A sequential quadratic programming method with line search is analyzed and studied for finding the local solution of a nonlinear semidefinite programming problem resulting from the discrete-time output feedback problem. The method requires an initial feasible point with respect to two positive definite constraints. By parameterizing the optimization problem we ease that requirement. The method is tested numerically on several test problems chosen from the benchmark collection (Leibfritz, 2004).

The stochastic restricted $r\text{-}k$ class estimator and stochastic restricted $r\text{-}d$ class estimator are proposed for the vector of parameters in a multiple linear regression model with stochastic linear restrictions. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a numerical example is given to show some of the theoretical results.

We introduce a general iteration method for a finite family of generalized asymptotically quasi-nonexpansive mappings. The results presented in the paper extend and improve some recent results in the works by Shahzad and Udomene (2006); L. Qihou (2001); Khan et al. (2008).

We consider the sleep mode with multimedia application in WiMAX 2 networks, where the real-time traffic includes the real-time and the best-effort traffic mixed. We present a queueing model with multiple heterogeneous vacations to characterize the system probability behavior in the networks with multimedia application. Taking into account the correlation of the real-time traffic, we assume the arrival process as a discrete-time Markovian arrival process (D-MAP) and analyze this queueing model by using the method of an embedded Markov chain. Then, we present the probability distribution for the number of data packets. Accordingly, we give the formulas for the performance measures in terms of the average response time of data packets, the energy saving ratio, and the standard deviation of the number of data packets. We also develop a cost function to determine the optimal length of the sleep cycle in order to maximize the energy saving ratio while satisfying the Quality of Service (QoS) constraint on the average response time of data packets. Finally, we provide numerical results to investigate the influence of the system parameters on the system performance.

Firstly, we show a connection between the first Lucas sequence and the determinants of some tridiagonal matrices. Secondly, we derive the complex factorizations of the first Lucas sequence by computing those determinants with the help of Chebyshev polynomials of the second kind. Furthermore, we also obtain the complex factorizations of the second Lucas sequence by the similar matrix method using Chebyshev polynomials of the first kind.

We present finite difference schemes for Burgers equation and Burgers-Fisher equation. A new version of exact finite difference scheme for Burgers equation and Burgers-Fisher equation is proposed using the solitary wave solution. Then nonstandard finite difference schemes are constructed to solve two equations. Numerical experiments are presented to verify the accuracy and efficiency of such NSFD schemes.

Tensor subspace analysis (TSA) and discriminant TSA (DTSA) are two effective two-sided projection methods for dimensionality reduction and feature extraction of face image matrices. However, they have two serious drawbacks. Firstly, TSA and DTSA iteratively compute the left and right projection matrices. At each iteration, two generalized eigenvalue problems are required to solve, which makes them inapplicable for high dimensional image data. Secondly, the metric structure of the facial image space cannot be preserved since the left and right projection matrices are not usually orthonormal. In this paper, we propose the orthogonal TSA (OTSA) and orthogonal DTSA (ODTSA). In contrast to TSA and DTSA, two trace ratio optimization problems are required to be solved at each iteration. Thus, OTSA and ODTSA have much less computational cost than their nonorthogonal counterparts since the trace ratio optimization problem can be solved by the inexpensive Newton-Lanczos method. Experimental results show that the proposed methods achieve much higher recognition accuracy and have much lower training cost.

This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM) for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.

We apply the Krasnoselskii’s fixed point theorem to study the existence of multiple positive periodic solutions for a class of impulsive functional differential equations with infinite delay and two parameters. In particular, the presented criteria improve and generalize some related results in the literature. As an application, we study some special cases of systems, which have been studied extensively in the literature.

A Riemannian gradient algorithm based on geometric structures of a manifold consisting of all positive definite matrices is proposed to calculate the numerical solution of the linear matrix equation $Q=X+{\sum }_{i=1}^m{A}_i^{T}X{A}_i$. In this algorithm, the geodesic distance on the curved Riemannian manifold is taken as an objective function and the geodesic curve is treated as the convergence path. Also the optimal variable step sizes corresponding to the minimum value of the objective function are provided in order to improve the convergence speed. Furthermore, the convergence speed of the Riemannian gradient algorithm is compared with that of the traditional conjugate gradient method in two simulation examples. It is found that the convergence speed of the provided algorithm is faster than that of the conjugate gradient method.

This paper investigates a general form of guaranteed descent conjugate gradient methods which satisfies the descent condition $g_k^T{d}_k\le -\left(\mathrm{1}-\mathrm{1}/\left(\mathrm{4}{\theta }_k\right)\right){∥g_k∥}^2\hspace{0.17em}\hspace{0.17em}\left({\theta }_k>\mathrm{1}/\mathrm{4}\right)$ and which is strongly convergent whenever the weak Wolfe line search is fulfilled. Moreover, we present several specific guaranteed descent conjugate gradient methods and give their numerical results for large-scale unconstrained optimization.

Recently, hybrid stochastic and local volatility models have become an industry standard for the pricing of derivatives and other problems in finance. In this study, we use a multiscale stochastic volatility model incorporated by the constant elasticity of variance to understand the price structure of continuous arithmetic average Asian options. The multiscale partial differential equation for the option price is approximated by a couple of single scale partial differential equations. In terms of the elasticity parameter governing the leverage effect, a correction to the stochastic volatility model is made for more efficient pricing and hedging of Asian options.

Service-oriented architecture (SOA) provides an elastic and automatic way to discover, publish, and compose individual services. SOA enables faster integration of existing software components from different parties, makes fault tolerance (FT) feasible, and is also one of the fundamentals of cloud computing. However, the unpredictable nature of SOA systems introduces new challenges for reliability evaluation, while reliability and dependability have become the basic requirements of enterprise systems. This paper proposes an SOA system reliability model which incorporates three common fault-tolerance strategies. Sensitivity analysis of SOA at both coarse and fine grain levels is also studied, which can be used to efficiently identify the critical parts within the system. Two SOA system scenarios based on real industrial practices are studied. Experimental results show that the proposed SOA model can be used to accurately depict the behavior of SOA systems. Additionally, a sensitivity analysis that quantizes the effects of system structure as well as fault tolerance on the overall reliability is also studied. On the whole, the proposed reliability modeling and analysis framework may help the SOA system service provider to evaluate the overall system reliability effectively and also make smarter improvement plans by focusing resources on enhancing reliability-sensitive parts within the system.

In order to well maintain the diversity of obtained solutions, a new multiobjective evolutionary algorithm based on decomposition of the objective space for multiobjective optimization problems (MOPs) is designed. In order to achieve the goal, the objective space of a MOP is decomposed into a set of subobjective spaces by a set of direction vectors. In the evolutionary process, each subobjective space has a solution, even if it is not a Pareto optimal solution. In such a way, the diversity of obtained solutions can be maintained, which is critical for solving some MOPs. In addition, if a solution is dominated by other solutions, the solution can generate more new solutions than those solutions, which makes the solution of each subobjective space converge to the optimal solutions as far as possible. Experimental studies have been conducted to compare this proposed algorithm with classic MOEA/D and NSGAII. Simulation results on six multiobjective benchmark functions show that the proposed algorithm is able to obtain better diversity and more evenly distributed Pareto front than the other two algorithms.

This paper is concerned with a stochastic nonautonomous logistic model with jumps. In the model, the martingale and jump noise are taken into account. This model is new and more feasible and applicable. Sufficient criteria for the existence of global positive solutions are obtained; then asymptotic boundedness in pth moment, stochastically ultimate boundedness, and asymptotic pathwise behavior are to be considered.

This paper studies the effect of jump-diffusion random environmental perturbations on the asymptotic behaviour and extinction of Lotka-Volterra population dynamics with delays. The contributions of this paper lie in the following: (a) to consider delay stochastic differential equation with jumps, we introduce a proper initial data space, in which the initial data may be discontinuous function with downward jumps; (b) we show that the delay stochastic differential equation with jumps associated with our model has a unique global positive solution and give sufficient conditions that ensure stochastically ultimate boundedness, moment average boundedness in time, and asymptotic polynomial growth of our model; (c) the sufficient conditions for the extinction of the system are obtained, which generalized the former results and showed that the sufficiently large random jump magnitudes and intensity (average rate of jump events arrival) may lead to extinction of the population.

Based on the Hermitian and skew-Hermitian splitting (HSS) iteration technique, we establish a generalized HSS (GHSS) iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semidefinite matrices. The GHSS method is essentially a four-parameter iteration which not only covers the standard HSS iteration but also enables us to optimize the iterative process. An exact parameter region of convergence for the method is strictly proved and a minimum value for the upper bound of the iterative spectrum is derived. Moreover, to reduce the computational cost, we establish an inexact variant of the GHSS (IGHSS) iteration method whose convergence property is discussed. Numerical experiments illustrate the efficiency and robustness of the GHSS iteration method and its inexact variant.

The stability of a class of static interval neural networks with time delay in the leakage term is investigated. By using the method of $M$-matrix and the technique of delay differential inequality, we obtain some sufficient conditions ensuring the global exponential robust stability of the networks. The results in this paper extend the corresponding conclusions without leakage delay. An example is given to illustrate the effectiveness of the obtained results.

We propose a BDDC preconditioner for the rotated $Q_{\mathrm{1}}$ finite element method for second order elliptic equations with piecewise but discontinuous coefficients. In the framework of the standard additive Schwarz methods, we describe this method by a complete variational form. We show that our method has a quasioptimal convergence behavior; that is, the condition number of the preconditioned problem is independent of the jumps of the coefficients and depends only logarithmically on the ratio between the subdomain size and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

Solutions are constructed for the Kalman-Yakubovich-transpose equation $X-A{X}^{T}B=C$. The solutions are stated as a polynomial of parameters of the matrix equation. One of the polynomial solutions is expressed by the symmetric operator matrix, controllability matrix, and observability matrix. Moreover, the explicit solution is proposed when the Kalman-Yakubovich-transpose matrix equation has a unique solution. The provided approach does not require the coefficient matrices to be in canonical form. In addition, the numerical example is given to illustrate the effectiveness of the derived method. Some applications in control theory are discussed at the end of this paper.

This paper investigates the finite-time stability problem of switching genetic regulatory networks (GRNs) with interval time-varying delays and unbounded continuous distributed delays. Based on the piecewise Lyapunov-Krasovskii functional and the average dwell time method, some new finite-time stability criteria are obtained in the form of linear matrix inequalities (LMIs), which are easy to be confirmed by the Matlab toolbox. The finite-time stability is taken into account in switching genetic regulatory networks for the first time and the average dwell time of the switching signal is obtained. Two numerical examples are presented to illustrate the effectiveness of our results.

