We prove that viscosity solutions of geometric equations in step two Carnot groups can be equivalently reformulated by restricting the set of test functions at the singular points. These are characteristic points for the level sets of the solutions and are usually difficult to deal with. A similar property is known in the Euclidian space, and in Carnot groups, it is based on appropriate properties of a suitable homogeneous norm. We also use this idea to extend to Carnot groups the definition of generalised flow, and it works similarly to the Euclidian setting. These results simplify the handling of the singularities of the equation, for instance, to study the asymptotic behaviour of singular limits of reaction diffusion equations. We provide examples of using the simplified definition, showing, for instance, that boundaries of strictly convex subsets in the Carnot group structure become extinct in finite time when subject to the horizontal mean curvature flow even if characteristic points are present.

A family of linear singularly perturbed difference differential equations is examined. These equations stand for an analog of singularly perturbed PDEs with irregular and Fuchsian singularities in the complex domain recently investigated by A. Lastra and the author. A finite set of sectorial holomorphic solutions is constructed by means of an enhanced version of a classical multisummability procedure due to W. Balser. These functions share a common asymptotic expansion in the perturbation parameter, which is shown to carry a double scale structure, which pairs q-Gevrey and Gevrey bounds.

In this paper, variable exponent function spaces ${\mathbb{L}}^{p\left(·\right)}$, ${\mathbb{L}}_b^{p\left(·\right)}$, and ${\mathbb{L}}_c^{p\left(·\right)}$ are introduced in the framework of sublinear expectation, and some basic and important properties of these spaces are given. A version of Kolmogorov’s criterion on variable exponent function spaces is proved for continuous modification of stochastic processes.

In this paper, we investigate the existence of solution for differential systems involving a $\varphi -$Laplacian operator which incorporates as a special case the well-known $p-$Laplacian operator. In this purpose, we use a variational method which relies on Szulkin’s critical point theory. We obtain the existence of solution when the corresponding Euler–Lagrange functional is coercive.

The aim of this paper is to give fixed point theorems for $G$-monotone $\rho$-nonexpansive mappings over $\rho$-compact or $\rho$-a.e. compact sets in modular function spaces endowed with a reflexive digraph not necessarily transitive. Examples are given to support our work.

The main purpose of this article is to make use of the Horadam polynomials $h_n\left(x\right)$ and the generating function $\mathrm{\Pi }\left(x,z\right)$, in order to introduce three new subclasses of the bi-univalent function class $\sigma .$ For functions belonging to the defined classes, we then derive coefficient inequalities and the Fekete–Szegö inequalities. Some interesting observations of the results presented here are also discussed. We also provide relevant connections of our results with those considered in earlier investigations.

The Multivariate Geographically Weighted Regression (MGWR) model is a development of the Geographically Weighted Regression (GWR) model that takes into account spatial heterogeneity and autocorrelation error factors that are localized at each observation location. The MGWR model is assumed to be an error vector $\left(\mathbf{\epsilon }\right)$ that distributed as a multivariate normally with zero vector mean and variance-covariance matrix $\mathbf{\Sigma }$ at each location $\left(u_i,v_i\right)$, which $\mathbf{\Sigma }$ is sized $qxq$ for samples at the $i$-location. In this study, the estimated error variance-covariance parameters is obtained from the MGWR model using Maximum Likelihood Estimation (MLE) and Weighted Least Square (WLS) methods. The selection of the WLS method is based on the weighting function measured from the standard deviation of the distance vector between one observation location and another observation location. This test uses a statistical inference procedure by reducing the MGWR model equation so that the estimated error variance-covariance parameters meet the characteristics of unbiased. This study also provides researchers with an understanding of statistical inference procedures.

In this paper, we study generic properties of the optimal, in a certain sense, highly active antiretroviral therapy (or HAART). To address this problem, we consider a control model based on the $3$-dimensional Nowak–May within-host HIV dynamics model. Taking into consideration that precise forms of functional responses are usually unknown, we introduce into this model a nonlinear incidence rate of a rather general form given by an unspecified function of the susceptible cells and free virus particles. We also add a term responsible to the loss of free virions due to infection of the target cells. To mirror the idea of highly active anti-HIV therapy, in this model we assume six controls that can act simultaneously. These six controls affecting different stage of virus life cycle comprise all controls possible for this model and account for all feasible actions of the existing anti-HIV drugs. With this control model, we consider an optimal control problem of minimizing the infection level at the end of a given time interval. Using an analytical mathematical technique, we prove that the optimal controls are bang-bang, find accurate estimates for the maximal possible number of switchings of these controls and establish qualitative types of the optimal controls as well as mutual relationships between them. Having the estimate for the number of switchings found, we can reduce the two-point boundary value problem for Pontryagin Maximum Principle to a considerably simpler problem of the finite-dimensional optimization, which can be solved numerically. Despite this possibility, the obtained theoretical results are illustrated by numerical calculations using BOCOP–2.0.5 software package, and the corresponding conclusions are made.

