The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order models are considered, since they can be seen as proper representatives of a larger class of systems. The explicit relationship between the control input and the Hopf bifurcation nature is obtained via a frequency approach, that does not need the computation of the center manifold.

The transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain is derived to Hamiltonian system. In symplectic geometry space with the origin variables—displacements, electric potential, and magnetic potential, as well as their duality variables—lengthways stress, electric displacement, and magnetic induction, on the basis of the obtained eigensolutions of zero-eigenvalue, the eigensolutions of nonzero-eigenvalues are also obtained. The former are the basic solutions of Saint-Venant problem, and the latter are the solutions which have the local effect, decay drastically with respect to distance, and are covered in the Saint-Venant principle. So the complete solution of the problem is given out by the symplectic eigensolutions expansion. Finally, a few examples are selected and their analytical solutions are presented.

The Problem of peristaltic transport of a magnetic fluid with variable viscosity through the gap between coaxial tubes where the outer tube is nonuniform with sinusoidal wave traveling down its wall and the inner tube is rigid. The relation between the pressure gradient and friction force on the inner and outer tubes is obtained in terms of magnetic and viscosity parameter. The numerical solutions of pressure gradient, outer friction and inner friction force, and flow rate are shown graphically.

We introduce algorithms marching over a polygonal mesh with elements consistent with the propagation directions of the particle (radiation) flux. The decision for adopting this kind of mesh to solve the one-speed Boltzmann transport equation is due to characteristics of the domain of the transport operator which controls derivatives only in the direction of propagation of the particles (radiation) flux in the absorbing and scattering media. This a priori adaptivity has the advantages that it formulates a consistent scheme which makes appropriate the application of the Lax equivalence theorem framework to the problem. In this work, we present the main functional spaces involved in the formalism and a description of the algorithms for the mesh generation and the transport equation solution. Some numerical examples related to the solution of a transmission problem in a high-contrast model with absorption and scattering are presented. Also, a comparison with benchmarks problems for source and reactor criticality simulations shows the compatibility between calculations with the algorithms proposed here and theoretical results.

The aim of this paper is to prove a common fixed point theorem for six mappings on fuzzy metric space using notion of semicompatibility and reciprocal continuity of maps satisfying an implicit relation. We proposed to reanalysis the theorems of Imdad et al. (2002), Popa (2001), Popa (2002) and Singh and Jain (2005).

A nonlinear Schrödinger (NLS) equation with an effect of viscosity is derived from a Korteweg-de Vries (KdV) equation modified with viscosity using the method of multiple time scale. It is well known that the plane-wave solution of the NLS equation exhibits modulational instability phenomenon. In this paper, the modulational instability of the plane-wave solution of the NLS equation modified with viscosity is investigated. The corresponding modulational dispersion relation is expressed as a quadratic equation with complex-valued coefficients. By restricting the modulational wavenumber into the case of narrow-banded spectra, it is observed that a type of dissipation, in this case the effect of viscosity, stabilizes the modulational instability, as confirmed by earlier findings.

The magnetohydrodynamic (MHD) and rotating flow of second-grade fluid over a suddenly moved flat plate is investigated, where the second-grade fluid saturates the porous medium. The new exact solution is derived by using the Fourier sine and Laplace transforms. Many interesting available results in the literature are obtained as limiting cases of our solution. Finally, some graphical results are presented for different values of the material constants.

This work is devoted to contribute with two algorithms for performing, in an efficient way, connected components labeling and boundary extraction from orthogonal pseudo-polytopes. The proposals are specified in terms of the extreme vertices model in the $n$-dimensional space ($n$D-EVM). An overview of the model is presented, considering aspects such as its fundamentals and basic algorithms. The temporal efficiency of the two proposed algorithms is sustained in empirical way and by taking into account both lower dimensional cases (2D and 3D) and higher-dimensional cases (4D and 5D).

Motivated essentially by the success of the applications of the Mittag-Leffler functions in many areas of science and engineering, the authors present, in a unified manner, a detailed account or rather a brief survey of the Mittag-Leffler function, generalized Mittag-Leffler functions, Mittag-Leffler type functions, and their interesting and useful properties. Applications of G. M. Mittag-Leffler functions in certain areas of physical and applied sciences are also demonstrated. During the last two decades this function has come into prominence after about nine decades of its discovery by a Swedish Mathematician Mittag-Leffler, due to the vast potential of its applications in solving the problems of physical, biological, engineering, and earth sciences, and so forth. In this survey paper, nearly all types of Mittag-Leffler type functions existing in the literature are presented. An attempt is made to present nearly an exhaustive list of references concerning the Mittag-Leffler functions to make the reader familiar with the present trend of research in Mittag-Leffler type functions and their applications.

Let $F$ be a distribution in $𝒟\text{'}$ and let $f$ be a locally summable function. The composition $F\left(f\right(x\left)\right)$ of $F$ and $f$ is said to exist and be equal to the distribution $h\left(x\right)$ if the limit of the sequence $\left\{F_n\left(f\right(x\left)\right)\right\}$ is equal to $h\left(x\right)$, where $F_n\left(x\right)=F\left(x\right)*{\delta }_n\left(x\right)$ for $n=1,2,\dots$ and $\left\{{\delta }_n\left(x\right)\right\}$ is a certain regular sequence converging to the Dirac delta function. In the ordinary sense, the composition ${\delta }^{\left(s\right)}\left[\right({\sinh }^{-1}{x}_{+}{)}^r]$ does not exists. In this study, it is proved that the neutrix composition ${\delta }^{\left(s\right)}\left[\right({\sinh }^{-1}{x}_{+}{)}^r]$ exists and is given by ${\delta }^{\left(s\right)}\left[{\left({\sinh }^{-1}{x}_{+}\right)}^r\right]={\displaystyle \sum _{k=0}^{sr+r-1}}{\displaystyle \sum _{i=0}^k}\left(\genfrac{}{}{0ex}{}{\text{k}}{\text{i}}\right)({(-1)}^{k}r{c}_{s,k,i}/2^{k+1}k!){\delta }^{\left(k\right)}\left(x\right)$, for $s=0,1,2,\dots$ and $s=1,2,\dots$, where $c_{s,k,i}=(-1{)}^{s}s!\left[\right(k-2i+1{)}^{rs-1}+(k-2i-1{)}^{rs+r-1}]/\left(2\right(rs+r-1)!)$. Further results are also proved.

