Abstract: In this work, we consider the Darboux frame of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a -direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices is a vector of the Darboux frame, a Darboux vector field. Finally, we give some examples for special curves such as the asymptotic line, geodesic curve, and principal line, with illustrations of the different cases studied. PubDate: Sat, 11 Sep 2021 05:50:01 +000

Abstract: We present the concept of -contractive multivalued mappings in -metric spaces and prove some fixed point results for these mappings in this study. Our results expand and refine some of the literature’s findings in fixed point theory. PubDate: Thu, 02 Sep 2021 07:35:00 +000

Abstract: In this paper, we introduce original definitions of Partner ruled surfaces according to the Darboux frame of a curve lying on an arbitrary regular surface in . It concerns Partner ruled surfaces, Partner ruled surfaces, and Partner ruled surfaces. We aim to study the simultaneous developability conditions of each couple of two Partner ruled surfaces. Finally, we give an illustrative example for our study. PubDate: Sat, 28 Aug 2021 03:50:01 +000

Abstract: In this paper, we consider a source problem for a time harmonic acoustic wave in two-dimensional space. Based on the boundary integral equation method, a Dirichlet-to-Neumann map in terms of boundary integral operators on the boundary of the source is constructed to transform this problem into two boundary value problems for the Helmholtz equation. PubDate: Mon, 23 Aug 2021 03:20:01 +000

Abstract: In this article, we propose two Banach-type fixed point theorems on bipolar metric spaces. More specifically, we look at covariant maps between bipolar metric spaces and consider iterates of the map involved. We also propose a generalization of the Banach fixed point result via Caristi-type arguments. PubDate: Fri, 13 Aug 2021 05:35:06 +000

Abstract: In the present paper, we establish some composition formulas for Marichev-Saigo-Maeda (MSM) fractional calculus operators with -function as the kernel. In addition, on account of -function, a variety of known results associated with special functions such as the Mittag-Leffler function, exponential function, Struve’s function, Lommel’s function, the Bessel function, Wright’s generalized Bessel function, and the generalized hypergeometric function have been discovered by defining suitable values for the parameters. PubDate: Thu, 12 Aug 2021 05:35:06 +000

Abstract: Let and be two closed linear relations acting between two Banach spaces and , and let be a complex number. We study the stability of the nullity and deficiency of when it is perturbed by . In particular, we show the existence of a constant for which both the nullity and deficiency of remain stable under perturbation by for all inside the disk . PubDate: Tue, 10 Aug 2021 11:05:04 +000

Abstract: Abstracts. A method for the group classification of differential equations is proposed. It is based on the determination of all possible cases of linear dependence of certain indeterminates appearing in the determining equations of symmetries of the equation. The method is simple and systematic and applied to a family of hyperbolic equations. Moreover, as the given family contains several known equations with important physical applications, low-order conservation laws of some relevant equations from the family are computed, and the results obtained are discussed with regard to the symmetry integrability of a particular class from the underlying family of hyperbolic equations. PubDate: Fri, 06 Aug 2021 14:35:05 +000

Abstract: The nonlinear wave equation is a significant concern to describe wave behavior and structures. Various mathematical models related to the wave phenomenon have been introduced and extensively being studied due to the complexity of wave behaviors. In the present work, a mathematical model to obtain the solution of the nonlinear wave by coupling the classical Camassa-Holm equation and the Rosenau-RLW-Kawahara equation with the dual term of nonlinearities is proposed. The solution properties are analytically derived. The new model still satisfies the fundamental energy conservative property as the original models. We then apply the energy method to prove the well-posedness of the model under the solitary wave hypothesis. Some categories of exact solitary wave solutions of the model are described by using the Ansatz method. In addition, we found that the dual term of nonlinearity is essential to obtain the class of analytic solution. Besides, we provide some graphical representations to illustrate the behavior of the traveling wave solutions. PubDate: Mon, 19 Jul 2021 09:05:03 +000

Abstract: The main goal of this paper is to investigate the boundedness and essential norm of a class of product-type operators from Hardy spaces into th weighted-type spaces. As a corollary, we obtain some equivalent conditions for compactness of such operators. PubDate: Fri, 16 Jul 2021 08:50:00 +000