Cholera is an infectious intestinal disease which occurs as a result of poor sanitation and lack of basic education in its transmission. It is characterized by profuse vomiting and severe diarrhea when an individual eats food or drinks water contaminated with the Vibrio cholerae. A dynamic mathematical model that explicitly simulates the transmission mechanism of cholera by taking into account the role of control measures and the environment in the transmission of the disease is developed. The model comprises two populations: the human population and bacteria population. The next-generation method is used to compute the basic reproduction number, $R_0$. Both the disease-free and endemic equilibria are shown to be locally and globally stable for $R_0$ values less than unity and unstable otherwise. Necessary conditions of the optimal control problem were analyzed using Pontryagin’s maximum principle with control measures such as educational campaign and treatment of water bodies used to optimize the objective function. Numerical values of model parameters were estimated using the nonlinear least square method. The model simulations confirm the significant role played by control measures (education and treatment of water bodies) and the bacteria in the environment in the transmission dynamics as well as reducing the spread of cholera.

In this work, the Sumudu decomposition method (SDM) is utilized to obtain the approximate solution of two-dimensional nonlinear system of Burger’s differential equations. This method is considered to be an effective tool in solving many problems. Our results have shown that the SDM offers a much better approximation for solving several numbers of systems of two-dimensional nonlinear Burger’s differential equations. To clarify the facility and accuracy of the strategy, two examples are provided.

In this paper, we introduce the concept of a set-valued or multivalued quasi-contraction mapping in V-fuzzy metric spaces. Using this new concept, a fixed-point theorem is established. We also provide an example verifying and illustrating the fixed-point theorem in action.

In this paper, a class of linear second-order singularly perturbed differential-difference turning point problems with mixed shifts exhibiting two exponential boundary layers is considered. For the numerical treatment of these problems, first we employ a second-order Taylor’s series approximation on the terms containing shift parameters and obtain a modified singularly perturbed problem which approximates the original problem. Then a hybrid finite difference scheme on an appropriate piecewise-uniform Shishkin mesh is constructed to discretize the modified problem. Further, we proved that the method is almost second-order ɛ-uniformly convergent in the maximum norm. Numerical experiments are considered to illustrate the theoretical results. In addition, the effect of the shift parameters on the layer behavior of the solution is also examined.

In this article, we investigate spectrum estimation of law order moving average (MA) process. The main tool is the lag window which is one of the important components of the consistent form to estimate spectral density function (SDF). We show, based on a computer simulation, that the Blackman window is the best lag window to estimate the SDF of $\text{MA}\left(1\right)$ and $\text{MA}\left(2\right)$ at the most values of parameters ${\beta }_i$ and series sizes $n$, except for a special case when $\beta =-1$ and $n\ge 40$ in $\text{MA}\left(1\right)$. In addition, the Hanning–Poisson window appears as the best to estimate the SDF of$\hspace{0.17em}\text{MA}\left(2\right)$ when ${\beta }_1={\beta }_2=-0.5$ and $n\ge 40$.

In this paper, we introduce a new iterative method in a real Hilbert space for approximating a point in the solution set of a pseudomonotone equilibrium problem which is a common fixed point of a finite family of demicontractive mappings. Our result does not require that we impose the condition that the sum of the control sequences used in the finite convex combination is equal to 1. Furthermore, we state and prove a strong convergence result and give some numerical experiments to demonstrate the efficiency and applicability of our iterative method.

In this paper, the authors studied oscillatory behavior of solutions of fourth-order delay difference equation $\Delta \left(c_3\left(n\right)\Delta \left(c_2\left(n\right)\Delta \left(c_1\left(n\right)\Delta u\left(n\right)\right)\right)\right)+p\left(n\right)f\left(u\left(n-k\right)\right)=0$ under the conditions . New oscillation criteria have been obtained which greatly reduce the number of conditions required for the studied equation. Some examples are presented to show the strength and applicability of the main results.