The nonlinear tumor equation in spherical coordinates assuming that both the diffusivity and the killing rate are functions of concentration of tumor cell is studied. A complete classification with regard to the diffusivity and net killing rate is obtained using Lie symmetry analysis. The reduction of the nonlinear governing equation is carried out in some interesting cases and exact solutions are obtained.

Based on the availability of symbolic computation, the tanh-coth method is used to obtain a number of travelling wave solutions for several coupled improved Boussinesq equations. The abundant new solutions can be seen as improvement of the previously known data. The obtained results in this work also demonstrate the efficiency of the method.

Given $k$ pairs of complex numbers and vectors (closed under conjugation), we consider the inverse quadratic eigenvalue problem of constructing $n\times n$ real matrices $M$, $D$, $G$, and $K$, where $M>0$, $K$ and $D$ are symmetric, and $G$ is skew-symmetric, so that the quadratic pencil $Q(\lambda )={\lambda }^{2}M+\lambda (D+G)+K$ has the given $k$ pairs as eigenpairs. First, we construct a general solution to this problem with $k\le n$. Then, with the special properties $D=0$ and , we construct a particular solution. Numerical results illustrate these solutions.

The evolution simulation of dust particles provides an important way to analyze the impact of dust on the environment. KMC-based parallel algorithm is proposed to simulate the evolution of dust particles. In the parallel evolution simulation algorithm of dust particles, data distribution way and communication optimizing strategy are raised to balance the load of every process and reduce the communication expense among processes. The experimental results show that the simulation of diffusion, sediment, and resuspension of dust particles in virtual campus is realized and the simulation time is shortened by parallel algorithm, which makes up for the shortage of serial computing and makes the simulation of large-scale virtual environment possible.

We present the two-dimensional quaternion Wigner-Ville distribution (QWVD). The transform is constructed by substituting the Fourier transform kernel with the quaternion Fourier transform (QFT) kernel in the classical Wigner-Ville distribution definition. Based on the properties of quaternions and the QFT kernel we obtain three types of the QWVD. We discuss some useful properties of various definitions for the QWVD, which are extensions of the classical Wigner-Ville distribution properties.

This paper develops a probabilistic decomposition method for an ${\text{M}}^{\xi }$/G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probability p. Such a novel method is used to analyze the main performance indices of the server, such as the unavailability and the mean failure number during $(0,t]$. It is derived that the structures of server indices are two convolution equations. Further, comparisons with existing methods indicate that our method is effective and applicable for studying server performances in single-server ${\text{M}}^{\xi }$/G/1 vacation queues and their complex variants. Finally, a stochastic order and production system with a multipurpose production facility is numerically presented for illustrative purpose.

A two-city SIR epidemic model with transport-related infections is proposed. Some good analytical results are given for this model. If the basic reproduction number ${\Re }_{0\gamma }\le 1$, there exists a disease-free equilibrium which is globally asymptotically stable. There exists an endemic equilibrium which is locally asymptotically stable if the basic reproduction number ${\Re }_{0\gamma }>1$. We also show the permanence of this SIR model. In addition, sufficient conditions are established for global asymptotic stability of the endemic equilibrium.

The row first-minus-last right (RFMLR) circulant matrix and row last-minus-first left (RLMFL) circulant matrices are two special pattern matrices. By using the inverse factorization of polynomial, we give the exact formulae of determinants of the two pattern matrices involving Perrin, Padovan, Tribonacci, and the generalized Lucas sequences in terms of finite many terms of these sequences.

We consider stochastic suppression and stabilization for nonlinear delay differential system. The system is assumed to satisfy local Lipschitz condition and one-side polynomial growth condition. Since the system may explode in a finite time, we stochastically perturb this system by introducing independent Brownian noises and Lévy noise feedbacks. The contributions of this paper are as follows. (a) We show that Brownian noises or Lévy noise may suppress potential explosion of the solution for some appropriate parameters. (b) Using the exponential martingale inequality with jumps, we discuss the fact that the sample Lyapunov exponent is nonpositive. (c) Considering linear Lévy processes, by the strong law of large number for local martingale, sufficient conditions for a.s. exponentially stability are investigated in Theorem 13.

We consider the boundary value problem for a fourth order nonlinear p-Laplacian difference equation containing both advance and retardation. By using Mountain pass lemma and some established inequalities, sufficient conditions of the existence of solutions of the boundary value problem are obtained. And an illustrative example is given in the last part of the paper.

The modified decomposition method (MDM) and homotopy perturbation method (HPM) are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM) is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.

This paper proposes a decision tree model for specifying the importance of 21 factors causing the landslides in a wide area of Penang Island, Malaysia. These factors are vegetation cover, distance from the fault line, slope angle, cross curvature, slope aspect, distance from road, geology, diagonal length, longitude curvature, rugosity, plan curvature, elevation, rain perception, soil texture, surface area, distance from drainage, roughness, land cover, general curvature, tangent curvature, and profile curvature. Decision tree models are used for prediction, classification, and factors importance and are usually represented by an easy to interpret tree like structure. Four models were created using Chi-square Automatic Interaction Detector (CHAID), Exhaustive CHAID, Classification and Regression Tree (CRT), and Quick-Unbiased-Efficient Statistical Tree (QUEST). Twenty-one factors were extracted using digital elevation models (DEMs) and then used as input variables for the models. A data set of 137570 samples was selected for each variable in the analysis, where 68786 samples represent landslides and 68786 samples represent no landslides. 10-fold cross-validation was employed for testing the models. The highest accuracy was achieved using Exhaustive CHAID (82.0%) compared to CHAID (81.9%), CRT (75.6%), and QUEST (74.0%) model. Across the four models, five factors were identified as most important factors which are slope angle, distance from drainage, surface area, slope aspect, and cross curvature.

We propose a novel method, called Kernel Neighborhood Discriminant Analysis (KNDA), which can be regarded as a supervised kernel extension of Locality Preserving Projection (LPP). KNDA nonlinearly maps the original data into a kernel space in which two graphs are constructed to depict the within-class submanifold and the between-class submanifold. Then a criterion function which minimizes the quotient between the within-class representation and the between-class representation of the submanifolds is designed to separate each submanifold constructed by each class. The real contribution of this paper is that we bring and extend the submanifold based algorithm to a general model and by some derivation a simple result is given by which we can classify a given object to a predefined class effectively. Experiments on the MNIST Handwritten Digits database, the Binary Alphadigits database, the ORL face database, the Extended Yale Face Database B, and a downloaded documents dataset demonstrate the effectiveness and robustness of the proposed method.

We consider the following inverse eigenvalue problem: to construct a special kind of matrix (real symmetric doubly arrow matrix) from the minimal and maximal eigenvalues of all its leading principal submatrices. The necessary and sufficient condition for the solvability of the problem is derived. Our results are constructive and they generate algorithmic procedures to construct such matrices.

In real-life games, the consequence or payoff of a strategy profile and a player's belief about the consequence of a strategy profile are often ambiguous, and players may have different optimistic attitudes with respect to a strategy profile. To handle this problem, this paper proposes a decision rule using the Hurwicz criterion and Dempster-Shafer theory. Based on this rule, we introduce a new kind of games, called ambiguous games, and propose a solution concept that is appropriate for this sort of games. Moreover, we also study how the beliefs regarding possible payoffs and optimistic attitudes may affect the solutions of such a game. To illustrate our model, we provide an analysis of a scenario concerning allocating resource of defending and attacking in military contexts.

A generalized predator-prey model concerning integrated pest management and nonlinear impulsive control measures is proposed and analyzed. The main purpose is to understand how resource limitation affects the successful pest control and pest outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given firstly. Once the threshold value exceeds a critical level, both pest and its natural enemy populations can oscillate periodically. Secondly, in order to address how the limited resources affect the pest control, as an example the Holling II functional response function is chosen. The numerical results show that predator-prey model with limited resource has complex dynamical behavior. In addition, it is confirmed that the model has the coexistence of pests and natural enemies for a wide range of parameters.

A class of shunting inhibitory cellular neural networks of neutral type with time-varying delays in the leakage term on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, fixed point theorems, and calculus on time scales we obtain some sufficient conditions for the existence and global exponential stability of periodic solutions for that class of neural networks. The results of this paper are completely new and complementary to the previously known results even if the time scale $𝕋=ℝ$ or $\mathbb{Z}$. Moreover, we present illustrative numerical examples to show the feasibility of our results.

In recent years, countries all over the world consider the future internet as the country’s strategic development directions, so projects about future internet have been launched by these countries. Load balancing algorithms and job allocations are main research problems in areas of resource management of future internet. In this paper, we introduce a load balancing model for future internet. We formulate the static load balancing problem in the model proposed above as noncooperative game among users and cooperative game among processors. Based on this model, we derive a load balancing algorithm for computing center. Finally, we execute the algorithm presented in this paper with another three algorithms for comparison purpose. The advantages of our algorithm are better scalability to the model, improving system performance, and low cost on maintaining system information.

To reflect uncertain data in practical problems, stochastic versions of the mathematical program with complementarity constraints (MPCC) have drawn much attention in the recent literature. Our concern is the detailed analysis of convergence properties of a regularization sample average approximation (SAA) method for solving a stochastic mathematical program with complementarity constraints (SMPCC). The analysis of this regularization method is carried out in three steps: First, the almost sure convergence of optimal solutions of the regularized SAA problem to that of the true problem is established by the notion of epiconvergence in variational analysis. Second, under MPCC-MFCQ, which is weaker than MPCC-LICQ, we show that any accumulation point of Karash-Kuhn-Tucker points of the regularized SAA problem is almost surely a kind of stationary point of SMPCC as the sample size tends to infinity. Finally, some numerical results are reported to show the efficiency of the method proposed.

Determining the winners in combinatorial auctions to maximize the auctioneer's revenue is an NP-complete problem. Computing an optimal solution requires huge computation time in some instances. In this paper, we apply three concepts of the game theory to design an approximation algorithm: the stability of the Nash equilibrium, the self-learning of the evolutionary game, and the mistake making of the trembling hand assumption. According to our simulation results, the proposed algorithm produces near-optimal solutions in terms of the auctioneer's revenue. Moreover, reasonable computation time is another advantage of applying the proposed algorithm to the real-world services.