Abstract: In this article, small modification to the Modified Euler Method is proposed. Stability and consistency were tested to determine the end result, and some numerical results were presented, and the CPU time was compared again, and it is recognized that the proposed method is more reliable and compatible with higher efficiency. PubDate: Mon, 12 Jul 2021 10:35:02 +000

Abstract: In this work, the existence of at least one solution for the following third-order integral and -point boundary value problem on the half-line at resonance will be investigated. The Mawhin’s coincidence degree theory will be used to obtain existence results while an example will be used to validate the result obatined. PubDate: Fri, 02 Jul 2021 06:35:01 +000

Abstract: This paper presents the study of singularly perturbed differential-difference equations of delay and advance parameters. The proposed numerical scheme is a fitted fourth-order finite difference approximation for the singularly perturbed differential equations at the nodal points and obtained a tridiagonal scheme. This is significant because the proposed method is applicable for the perturbation parameter which is less than the mesh size where most numerical methods fail to give good results. Moreover, the work can also help to introduce the technique of establishing and making analysis for the stability and convergence of the proposed numerical method, which is the crucial part of the numerical analysis. Maximum absolute errors range from up to , and computational rate of convergence for different values of perturbation parameter, delay and advance parameters, and mesh sizes are tabulated for the considered numerical examples. Concisely, the present method is stable and convergent and gives more accurate results than some existing numerical methods reported in the literature. PubDate: Thu, 01 Jul 2021 10:50:02 +000

Abstract: For the superreplication problem with discrete time, a guaranteed deterministic formulation is considered: the problem is to guarantee coverage of the contingent liability on sold option under all admissible scenarios. These scenarios are defined by means of a priori defined compacts dependent on price prehistory: the price increments at each point in time must lie in the corresponding compacts. In a general case, we consider a market with trading constraints and assume the absence of transaction costs. The formulation of the problem is game theoretic and leads to the Bellman–Isaacs equations. This paper analyses the solution to these equations for a specific pricing problem, i.e., for a binary option of the European type, within a multiplicative market model, with no trading constraints. A number of solution properties and an algorithm for the numerical solution of the Bellman equations are derived. The interest in this problem, from a mathematical prospective, is related to the discontinuity of the option payoff function. PubDate: Fri, 18 Jun 2021 08:35:01 +000

Abstract: This paper uses the generalization of the Hukuhara difference for compact convex set to extend the classical notions of Carathéodory differentiability to multifunctions (set-valued maps). Using the Hukuhara difference and affine multifunctions as a local approximation, we introduce the notion of CH-differentiability for multifunctions. Finally, we tackle the study of the relation among the Fréchet differentiability, Hukuhara differentiability, and CH-differentiability. PubDate: Tue, 01 Jun 2021 08:35:00 +000

Abstract: This paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. To observe the effectiveness of this method, few numerical examples are given. The study points out that, using the generalized refinement of Gauss-Seidel method, we obtain a solution of a problem with a minimum number of iteration and obtain a greater rate of convergence than other previous methods. PubDate: Tue, 01 Jun 2021 08:20:01 +000

Abstract: We discuss martingale transforms between martingale Hardy-amalgam spaces and Let and and let be a martingale in ; then, we show that its martingale transforms are the martingales in for some and similarly for and PubDate: Sun, 30 May 2021 10:50:00 +000

Abstract: This paper introduces novel concepts of joint cyclic -weak contraction and joint cyclic -weak nonexpansive mappings and then proves the existence of a unique common fixed point of such mappings in case of complete and compact metric spaces, respectively, in particular, it proves the existence of a unique fixed point for both cyclic -weak contraction and cyclic -weak nonexpansive mappings, and hence, it also proves the existence of a unique fixed point for both cyclic -weak contraction and cyclic -weak nonexpansive mappings. The results of this research paper extend and generalize some fixed point theorems previously proved via the attached references. PubDate: Fri, 21 May 2021 11:35:00 +000

Abstract: We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two properties for set-valued functions and generalize some results from a single-valued case to a set-valued case. We also show that both properties of set-valued dynamical systems are equivalence for any compact intervals. PubDate: Sat, 15 May 2021 10:50:00 +000