The Bregman Proximal Gradient (BPG) algorithm is an algorithm for minimizing the sum of two convex functions, with one being nonsmooth. The supercoercivity of the objective function is necessary for the convergence of this algorithm precluding its use in many applications. In this paper, we give an inexact version of the BPG algorithm while circumventing the condition of supercoercivity by replacing it with a simple condition on the parameters of the problem. Our study covers the existing results, while giving other.

In this paper, a cyclic algorithm for approximating a class of split variational inequality problem is introduced and studied in some Banach spaces. A strong convergence theorem is proved. Some applications of the theorem are presented. The results presented here improve, unify, and generalize certain recent results in the literature.

In this work, the forced Duffing equation with secondary resonance will be considered our subject by assuming that the initial values has uncertainty in terms of a fuzzy number. The resulted fuzzy models will be studied by three fuzzy differential approaches, namely, Hukuhara differential and its generalization and fuzzy differential inclusion. Applications of fuzzy arithmetics to the models lead to a set of alpha-cut deterministic systems with some additional equations. These systems are then solved by the extended Runge-Kutta method. The extended Runge-Kutta method is chosen as our numerical approach in order to enhance the order of accuracy of the solutions by including both function and its first derivative values in calculations. Among our fuzzy approaches, our simulations show that the fuzzy differential inclusion is the most appropriate approach to capture oscillation behaviors of the model. Using the aforementioned fuzzy approach, we then demonstrate how to estimate parameters to our generated fuzzy simulation data.

We prove Browder’s convergence theorem for multivalued mappings in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm by using the notion of diametrically regular mappings. Our results are significant improvement on results of Jung (2007) and Panyanak and Suantai (2020).

Several essential properties of the linear canonical transform (LCT) are provided. Some results related to the sampling theorem in the LCT domain are investigated. Generalized wave and heat equations on the real line are introduced, and their solutions are constructed using the sampling formulae. Some examples are presented to illustrate our results.

In this paper, we explore a certain class of Non-selfadjoint operators acting on a complex separable Hilbert space. We consider a perturbation of a nonselfadjoint operator by an operator that is also nonselfadjoint. Our consideration is based on known spectral properties of the real component of a nonselfadjoint compact operator. Using a technique of the sesquilinear forms theory, we establish the compactness property of the resolvent and obtain the asymptotic equivalence between the real component of the resolvent and the resolvent of the real component for some class of nonselfadjoint operators. We obtain a classification of nonselfadjoint operators in accordance with belonging their resolvent to the Schatten-von Neumann class and formulate a sufficient condition of completeness of the root vector system. Finally, we obtain an asymptotic formula for the eigenvalues.

In this paper, we present a survey of the inverse eigenvalue problem for a Laplacian equation based on available Cauchy data on a known part ${\Gamma }_0$ and a homogeneous Dirichlet condition on an unknown part ${\Gamma }_0$ of the boundary of a bounded domain, $\Omega \subset {ℝ}^N$ . We consider variations in the eigenvalues and propose a conformal mapping tool to reconstruct a part of the boundary curve of the two-dimensional bounded domain based on the Cauchy data of a holomorphic function that maps the unit disk onto the unknown domain. The boundary values of this holomorphic function are obtained by solving a nonlocal differential Bessel equation. Then, the unknown boundary is obtained as the image of the boundary of the unit disk by solving an ill-posed Cauchy problem for holomorphic functions via a regularized power expansion. The Cauchy data were restricted to a nonvanishing function and to the normal derivatives without zeros. We prove the existence and uniqueness of the holomorphic function being considered and use the fixed-point method to numerically analyze the results of convergence. We’ll calculate the eigenvalues and compare the result with the shape obtained via minimization functional method, as developed in a previous study. Further, we’ll observe via simulations the shape of $\Gamma$ and if it preserves its properties with varying the eigenvalues.

Two identities extracted from the literature are coupled to obtain an integral equation for Riemann’s $\xi (s)$ function and thus $\zeta (s)$ indirectly. The equation has a number of simple properties from which useful derivations flow, the most notable of which relates $\zeta (s)$ anywhere in the critical strip to its values on a line anywhere else in the complex plane. From this, both an analytic expression for $\zeta (\sigma +it)$, everywhere inside the asymptotic $(t\to \infty )$ critical strip, as well as an approximate solution can be obtained, within the confines of which the Riemann Hypothesis is shown to be true. The approximate solution predicts a simple, but strong correlation between the real and imaginary components of $\zeta (\sigma +it)$ for different values of $\sigma$ and equal values of $t$; this is illustrated in a number of figures.