Let $G$ be a connected graph. The first and second Zagreb eccentricity indices of $G$ are defined as $M_{\mathrm{1}}^{\mathrm{*}}(G)={\sum }_{v\in V(G)}\mathrm{‍}{\epsilon }_G^{\mathrm{2}}(v)$ and $M_{\mathrm{2}}^{\mathrm{*}}(G)={\sum }_{uv\in E(G)}\mathrm{‍}{\epsilon }_G(u){\epsilon }_G(v)$, where ${\epsilon }_G(v)$ is the eccentricity of the vertex $v$ in $G$ and ${\epsilon }_G^{\mathrm{2}}(v)=({\epsilon }_G(v){)}^{\mathrm{2}}$. Suppose that $G(U)\sqcap H(\mathrm{\varnothing }\ne U\subseteq V(G))$ is the generalized hierarchical product of two connected graphs $G$ and $H$. In this paper, the Zagreb eccentricity indices $M_{\mathrm{1}}^{\mathrm{*}}$ and $M_{\mathrm{2}}^{\mathrm{*}}$ of $G(U)\sqcap H$ are computed. Moreover, we present explicit formulas for the $M_{\mathrm{1}}^{\mathrm{*}}$ and $M_{\mathrm{2}}^{\mathrm{*}}$ of S-sum graph, Cartesian, cluster, and corona product graphs by means of some invariants of the factors.

Consider dividend problems in the diffusion model with interest and exponentially distributed observation time where dividends are paid according to a barrier strategy. Assume that dividends can only be paid with a certain probability at each point of time; that is, on each observation, if the surplus exceeds the barrier level, the excess is paid as dividend. In this paper, integrodifferential equations for the moment-generating function, the nth moment function, and the Laplace transform of ruin time are derived; explicit expressions for the expected discounted dividends paid until ruin and the Laplace transform of ruin time are also obtained.

The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially greedy algorithm design which plays an important role in the reduction problems. Therefore, it is meaningful to combine coverings with geometric lattices to solve the optimization problems. In this paper, we obtain geometric lattices from coverings through matroids and then apply them to the issue of attribute reduction. First, a geometric lattice structure of a covering is constructed through transversal matroids. Then its atoms are studied and used to describe the lattice. Second, considering that all the closed sets of a finite matroid form a geometric lattice, we propose a dependence space through matroids and study the attribute reduction issues of the space, which realizes the application of geometric lattices to attribute reduction. Furthermore, a special type of information system is taken as an example to illustrate the application. In a word, this work points out an interesting view, namely, geometric lattice, to study the attribute reduction issues of information systems.

In mathematics, to a large extent, control theory addresses the stability of solutions of differential equations, which can describe the behavior of dynamic systems. In this paper, a class of fractional-order nonautonomous systems with multiple time delays modeled by differential equations is considered. A sufficient condition is established for the existence and uniqueness of solutions for such systems involving Caputo fractional derivative, and the uniform stability of solution is studied. At last, two examples are given to demonstrate the applicability of our results.

The r-Whitney numbers of the second kind are a generalization of all the Stirling-type numbers of the second kind which are in line with the unified generalization of Hsu and Shuie. In this paper, asymptotic formulas for r-Whitney numbers of the second kind with integer and real parameters are obtained and the range of validity of each formula is established.

For a vertex $v$ of a graph $G$, the lower connectivity, denoted by $s_v(G)$, is the smallest number of vertices that contains $v$ and those vertices whose deletion from $G$ produces a disconnected or a trivial graph. The average lower connectivity denoted by ${\kappa }_{\text{a}\text{v}}(G)$ is the value $({\sum }_{v\in V\left(G\right)}{s}_v\left(G\right))/\left|V\left(G\right)\right|$. It is shown that this parameter can be used to measure the vulnerability of networks. This paper contains results on bounds for the average lower connectivity and obtains the average lower connectivity of some graphs.

A mathematical model on schistosomiasis governed by periodic differential equations with a time delay was studied. By discussing boundedness of the solutions of this model and construction of a monotonic sequence, the existence of positive periodic solution was shown. The conditions under which the model admits a periodic solution and the conditions under which the zero solution is globally stable are given, respectively. Some numerical analyses show the conditional coexistence of locally stable zero solution and periodic solutions and that it is an effective treatment by simply reducing the population of snails and enlarging the death ratio of snails for the control of schistosomiasis.

We consider a SVR-B cholera model with imperfect vaccination. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. We calculate the certain threshold known as the control reproduction number ${ℛ}_v$. If ${ℛ}_v$ $1$, we obtain sufficient conditions for the global asymptotic stability of the disease-free equilibrium; the diseases will be eliminated from the community. By comparison of arguments, it is proved that if ${ℛ}_v$ $>$ $1$, the disease persists and the unique endemic equilibrium is globally asymptotically stable, which is obtained by the second compound matrix techniques and autonomous convergence theorems. We perform sensitivity analysis of ${ℛ}_v$ on the parameters in order to determine their relative importance to disease transmission and show that an imperfect vaccine is always beneficial in reducing disease spread within the community.

The simplest equation method has been used for finding the exact solutions of coupled sine-Gordon equations. Such equations have some useful applications in physics and biology, so finding their exact solutions is of great importance.

Ranking Efficient Decision Making Units (DMUs) are an important issue in Data Envelopment Analysis (DEA). This is one of the main areas for the researcher. Different methods for this purpose have been suggested. Appearing nonzero slack in optimal solution makes the method problematic. In this paper, we modify the nonradial supper efficiency model to remove this difficulty. Some numerical examples are solved by modified model.

This paper investigates the analysis problem for stability of discrete-time neural networks (NNs) with discrete- and distribute-time delay. Stability theory and a linear matrix inequality (LMI) approach are developed to establish sufficient conditions for the NNs to be globally asymptotically stable and to design a state estimator for the discrete-time neural networks. Both the discrete delay and distribute delays employ decomposing the delay interval approach, and the Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals, such that a new stability criterion is proposed in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness of the proposed method and the applicability of the proposed method.

The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we apply the coefficient theorem on the characteristic polynomial of a signed graph and give two formulae on the nullity of signed graphs with cut-points. As applications of the above results, we investigate the nullity of the bicyclic signed graph $\Gamma \left(\infty \left(p,q,l\right)\right)$, obtain the nullity set of unbalanced bicyclic signed graphs, and thus determine the nullity set of bicyclic signed graphs.

We model a Basel III compliant commercial bank that operates in a financial market consisting of a treasury security, a marketable security, and a loan and we regard the interest rate in the market as being stochastic. We find the investment strategy that maximizes an expected utility of the bank’s asset portfolio at a future date. This entails obtaining formulas for the optimal amounts of bank capital invested in different assets. Based on the optimal investment strategy, we derive a model for the Capital Adequacy Ratio (CAR), which the Basel Committee on Banking Supervision (BCBS) introduced as a measure against banks’ susceptibility to failure. Furthermore, we consider the optimal investment strategy subject to a constant CAR at the minimum prescribed level. We derive a formula for the bank’s asset portfolio at constant (minimum) CAR value and present numerical simulations on different scenarios. Under the optimal investment strategy, the CAR is above the minimum prescribed level. The value of the asset portfolio is improved if the CAR is at its (constant) minimum value.

We study the existence of positive solutions and multiplicity of nontrivial solutions for a class of quasilinear elliptic equations by using variational methods. Our obtained results extend some existing ones.

An unfitted discontinuous Galerkin method is proposed for the elliptic interface problems. Based on a variant of the local discontinuous Galerkin method, we obtain the optimal convergence for the exact solution u in the energy norm and its flux p in the L ² norm. These results are the same as those in the case of elliptic problems without interface. Finally, some numerical experiments are presented to verify our theoretical results.

We study the nonlinear wave solutions for the Broer-Kaup equation. Many exact explicit expressions of the nonlinear wave solutions for the equation are obtained by exploiting the bifurcation method and qualitative theory of dynamical systems. These solutions contain solitary wave solutions, singular solutions, periodic singular solutions, and kink-shaped solutions, most of which are new. Some previous results are extended.

We consider the second dynamic operators of elliptic type on time scales. We establish basic generalized maximum principles and apply them to obtain weak comparison principle for second dynamic elliptic operators and to obtain the uniqueness of Dirichlet boundary value problems for dynamic elliptic equations.

We prove the existence of homoclinic solutions of a class of nonlinear difference equations with superlinear nonlinearity by using the generalized Nehari manifold approach. For the case where the nonlinearity is odd, we obtain infinitely many homoclinic solutions of the equations. Recent results in the literature are generalized and improved.

The Cauchy problem for a generalized two-component Camassa-Holm system is investigated. Following the idea of fixed points and using new sets of independent and dependent variables, the existence of the global conservative solutions for the system is established.

A computer virus model with infection delay and recovery delay is considered. The sufficient conditions for the global stability of the virus infection equilibrium are established. We show that the time delay can destabilize the virus infection equilibrium and give rise to Hopf bifurcations and stable periodic orbits. By the normal form and center manifold theory, the direction of the Hopf bifurcation and stability of the bifurcating periodic orbits are determined. Numerical simulations are provided to support our theoretical conclusions.

New exact traveling wave solutions of a higher-order KdV equation type are studied by the $(G^{\prime }/G)$-expansion method, where $G=G(\xi )$ satisfies a second-order linear differential equation. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. The property of this method is that it is quite simple and understandable.

We study the well-posedness of a 3D nonlinear stochastic wave equation which derives from the Maxwell system by the Galerkin method. Then we study the approximate controllability of this system by the Hilbert uniqueness method.

Two efficient iterative algorithms are presented to solve a system of matrix equations $A_1{X}_1{B}_1$ + $A_2{X}_2{B}_2$ $=E$, $C_1{X}_1{D}_1$ + $C_2{X}_2{D}_2$ $=F$ over generalized reflexive and generalized antireflexive matrices. By the algorithms, the least norm generalized reflexive (antireflexive) solutions and the unique optimal approximation generalized reflexive (antireflexive) solutions to the system can be obtained, too. For any initial value, it is proved that the iterative solutions obtained by the proposed algorithms converge to their true values. The given numerical examples demonstrate that the iterative algorithms are efficient.

We consider a modification of the $K(\mathrm{2,2})$ equation $u_t=2u{u}_{xxx}+2k{u}_x{u}_{xx}+2u{u}_x$ using the bifurcation method of dynamical systems and the method of phase portraits analysis. From dynamic point of view, some peakons, solitary, and smooth periodic waves are found and their exact parametric representations are presented. Also, the coexistence of peakon and solitary wave solutions is investigated.

The notion of unisoft subfields, unisoft algebras over unisoft subfields, and unisoft hypervector spaces are introduced, and their properties and characterizations are considered. In connection with linear transformations, unisoft hypervector spaces are discussed.

A new two-part parametric linearization technique is proposed globally to a class of nonconvex programming problems (NPP). Firstly, a two-part parametric linearization method is adopted to construct the underestimator of objective and constraint functions, by utilizing a transformation and a parametric linear upper bounding function (LUBF) and a linear lower bounding function (LLBF) of a natural logarithm function and an exponential function with e as the base, respectively. Then, a sequence of relaxation lower linear programming problems, which are embedded in a branch-and-bound algorithm, are derived in an initial nonconvex programming problem. The proposed algorithm is converged to global optimal solution by means of a subsequent solution to a series of linear programming problems. Finally, some examples are given to illustrate the feasibility of the presented algorithm.