We will study oscillation of bounded solutions of higher-order nonlinear neutral delay differential equations of the following type: ${[y\left(t\right)+p\left(t\right)f\left(y\right(\tau \left(t\right)\left)\right)]}^{\left(n\right)}+q\left(t\right)h\left(y\right(\sigma \left(t\right)\left)\right)=0$, $t\ge t_0$, $t\in ℝ$, where $p\in C\left(\right[t_0,\infty ),ℝ)$, ${\text{lim}}_{t\to \infty }p\left(t\right)=0$, $q\in C\left(\right[t_0,\infty ),{ℝ}^{+})$, $\tau \left(t\right)$, $\sigma \left(t\right)\in C\left(\right[t_0,\infty ),ℝ)$, $\tau \left(t\right)$, $\sigma \left(t\right)<t$, ${\lim }_{t\to \infty }\tau \left(t\right)$, $\sigma \left(t\right)=\infty$, and $f,h\in C(ℝ,ℝ)$. We obtain sufficient conditions for the oscillation of all solutions of this equation.

The challenge of tensor field visualization is to provide simple and comprehensible representations of data which vary both directionally and spatially. We explore the use of differential operators to extract features from tensor fields. These features can be used to generate skeleton representations of the data that accurately characterize the global field structure. Previously, vector field operators such as gradient, divergence, and curl have previously been used to visualize of flow fields. In this paper, we use generalizations of these operators to locate and classify tensor field degenerate points and to partition the field into regions of homogeneous behavior. We describe the implementation of our feature extraction and demonstrate our new techniques on synthetic data sets of order 2, 3 and 4.

We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given.

We study the multiplicity of periodic solutions of nonautonomous delay differential equations which are asymptotically linear both at zero and at infinity. By making use of a theorem of Benci, some sufficient conditions are obtained to guarantee the existence of multiple periodic solutions.

The sharp estimates of the $m$-linear $p$-adic Hardy and Hardy-Littlewood-Pólya operators on Lebesgue spaces with power weights are obtained in this paper.

Dispersion of Love waves is studied in a fibre-reinforced layer resting on monoclinic half-space. The wave velocity equation has been obtained for a fiber-reinforced layer resting on monoclinic half space. Shear wave velocity ratio curve for Love waves has been shown graphically for fibre reinforced material layer resting on various monoclinic half-spaces. In a similar way, shear wave velocity ratio curve for Love waves has been plotted for an isotropic layer resting on various monoclinic half-spaces. From these curves, it has been observed that the curves are of similar type for a fibre reinforced layer resting on monoclinic half-spaces, and the shear wave velocity ratio ranges from 1.14 to 7.19, whereas for the case isotropic layer, this range varies from 1.0 to 2.19.

This paper presents a global optimization method for solving general nonlinear programming problems subjected to box constraints. Regardless of convexity or nonconvexity, by introducing a differential flow on the dual feasible space, a set of complete solutions to the original problem is obtained, and criteria for global optimality and existence of solutions are given. Our theorems improve and generalize recent known results in the canonical duality theory. Applications to a class of constrained optimal control problems are discussed. Particularly, an analytical form of the optimal control is expressed. Some examples are included to illustrate this new approach.

We define here an integral operator ${\mathscr{H}}_{{\gamma }_1,\dots ,{\gamma }_n}$ for meromorphic functions in the punctured open unit disk. Several starlikeness conditions for the integral operator ${\mathscr{H}}_{{\gamma }_1,\dots ,{\gamma }_n}$ are derived.

In batch culture of glycerol biodissimilation to 1,3-propanediol (1,3-PD), the aim of adding glycerol is to obtain as much 1,3-PD as possible. Taking the yield intensity of 1,3-PD as the performance index and the initial concentration of biomass, glycerol, and terminal time as the control vector, we propose an optimal control model subject to a multistage nonlinear dynamical system and constraints of continuous state. A computational approach is constructed to seek the solution of the above model. Firstly, we transform the optimal control problem into the one with fixed terminal time. Secondly, we transcribe the optimal control model into an unconstrained one based on the penalty functions and an extension of the state space. Finally, by approximating the control function with simple functions, we transform the unconstrained optimal control problem into a sequence of nonlinear programming problems, which can be solved using gradient-based optimization techniques. The convergence analysis and optimality function of the algorithm are also investigated. Numerical results show that, by employing the optimal control, the concentration of 1,3-PD at the terminal time can be increased, compared with the previous results.

We study the problem of pricing an inflation adjusted annuity in a forward rates market with jumps. Since the market will be incomplete, we use the minimal $f^q$-martingale measure $Q_q$ which we use for computing discounted expectations. We give explicit results for $Q_q$ together with explicit results for the price of the annuity.

The aim of this paper is to investigate the solution and the superstability of the Pexiderized Lobacevski equation $f{\left(\right(x+y)/2)}^2=g\left(x\right)h\left(y\right)$, where $f$, $g$, $h:G^2\to C$ are unknown functions on an Abelian semigroup $(G,+)$. The obtained result is a generalization of Gavruta's result in 1994 and Kim's result in 2010.