In this paper, we present a mathematical model that describes agree-disagree opinions during polls. We first present the different compartments of the model. Then, using the next-generation matrix method, we derive thresholds of the stability of equilibria. We consider two sets of data from the Reuters polling system regarding the approval rating of the U.S presidential in two terms. These two weekly polls data track the percentage of Americans who approve and disapprove of the way the President manages his work. To validate the reality of the underlying model, we use nonlinear least-squares regression to fit the model to actual data. In the first poll, we consider only $31$ weeks to estimate the parameters of the model, and then, we compare the rest of the data with the outcome of the model over the remaining $21$ weeks. We show that our model fits correctly the real data. The second poll data is collected for $115$ weeks. We estimate again the parameters of the model, and we show that our model can predict the poll outcome in the next weeks, thus, whether the need for some control strategies or not. Finally, we also perform several computational and statistical experiments to validate the proposed model in this paper. To study the influence of various parameters on these thresholds and to identify the most influential parameters, sensitivity analysis is carried out to investigate the effect of the small perturbation near a parameter value on the value of the threshold. An uncertainty analysis is performed to evaluate the forecast inaccuracy in the outcome variable due to uncertainty in the estimation of the parameters.

In this article, we survey the Lyapunov direct method for distributed-order nonlinear time-varying systems with the Prabhakar fractional derivatives. We provide various ways to determine the stability or asymptotic stability for these types of fractional differential systems. Some examples are applied to determine the stability of certain distributed-order systems.

In this paper, we establish the existence of nontrivial positive solution to the following integral-infinite point boundary-value problem involving $\varphi$-Laplacian operator $D_{0^{+}}^{\alpha }\varphi (\text{x},D_{0^{+}}^{\beta }u(x))+f(x,u(x))=0,$ $x\in (0,1),D_{0^{+}}^{\sigma }u(0)=D_0^{\beta }+u(0)=0$, $u(1)={\displaystyle {\int }_0^{1}g(t)u(t)dt}+{\displaystyle {\sum }_{n=1}^{n=+\infty }{\alpha }_{n}u({\eta }_n)}$, where $\varphi :[0,1]\times R\to R$ is a continuous function and $D_{0^{+}}^p$ is the Riemann-Liouville derivative for $p\in \{a,\beta ,\text{ σ}\}.$ By using some properties of fixed point index, we obtain the existence results and give an example at last.

In this paper, the notion of generalized set-valued weak $\theta$-contractions is introduced and a new fixed point theorem for such contractions is established in the setting metric spaces. The main result is a generalization of fixed point theorems in the literature. An example and an application to generalized differential equation are given to support the validity of the main theorem.

This paper deals with some existence of mild solutions for two classes of impulsive integrodifferential equations in Banach spaces. Our results are based on the fixed point theory and the concept of measure of noncompactness with the help of the resolvent operator. Two illustrative examples are given in the last section.

In this paper, we study the split feasibility problem in Banach spaces. At first, we prove that a solution of this problem is a solution of the equivalent equation defined by using a metric projection, a generalized projection, and sunny generalized nonexpansive retraction, respectively. Then, using the hybrid method with these projections, we prove strong convergence theorems in mathematical programing in order to find a solution of the split feasibility problem in Banach spaces.

In cases of nonpoint pollution sources, the regulator can observe the total emission but unable to distinguish between the firms. The regulator then selects an environmental standard. If the total emission level is higher than the standard, then the firms are uniformly punished, and if lower, then uniformly awarded. This environmental regulation is added to $n$-firm dynamic oligopolies, and the asymptotical behavior of the corresponding dynamic systems is examined. Two particular models are considered with linear and hyperbolic price functions. Without delays, the equilibrium is always (locally) asymptotically stable. It is shown how the stability can be lost if time delays are introduced in the output quantities of the competitors as well as in the firms’ own output levels. Complete stability analysis is presented for the resulting one- and two-delay models including the derivations of stability thresholds, stability switching curves, and directions of the stability switches.