This paper features a numerical study that is carried out by using discontinuous deformation method (DDA) and fractal geometry. The configurations of rock strata calculated by DDA were imported into a code that is written by using VC++ called “Fractal” to calculate the fractal dimension of the rock strata. As illustrated, a long wall mining case in China was presented. The relationship of the fractal dimension, excavation length, stress, and movement of strata were discussed. The evolution of fractal dimension can be considered as an index of instability or failure. The method proposed in this paper can be employed to predict the period weighting in long wall mining engineering.

This paper mainly deals with how kernel method can be used for software defect prediction, since the class imbalance can greatly reduce the performance of defect prediction. In this paper, two classifiers, namely, the asymmetric kernel partial least squares classifier (AKPLSC) and asymmetric kernel principal component analysis classifier (AKPCAC), are proposed for solving the class imbalance problem. This is achieved by applying kernel function to the asymmetric partial least squares classifier and asymmetric principal component analysis classifier, respectively. The kernel function used for the two classifiers is Gaussian function. Experiments conducted on NASA and SOFTLAB data sets using F-measure, Friedman’s test, and Tukey’s test confirm the validity of our methods.

The main contribution of this paper is the homogenization of the linear parabolic equation ${\partial }_t{u}^{\epsilon }(x,t)-\nabla ·(a(x/{\epsilon }^{q_{\mathrm{1}}},...,x/{\epsilon }^{q_n},t/{\epsilon }^{r_{\mathrm{1}}},...,t/{\epsilon }^{r_m})\nabla u^{\epsilon }(x,t))=f(x,t)$ exhibiting an arbitrary finite number of both spatial and temporal scales. We briefly recall some fundamentals of multiscale convergence and provide a characterization of multiscale limits for gradients, in an evolution setting adapted to a quite general class of well-separated scales, which we name by jointly well-separated scales (see appendix for the proof). We proceed with a weaker version of this concept called very weak multiscale convergence. We prove a compactness result with respect to this latter type for jointly well-separated scales. This is a key result for performing the homogenization of parabolic problems combining rapid spatial and temporal oscillations such as the problem above. Applying this compactness result together with a characterization of multiscale limits of sequences of gradients we carry out the homogenization procedure, where we together with the homogenized problem obtain $n$ local problems, that is, one for each spatial microscale. To illustrate the use of the obtained result, we apply it to a case with three spatial and three temporal scales with $q_{\mathrm{1}}=\mathrm{1}$, $q_{\mathrm{2}}=\mathrm{2}$, and .

In this paper we define nonnull and null pseudospherical Smarandache curves according to the Sabban frame of a spacelike curve lying on pseudosphere in Minkowski 3-space. We obtain the geodesic curvature and the expressions for the Sabban frame’s vectors of spacelike and timelike pseudospherical Smarandache curves. We also prove that if the pseudospherical null straight lines are the Smarandache curves of a spacelike pseudospherical curve $\alpha$, then $\alpha$ has constant geodesic curvature. Finally, we give some examples of pseudospherical Smarandache curves.

This paper presents a $p$-step-ahead forecasting strategy based on two stages to improve pelagic fish-catch time-series modeling by considering annual and interannual fluctuations for northern Chile (18°S–24°S). In the first stage, the stationary wavelet transform is used to separate the raw time series into an annual component and an interannual component, whereas the periodicities of each component are obtained using the Morlet wavelet power spectrum. In the second stage, a linear autoregressive model is constructed to predict each component and the unknown $p$-next values are forecasted by the addition of the two predicted components. We demonstrate the utility of the proposed forecasting model on monthly anchovy-catches time series for periods from January 1963 to December 2007. Empirical results obtained for 10-month-ahead forecasting showed the effectiveness of the proposed wavelet autoregressive strategy.

We studied the thin film flow for lifting and drainage problems using an incompressible, nonisothermal modified second grade fluid. We developed nonlinear differential equations from momentum and energy equations, respectively. Series solutions for both lifting and drainage problems are obtained. Expressions for the velocity profile, temperature distribution, volume flux, average film velocity, and shear stress on cylinder for both cases are obtained. Effects of different parameters on the flow problems are presented graphically.

A delayed predator-prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of persistence theory on infinite dimensional systems, it is proved that the system is permanent. By using Lyapunov functions and the LaSalle invariant principle, the global stability of each of the feasible equilibria of the model is discussed. Numerical simulations are carried out to illustrate the main theoretical results.

An average linear finite difference scheme for the numerical solution of the initial-boundary value problem of Generalized Rosenau-KdV equation is proposed. The existence, uniqueness, and conservation for energy of the difference solution are proved by the discrete energy norm method. It is shown that the finite difference scheme is 2nd-order convergent and unconditionally stable. Numerical experiments verify that the theoretical results are right and the numerical method is efficient and reliable.

The structural holes have been a key issue in fuzzy social network analysis. For undirected fuzzy social networks where edges are just present or absent undirected fuzzy relation and have no more information attached, many structural holes measures have been presented, such as key fuzzy structural holes, general fuzzy structural holes, strong fuzzy structural holes, and weak fuzzy structural holes. There has been a growing need to design structural holes measures for directed fuzzy social networks, because directed fuzzy social networks where edges are attached by directed fuzzy relation would contain rich information. In this paper, we extend structural holes theory to directed fuzzy social network and propose the algorithm of unidirectional fuzzy structural holes and bidirectional fuzzy structural holes, which unveil more structural information of directed fuzzy social networks. Furthermore, we investigate the validness of the algorithm by illustrating this method to a case called G-Y Research Team and obtain reliable results, which provide strong evidences of the new measure’s utility.

Software defect prediction studies usually build models without analyzing the data used in the procedure. As a result, the same approach has different performances on different data sets. In this paper, we introduce discrimination analysis for providing a good method to give insight into the inherent property of the software data. Based on the analysis, we find that the data sets used in this field have nonlinearly separable and class-imbalanced problems. Unlike the prior works, we try to exploit the kernel method to nonlinearly map the data into a high-dimensional feature space. By combating these two problems, we propose an algorithm based on kernel discrimination analysis called KDC to build more effective prediction model. Experimental results on the data sets from different organizations indicate that KDC is more accurate in terms of $F$-measure than the state-of-the-art methods. We are optimistic that our discrimination analysis method can guide more studies on data structure, which may derive useful knowledge from data science for building more accurate prediction models.

We prove the demiclosedness principle for a class of mappings which is a generalization of all the forms of nonexpansive, asymptotically nonexpansive, and nearly asymptotically nonexpansive mappings. Moreover, we establish the existence theorem and convergence theorems for modified Ishikawa iterative process in the framework of $CAT(0)$ spaces. Our results generalize, extend, and unify the corresponding results on the topic in the literature.

The Particle Swarm Optimization (PSO) Algorithm is a popular optimization method that is widely used in various applications, due to its simplicity and capability in obtaining optimal results. However, ordinary PSOs may be trapped in the local optimal point, especially in high dimensional problems. To overcome this problem, an efficient Global Particle Swarm Optimization (GPSO) algorithm is proposed in this paper, based on a new updated strategy of the particle position. This is done through sharing information of particle position between the dimensions (variables) at any iteration. The strategy can enhance the exploration capability of the GPSO algorithm to determine the optimum global solution and avoid traps at the local optimum. The proposed GPSO algorithm is validated on a 12-benchmark mathematical function and compared with three different types of PSO techniques. The performance of this algorithm is measured based on the solutions’ quality, convergence characteristics, and their robustness after 50 trials. The simulation results showed that the new updated strategy in GPSO assists in realizing a better optimum solution with the smallest standard deviation value compared to other techniques. It can be concluded that the proposed GPSO method is a superior technique for solving high dimensional numerical function optimization problems.

Toshka Depression (TD), located about 250 km south west of the High Aswan Dam (HAD), consists of four deep-cut basins connected by natural sills. It is required to assess the contribution of TD as a spillway, in enhancing the effectiveness of Lake Nasser in flood control and water availability. However, most related previous works are descriptive and use qualitative methods. In order to provide the required assessment quantitatively, we developed a numerical model which computes TD mass balance and interbasin water movements. The model computes the variation of water volume, surface area, and water level in each one of the four basins (subdepressions), thus depicting their filling sequence, for the past 130 years. This TD response to realistic time series of water inflow gains and evaporation losses is analyzed to compute the TD overflow time series. This response helps assess water availability for agricultural use and effectiveness in alleviating flood risks. Furthermore, the developed model compares between three TD configurations to help the decision maker and recommends (i) building a dam—height 10 m—at the end of the fourth subdepression near Kharga Oasis and/or (ii) incorporating the third subdepression into TD by digging a canal through the hill that blocks it from the first subdepression.

We report a characteristic function to determine whether repetitive static plate load test (RSPLT) moduli are within an acceptable quality range, based on a comparison between the initial loading values and reloading moduli. The results of RSPLTs depend on the experience and expertise of the engineer carrying out the test, as well as the loading device, hydraulic jack assembly, and bearing plates. To identify outlier data points, well-tested data were used to develop a characteristic function model using a harmony search algorithm error minimization technique. This measure was applied to determine the reliability of RSPLT data.

The main purpose of this paper is using the properties of Gauss sums and the estimate for character sums to study the hybrid mean value problem involving the two-term exponential sums and two-term character sums and give an interesting asymptotic formula for it.

A linearized Crank-Nicolson difference scheme is constructed to solve a type of variable coefficient delay partial differential equations. The difference scheme is proved to be unconditionally stable and convergent, where the convergence order is two in both space and time. A numerical test is provided to illustrate the theoretical results.

This paper studies the multiattribute decision making (MADM) problems in which the attribute values take the form of dual hesitant fuzzy triangular linguistic elements and the weights of attributes take the form of real numbers. Firstly, to solve the situation where the membership degree and the nonmembership degree of an element to a triangular linguistic variable, the concept, operational laws, score function, and accuracy function of dual hesitant fuzzy triangular linguistic elements (DHFTLEs) are defined. Then, some dual hesitant fuzzy triangular linguistic geometric aggregation operators are developed for aggregating the DHFTLEs, including dual hesitant fuzzy triangular linguistic weighted geometric (DHFTLWG) operator, dual hesitant fuzzy triangular linguistic ordered weighted geometric (DHFTLOWG) operator, dual hesitant fuzzy triangular linguistic hybrid geometric (DHFTLHG) operator, generalized dual hesitant fuzzy triangular linguistic weighted geometric (GDHFTLWG) operator, and generalized dual hesitant fuzzy triangular linguistic ordered weighted geometric (GDHFTLOWG) operator. Furthermore, some desirable properties of these operators are investigated in detail. Based on the proposed operators, an approach to MADM with dual hesitant fuzzy triangular linguistic information is proposed. Finally, a numerical example for investment alternative selection is given to illustrate the application of the proposed method.