Let $F$ be a distribution in $𝒟\text{'}$ and let $f$ be a locally summable function. The composition $F\left(f\right(x\left)\right)$ of $F$ and $f$ is said to exist and be equal to the distribution $h\left(x\right)$ if the limit of the sequence $\left\{F_n\left(f\right(x\left)\right)\right\}$ is equal to $h\left(x\right)$, where $F_n\left(x\right)=F\left(x\right)*{\delta }_n\left(x\right)$ for $n=\mathrm{1,2},\dots$ and $\left\{{\delta }_n\left(x\right)\right\}$ is a certain regular sequence converging to the Dirac delta function. It is proved that the neutrix composition ${\delta }^{(rs-1)}\left(\right(\tanh x_{+}{)}^{1/r})$ exists and ${\delta }^{(rs-1)}\left({\left(\tanh x_{+}\right)}^{1/r}\right)={{\displaystyle \sum }}_{k=0}^{s-1}{{\displaystyle \sum }}_{i=0}^{K_k}\left({(-1)}^k{c}_{s-2i-1,k}\right(rs)!/2sk!){\delta }^{\left(k\right)}\left(x\right)$ for $r,s=\mathrm{1,2},\dots$, where $K_k$ is the integer part of $(s-k-1)/2$ and the constants $c_{j,k}$ are defined by the expansion ${\left({\tanh }^{-1}x\right)}^k={\left\{{\displaystyle \sum _{i=0}^{\infty }}(x^{2i+1}/(2i+1\left)\right)\right\}}^k={\displaystyle \sum _{j=k}^{\infty }}{c}_{j,k}{x}^j$, for $k=0,1,2,\dots$. Further results are also proved.

A class of nonlinear fourth-order telegraph-diffusion equations (TDE) for image restoration are proposed based on fourth-order TDE and bilateral filtering. The proposed model enjoys the benefits of both fourth-order TDE and bilateral filtering, which is not only edge preserving and robust to noise but also avoids the staircase effects. The existence, uniqueness, and stability of the solution for our model are proved. Experiment results show the effectiveness of the proposed model and demonstrate its superiority to the existing models.

Both the forward and backward kinematics of the Gough-Stewart mechanism exhibit nonlinear behavior. It is critically important to take account of this nonlinearity in some applications such as path control in parallel kinematics machine tools. The nonlinearity of inverse kinematics is straightforward and has been first studied in this paper. However the nonlinearity of forward kinematics is more challenging to be considered as there is no analytic solution to the forward kinematic solution of the mechanism. A statistical approach including the Bates and Watts measures of nonlinearity has been employed to investigate the nonlinearity of the forward kinematics. The concept of standard sphere has been used to check the significance of the nonlinearity of the mechanism. It is demonstrated that the length of the region, defined as the linear approximation of the lifted line, has a significant impact on the nonlinearity of the mechanism.

The existence of the solution for a new system of generalized nonlinear mixed quasi variational inclusions with H-monotone operators is proved by using implicit resolvent technique, and the sensitivity analysis of solution in Hilbert spaces is given. Our results improve and generalize some results of the recent ones.

Convex multiobjective programming problems and multiplicative programming problems have important applications in areas such as finance, economics, bond portfolio optimization, engineering, and other fields. This paper presents a quite easy algorithm for generating a number of efficient outcome solutions for convex multiobjective programming problems. As an application, we propose an outer approximation algorithm in the outcome space for solving the multiplicative convex program. The computational results are provided on several test problems.

Regularity criterion for the 3D micropolar fluid equations is investigated. We prove that, for some $T>0$, if ${{\displaystyle \int }}_0^T\parallel v_{x_3}{\parallel }_{L^{\varrho }}^{\rho }dt<\infty$, where $3/\varrho +2/\rho \le 1$ and $\varrho \ge 3$, then the solution $(v,w)$ can be extended smoothly beyond $t=T$. The derivative $v_{x_3}$ can be substituted with any directional derivative of v.

We derive a new iteration method for finding solution of the generalized Blasius problem. This method results in the analytical series solutions which are consistent with the existing series solutions for some special cases.

This paper considers the approximate controllability for a class of semilinear delay control systems described by a semigroup formulation with boundary control. Sufficient conditions for approximate controllability are established provided the approximate controllability of corresponding linear systems.

We prove some common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces both in the sense of Kramosil and Michalek and in the sense of George and Veeramani by using the new property and give some examples. Our results improve and generalize the main results of Mihet in (Mihet, 2010) and many fixed point theorems in fuzzy metric spaces.

This paper is an extension to the recent results presented by M. Sabatini about the existence and uniqueness of limit cycles of a certain class of planar differential systems in order to include other new classes. A concrete example exhibiting the applicability of the result is introduced.

We study a three-firm contagion model with counterparty risk and apply this model to price defaultable bonds and credit default swap (CDS). This model assumes that default intensities are driven by external common factors as well as other defaults in the system. Using the “total hazard” approach, default times can be generated and the joint density function is obtained. We represent the pricing method of defaultable bonds and obtain the closed-form pricing formulas. By the approach of “change of measure,” analytical solutions of CDS swap rate (swap premuim) are derived in the continuous time framework and the discrete time framework, respectively.

The dilogarithm integral Li($x^s$) and its associated functions ${\text{Li}}_{+}\left(x^s\right)$ and ${\text{Li}}_{-}\left(x^s\right)$ are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of these functions and other functions are then found.

A nondifferentiable multiobjective optimization problem with nonempty set constraints is considered, and the equivalence of weakly efficient solutions, the critical points for the nondifferentiable multiobjective optimization problems, and solutions for vector variational-like inequalities is established under some suitable conditions. Nonemptiness and compactness of the solutions set for the nondifferentiable multiobjective optimization problems are proved by using the FKKM theorem and a fixed-point theorem.

We introduce a new iterative scheme that converges strongly to a common fixed point of a countable family of nonexpansive mappings in a Hilbert space such that the common fixed point is a solution of a hierarchical fixed point problem. Our results extend the ones of Moudafi, Xu, Cianciaruso et al., and Yao et al.