Let $0<\gamma <n$ and $I_{\gamma }$ be the fractional integral operator of order $\gamma ,I_{\gamma }f(x)={\displaystyle {\int }_{{ℝ}^n}|x-y{|}^{\gamma -n}f(y)\text{d}y}$ and let $[b,I_{\gamma }]$ be the linear commutator generated by a symbol function $b$ and $I_{\gamma },[b,I_{\gamma }]f(x)=b(x)·I_{\gamma }f(x)-I_{\gamma }(bf)(x)$. This paper is concerned with two-weight, weak-type norm estimates for such operators on the weighted Morrey and amalgam spaces. Based on weak-type norm inequalities on weighted Lebesgue spaces and certain $A_p$-type conditions on pairs of weights, we can establish the weak-type norm inequalities for fractional integral operator $I_{\gamma }$ as well as the corresponding commutator in the framework of weighted Morrey and amalgam spaces. Furthermore, some estimates for the extreme case are also obtained on these weighted spaces.

Let ${\mathcal{T}}_{\alpha }(0\le \alpha <n)$ be a class of sublinear operators satisfying certain size conditions introduced by Soria and Weiss, and let $[b,{\mathcal{T}}_{\alpha }](0\le \alpha \le n)$ be the commutators generated by BMO(${ℝ}^n$) functions and ${\mathcal{T}}_{\alpha }$. This paper is concerned with two-weight, weak-type norm estimates for these sublinear operators and their commutators on the weighted Morrey and amalgam spaces. Some boundedness criteria for such operators are given, under the assumptions that weak-type norm inequalities on weighted Lebesgue spaces are satisfied. As applications of our main results, we can obtain the weak-type norm inequalities for several integral operators as well as the corresponding commutators in the framework of weighted Morrey and amalgam spaces.

In this paper, we discuss a class of mappings more general than $\rho$-nonexpansive mapping defined on a modular space endowed with a graph. In our investigation, we prove the existence of fixed point results of these mappings. Then, we also introduce an iterative scheme for which proves the convergence to a fixed point of such mapping in a modular space with a graph.

In this article, we applied a new technique for solving the time-fractional coupled Korteweg-de Vries (KdV) equation. This method is a combination of the natural transform method with the Adomian decomposition method called the natural decomposition method (NDM). The solutions have been made in a convergent series form. To demonstrate the performances of the technique, two examples are provided.

Existing literature in nonparametric regression has established a model that only applies one estimator to all predictors. This study is aimed at developing a mixed truncated spline and Fourier series model in nonparametric regression for longitudinal data. The mixed estimator is obtained by solving the two-stage estimation, consisting of a penalized weighted least square (PWLS) and weighted least square (WLS) optimization. To demonstrate the performance of the proposed method, simulation and real data are provided. The results of the simulated data and case study show a consistent finding.

The primary purpose of this research is to demonstrate an efficient replacement double transform named the Laplace–Sumudu transform (DLST) to unravel integral differential equations. The theorems handling fashionable properties of the Laplace–Sumudu transform are proved; the convolution theorem with an evidence is mentioned; then, via the usage of these outcomes, the solution of integral differential equations is built.

In this paper, we construct a connected path of real roots of odd-degree real polynomials depending on parameters continuously, which joins with all parameters. Moreover, most of the points on the path are odd-multiple real roots except for at most countable even-multiple real roots. Furthermore, some geometrical features of the path can be seen easily from the construction.

The objective of this article is to discuss the existence and the uniqueness of a weighted extended B-spline- (WEB-spline-) based discrete solution for the 2D Navier-Lamé equation of linear elasticity with a different type of mixed boundary condition called $C_{A,B}$ boundary condition. Along with the usual weak mixed formulation, we give existence and uniqueness results for weak solution. Then, we illustrate the performance of Ritz–Galerkin schemes for a model problem and applications in linear elasticity. Finally, we discuss several implementation aspects. The numerical tests confirm that, due to the new integration routines, the weighted B-spline solvers have become considerably more efficient.