Abstract: Frame theory has a great revolution for recent years. This theory has been extended from Hilbert spaces to Hilbert -modules. In this paper, we define and study the new concept of controlled continuous ---frames for Hilbert -modules and we establish some properties. PubDate: Thu, 29 Apr 2021 08:50:00 +000

Abstract: In this paper, we give an equivalent characterization of the Besov space. This reveals the equivalent relation between the mixed derivative norm and single-variable norm. Fourier multiplier, real interpolation, and Littlewood-Paley decomposition are applied. PubDate: Mon, 26 Apr 2021 08:50:00 +000

Abstract: The Jacobi elliptic function method is applied to solve the generalized Benjamin-Bona-Mahony equation (BBM). Periodic and soliton solutions are formally derived in a general form. Some particular cases are considered. A power series method is also applied in some particular cases. Some solutions are expressed in terms of the Weierstrass elliptic function. PubDate: Fri, 23 Apr 2021 11:35:01 +000

Abstract: The aim of this paper is to extend the notion of -Riemann integrability of functions defined over to functions defined over a rectangular box of . As a generalization of step functions, we introduce a notion of -step functions which allows us to give an equivalent definition of the -Riemann integrable functions. PubDate: Thu, 22 Apr 2021 11:20:01 +000

Abstract: This article deals with some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer Fractional derivative. The results are obtained using the Banach contraction principle and Krasnoselskii’s and Schaefer’s fixed-point theorems. PubDate: Wed, 21 Apr 2021 06:50:01 +000

Abstract: This paper is aimed at proving a common fixed point theorem for -Kannan mappings in metric spaces with an application to integral equations. The main result of the paper will extend and generalise the recent existing fixed point results in the literature. We also provided illustrative examples and some applications to integral equation, nonlinear fractional differential equation, and ordinary differential equation for damped forced oscillations to support the results. PubDate: Sat, 17 Apr 2021 07:05:01 +000

Abstract: The ultimate objective of the problem under study is to apply the min-max tool, thus making it possible to optimize the default risks linked to several areas: the agricultural sector, for example, which requires the optimization of the default risk using the following elements: silage crops, annual consumption requirements, and crops produced for a given year. To minimize the default risk in the future, we start, in the first step, by forecasting the total budget of agriculture investment for the next 20 years, then distribute this budget efficiently between the irrigation and construction of silos. To do this, Bangladesh was chosen as an empirical case study given the availability of its data on the FAO website; it is considered a large agricultural country in South Asia. In this article, we give a detailed and original in-depth study of the agricultural planning model through a calculating algorithm suggested to be coded on the R software thereafter. Our approach is based on an original statistical modeling using nonparametric statistics and considering an example of a simulation involving agricultural data from the country of Bangladesh. We also consider a new pollution model, which leads to a vector optimization problem. Graphs illustrate our quantitative analysis. PubDate: Thu, 15 Apr 2021 07:05:01 +000

Abstract: This paper intends to obtain accurate and convergent numerical solutions of linear space-time matching telegraph fractional equations by means of a double Sumudu matching transformation method. Moreover, the numerical model is equipped to explain the work, the accuracy of the work, and sobriety in its presentation method, and as a result, the proposed method shows an effective and convenient way, to employ proven problems in science and engineering. PubDate: Fri, 09 Apr 2021 08:20:01 +000

Abstract: In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in . It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations. PubDate: Thu, 01 Apr 2021 08:50:01 +000

Abstract: This paper is devoted to study the null controllability properties of a nonlinear age and two-sex population dynamics structured model without spatial structure. Here, the nonlinearity and the couplage are at the birth level. In this work, we consider two cases of null controllability problem. The first problem is related to the extinction of male and female subpopulation density. The second case concerns the null controllability of male or female subpopulation individuals. In both cases, if is the maximal age, a time interval of duration after the extinction of males or females, one must get the total extinction of the population. Our method uses first an observability inequality related to the adjoint of an auxiliary system, a null controllability of the linear auxiliary system, and after Kakutani’s fixed-point theorem. PubDate: Mon, 29 Mar 2021 10:50:00 +000