We introduce a new iterative scheme by shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of variational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotone mappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above four sets under some mind conditions. Furthermore, by using the above result, an iterative algorithm for solution of an optimization problem was obtained. Our results improve and extend the corresponding results of Martinez-Yanes and Xu (2006), Shehu (2011), Zhang et al. (2008), and many authors.

A new system of generalized mixed quasivariational inclusions (for short, SGMQVI) with relaxed cocoercive operators, which develop some preexisting variational inequalities, is introduced and investigated in Banach spaces. Next, the existence and uniqueness of solutions to the problem (SGMQVI) are established in real Banach spaces. From fixed point perspective, we propose some new iterative algorithms for solving the system of generalized mixed quasivariational inclusion problem (SGMQVI). Moreover, strong convergence theorems of these iterative sequences generated by the corresponding algorithms are proved under suitable conditions. As an application, the strong convergence theorem for a class of bilevel variational inequalities is derived in Hilbert space. The main results in this paper develop, improve, and unify some well-known results in the literature.

We investigate the initial value problem for a class of fractional evolution equations in a Banach space. Under some monotone conditions and noncompactness measure conditions of the nonlinearity, the well-known monotone iterative technique is then extended for fractional evolution equations which provides computable monotone sequences that converge to the extremal solutions in a sector generated by upper and lower solutions. An example to illustrate the applications of the main results is given.

Due to the difficulty for constructing two-dimensional wavelet filters, the commonly used wavelet filters are tensor-product of one-dimensional wavelet filters. In some applications, more perfect reconstruction filters should be provided. In this paper, we introduce a transformation which is referred to as Shift Unitary Transform (SUT) of Conjugate Quadrature Filter (CQF). In terms of this transformation, we propose a parametrization method for constructing two-dimensional orthogonal wavelet filters. It is proved that tensor-product wavelet filters are only special cases of this parametrization method. To show this, we introduce the SUT of one-dimensional CQF and present a complete parametrization of one-dimensional wavelet system. As a result, more ways are provided to randomly generate two-dimensional perfect reconstruction filters.

We investigate the stability of the functional equation $\mathrm{2f}(x+y)+f(x-y)+f(y-x)-\mathrm{3f}\left(x\right)-f(-x)-\mathrm{3f}\left(y\right)-f(-y)=0$ by using the fixed point theory in the sense of Cadariu and Radu.

The techniques for parametrizing nonsingular cubic surfaces have shown to be of great interest in recent years. This paper is devoted to the rational parametrization of nonsingular cubic blending surfaces. We claim that these nonsingular cubic blending surfaces can be parametrized using the symbolic computation due to their excellent geometric properties. Especially for the specific forms of these surfaces, we conclude that they must be $F_3$, $F_4$, or $F_5$ surfaces, and a criterion is given for deciding their surface types. Besides, using the algorithm proposed by Berry and Patterson in 2001, we obtain the uniform rational parametric representation of these specific forms. It should be emphasized that our results in this paper are invariant under any nonsingular real projective transform. Two explicit examples are presented at the end of this paper.

We deal with the extinction of the solutions of the initial-boundary value problem of the discrete p-Laplacian equation with absorption $u_t={\Delta }_{p,\omega }u-u^q$ with $p>1$, $q>0$, which is said to be the discrete p-Laplacian equation on weighted graphs. For $0<q<1$, we show that the nontrivial solution becomes extinction in finite time while it remains strictly positive for $p\ge 2$, $q\ge 1$ and $q\ge p-1$. Finally, a numerical experiment on a simple graph with standard weight is given.

A class of generalized definitions of expectation value is often employed in nonequilibrium statistical mechanics for complex systems. Here, the necessary and sufficient condition is presented for such a class to be stable under small deformations of a given arbitrary probability distribution.

The enlargement and rupture of intracranial and abdominal aortic aneurysms constitutes a major medical problem. It has been suggested that enlargement and rupture are due to mechanical instabilities of the associated complex fluid-solid interaction in the lesions. In this paper, we examine a coupled fluid-structure mathematical model for a cylindrical geometry representing an idealized aneurysm using both analytical and numerical techniques. A stability analysis for this subclass of aneurysms is presented. It is shown that this subclass of aneurysms is dynamically stable both with and without a viscoelastic contribution to the arterial wall.

Some properties of the weak subdifferential are considered in this paper. By using the definition and properties of the weak subdifferential which are described in the papers (Azimov and Gasimov, 1999; Kasimbeyli and Mammadov, 2009; Kasimbeyli and Inceoglu, 2010), the author proves some theorems connecting weak subdifferential in nonsmooth and nonconvex analysis. It is also obtained necessary optimality condition by using the weak subdifferential in this paper.

The moving bullet out of a rifle barrel is propelled by a fired explosive charge. Subsequently, a disturbed muzzle blast wave is initiated which lasts several milliseconds. In this study, axially symmetric, unsteady, Large Eddy Simulation (LES), and Ffowcs Williams and Hawkins (FWH) equations were solved by the implicit-time formulation. For the spatial discretization, second order upwind scheme was employed. In addition, dynamic mesh model was used to where the ballistic domain changed with time due to the motion of bullet. Results obtained for muzzle flow field and for noise recorded were compared with those obtained from experimental data; these two batches of results were in agreement. Five cases of gunshot including one model of an unsuppressed rifle and four models of suppressors were simulated. Besides, serial images of species distributions and velocity vectors-pressure contours in suppressors and near muzzle field were displayed. The sound pressure levels (dB) in far field that were post-processed by the fast Fourier transform (FFT) were compared. The proposed physical model and the numerical simulations used in the present work are expected to be extended to solve other shooting weapon problems with three-dimensional and complex geometries.