Due to the difficulty of representing problem parameters fuzziness using the soft set theory, the fuzzy soft set is regarded to be more general and flexible than using the soft set. In this paper, we define the fuzzy soft linear operator $\tilde{T}$ in the fuzzy soft Hilbert space $\tilde{H}$ based on the definition of the fuzzy soft inner product space in terms of the fuzzy soft vector ${\tilde{v}}_{f_{G\left(e\right)}}$ modified in our work. Moreover, it is shown that ${ℂ}^n\left(A\right),{ℝ}^n\left(A\right)$ and $l_2\left(A\right)$ are suitable examples of fuzzy soft Hilbert spaces and also some related examples, properties and results of fuzzy soft linear operators are introduced with proofs. In addition, we present the definition of the fuzzy soft orthogonal family and the fuzzy soft orthonormal family and introduce examples satisfying them. Furthermore, the fuzzy soft resolvent set, the fuzzy soft spectral radius, the fuzzy soft spectrum with its different types of fuzzy soft linear operators and the relations between those types are introduced. Moreover, the fuzzy soft right shift operator and the fuzzy soft left shift operator are defined with an example of each type on ${𝓁}_2\left(A\right)$.In addition, it is proved, on ${𝓁}_2\left(A\right)$, that the fuzzy soft point spectrum of fuzzy soft right shift operator has no fuzzy soft eigenvalues, the fuzzy soft residual spectrum of fuzzy soft right shift operator is equal to the fuzzy soft comparison spectrum of it and the fuzzy soft point spectrum of fuzzy soft left shift operator is the fuzzy soft open disk $\left|\widetilde{\text{λ}}\right|\widetilde{<}\tilde{1}$. Finally, it is shown that the fuzzy soft Hilbert space is fuzzy soft self-dual in this generalized setting.

Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear is used to obtain a strong convergence result for nonlinear equations of $\left(p,\eta \right)$-strongly monotone type, where , . An example is presented for the nonlinear equations of $\left(p,\eta \right)$-strongly monotone type. As a consequence of the main result, the solutions of convex minimization and variational inequality problems are obtained. This solution has applications in other fields such as engineering, physics, biology, chemistry, economics, and game theory.

The model system of ordinary differential equations considers two classes of latently infected individuals, with different risk of becoming infectious. The system has positive solutions. By constructing a Lyapunov function, it is proved that if the basic reproduction number is less than unity, then the disease-free equilibrium point is globally asymptotically stable. The Routh-Hurwitz criterion is used to prove the local stability of the endemic equilibrium when . The model is illustrated using parameters applicable to Ethiopia. A variety of numerical simulations are carried out to illustrate our main results.

Using standard techniques from geometric quantization, we rederive the integral product of functions on ${ℝ}^2$ (non-Euclidian) which was introduced by Pierre Bieliavsky as a contribution to the area of strict quantization. More specifically, by pairing the nontransverse real polarization on the pair groupoid ${ℝ}^2\times {\overline{ℝ}}^2$, we obtain the well-defined integral transform. Together with a convolution of functions, which is a natural deformation of the usual convolution of functions on the pair groupoid, this readily defines the Bieliavsky product on a subset of $L^2({ℝ}^2)$.

We explore the relationship between unemployment and inflation in the United States (1949-2019) through both Bayesian and spectral lenses. We employ Bayesian vector autoregression (“BVAR”) to expose empirical interrelationships between unemployment, inflation, and interest rates. Generally, we do find short-run behavior consistent with the Phillips curve, though it tends to break down over the longer term. Emphasis is also placed on Phelps’ and Friedman’s NAIRU theory using both a simplistic functional form and BVAR. We find weak evidence supporting the NAIRU theory from the simplistic model, but stronger evidence using BVAR. A wavelet analysis reveals that the short-run NAIRU theory and Phillips curve relationships may be time-dependent, while the long-run relationships are essentially vertical, suggesting instead that each relationship is primarily observed over the medium-term (2-10 years), though the economically significant medium-term region has narrowed in recent decades to roughly 4-7 years. We pay homage to Phillips’ original work, using his functional form to compare potential differences in labor bargaining power attributable to labor scarcity, partitioned by skill level (as defined by educational attainment). We find evidence that the wage Phillips curve is more stable for individuals with higher skill and that higher skilled labor may enjoy a lower natural rate of unemployment.

In this paper, we investigate the existence and uniqueness of solutions for a class of integral boundary value problems of nonlinear fractional differential equations with $p$-Laplacian operator. We obtain some existence and uniqueness results concerned with our problem by using Schaefer’s fixed-point theorem and Banach contraction mapping principle. Finally, we present some examples to illustrate our main results.

We discuss the existence issue to an optimal control problem for one class of nonlinear elliptic equations with an exponential type of nonlinearity. We deal with the control object when we cannot expect to have a solution of the corresponding boundary value problem in the standard functional space for all admissible controls. To overcome this difficulty, we make use of a variant of the classical Tikhonov regularization scheme. In particular, we eliminate the PDE constraints between control and state and allow such pairs run freely by introducing an additional variable which plays the role of “compensator” that appears in the original state equation. We show that this fictitious variable can be determined in a unique way. In order to provide an approximation of the original optimal control problem, we define a special family of regularized optimization problems. We show that each of these problems is consistent, well-posed, and their solutions allow to attain an optimal solution of the original problem as the parameter of regularization tends to zero. As a consequence, we prove the existence of optimal solutions to the original problem and propose a way for their approximation.