In this paper, we develop a modified gradient based algorithm for solving matrix equations $AXB+C{X}^{T}D\mathrm{}=F$. Different from the gradient based method introduced by Xie et al., 2010, the information generated in the first half-iterative step is fully exploited and used to construct the approximate solution. Theoretical analysis shows that the new method converges under certain assumptions. Numerical results are given to verify the efficiency of the new method.

By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for $k$-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse: $x\mathrm{\text{'}}(t)=x(t)[a(t)-f(t,x(t),x(t-{\tau }_{\mathrm{1}}(t,x(t))),\dots ,x(t-{\tau }_n(t,x(t))),x\mathrm{\text{'}}(t-{\gamma }_{\mathrm{1}}(t,x(t))),\dots ,x\mathrm{\text{'}}(t-{\gamma }_m(t,x(t))))],t\ne t_k,k\in Z_{+};x(t_k^{+})=x(t_k^{-})+{\theta }_k(x(t_k)),k\in Z_{+}$. As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.

We investigate the controllability for a one-dimensional wave equation in domains with moving boundary. This model characterizes small vibrations of a stretched elastic string when one of the two endpoints varies. When the speed of the moving endpoint is less than $1-1/\sqrt{e}$, by Hilbert uniqueness method, sidewise energy estimates method, and multiplier method, we get partial Dirichlet boundary controllability. Moreover, we will give a sharper estimate on controllability time that only depends on the speed of the moving endpoint.

For the complex industrial process, it has become increasingly challenging to effectively diagnose complicated faults. In this paper, a combined measure of the original Support Vector Machine (SVM) and Principal Component Analysis (PCA) is provided to carry out the fault classification, and compare its result with what is based on SVM-RFE (Recursive Feature Elimination) method. RFE is used for feature extraction, and PCA is utilized to project the original data onto a lower dimensional space. PCA $T^2$, SPE statistics, and original SVM are proposed to detect the faults. Some common faults of the Tennessee Eastman Process (TEP) are analyzed in terms of the practical system and reflections of the dataset. PCA-SVM and SVM-RFE can effectively detect and diagnose these common faults. In RFE algorithm, all variables are decreasingly ordered according to their contributions. The classification accuracy rate is improved by choosing a reasonable number of features.

This paper discussed the local control of interpolating function by using rational cubic spline (cubic/quadratic) with three parameters originally proposed by the authors. The rational spline has $C^1$ continuity. The bounded properties of the rational cubic interpolants and shape controls of the rational interpolants are discussed in detail. The value control, inflection point control, and convexity control at a point by using the proposed rational cubic spline are constructed. Several numerical results are presented to show the capability of the method. Numerical comparisons with the existing scheme are also further elaborated. From the results, it was indicated that the scheme works well and it is comparable with the established existing scheme.

We prove that a continuous $g$-supermartingale with uniformly continuous coeffcient $g$ on finite or infinite horizon, is a $g$-supersolution of the corresponding backward stochastic differential equation. It is a new nonlinear Doob-Meyer decomposition theorem for the $g$-supermartingale with continuous trajectory.

Training of an artificial neural network (ANN) adjusts the internal weights of the network in order to minimize a predefined error measure. This error measure is given by an error function. Several different error functions are suggested in the literature. However, the far most common measure for regression is the mean square error. This paper looks into the possibility of improving the performance of neural networks by selecting or defining error functions that are tailor-made for a specific objective. A neural network trained to simulate tension forces in an anchor chain on a floating offshore platform is designed and tested. The purpose of setting up the network is to reduce calculation time in a fatigue life analysis. Therefore, the networks trained on different error functions are compared with respect to accuracy of rain flow counts of stress cycles over a number of time series simulations. It is shown that adjusting the error function to perform significantly better on a specific problem is possible. On the other hand. it is also shown that weighted error functions actually can impair the performance of an ANN.

A new epidemiological model is introduced with nonlinear incidence, in which the infected disease may lose infectiousness and then evolves to a chronic noninfectious disease when the infected disease has not been cured for a certain time $\tau$. The existence, uniqueness, and stability of the disease-free equilibrium and endemic equilibrium are discussed. The basic reproductive number $R_0$ is given. The model is studied in two cases: with and without time delay. For the model without time delay, the disease-free equilibrium is globally asymptotically stable provided that $R_0\le 1$; if $R_0>1$, then there exists a unique endemic equilibrium, and it is globally asymptotically stable. For the model with time delay, a sufficient condition is given to ensure that the disease-free equilibrium is locally asymptotically stable. Hopf bifurcation in endemic equilibrium with respect to the time $\tau$ is also addressed.

The paper constructs a class of simple high-accurate schemes (SHA schemes) with third order approximation accuracy in both space and time to solve linear hyperbolic equations, using linear data reconstruction and Lax-Wendroff scheme. The schemes can be made even fourth order accurate with special choice of parameter. In order to avoid spurious oscillations in the vicinity of strong gradients, we make the SHA schemes total variation diminishing ones (TVD schemes for short) by setting flux limiter in their numerical fluxes and then extend these schemes to solve nonlinear Burgers’ equation and Euler equations. The numerical examples show that these schemes give high order of accuracy and high resolution results. The advantages of these schemes are their simplicity and high order of accuracy.

Based on recent progress on moment problems, semidefinite optimization approach is proposed for estimating upper and lower bounds on linear functionals defined on solutions of linear integral equations with smooth kernels. The approach is also suitable for linear integrodifferential equations with smooth kernels. Firstly, the primal problem with smooth kernel is converted to a series of approximative problems with Taylor polynomials obtained by expanding the smooth kernel. Secondly, two semidefinite programs (SDPs) are constructed for every approximative problem. Thirdly, upper and lower bounds on related functionals are gotten by applying SeDuMi 1.1R3 to solve the two SDPs. Finally, upper and lower bounds series obtained by solving two SDPs, respectively infinitely approach the exact value of discussed functional as approximative order of the smooth kernel increases. Numerical results show that the proposed approach is effective for the discussed problems.

The Legendre multiwavelet Galerkin method is adopted to give the approximate solution for the nonlinear fractional partial differential equations (NFPDEs). The Legendre multiwavelet properties are presented. The main characteristic of this approach is using these properties together with the Galerkin method to reduce the NFPDEs to the solution of nonlinear system of algebraic equations. We presented the numerical results and a comparison with the exact solution in the cases when we have an exact solution to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.

We deal with discrete weighted pseudo almost automorphy which extends some classical concepts and systematically explore its properties in Banach space including a composition result. As an application, we establish some sufficient criteria for the existence and uniqueness of the discrete weighted pseudo almost automorphic solutions to the Volterra difference equations of convolution type and also to nonautonomous semilinear difference equations. Some examples are presented to illustrate the main findings.

This paper studies systematically a differential-algebraic prey-predator model with time delay and Allee effect. It shows that transcritical bifurcation appears when a variation of predator handling time is taken into account. This model also exhibits singular induced bifurcation as the economic revenue increases through zero, which causes impulsive phenomenon. It can be noted that the impulsive phenomenon can be much weaker by strengthening Allee effect in numerical simulation. On the other hand, at a critical value of time delay, the model undergoes a Hopf bifurcation; that is, the increase of time delay destabilizes the model and bifurcates into small amplitude periodic solution. Moreover, a state delayed feedback control method, which can be implemented by adjusting the harvesting effort for biological populations, is proposed to drive the differential-algebraic system to a steady state. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results.

Two kinds of homomorphisms of fuzzy approximation spaces based on complete residuated lattice are proposed. The homomorphisms are structure-preserving maps in some sense. We also introduce the fuzzy approximation subspaces and investigate their correspondence with the homomorphisms. Given a fuzzy equivalence relation, the factor set of the fuzzy approximation space is discussed.

The Behrens-Fisher problem concerns the inferences for the difference between the means of two normal populations without making any assumption about the variances. Although the problem has been extensively studied in the literature, researchers cannot agree on its solution at present. In this paper, we propose a new method for dealing with the Behrens-Fisher problem in the Bayesian framework. The Bayesian evidence for testing the equality of two normal means and a credible interval at a specified level for the difference between the means are derived. Simulation studies are carried out to evaluate the performance of the provided Bayesian evidence.

Let ${\mathrm{\Gamma }}_n$ and ${\mathrm{\Lambda }}_n$ be the $n$-dimensional Fibonacci cube and Lucas cube, respectively. Denote by $\mathrm{\Gamma }[u_{n,k,z}]$ the subgraph of ${\mathrm{\Gamma }}_n$ induced by the end-vertex $u_{n,k,z}$ that has no up-neighbor. In this paper, the number of end-vertices and domination number $\gamma$ of ${\mathrm{\Gamma }}_n$ and ${\mathrm{\Lambda }}_n$ are studied. The formula of calculating the number of end-vertices is given and it is proved that $\gamma (\mathrm{\Gamma }[u_{n,k,z}])\le 2^{k-1}+1$. Using these results, the larger bound on the domination number $\gamma$ of ${\mathrm{\Gamma }}_n$ and ${\mathrm{\Lambda }}_n$ is determined.

This paper focuses on a class of stochastic differential equations with mixed delay based on Lyapunov stability theory, Itô formula, stochastic analysis, and inequality technique. A sufficient condition for existence and uniqueness of the adapted solution to such systems is established by employing fixed point theorem. Some sufficient conditions of exponential stability and corollaries for such systems are obtained by using Lyapunov function. By utilizing Doob’s martingale inequality and Borel-Cantelli lemma, it is shown that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. In particular, our theoretical results show that if stochastic differential equation is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic differential equation with mixed delay will remain exponentially stable. Moreover, time delay upper limit is solved by using our theoretical results when the system is exponentially stable, and they are more easily verified and applied in practice.

Project priority strategy is the benchmarking of a corporate operation management strategy and in particular is used by a projects-based research and development firm in the complex competence environment of the information and communication technology (ICT) industry. This research takes the variables of external environments and internal resources into account for a firm’s market, technology, and finance assets in order to present a decision process on a project priority strategy. This empirical study also addresses the key factors of the interaction between business on a project development’s supply chain: clients, the examined firm, and suppliers. The findings indicate that a profit-driven project can dominate the firm’s strategic operations and management from the resource-based view and analytic hierarchy process technique perspectives. At the same time, the analysis results contribute significant values to project decision management, which is highly recommended for small-medium enterprises conducting product/project development, project portfolio management, and strategic business management.