Global well-posedness is proved for a family of n-dimensional MHD-alpha-like models.

The equations of motion of a missile under the air drag effects are constructed. The modified TD88 is surveyed. Using Lagrange's planetary equations in Gauss form, the perturbations, due to the air drag in the orbital elements, are computed between the eccentric anomalies of the burn out and the reentry points $[E_{bo},2\pi -E_{bo}]$, respectively. The range equation is expressed as an infinite series in terms of the eccentricity e and the eccentric anomaly E. The different errors in the missile-free range due to the drag perturbations in the missile trajectory are obtained.

We are concerned with the valuation of European options in the Heston stochastic volatility model with correlation. Based on Mellin transforms, we present new solutions for the price of European options and hedging parameters. In contrast to Fourier-based approaches, where the transformation variable is usually the log-stock price at maturity, our framework focuses on directly transforming the current stock price. Our solution has the nice feature that it requires only a single integration. We make numerical tests to compare our results with Heston's solution based on Fourier inversion and investigate the accuracy of the derived pricing formulae.

Some new Gronwall-Bellman-type delay integral inequalities in two independent variables on time scales are established, which provide a handy tool in the research of qualitative and quantitative properties of solutions of delay dynamic equations on time scales. The established inequalities generalize some of the results in the work of Zhang and Meng 2008, Pachpatte 2002, and Ma 2010.

We prove the existence of the random attractor for the stochastic discrete long wave-short wave resonance equations in an infinite lattice. We prove the asymptotic compactness of the random dynamical system and obtain the random attractor.

After reducing a system of higher-order regular Lagrangian into first-order singular Lagrangian using constrained auxiliary description, the Hamilton-Jacobi function is constructed. Besides, the quantization of the system is investigated using the canonical path integral approximation.

In this paper, we consider b-family equations with a strong dispersive term. First, we present a criterion on blow-up. Then global existence and persistence property of the solution are also established. Finally, we discuss infinite propagation speed of this equation.

The purpose of this paper is to study the existence of fixed point for a nonlinear integral operator in the framework of Banach space $X:=C([a,b],R^n)$. Later on, we give some examples of applications of this type of results.

Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. This paper discusses five types of existing neighborhood-based generalized rough sets. The concepts of minimal neighborhood description and maximal neighborhood description of an element are defined, and by means of the two concepts, the properties and structures of the third and the fourth types of neighborhood-based rough sets are deeply explored. Furthermore, we systematically study the covering reduction of the third and the fourth types of neighborhood-based rough sets in terms of the two concepts. Finally, two open problems proposed by Yun et al. (2011) are solved.

We first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related with Ekeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi's nonconvex minimization theorem, and common fuzzy fixed point theorem. We also obtain some fixed point theorems for weakly contractive maps in the setting of cone metric spaces and focus our research on the equivalence between scalar versions and vectorial versions of some results of fixed point and others.

We investigate the asymptotic behavior of the solutions of a neutral type difference equation of the form $\Delta [x\left(n\right)+cx\left(\tau \right(n\left)\right)]+p\left(n\right)x\left(\sigma \right(n\left)\right)=0$, where $\tau \left(n\right)$ is a general retarded argument, $\sigma \left(n\right)$ is a general deviated argument (retarded or advanced), $c\in R$, ${\left(p\right(n\left)\right)}_{n\ge 0}$ is a sequence of positive real numbers such that $p\left(n\right)\ge p$, $p\in R_{+}$, and $\Delta$ denotes the forward difference operator $\Delta x\left(n\right)=x(n+1)-x\left(n\right)$. Also, we examine the asymptotic behavior of the solutions in case they are continuous and differentiable with respect to cc.

Some new higher algebraic order symmetric various-step methods are introduced. For these methods a direct formula for the computation of the phase-lag is given. Basing on this formula, calculation of free parameters is performed to minimize the phase-lag. An explicit symmetric multistep method is presented. This method is of higher algebraic order and is fitted both exponentially and trigonometrically. Such methods are needed in various branches of natural science, particularly in physics, since a lot of physical phenomena exhibit a pronounced oscillatory behavior. Many exponentially-fitted symmetric multistepmethods for the second-order differential equation are already developed. The stability properties of several existing methods are analyzed, and a new $P$-stable method is proposed, to establish the existence of methods to which our definition applies and to demonstrate its relevance to stiff oscillatory problems. The work is mainly concerned with two-stepmethods but extensions tomethods of larger step-number are also considered. To have an idea about its accuracy, we examine their phase properties. The efficiency of the proposed method is demonstrated by its application to well-known periodic orbital problems. The new methods showed better stability properties than the previous ones.

We study a system of delay difference equations modeling four-dimensional discrete-time delayed neural networks with no internal decay. Such a discrete-time system can be regarded as the discrete analog of a differential equation with piecewise constant argument. By using semicycle analysis method, it is shown that every bounded solution of this discrete-time system is eventually periodic. The obtained results are new, and they complement previously known results.

Based on the concept of an interval-valued function which is motivated by the goal to represent an uncertain function, we define the Choquet integral with respect to a fuzzy measure of interval-valued functions. We also discuss convergence in the (C) mean and convergence in a fuzzy measure of sequences of measurable interval-valued functions. In particular, we investigate the convergence theorem for the Choquet integral of measurable interval-valued functions.

Transitivity of generalized fuzzy matrices over a special type of semiring is considered. The semiring is called incline algebra which generalizes Boolean algebra, fuzzy algebra, and distributive lattice. This paper studies the transitive incline matrices in detail. The transitive closure of an incline matrix is studied, and the convergence for powers of transitive incline matrices is considered. Some properties of compositions of incline matrices are also given, and a new transitive incline matrix is constructed from given incline matrices. Finally, the issue of the canonical form of a transitive incline matrix is discussed. The results obtained here generalize the corresponding ones on fuzzy matrices and lattice matrices shown in the references.