The Perona-Malik (PM) model is used successfully in image processing to eliminate noise while preserving edges; however, this model has a major drawback: it tends to make the image look blocky. This work proposes to modify the PM model by introducing the Caputo-Fabrizio fractional gradient inside the diffusivity function. Experiments with natural images show that our model can suppress efficiently the blocky effect. Also, our model has good performance in visual quality, high peak signal-to-noise ratio (PSNR), and lower value of mean absolute error (MAE) and mean square error (MSE).

The focus of this research work is to obtain the chaotic behaviour and bifurcation in the real dynamics of a newly proposed family of functions $f_{\lambda ,a}(x)=x+(1–\lambda x)$ ln , depending on two parameters in one dimension, where assume that $\lambda$ is a continuous positive real parameter and $a$ is a discrete positive real parameter. This proposed family of functions is different from the existing families of functions in previous works which exhibits chaotic behaviour. Further, the dynamical properties of this family are analyzed theoretically and numerically as well as graphically. The real fixed points of functions $f_{\lambda ,a}(x)$ are theoretically simulated, and the real periodic points are numerically computed. The stability of these fixed points and periodic points is discussed. By varying parameter values, the plots of bifurcation diagrams for the real dynamics of $f_{\lambda ,a}(x)$ are shown. The existence of chaos in the dynamics of $f_{\lambda ,a}(x)$ is explored by looking period-doubling in the bifurcation diagram, and chaos is to be quantified by determining positive Lyapunov exponents.

The continuous dependence of the two fluids which interface with each other in a bounded domain is derived. It is first shown how to establish the a priori results for the solutions for the flow in a bounded domain occupied by a viscous fluid in contact with a porous solid. It is also proved that the solution depends continuously on the Forchheimer coefficient.

The object of the present paper is to establish some interested theorems on Euler-type integrals involving $\mathcal{S}$-function, which is defined by Saxena and Daiya. Further, we reduce some special cases involving various known functions like the $k$-Mittag-Leffler function, $\mathcal{K}$-function, and $ℳ$-series.

This study investigates the geographically weighted multivariate logistic regression (GWMLR) model, parameter estimation, and hypothesis testing procedures. The GWMLR model is an extension to the multivariate logistic regression (MLR) model, which has dependent variables that follow a multinomial distribution along with parameters associated with the spatial weighting at each location in the study area. The parameter estimation was done using the maximum likelihood estimation and Newton-Raphson methods, and the maximum likelihood ratio test was used for hypothesis testing of the parameters. The performance of the GWMLR model was evaluated using a real dataset and it was found to perform better than the MLR model.

In this paper, we introduce new subclasses of the function class $\Sigma$ of bi-univalent functions connected with a $q$-analogue of Bessel function and defined in the open unit disc. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients $\left|a_2\right|$ and $\left|a_3\right|$ for functions in these new subclasses.

In this paper, we develop an a posteriori error analysis for the stationary Stokes-Darcy coupled problem approximated by conforming the finite element method on isotropic meshes in ${ℝ}^d,d\in \{2,3\}$. The approach utilizes a new robust stabilized fully mixed discretization. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution plus the stabilization terms. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.

The purpose of the present paper is to obtain some inclusion relation between various subclasses of harmonic univalent functions by applying certain convolution operators associated with Wright’s generalized hypergeometric functions.

This paper is devoted to the study of approximate Lie point symmetries of general autoparallel systems. The significance of such systems is that they characterize the equations of motion of a Riemannian space under an affine parametrization. In particular, we formulate the first-order symmetry determining equations based on geometric requirements and stipulate that the underlying Riemannian space be approximate in nature. Lastly, we exemplify the results by application to some approximate wave-like manifolds.

The Banach contraction principle is the most celebrated fixed point theorem and has been generalized in various directions. In this paper, inspired by the concept of $\theta -\varphi$-contraction in metric spaces, introduced by Zheng et al., we present the notion of $\theta -\varphi$-contraction in $b$-rectangular metric spaces and study the existence and uniqueness of a fixed point for the mappings in this space. Our results improve many existing results.

