By employing a simple method that relies on known results for the circulant matrix A(1), and by analyzing the eigenvalues and eigenvectors of four circulant matrices (B,B & lowast; , D and D-& lowast;), in the twisted configurations of the spatial Newtonian 6-body problem formed by two parallel equilateral triangles with a distance h > 0, we demonstrate that when the twist angle 0 is an element of [0, 2 pi), there is no spatial twisted central configuration with unequal masses located at the vertices of each separate equilateral triangle.
This article presents a new approach so-called the Laplace-residual power series method (L-RPSM) for estimating the solution of a coupled system of fractional partial differential equation (FPDE). To demonstrate the efficiency of the L-RPSM, we found the solution of the time-fractional Whitham-Broer-Kaup (WBK) equations, where the derivative is given in the Liouville-Caputo sense. A comparison of the numerical results obtained using our method and the results obtained using Adomian decomposition method (ADM), Variational iteration method (VIM), Optimal homotopy asymptotic method (OHAM), Daftardar-Gejji and Jafari method (DJM) and Laplace transform Adomian decomposition method (LADM) is given. Consequently the results show that the L-RPSM is reliable and effective for solving coupled systems of the FPDE. Moreover, the solutions obtained by the L-RPSM converge faster than the solutions obtained using ADM, VIM, OHAM, DJM and LADM to the exact solution.
In this paper, we define three types of slant submanifolds of para-quaternion Hermitian manifolds by classifying. Accordingly, we arrive at some results for the slant submanifolds with parallel canonical structures in the para-quaternion Kaehler manifolds.
. This paper generalizes fixed point results in non-traditional metric spaces by introducing dislocated quasi-ultrametric spaces (dq-ultrametric spaces). It establishes fixed point existence and uniqueness using specific contractions, explores implications for integral equations, and expands upon prior findings. Key results are illustrated with examples, broadening the ultrametric framework's applicability.
. In this paper, the Cauchy problem for fractional-order linear differential equations with constant coefficients is considered. Firstly, the given equation is reduced to the normal system, where only two elements of the initial condition vector are known. Then, the quadratic functional is introduced for defining the optimal program trajectory and optimal control. The extended functional is constructed and some transformations in this functional have been done for obtaining the Euler-Lagrange equations with boundary conditions. Using the Mittag-Leffler function, we construct the fundamental solution matrix for the general case. Using this solution, initial condition and boundary condition with Lagrange multipliers, we find the optimal program trajectory and optimal control.
. This article presents the results of concerning two mathematical works by N. Tusi: "Exposition of Euclid" and "Collection of Arithmetic Using a Blackboard and Dust" with the aim of revealing the mathematical views of Tusi. We were able to obtain some facts heretofore unknown that help to see more clearly the ways of development of mathematical thought, and the history of introduction of certain key mathematical notions.
The aim of the present work is to investigate the source identification problem for a reverse parabolic equation. The existence and uniqueness of the solution are established, along with stability estimates. These theoretical results are applied to proof of well-posedness of three specific source identification problems for the reverse parabolic partial differential equations.
. There are lots of specific error bounds of the Gaussian quadrature rules with simple and multiple nodes for functions analytic in a region of the complex plane that contains the interval of integration. They depend on the kind of a quadrature and the measure relative to which the quadrature is considered. We are aware of only one kind of error bound for the standard Gauss quadrature rule with respect to a general measure, given by von Sydow [34], and its generalization to the Gauss-Turan quadrature rule, given by the author [32]. In this paper we consider that kind of the general error bound for the positive interpolatory quadrature rules, in particular for some of their important subclasses. In many numerical experiments we performed, the results show that the proposed general error bound is of the same order as the existing specific error bounds.
In the present investigation, we introduce a class Khq(p, x, , alpha, S) of analytic functions which is defined in terms of a quasi-subordination. The coefficient estimates including the classical Fekete-Szego inequality of functions belonging to this class are then derived. The results presented in this paper are the generalization of the results that given in [27].
We consider a problem of the topology design and optimization of a utility communication network. Mathematically, it is represented by a hierarchical two-level network which allows us to take into account the fact that a communication line (trench or tunnel) of a primary network can be used multiple times for laying edges (various utility communications) of a secondary network while the expenses for preparation of that line are made just once. Another advantage is that we can consider a failure in a primary network along with its influence on all secondary network elements lying in it. For a given topology of a secondary network and a redundant topology of a primary network, we analyze the complexity of the problem of the cheapest choice of the primary network elements for laying into them secondary network elements. The methods for solving this problem are proposed, along with results of the numerical experiments.
. This study explores the feasibility of installing air filtration systems on building facades to monitor vehicle-induced pollution and mitigate its effects in urban environments. Additionally, the study addresses the optimal placement of sensor-equipped air filtration systems to maximize their effectiveness. This proposed approach not only curtails the spread of polluted air throughout urban spaces but also facilitates its immediate purification.
The aim of this paper is to study interesting combinatorial identities for ct-analogues of r-Stiring numbers of the first and second kind via Boson operators, respectively.
In this paper, we construct the convergence and stability of iterative algorithms for fixed points under a weaker condition of the generalized nonexpansive mappings in Banach spaces. Some new data dependence theorems are also presented. Finally, our results are applied to consider the existence, uniqueness and approximation of solutions for a class of nonlinear fractional differential equations.
In this paper, we establish some new monotonicity properties of ratios defined by finitely many polygamma functions and their divided difference functions, which give an answer to Qi's guess and extend some known results.
In this article, existence and uniqueness theorems are proved by considering the nonlinear impulsive singular q-Sturm-Liouville problem in the case of Weyl's limit circle.
In this paper, we study the abstract nonlo cal boundary value problem for the elliptic equation in an arbitrary Banach space with the positive operator. We establish the well posedness of this nonlo cal boundary value problem across several Banach spaces. Additionally, we derive new Schauder types of coercive stability estimates for the solutions of several nonlo cal boundary value problems involving elliptic equations.
In this article, the umbral-operational methods are used to reformulate the theory of multi-variable generalized Bessel functions. Further, certain results concerning the multi-variable argument expansion are derived.
. In this article, we present some new fixed point results for F-Kannan contraction mappings in non-triangular metric spaces. As a part of applications, the claimed results are synthesized by the existence and the uniqueness of the solution of a general Volterra integral equation and a fractional differential equation along with a fractional differential operator in Riemann-Liouville sense. We have also designated examples to support our results.
It is studied that pointwise estimates and continuities on Hardy spaces of the pseudo-differential operators (PDOs for short) with the symbol in general Hormander's classes. We get weighted weak-type (1, 1) estimate, weighted normal inequalities, (H-p, H-p) continuities and (H-p, L-p) continuities for the PDOs, where 0 < p < 1.
The representation of an explicit solution to the Prabhakar fractional differential delayed system is studied employing the far-famed Laplace transform technique. Second, the existence uniqueness of the solution is debated together with the Ulam-Hyers stability of a semilinear Prabhakar fractional differential delayed system. Thirdly, the necessary and sufficient circumstances for the controllability of linear Prabhakar fractional differential delayed system are determined by describing the Gramian matrix. A sufficient circumstance for the relative controllability of a semilinear Prabhakar fractional differential delayed system is studied via the Krasnoselskii’s fixed point theorem. Numerical examples are offered to verify the theoretical findings.