This paper presents a 1-opt heuristic approach to solve resource allocation/reallocation problem which is known as 0/1 multichoice multidimensional knapsack problem (MMKP). The intercept matrix of the constraints is employed to find optimal or near-optimal solution of the MMKP. This heuristic approach is tested for 33 benchmark problems taken from OR library of sizes upto 7000, and the results have been compared with optimum solutions. Computational complexity is proved to be $O\left(klm{n}^2\right)$ of solving heuristically MMKP using this approach. The performance of our heuristic is compared with the best state-of-art heuristic algorithms with respect to the quality of the solutions found. The encouraging results especially for relatively large-size test problems indicate that this heuristic approach can successfully be used for finding good solutions for highly constrained NP-hard problems.

We establish several new Lyapunov-type inequalities for some quasilinear dynamic system involving the $(p_1,p_2,\dots ,p_m)$-Laplacian on an arbitrary time scale $𝕋$, which generalize and improve some related existing results including the continuous and discrete cases.

We find the least values $p$, $q$, and $s$ in (0, 1/2) such that the inequalities $H(pa+(1-p)b$, $pb+(1-p)a)>\mathrm{AG}(a,b)$, $G(qa+(1-q)b,qb+(1-q\left)a\right)>\mathrm{AG}(a,b)$, and $L(sa+(1-s)b,sb+(1-s\left)a\right)>\mathrm{AG}(a,b)$ hold for all $a,b>0$ with $a\ne b$, respectively. Here $\mathrm{AG}(a,b),H(a,b),G(a,b)$, and $L(a,b)$ denote the arithmetic-geometric, harmonic, geometric, and logarithmic means of two positive numbers a and b, respectively.

The interaction between fluid and structure occurs in a wide range of engineering problems. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid-structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. One possibility for reducing the computational effort of fluid-structure simulations is the use of one-way coupled simulations. In this paper, different problems are investigated with one-way and two-way coupled methods. After an explanation of the solution strategy for both models, a closer look at the differences between these methods will be provided, and it will be shown under what conditions a one-way coupling solution gives plausible results.

In 2000, Biehl et al. proposed a fault-based attack on elliptic curve cryptography. In this paper, we refined the fault attack method. An elliptic curve E is defined over prime field ${⊩}_p$ with base point $P\in E\left({⊩}_p\right)$. Applying the fault attack on these curves, the discrete logarithm on the curve can be computed in subexponential time of $L_p(1/\mathrm{2,1}+o(1\left)\right)$. The runtime bound relies on heuristics conjecture about smooth numbers similar to the ones used by Lenstra, 1987.

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic PDE on two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz asssumption on the nonlinearity, we establish, on each subdomain, an optimal $L^{\infty }$ error estimate between the discrete Schwarz sequence and the exact solution of the PDE.

We consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one-level ones. We generalize a pseudo-$\nabla$-monotonicity concept from $\nabla$-monotonicity and prove that under pseudo-$\nabla$-monotonicity property any stationary point of a regularized gap function is a solution of the penalized equilibrium problem. As an application, we discuss a special case that arises from the Tikhonov regularization method for pseudomonotone equilibrium problems.

We study the normality of families of meromorphic functions concerning shared values. We consider whether a family of meromorphic functions F is normal in $D$, if, for every pair of functions $f$ and $g$ in F, $f^{\prime }-a{f}^{-n}$ and $g^{\prime }-a{g}^{-n}$ share the value b, where a and b are two finite complex numbers such that $a\ne 0$, n is a positive integer. Some examples show that the conditions in our results are best possible.

We consider the weighted q-Genocchi numbers and polynomials. From the construction of the weighted q-Genocchi numbers and polynomials, we investigate many interesting identities and relations satisfied by these new numbers and polynomials.

We discuss the convergence of GAOR method for linear systems with strictly $\alpha$ diagonally dominant matrices. Moreover, we show that our results are better than ones of Darvishi and Hessari (2006), Tian et al. (2008) by using three numerical examples.

The nonlinear two-dimensional forced-convection boundary-layer magneto hydrodynamic (MHD) incompressible flow of nanofluid over a horizontal stretching flat plate with variable magnetic field including the viscous dissipation effect is solved using the homotopy perturbation method (HPM). In the present work, our results of the HPM are compared with the results of simulation using the finite difference method, Keller's box-scheme. The comparisons of the results show that the HPM has the capability of solving the nonlinear boundary layer MHD flow of nanofluid with sufficient accuracy.

This paper presents Rayleigh mixtures of distributions in which the weight functions are assumed to be chi-square, t and F sampling distributions. The exact probability density functions of the mixture of two correlated Rayleigh random variables have been derived. Different moments, characteristic functions, shape characteristics, and the estimates of the parameters of the proposed mixture distributions using method of moments have also been provided.

We construct a new type of q-Euler numbers and polynomials with weak weight $\alpha :E_{n,q}^{\left(\alpha \right)}$, $E_{n,q}^{\left(\alpha \right)}\left(x\right)$, respectively. Some interesting results and relationships are obtained. Also, we observe the behavior of roots of the q-Euler numbers $E_{n,q}^{\left(\alpha \right)}$ and polynomials $E_{n,q}^{\left(\alpha \right)}\left(x\right)$ with weak weight α. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of q-Euler polynomials $E_{n,q}^{\left(\alpha \right)}$ with weak weight α.

We investigated a singular multipoint boundary value problem for fractional differential equation in Banach space. The nonlinear term $f(t,x,y)$ is positive and singular at $x=\theta$ and (or) $x=\theta$. Employing regularization, sequential techniques, and diagonalization methods, we obtained some new existence results of positive solution.