Let $X$ be a topological space equipped with a complete positive $\sigma$-finite measure and $T$ a subset of the reals with $0$ as an accumulation point. Let $a_t\left(x,y\right)$ be a nonnegative measurable function on $X\times X$ which integrates to $1$ in each variable. For a function $f\in L_2\left(X\right)$ and $t\in T$, define $A_{t}f\left(x\right)\equiv {\int }^{\text{}}{a}_t\left(x,y\right)f\left(y\right)dy$. We assume that $A_{t}f$ converges to $f$ in $L_2$, as $t\to 0$ in $T$. For example, $A_t$ is a diffusion semigroup $(withT=[0,\infty )).$ For $W$ a finite measure space and $w\in W$, select real-valued $h_w\in L_2\left(X\right)$, defined everywhere, with ${\Vert h_w\Vert }_{L_2(X)}\le 1$. Define the distance $D$ by $D\left(x,y\right)\equiv \Vert h_w\left(x\right)-h_w\left(y\right){\Vert }_{L_2\left(w\right)}$. Our main result is an equivalence between the smoothness of an $L_2\left(X\right)$ function $f$ (as measured by an $L_2$-Lipschitz condition involving $a_t\left(.,.\right)$and the distance $D$) and the rate of convergence of $A_{t}f$ to $f$.

The linear complementarity problem is receiving a lot of attention and has been studied extensively. Recently, El foutayeni et al. have contributed many works that aim to solve this mysterious problem. However, many results exist and give good approximations of the linear complementarity problem solutions. The major drawback of many existing methods resides in the fact that, for large systems, they require a large number of operations during each iteration; also, they consume large amounts of memory and computation time. This is the reason which drives us to create an algorithm with a finite number of steps to solve this kind of problem with a reduced number of iterations compared to existing methods. In addition, we consider a new class of matrices called the E-matrix.

This manuscript proves the existence of a single common fixed point of two joint $\left(A,B\right)$ generalized cyclic $\varphi -abc$ weak nonexpansive mappings, where $A$ and $B$ are compact sets. The result in particular demonstrated a single fixed point of generalized cyclic $\varphi -abc$ weak nonexpansive mappings, without the assumption of a single contracting point. Additionally, it introduces new types of generalized cyclic $abc;r$ contraction mappings and describes the existence of a single fixed point of them in $b$-metric spaces. Finally, the presented results establish a simpler convergence theorem for a sequence of generalized cyclic $abc;r$ contraction mappings, extend, and generalize some of the previous reported results.

Several fixed point results for the existence of common fixed points of multivalued contractive mappings have been established in complex-valued metric space. In this paper, we study the existence of common fixed points for a pair of multivalued contractive mappings satisfying some rational inequalities in the framework of complex-valued $b$-metric spaces. The contractive condition used in this paper generalizes many contractive conditions used by other authors in the literature. Employing our results, we check the existence solution to the Riemann-Liouville equation.

The boundary layer flow of an incompressible viscoelastic Jeffrey’s nanofluid from a vertical permeable flat plate is investigated. We consider the effects of heat generation, thermal radiation, and chemical reaction on the fluid flow. The nonlinear transformed coupled differential equations that describe the transport processes are solved numerically using a multidomain bivariate spectral quasilinearization method (MD-BSQLM). This innovative method involves blending the quasilinearization idea with the bivariate Lagrange interpolation. The solutions of the resulting system of equations are then obtained sequentially on multiple intervals using the Chebyshev spectral collocation method. The method is shown to give accurate solutions for boundary layer-type equations. The influence of various physical parameters on velocity, temperature, and nanoparticle concentration fields, as well as on the skin friction and heat and mass transfer coefficients, is shown and discussed in detail. The range of the values of the governing parameters considered in this study is between $[0,4]$. For qualitative validation of the results and the numerical method used, calculations were carried out to graphically obtain the velocity, temperature, and nanoparticle concentration fields for selected physical parameter values. The results obtained were found to correlate with the results from published literature. For quantitative verification of our findings, the MD-BSQLM numerical solutions were again confirmed against published results reported in the literature, and the results were observed to be in perfect agreement. This study’s findings indicate that the Deborah number and suction parameter have related effects on the velocity profile, which is to suppress both the flow velocity and the momentum boundary layer thickness. Increasing the heat generation and thermal radiation parameters enhances both the temperature and thermal boundary layer depths. In contrast, an increase in the chemical reaction parameter causes a decrease in the fluid concentration.