This paper examines the forecasting performance of ARIMA and artificial neural networks model with published stock data obtained from New York Stock Exchange. The empirical results obtained reveal the superiority of neural networks model over ARIMA model. The findings further resolve and clarify contradictory opinions reported in literature over the superiority of neural networks and ARIMA model and vice versa.

This paper studies axiom systems of supermatroids. Barnabei et al.'s base axioms concerning poset matroids (i.e., distributive supermatroids) are generalized to modular supermatroids, and a mistake in the proof of base axioms of poset matroids is pointed out.

A class of nonlinear multipoint boundary value problems for singular fractional differential equations is considered. By means of a coupled fixed point theorem on ordered sets, some results on the existence and uniqueness of positive solutions are obtained.

We focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main claim amount. In addition, the premium number process is assumed as a Poisson process. We derive the integral equation satisfied by the expected discounted penalty function. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the expected discounted penalty function is derived. Finally, for the exponential claim sizes, we present the explicit formula for the expected discounted penalty function.

The asymptotic equilibrium results for fuzzy differential systems $\left(GCP\right)\hspace{0.17em}{x}^{\prime }=f_1\left(t,x,y\right),y^{\prime }=f_2(t,x,y)$ are investigated, where $f_1\left(t,x,y\right)$ satisfies the compactness-type and $f_2\left(t,x,y\right)$ satisfies the dissipative-type conditions. It is worth mentioning that the uniformly continuous conditions of $f\left(t,x,y\right)$ are removed in Song et al. (2005). That is to say, the results of Song et al. (2005) are extended. In addition, the global existence and asymptotic equilibrium results of fuzzy differential systems $\left(CP\right)\hspace{0.17em}{x}^{\prime }\left(t\right)=f\left(t,x\right),x\left(0\right)=x_0$ are obtained.

Considering the uncertainty of a financial market includes two aspects: risk and vagueness; in this paper, fuzzy sets theory is applied to model the imprecise input parameters (interest rate and volatility). We present the fuzzy price of compound option by fuzzing the interest and volatility in Geske’s compound option pricing formula. For each $\alpha$, the $\alpha$-level set of fuzzy prices is obtained according to the fuzzy arithmetics and the definition of fuzzy-valued function. We apply a defuzzification method based on crisp possibilistic mean values of the fuzzy interest rate and fuzzy volatility to obtain the crisp possibilistic mean value of compound option price. Finally, we present a numerical analysis to illustrate the compound option pricing under fuzzy environment.

On the basis of the family of quasifiliform Lie algebra laws of dimension 9 of 16 parameters and 17 constraints, this paper is devoted to identify the invariants that completely classify the algebras over the complex numbers except for isomorphism. It is proved that the nullification of certain parameters or of parameter expressions divides the family into subfamilies such that any couple of them is nonisomorphic and any quasifiliform Lie algebra of dimension 9 is isomorphic to one of them. The iterative and exhaustive computation with Maple provides the classification, which divides the original family into 263 subfamilies, composed of 157 simple algebras, 77 families depending on 1 parameter, 24 families depending on 2 parameters, and 5 families depending on 3 parameters.

A paraconsistent semantics has been presented for hybrid MKNF knowledge bases—a combination method for description logics and rules. However, it is invalid when incoherency occurs in the knowledge base. In this paper, we introduce a semi-$S_5$ semantics for hybrid MKNF knowledge bases on the basis of nine-valued lattice, such that it is paraconsistent for incoherent knowledge base. It is shown that a semi-$S_5$ model can be computed via a fixpoint operator and is in fact a paraconsistent MKNF model when the knowledge base is incoherent. Moreover, we apply six-valued lattice to hybrid MKNF knowledge bases and present a suspicious semantics to distinguish different trust level information. At last, we investigate the relationship between suspicious semantics and paraconsistent semantics.

A Cohen-Grossberg neural network with discrete delays is investigated in this paper. Sufficient conditions for the existence of local Hopf bifurcation are obtained by analyzing the distribution of roots of characteristic equation. Moreover, the direction and stability of Hopf bifurcation are obtained by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the obtained results.

Type-2 fuzzy reasoning relations are the type-2 fuzzy relations obtained from a group of type-2 fuzzy reasonings by using extended t-(co)norm, which are essential for implementing type-2 fuzzy logic systems. In this paper an algorithm is provided for constructing type-2 fuzzy reasoning relations of SISO type-2 fuzzy logic systems. First, we give some properties of extended t-(co)norm and simplify the expression of type-2 fuzzy reasoning relations in accordance with different input subdomains under certain conditions. And then different techniques are discussed to solve the simplified expressions on the input subdomains by using the related methods on solving fuzzy relation equations. Besides, it is pointed out that the computation amount level of the proposed algorithm is the same as that of polynomials and the possibility of applying the proposed algorithm in the construction of type-2 fuzzy reasoning relations is illustrated on several examples. Finally, the calculation of an arbitrary extended continuous t-norm can be obtained as the special case of the proposed algorithm.

By using the polynomial expansion in the even order Bernoulli polynomials and using the linear combinations of the shifts of the function $f(x)(x\in ℝ)$ to approximate the derivatives of $f(x)$, we propose a family of modified even order Bernoulli-type multiquadric quasi-interpolants which do not require the derivatives of the function approximated at each node and can satisfy any degree polynomial reproduction property. Error estimate indicates that our operators could provide the desired precision by choosing a suitable shape-preserving parameter $c$ and a nonnegative integer $m$. Numerical comparisons show that this technique provides a higher degree of accuracy. Finally, applying our operators to the fitting of discrete solutions of initial value problems, we find that our method has smaller errors than the Runge-Kutta method of order 4 and Wang et al.’s quasi-interpolation scheme.

Based on a fourth order compact difference scheme, a Richardson cascadic multigrid (RCMG) method for 2D Poisson equation is proposed, in which the an initial value on the each grid level is given by the Richardson extrapolation technique (Wang and Zhang (2009)) and a cubic interpolation operator. The numerical experiments show that the new method is of higher accuracy and less computation time.

Impact on petroleum based vehicles on the environment, cost, and availability of fuel has led to an increased interest in electric vehicle as a means of transportation. Battery is a major component in an electric vehicle. Economic viability of these vehicles depends on the availability of cost-effective batteries. This paper presents a generalized formulation for determining the optimal operating strategy and cost optimization for battery. Assume that the deterioration of the battery is stochastic. Under the assumptions, the proposed operating strategy for battery is formulated as a nonlinear optimization problem considering reliability and failure number. And an explicit expression of the average cost rate is derived for battery lifetime. Results show that the proposed operating strategy enhances the availability and reliability at a low cost.

Global synchronization analysis for complex networks with coupling delay is investigated. Firstly the constant time delay is analyzed and then the case for time-varying delay is considered. Sufficient conditions for network synchronization are given based on Lyapunov functional, linear matrix inequality, and Kronecker product technique. The unknown variables in the sufficient conditions are fewer than those in the recent reference. Moreover, for the time-varying delay case, we find that the conditions are dependent on the bounds of both time delay and its derivative, and the derivative of the time-varying delay can be any value in the bounds. Finally, numerical examples are given to validate the effectiveness of the obtained results.

Universal projective synchronization (UPS) of two chaotic systems is defined. Based on the Lyapunov stability theory, an adaptive control method is derived such that UPS of two different hyperchaotic systems with unknown parameters is realized, which is up to a scaling function matrix and three kinds of reference systems, respectively. Numerical simulations are used to verify the effectiveness of the scheme.

To solve an unconstrained nonlinear minimization problem, we propose an optimal algorithm (OA) as well as a globally optimal algorithm (GOA), by deflecting the gradient direction to the best descent direction at each iteration step, and with an optimal parameter being derived explicitly. An invariant manifold defined for the model problem in terms of a locally quadratic function is used to derive a purely iterative algorithm and the convergence is proven. Then, the rank-two updating techniques of BFGS are employed, which result in several novel algorithms as being faster than the steepest descent method (SDM) and the variable metric method (DFP). Six numerical examples are examined and compared with exact solutions, revealing that the new algorithms of OA, GOA, and the updated ones have superior computational efficiency and accuracy.

The dynamical behavior of different Steffensen-type methods is analyzed. We check the chaotic behaviors alongside the convergence radii (understood as the wideness of the basin of attraction) needed by Steffensen-type methods, that is, derivative-free iteration functions, to converge to a root and compare the results using different numerical tests. We will conclude that the convergence radii (and the stability) of Steffensen-type methods are improved by increasing the convergence order. The computer programming package MATHEMATICA provides a powerful but easy environment for all aspects of numerics. This paper puts on show one of the application of this computer algebra system in finding fixed points of iteration functions.

We present new results on the existence and uniqueness of tripled fixed points for nonlinear mappings in partially ordered complete metric spaces that extend the results in the previous works: Berinde and Borcut, 2011, Borcut and Berinde, 2012, and Borcut, 2012. An example and an application to support our new results are also included in the paper.

A novel active disturbance rejection control (ADRC) controller is proposed based on support vector regression (SVR). The SVR-ADRC is designed to force an underactuated autonomous underwater vehicle (AUV) to follow a path in the horizontal plane with the ocean current disturbance. It is derived using SVR algorithm to adjust the coefficients of the nonlinear state error feedback (ELSEF) part in ADRC to deal with nonlinear variations at different operating points. The trend of change about ELSEF coefficients in the simulation proves that the designed SVR algorithm maintains the characteristics of astringency and stability. Furthermore, the path following errors under current in simulation has proved the high accuracy, strong robustness, and stability of the proposed SVR-ADRC. The contributions of the proposed controller are to improve the characteristics of ADRC considering the changing parameters in operating environment which make the controller more adaptive for the situation.

The purpose of this paper is to present two new forward-backward splitting schemes with relaxations and errors for finding a common element of the set of solutions to the variational inclusion problem with two accretive operators and the set of fixed points of nonexpansive mappings in infinite-dimensional Banach spaces. Under mild conditions, some weak and strong convergence theorems for approximating this common elements are proved. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as the improvement, supplementation, development, and extension of the corresponding results in the very recent literature.

We study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for countable Markov chains indexed by an infinite tree with uniformly bounded degree, which extends the corresponding results of countable Markov chains indexed by a Cayley tree and generalizes the relative results of finite Markov chains indexed by a uniformly bounded tree.

The main objective of this paper is to propose an optimal finite duration treatment method for cancer. A mathematical model is proposed to show the interactions between healthy and cancerous cells in the human body. To extend the existing models, the effect of vaccine therapy and chemotherapy are also added to the model. The equilibrium points and the related local stability are derived and discussed. It is shown that the dynamics of the cancer model must be changed and modified for finite treatment duration. Therefore, the vaccine therapy is used to change the parameters of the system and the chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. For optimal chemotherapy, an optimal control is used based on state dependent Riccati equation (SDRE). It is shown that, in spite of eliminating the treatment, the system approaches the healthy state conditions. The results show that the development of optimal vaccine-chemotherapy protocols for removing tumor cells would be an appropriate strategy in cancer treatment. Also, the present study states that a proper treatment method not only reduces the population of the cancer cells but also changes the dynamics of the cancer.