This paper investigates the existence of solutions for a class of variable exponent integrodifferential system with multipoint and integral boundary value condition in half line. When the nonlinearity term f satisfies sub-$(p^{-}-1)$ growth condition or general growth condition, we give the existence of solutions and nonnegative solutions via Leray-Schauder degree at nonresonance, respectively. Moreover, the existence of solutions for the problem at resonance has been discussed.

We prove the global existence of cylinder symmetric solutions to the compressible Navier-Stokes equations with external forces and heat source in $R^3$ for any large initial data. Some new ideas and more delicate estimates are used to prove this result.

The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail asymptotics of the probabilities involved. We first derive a sample-path large deviation principle (LDP) for the portfolio's loss process, which enables the computation of the logarithmic decay rate of the probabilities of interest. In addition, we derive exact asymptotic results for a number of specific rare-event probabilities, such as the probability of the loss process exceeding some given function.

For $\alpha ,\beta \in (\mathrm{0,1}/2)$ we prove that the double inequality $G(\alpha a+(1-\alpha )b,\alpha b+(1-\alpha \left)a\right)<P(a,b)<G(\beta a+(1-\beta )b,\beta b+(1-\beta \left)a\right)$ holds for all $a,b>0$ with $a\ne b$ if and only if $\alpha \le (1-\sqrt{1-4/{\pi }^2})/2$ and $\beta \ge (3-\sqrt{3})/6$. Here, $G(a,b)$ and $P(a,b)$ denote the geometric and Seiffert means of two positive numbers a and b, respectively.

We give new lower bound and upper bound for Papenfuss-Bach inequality and improve Ruehr-Shafer inequality by providing a new lower bound.

The aim of this paper is to introduce and study the fuzzy neighborhood, the limit fuzzy number, the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence on the base which is adopted by Abdul Hameed (every real number r is replaced by a fuzzy number $\overline{r}$ (either triangular fuzzy number or singleton fuzzy set (fuzzy point))). And then, we will consider that some results respect effect of the upper sequence on the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence.

This paper focuses on new measures of performance in single-server Markovian queueing system. These measures depend on the moments of order statistics. The expected value and the variance of the maximum (minimum) number of customers in the system as well as the expected value and the variance of the minimum (maximum) waiting time are presented. Application to an M/M/1 model is given to illustrate the idea and the applicability of the proposed measures.

Some new Gronwall-Bellman-type delay integral inequalities in two independent variables on time scales are established, which can be used as a handy tool in the research of boundedness of solutions of delay dynamic equations on time scales. Some of the established results are 2D extensions of several known results in the literature, while some results unify existing continuous and discrete analysis.

Many problems in pure and applied mathematics reduce to a problem of common fixed point of some self-mapping operators which are defined on metric spaces. One of the generalizations of metric spaces is the partial metric space in which self-distance of points need not to be zero but the property of symmetric and modified version of triangle inequality is satisfied. In this paper, some well-known results on common fixed point are investigated and generalized to the class of partial metric spaces.

We study the interaction of a three-level atom with a single mode field through multiphoton transition in a cavity, taking explicitly into account the existence of forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. The analytical forms of the absorption spectrum is calculated using the dressed states of the system. The effects of photon multiplicities, mean photon number, detuning, Kerr-like medium, and the intensity-dependent coupling functional on the absorption spectrum are analyzed.

We study a modified Newton's method with fifth-order convergence for nonlinear equations in Banach spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations. The recurrence relations for the method are derived, and then an existence-uniqueness theorem is given to establish the R-order of the method to be five and a priori error bounds. Finally, a numerical application is presented to demonstrate our approach.

Let $\left(Z\right(3),\tau )$ be a 3-adic system. we prove in $\left(Z\right(3),\tau )$ the existence of uncountable distributional chaotic set of $A\left(\tau \right)$, which is an almost periodic points set, and further come to a conclusion that $\tau$ is chaotic in the sense of Devaney and Wiggins.

This paper is concerned with the robust stability for a class of switched discrete-time systems with state parameter uncertainty. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, a novel sufficient condition for robust stability of a class of uncertain switched discrete-time systems is presented. Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability have been derived for the uncertain switched discrete-time systems using the Lyapunov stability theorem, block matrix method and inequality technology. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Two kinds of the Levenberg-Marquardt-type methods for the solution of vertical complementarity problem are introduced. The methods are based on a nonsmooth equation reformulation of the vertical complementarity problem for its solution. Local and global convergence results and some remarks about the two kinds of the Levenberg-Marquardt-type methods are also given. Finally, numerical experiments are reported.

We prove the generalized Hyers-Ulam stability of the 2nd-order linear differential equation of the form $y\text{'}\text{'}+p\left(x\right)y^{\prime }+q\left(x\right)y=f\left(x\right)$, with condition that there exists a nonzero $y_1:I\to X$ in $C^2\left(I\right)$ such that ${y\text{'}\text{'}}_1+p\left(x\right)y_1^{\prime }+q\left(x\right)y_1=0$ and $I$is an open interval. As a consequence of our main theorem, we prove the generalized Hyers-Ulam stability of several important well-known differential equations.

Let $A$ be an algebra, and let $\theta$, $\phi$ be ring automorphisms of $A$. An additive mapping $H:A\to A$ is called a $(\theta ,\phi )$-derivation if $H\left(xy\right)=H\left(x\right)\theta \left(y\right)+\phi \left(x\right)H\left(y\right)$ for all $x,y\in A$. Moreover, an additive mapping $F:A\to A$ is said to be a generalized $(\theta ,\phi )$-derivation if there exists a $(\theta ,\phi )$-derivation $H:A\to A$ such that $F\left(xy\right)=F\left(x\right)\theta \left(y\right)+\phi \left(x\right)H\left(y\right)$ for all $x,y\in A$. In this paper, we investigate the superstability of generalized $(\theta ,\phi )$-derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy’s functional equation.

By using the variational method, some existence theorems are obtained for periodic solutions of autonomous $(q,p)$-Laplacian system with impulsive effects.

This paper is concerned with $p(\ge 2)$-cyclic self-mappings $T:\bigcup _{i\in \overline{p}}{A}_i\to \bigcup _{i\in \overline{p}}{A}_i$ in a metric space ($X$ $d$), with $A_i\subset X$, $T\left(A_i\right)\subseteq A_{i+1}$ for $i=\mathrm{1,2},\dots ,p$, under a general contractive condition which includes as particular cases several of the existing ones in the literature. The existence and uniqueness of fixed points and best proximity points is discussed as well as the convergence to them of the iterates generated by the self-mapping from given initial points.

We study the robust stability criteria for uncertain neutral systems with interval time-varying delays and time-varying nonlinear perturbations simultaneously. The constraint on the derivative of the time-varying delay is not required, which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive new delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature.

This paper studies the Euler-Maxwell system which is a model of a collisionless plasma. By energy estimation and the curl-div decomposition of the gradient, we rigorously justify a singular approximation of the incompressible Euler equations via a quasi-neutral regime.

We deduce the explicit expressions for ${(P+Q)}^D$ and ${\left(PQ\right)}^D$ of two matrices $P$ and $Q$ under the conditions $P^{2}Q=PQP$ and $Q^{2}P=QPQ$. Also, we give the upper bound of ${\left|\right|{(P+Q)}^D-P^D\left|\right|}_2$.

We consider low-Reynolds-number axisymmetric flow about two spheres using a novel, biharmonic stream function. This enables us to calculate analytically not only the forces, but also the dipole moments (stresslets and pressure moments) and the associated resistance functions. In this paper the basics properties of axisymmetric flow and the stream function are discussed. Explicit series expansions, obtained by separation in bispherical coordinates, will be presented in a follow-up paper.

We present an explicit formula which unifies the mask of $(2n-1)$-point ternary interpolating as well as approximating subdivision schemes. We observe that the odd point ternary interpolating and approximating schemes introduced by Lian (2009), Siddiqi and Rehan (2010, 2009) and Hassan and Dodgson (2003) are special cases of our proposed masks/schemes. Moreover, schemes introduced by Zheng et al. (2009) can easily be generated by our proposed masks. It is also proved from comparison that $(2n-1)$-point schemes are better than $2n$-scheme in the sense of computational cost, support and error bounds.

We have presented a derivation of the asymptotic equations for transverse magnetic multiple scattering coefficients of an infinite grating of penetrable circular cylinders for obliquely incident plane electromagnetic waves. We have first deducted an “Ansatz” delineating the asymptotic behavior of the transverse magnetic multiple scattering coefficients associated with the most generalized condition of oblique incidence (Kavaklıoğlu, 2000) by exploiting Schlömilch series corresponding to the special circumstance that the grating spacing is much smaller than the wavelength of the incident electromagnetic radiation. The validity of the asymptotic equations for the aforementioned scattering coefficients has been verified by collating them with the Twersky's asymptotic equations at normal incidence. Besides, we have deduced the consequences that the asymptotic forms of the equations at oblique incidence acquired in this paper reduce to Twersky's asymptotic forms at normal incidence by expanding the generalized scattering coefficients at oblique incidence into an asymptotic series as a function of the ratio of the cylinder radius to the grating spacing.

We consider flows on a spherical surface and use a transformation to transport some well-known periodic two-dimensional vortex streets to that spherical surface to arrive at some new expressions for vortex streets on a sphere.

We study the heat equation in n dimensional by Diamond Bessel operator. We find the solution by method of convolution and Fourier transform in distribution theory and also obtain an interesting kernel related to the spectrum and the kernel which is called Bessel heat kernel.

The objective of this study is to present a brief survey on the geometrically nonlinear free vibrations of the Bernoulli-Euler, the Rayleigh, shear, and the Timoshenko beams with simple end conditions using the Homotopy Analysis Method (HAM). Expressions for the natural frequencies, the transverse deflection, postbuckling load-deflection relation to, and critical buckling load are presented. The results of nonlinear analysis are validated with the published results, and excellent agreement is observed. The effects of some parameters, such as slender ratio, the rotary inertia, and the shear deformation, are examined as other parameters are fixed.

A new construction of authentication codes with arbitration and multireceiver from singular symplectic geometry over finite fields is given. The parameters are computed. Assuming that the encoding rules are chosen according to a uniform probability distribution, the probabilities of success for different types of deception are also computed.

The piecewise algebraic curve, as the set of zeros of a bivariate spline function, is a generalization of the classical algebraic curve. In this paper, an algorithm is presented to compute the real solutions of two piecewise algebraic curves. It is primarily based on the Krawczyk-Moore iterative algorithm and good initial iterative interval searching algorithm. The proposed algorithm is relatively easy to implement.

This paper processes a unification of Fuzzy TOPSIS and Data Envelopment Analysis (DEA) to select the units with most efficiency. This research is a two-stage model designed to fully rank the organizational alternatives, where each alternative has multiple inputs and outputs. First, the alternative evaluation problem is formulated by Data Envelopment Analysis (DEA) and separately formulates each pair of units. In the second stage, we use the opinion of experts to be applied into a model of group Decision-Making (DM) called the Intuitionistic Fuzzy TOPSIS (IFT) method. The results of both methods are then multiplied to obtain the results. DEA and Intuitionistic Fuzzy TOPSIS ranking do not replace the DEA classification model; rather, it furthers the analysis by providing full ranking in the DEA context for all units by aggregate individual opinions of decision makers for rating the importance of criteria and alternatives.

We obtain some new fixed point theorems for a ($\psi ,\phi$)-pair Meir-Keeler-type set-valued contraction map in metric spaces. Our main results generalize and improve the results of Klim and Wardowski, (2007).