We study the relationship of the Chebyshev polynomials, Fibonacci polynomials, and their rth derivatives. We get the formulas for the rth derivatives of Chebyshev polynomials being represented by Chebyshev polynomials and Fibonacci polynomials. At last, we get several identities about the Fibonacci numbers and Lucas numbers.

The aim of this paper is to address how the secondary market affects the strategy of the manufacturer’s new product introduction by using the optimization method. To do so, we develop a two-period model in which a monopolistic manufacturer sells its new durable products directly to end consumers in both periods, while an entrant operates a reverse channel selling used products in the secondary market. We assume that the manufacturer launches a higher quality product in the second period for the technological innovation. We find that the secondary market can actually increase the manufacturer’s profitability and drives the new product introduction in the second period. We also derive the effect of the durability and the degree of quality improvement on the pricing of supply chain partners.

We define the notions of Bosbach states and inf-Bosbach states on a bounded hyper BCK-algebra $(H,\circ ,0,e)$ and derive some basic properties of them. We construct a quotient hyper BCK-algebra via a regular congruence relation. We also define a $\circ \text{-}\mathrm{compatibled}$ regular congruence relation $\theta$ and a $\theta \text{-}\mathrm{compatibled}$ inf-Bosbach state $s$ on $(H,\circ ,\mathrm{0,}e)$. By inducing an inf-Bosbach state $\widehat{s}$ on the quotient structure $H$ / ${[0]}_{\theta }$, we show that $H$ / ${[0]}_{\theta }$ is a bounded commutative BCK-algebra which is categorically equivalent to an MV-algebra. In addition, we introduce the notions of hyper measures (states/measure morphisms/state morphisms) on hyper BCK-algebras, and present a relation between hyper state-morphisms and Bosbach states. Then we construct a quotient hyper BCK-algebra $H$ / $\text{Ker}(m)$ by a reflexive hyper BCK-ideal $\text{Ker}(m)$. Further, we prove that $H$ / $\text{Ker}(m)$ is a bounded commutative BCK-algebra.

We present a new technique for solving numerically stochastic Volterra integral equation based on modified block pulse functions. It declares that the rate of convergence of the presented method is faster than the method based on block pulse functions. Efficiency of this method and good degree of accuracy are confirmed by a numerical example.

In this paper, a plant disease model with continuous cultural control strategy and time delay is formulated. Then, how the time delay affects the overall disease progression and, mathematically, how the delay affects the dynamics of the model are investigated. By analyzing the transendental characteristic equation, stability conditions related to the time delay are derived for the disease-free equilibrium. Specially, when $R_0=1$, the Jacobi matrix of the model at the disease-free equilibrium always has a simple zero eigenvalue for all $\tau \ge 0$. The center manifold reduction and the normal form theory are used to discuss the stability and the steady-state bifurcations of the model near the nonhyperbolic disease-free equilibrium. Then, the sensitivity analysis of the threshold parameter $R_0$ and the positive equilibrium $E^{*}$ is carried out in order to determine the relative importance of different factors responsible for disease transmission. Finally, numerical simulations are employed to support the qualitative results.

Within the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric Bézier basis with two shape parameters $\lambda$ and $\mu$ given in Han et al. (2009) forms an optimal normalized totally positive basis for $\mathrm{\lambda ,}\mu \in (-\mathrm{2,1}]$. Moreover, we show that for $\lambda =-\mathrm{2}$ or $\mu =-\mathrm{2}$ the basis is not suited for curve design from the blossom point of view. In order to compute the corresponding cubic trigonometric Bézier curves stably and efficiently, we also develop a new corner cutting algorithm.

The magnetohydrodynamic (MHD) boundary layer flow of a nanofluid past a stretching/shrinking sheet with velocity, thermal, and solutal slip boundary conditions is studied. Numerical solutions to the governing equations were obtained using a shooting method. The skin friction coefficient and the local Sherwood number increase as the stretching/shrinking parameter increases. However, the local Nusselt number decreases with increasing the stretching/shrinking parameter. The range of the stretching/shrinking parameter for which the solution exists increases as the velocity slip parameter and the magnetic parameter increase. For the shrinking sheet, the skin friction coefficient increases as the velocity slip parameter and the magnetic parameter increase. For the stretching sheet, it decreases when the velocity slip parameter and the magnetic parameter increase. The local Nusselt number diminishes as the thermal slip parameter increases while the local Sherwood number decreases with increasing the solutal slip parameter. The local Nusselt number is lower for higher values of Lewis number, Brownian motion parameter, and thermophoresis parameter.

This paper presents a novel optimization algorithm, namely, hierarchical artificial bee colony optimization (HABC), to tackle complex high-dimensional problems. In the proposed multilevel model, the higher-level species can be aggregated by the subpopulations from lower level. In the bottom level, each subpopulation employing the canonical ABC method searches the part-dimensional optimum in parallel, which can be constructed into a complete solution for the upper level. At the same time, the comprehensive learning method with crossover and mutation operator is applied to enhance the global search ability between species. Experiments are conducted on a set of 20 continuous and discrete benchmark problems. The experimental results demonstrate remarkable performance of the HABC algorithm when compared with other six evolutionary algorithms.

We investigate connections between bialgebras and Atanassov’s intuitionistic fuzzy sets. Firstly we define an intuitionistic fuzzy subbialgebra of a bialgebra with an intuitionistic fuzzy subalgebra structure and also with an intuitionistic fuzzy subcoalgebra structure. Secondly we investigate the related properties of intuitionistic fuzzy subbialgebras. Finally we prove that the dual of an intuitionistic fuzzy strong subbialgebra is an intuitionistic fuzzy strong subbialgebra.

This paper deals with the derivation of a simple mathematical model of cyclic learning with a period of 24 hours. Various requirements are met with an emphasis and approach which relies on simple mathematical operations, the prediction of measurable quantities, and the creation of uncomplicated processes of calibration. The presented model can be used to answer questions such as the following. Will I be able to memorize a given set of information? How long will it take to memorize information? How long will I remember the information that was memorized? The model is based on known memory retention functions that are in good agreement with experimental results. By the use of these functions and by formalism of differential equations, the concurrent processes of learning and forgetting are described mathematically. The usability of this model is limited to scenarios where logical bonds (connections to prior learning) are not created and mnemonic devices cannot be utilized during the learning process.

For the marginal longitudinal generalized linear models (GLMs), we develop the empirical Cressie-Read (ECR) test statistic approach which has been proposed for the independent identically distributed (i.i.d.) case. The ECR test statistic includes empirical likelihood as a special case. By adopting this ECR test statistic approach and taking into account the within-subject correlation, the efficiency theory results of estimation and testing based on ECR are established under some regularity conditions. Although a working correlation matrix is assumed, there is no need to estimate the nuisance parameters in the working correlation matrix based on the quadratic inference function (QIF). Therefore, the proposed ECR test statistic is asymptotically a standard ${\chi }^2$ limit under the null hypothesis. It is shown that the proposed method is more efficient even when the working correlation matrix is misspecified. We also evaluate the finite sample performance of the proposed methods via simulation studies and a real data analysis.

The element-free Galerkin (EFG) method is one of the widely used meshfree methods for solving partial differential equations. In the EFG method, shape functions are derived from a moving least-squares (MLS) approximation, which involves the inversion of a small matrix for every point of interest. To avoid the calculation of matrix inversion in the formulation of the shape functions, an improved MLS approximation is presented, where an orthogonal function system with a weight function is used. However, it can also lead to ill-conditioned or even singular system of equations. In this paper, aspects of the IMLS approximation are analyzed in detail. The reason why singularity problem occurs is studied. A novel technique based on matrix triangular process is proposed to solve this problem. It is shown that the EFG method with present technique is very effective in constructing shape functions. Numerical examples are illustrated to show the efficiency and accuracy of the proposed method. Although our study relies on monomial basis functions, it is more general than existing methods and can be extended to any basis functions.

The equivalent conditions of complete convergence are established for weighted sums of $\tilde{\rho }$-mixing random variables with different distributions. Our results extend and improve the Baum and Katz complete convergence theorem. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequence of $\tilde{\rho }$-mixing random variables is obtained.

We study the existence and nonexistence of positive solutions for the following fourth-order two-point boundary value problem subject to nonlinear boundary conditions $u^{\mathrm{\prime \prime \prime \prime }}(t)=\lambda f(t,u(t)),t\in (\mathrm{0,1}),u(\mathrm{0})=\mathrm{0},u^{\prime }(\mathrm{0})=\mu h(u(\mathrm{0})),u^{\mathrm{\prime \prime }}(\mathrm{1})=\mathrm{0},u^{\mathrm{\prime \prime \prime }}(\mathrm{1})=\mu g(u(\mathrm{1}))$, where $\lambda >0, \mu \ge 0$ are parameters, and $f:\left[0, 1\right]\times \left[0,+\infty \right)\to \left(0, +\infty \right), h:\left[0, +\infty \right)\to \left[0, +\infty \right)$, and $g:\left[0, +\infty \right)\to \left(-\infty ,0\right]$ are continuous. By using the fixed-point index theory, we prove that the problem has at least one positive solution for $\lambda ,\mu$ sufficiently small and has no positive solution for $\lambda$ large enough.

The Chinese commodity futures markets neglect the existence of the risk hedge and diversification between futures contracts, thus leading to overcharge futures portfolio holders’ maintenance margins. To this end, this paper proposes a new method, namely, the multivariate t-Copula-POT-PSRM method, which combines three models, that is, the multivariate t-Copula, the peaks over threshold (POT), and the power spectral risk measures (PSRM), to set futures portfolios’ maintenance margins. In the empirical analysis, we first construct four kinds of futures portfolios and set their maintenance margins by using the new method. Then, we introduce two evaluation indicators, namely, the prudence index (PI) and the opportunity cost index (OCI), to assess the effectiveness of the proposed method. We also compare the outcomes of the two evaluation indicators of the new method with those of the widely used linear additive model. The empirical results show that the new method can, respectively, lower the OCI value of all four kinds of futures portfolios for the In-sample period and the Out-of-sample period without significantly reducing the PI value as against the traditional model, which implies that the proposed method can be used to balance security and investment efficiency in the futures market.

The cost-based system optimum problem in networks with continuously distributed value of time is formulated as a path-based form, which cannot be solved by the Frank-Wolfe algorithm. In light of magnitude improvement in the availability of computer memory in recent years, path-based algorithms have been regarded as a viable approach for traffic assignment problems with reasonably large network sizes. We develop a path-based gradient projection algorithm for solving the cost-based system optimum model, based on Goldstein-Levitin-Polyak method which has been successfully applied to solve standard user equilibrium and system optimum problems. The Sioux Falls network tested is used to verify the effectiveness of the algorithm.

The aim of this paper is to introduce the concepts of IFP-intuitionistic fuzzy soft h-ideals and IFP-equivalent intuitionistic fuzzy soft h-ideals of hemirings. Some characterizations and properties of them are given. In particular, some good examples are explored. Finally, we investigate aggregate intuitionistic fuzzy h-ideals of hemirings based on decision making.

We propose a fully discrete method for the multiscale Richards’ equation of van Genuchten-Mualem model which describes the flow transport in unsaturated heterogenous porous media. Under the framework of heterogeneous multiscale method (HMM), a fully discrete scheme combined with a regularized procedure is proposed. Including the numerical integration, the discretization is given by $C^0$ piecewise finite element in space and an implicit scheme in time. Error estimates between the numerical solution and the solution of homogenized problem are derived under the assumption that the permeability is periodic. Numerical experiments with periodic and random permeability are carried out for the van Genuchten-Mualem model of Richards’ equation to show the efficiency and accuracy of the proposed method.

A delayed SEIQRS model for the transmission of malicious objects in computer network is considered in this paper. Local stability of the positive equilibrium of the model and existence of local Hopf bifurcation are investigated by regarding the time delay due to the temporary immunity period after which a recovered computer may be infected again. Further, the properties of the Hopf bifurcation are studied by using the normal form method and center manifold theorem. Numerical simulations are also presented to support the theoretical results.

A ratio-dependent predator-prey model incorporating a prey refuge with disease in the prey population is formulated and analyzed. The effects of time delay due to the gestation of the predator and stage structure for the predator on the dynamics of the system are concerned. By analyzing the corresponding characteristic equations, the local stability of a predator-extinction equilibrium and a coexistence equilibrium of the system is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the coexistence equilibrium, when $\tau ={\tau }_0$. By comparison arguments, sufficient conditions are obtained for the global stability of the predator-extinction equilibrium. By using an iteration technique, sufficient conditions are derived for the global attractivity of the coexistence equilibrium of the proposed system.

This paper is concerned with the impulsive synchronization problem of chaotic delayed neural networks. By employing Lyapunov stability theorem, impulsive control theory and linear matrix inequality (LMI) technique, several new sufficient conditions ensuring the asymptotically synchronization for coupled chaotic delayed neural networks are derived. Based on these new sufficient conditions, an impulsive controller is designed. Moreover, the stable impulsive interval of synchronized neural networks is objectively estimated by combining the MATLAB LMI toolbox and one of the two given equations. Two examples with numerical simulations are given to illustrate the effectiveness of the proposed method.

For the Blasius velocity profile we propose a simple algebraic type approximate function which is uniformly accurate over the whole region. Moreover, for further improvement a correction method based on a weight function is introduced. The availability of the proposed method is shown by the result of numerical experiments.

The Olver equation is governing a unidirectional model for describing long and small amplitude waves in shallow water waves. The solitary wave solutions of the Olver and fifth-order KdV equations can be obtained by using extended tanh and sech-tanh methods. The present results are describing the generation and evolution of such waves, their interactions, and their stability. Moreover, the methods can be applied to a wide class of nonlinear evolution equations. All solutions are exact and stable and have applications in physics.

The flow field and the sand flow field constitutive equations are analyzed at first, then the different desert highway numerical models are established by considering the crossroad and by changing the road surface height and air stream flow field, then three kinds of different models with different complex air flow fields are made for simulating the sand ripple formation process by weak coupling of air and sand flow field, and finally the numerical simulations of these models are conducted and the affect process of sand morphology under complex air flow fields are discussed. The results show that under the uniform airflow field, the straight parallel ripple formed and the flared ripple formed in the middle region of the crossroad, and the wavelength of the ripples on the desert highway is bigger than that of the ripples around the road when the road height is higher than that of the sand surface height. Under the nonuniform complex airflow field, the complex curved ripples are formed, and some of the local area, where the whirlwind exits, no ripples are formed.

The grey prediction model with convolution integral GMC (1, n) is a multiple grey model with exact solutions. To further improve prediction accuracy and describe better the relationship between cause and effect, we introduce nonlinear parameters into GMC (1, n) model and additionally apply a convolution integral to produce an improved forecasting model here designated as NGMC (1, n). The model solving process applied the least-squares method to evaluate the structure parameters of the model: convolution was used to obtain an exact solution with this improved grey model. The nonlinear optimisation took the parameters as the decision variables with the objective of minimising forecasting errors. The GMC (1, 2) and NGMC (1, 2) models were used to predict China’s industrial SO₂ emissions from the basis of the economic output level as the influencing factor. Results indicated that NGMC (1, 2) can effectively describe the nonlinear relationship between China’s economic output and SO₂ emissions with an improved accuracy over current GMC (1, 2) models.

We study surfaces defined as graph of the function $z=f(x,y)$ in the product space ${ℍ}^2\times ℝ$. In particular, we completely classify flat or minimal surfaces given by $f(x,y)=u(x)+v(y)$, where $u(x)$ and $v(y)$ are smooth functions.

The objective of this paper is to present a numerical iterative method for solving systems of first-order ordinary differential equations subject to periodic boundary conditions. This iterative technique is based on the use of the reproducing kernel Hilbert space method in which every function satisfies the periodic boundary conditions. The present method is accurate, needs less effort to achieve the results, and is especially developed for nonlinear case. Furthermore, the present method enables us to approximate the solutions and their derivatives at every point of the range of integration. Indeed, three numerical examples are provided to illustrate the effectiveness of the present method. Results obtained show that the numerical scheme is very effective and convenient for solving systems of first-order ordinary differential equations with periodic boundary conditions.

Due to convenience and powerfulness in dealing with vagueness and uncertainty of real situation, hesitant fuzzy set has received more and more attention and has been a hot research topic recently. To differently process and effectively aggregate hesitant fuzzy information and capture their interrelationship, in this paper, we propose the hesitant fuzzy reducible weighted Bonferroni mean (HFRWBM) and present its four prominent characteristics, namely, reductibility, monotonicity, boundedness, and idempotency. Then, we further investigate its generalized form, that is, the generalized hesitant fuzzy reducible weighted Bonferroni mean (GHFRWBM). Based on the discussion of model parameters, some special cases of the HFRWBM and GHFRWBM are studied in detail. In addition, to deal with the situation that multicriteria have connections in hesitant fuzzy information aggregation, a three-step aggregation approach has been proposed on the basis of the HFRWBM and GHFRWBM. In the end, we apply the proposed aggregation operators to multicriteria aggregation and give an example to illustrate our results.

In market transactions, volatility, which is a very important risk measurement in financial economics, has significantly intimate connection with the future risk of the underlying assets. Identifying the implied volatility is a typical PDE inverse problem. In this paper, based on the total variation regularization strategy, a bivariate total variation regularization model is proposed to estimate the implied volatility. We not only prove the existence of the solution, but also provide the necessary condition of the optimal control problem—Euler-Lagrange equation. The stability and convergence analyses for the proposed approach are also given. Finally, numerical experiments have been carried out to show the effectiveness of the method.

The pricing problem of geometric average Asian option under fractional Brownian motion is studied in this paper. The partial differential equation satisfied by the option’s value is presented on the basis of no-arbitrage principle and fractional formula. Then by solving the partial differential equation, the pricing formula and call-put parity of the geometric average Asian option with dividend payment and transaction costs are obtained. At last, the influences of Hurst index and maturity on option value are discussed by numerical examples.

Much of the previous work in D-optimal design for regression models with correlated errors focused on polynomial models with a single predictor variable, in large part because of the intractability of an analytic solution. In this paper, we present a modified, improved simulated annealing algorithm, providing practical approaches to specifications of the annealing cooling parameters, thresholds, and search neighborhoods for the perturbation scheme, which finds approximate D-optimal designs for 2-way and 3-way polynomial regression for a variety of specific correlation structures with a given correlation coefficient. Results in each correlated-errors case are compared with traditional simulated annealing algorithm, that is, the SA algorithm without our improvement. Our improved simulated annealing results had generally higher D-efficiency than traditional simulated annealing algorithm, especially when the correlation parameter was well away from 0.

In this paper, the impact of urban surface roughness length $\left(z_0\right)$ parameterization scheme on the atmospheric environment simulation over Beijing has been investigated through two sets of numerical experiments using the Weather Research and Forecasting model coupled with the Urban Canopy Model. For the control experiment (CTL), the urban surface $z_0$ parameterization scheme used in UCM is the model default one. For another experiment (EXP), a newly developed urban surface $z_0$ parameterization scheme is adopted, which takes into account the comprehensive effects of urban morphology. The comparison of the two sets of simulation results shows that all the roughness parameters computed from the EXP run are larger than those in the CTL run. The increased roughness parameters in the EXP run result in strengthened drag and blocking effects exerted by buildings, which lead to enhanced friction velocity, weakened wind speed in daytime, and boosted turbulent kinetic energy after sunset. Thermal variables (sensible heat flux and temperature) are much less sensitive to $z_0$ variations. In contrast with the CTL run, the EXP run reasonably simulates the observed nocturnal low-level jet. Besides, the EXP run-simulated land surface-atmosphere momentum and heat exchanges are also in better agreement with the observation.

A new linearizing method is presented for globally solving sum of linear ratios problem with coefficients. By using the linearizing method, linear relaxation programming (LRP) of the sum of linear ratios problem with coefficients is established, which can provide the reliable lower bound of the optimal value of the initial problem. Thus, a branch and bound algorithm for solving the sum of linear ratios problem with coefficients is put forward. By successively partitioning the linear relaxation of the feasible region and solving a series of the LRP, the proposed algorithm is convergent to the global optimal solution of the initial problem. Compared with the known methods, numerical experimental results show that the proposed method has the higher computational efficiency in finding the global optimum of the sum of linear ratios problem with coefficients.

This paper studies identification problems of two-input single-output controlled autoregressive moving average systems by using an estimated noise transfer function to filter the input-output data. Through data filtering, we obtain two simple identification models, one containing the parameters of the system model and the other containing the parameters of the noise model. Furthermore, we deduce a data filtering based recursive least squares method for estimating the parameters of these two identification models, respectively, by replacing the unmeasurable variables in the information vectors with their estimates. The proposed algorithm has high computational efficiency because the dimensions of its covariance matrices become small. The simulation results indicate that the proposed algorithm is effective.