Abstract: Abstract Some theorems of Liouville type are given for such P-harmonic maps when target manifold have conformal vector field or convex function or have non-positive sectional curvature. PubDate: 2024-07-26
Abstract: Abstract Valerij G. Bardakov and P. Bellingeri introduced a new linear representation \(\bar{\rho }_F\) of degree \(n+1\) of the braid group \(B_n\) . We study the irreducibility of this representation. We prove that \(\bar{\rho }_F\) is reducible to the degree \(n-1\) . Moreover, we give necessary and sufficient conditions for the irreducibility of the complex specialization of its \(n-1\) degree composition factor \(\bar{\phi }_F\) . PubDate: 2024-07-17
Abstract: Abstract This study presents the Chebyshev pseudospectral approach in time and space to approximate a solution to the time-fractional multidimensional Burgers equation. The suggested approach utilizes Chebyshev–Gauss–Lobatto (CGL) points in both spatial and temporal directions. To figure out the fractional derivative matrix at CGL points, we use the Caputo fractional derivative formula. Further, the Chebyshev fractional derivative matrix is utilized to reduce the given problem in an algebraic system of equations. The numerical approach known as the Newton–Raphson is implemented to get the desired results for the system. Error analysis for the set of values of \( \nu \) is done for various model examples of fractional Burgers equations, where \(\nu \) represents the fractional order. The computed numerical results are in perfect agreement with the exact solutions. PubDate: 2024-07-09
Abstract: Abstract In the past few decades, the discrete dynamics of difference maps have attained the remarkable attention of researchers owing to their incredible applications in different domains, like cryptography, secure communications, weather forecasting, traffic flow models, neural network models, and population biology. In this article, a generalized chaotic system is proposed, and superior dynamics is disclosed through fixed point analysis, time-series evolution, cobweb representation, period-doubling, period-3 window, and Lyapunov exponent properties. The comparative bifurcation and Lyapunov plots report the superior stability and chaos performance of the generalized system. It is interesting to notice that the generalized system exhibits superior dynamics due to an additional control parameter \(\beta \) . Analytical and numerical simulations are used to explore the superior dynamical characteristics of the generalized system for some specific values of parameter \(\beta \) . Further, it is inferred that the superiority in dynamics of the generalized system may be efficiently used for better future applications. PubDate: 2024-07-01
Abstract: Abstract Sierpiński graphs are frequently related to fractals, and fractals apply in several fields of science, i.e., in chemical graph theory, computer networking, biology, and physical sciences. Functions and polynomials are powerful tools in computer mathematics for predicting the features of networks. Topological descriptors, frequently graph constraints, are absolute values that characterize the topology of a computer network. In this essay, Firstly, we compute the M-polynomials for Sierpiński-type fractals. We derive some degree-dependent topological invariants after applying algebraic operations on these M-polynomials. PubDate: 2024-07-01
Abstract: Abstract This paper aims to study the existence and stability results concerning a fractional partial differential equation with variable exponent source functions. The local existence result for \(\alpha \in (0,1)\) is established with the help of the \(\alpha \) -resolvent kernel and the Schauder-fixed point theorem. The non-continuation theorem is proved by the fixed point technique and accordingly the global existence of solution is achieved. The uniqueness of the solution is obtained using the contraction principle and the stability results are discussed by means of Ulam-Hyers and generalized Ulam-Hyers-Rassias stability concepts via the Picard operator. Examples are provided to illustrate the results. PubDate: 2024-06-15
Abstract: Abstract Fourth order extended Fisher Kolmogorov reaction diffusion equation has been solved numerically using a hybrid technique. The temporal direction has been discretized using Crank Nicolson technique. The space direction has been split into second order equation using twice continuously differentiable function. The space splitting results into a system of equations with linear heat equation and non linear reaction diffusion equation. Quintic Hermite interpolating polynomials have been implemented to discretize the space direction which gives a system of collocation equations to be solved numerically. The hybrid technique ensures the fourth order convergence in space and second order in time direction. Unconditional stability has been obtained by plotting the eigen values of the matrix of iterations. Travelling wave behaviour of dependent variable has been obtained and the computed numerical values are shown by surfaces and curves for analyzing the behaviour of the numerical solution in both space and time directions. PubDate: 2024-04-24
Abstract: Abstract The aim of this paper is twofold: first, we obtain various curvature inequalities which involve the Ricci and scalar curvatures of horizontal and vertical distributions of anti-invariant Riemannian submersion defined from conformal Kenmotsu space form onto a Riemannian manifold. Second, we obtain the Chen–Ricci inequality for the said Riemannian submersion. The equality cases of all the inequalities are studied. Moreover, these curvature inequalities are studied under two different cases: the structure vector field \(\xi \) being vertical or horizontal. PubDate: 2024-04-20
Abstract: Abstract In this study, the theory of curves is reconstructed with fractional calculus. The condition of a naturally parametrized curve is described, and the orthonormal conformable frame of the naturally parametrized curve at any point is defined. Conformable helix and conformable slant helix curves are defined with the help of conformable frame elements at any point of the conformable curve. The characterizations of these curves are obtained in parallel with the conformable analysis Finally, examples are given for a better understanding of the theories and their drawings are given with the help of Mathematics. PubDate: 2024-04-15
Abstract: Abstract We prove that any homogeneous local representation \(\varphi :B_n \rightarrow GL_n(\mathbb {C})\) of type 1 or 2 of dimension \(n\ge 6\) is reducible. Then, we prove that any representation \(\varphi :B_n \rightarrow GL_n(\mathbb {C})\) of type 3 is equivalent to a complex specialization of the standard representation \(\tau _n\) . Also, we study the irreducibility of all local linear representations of the braid group \(B_3\) of degree 3. We prove that any local representation of type 1 of \(B_3\) is reducible to a Burau type representation and that any local representation of type 2 of \(B_3\) is equivalent to a complex specialization of the standard representation. Moreover, we construct a representation of \(B_3\) of degree 6 using the tensor product of local representations of type 2. Let \(u_i\) , \(i=1,2\) , be non-zero complex numbers on the unit circle. We determine a necessary and sufficient condition that guarantees the irreducibility of the obtained representation. PubDate: 2024-04-15
Abstract: Abstract In this paper, a discrete-time model of a plant–herbivore system is qualitatively analyzed using difference equations to describe population dynamics over time. The goal is to examine how the model behaves under varying parameter values and initial conditions. Results reveal that the model exhibits diverse dynamical behaviors such as stable equilibria, period-doubling cascade, and chaotic attractors. The analysis indicates that changes in crucial parameters greatly affect the system’s dynamics. This study offers crucial insights into plant–herbivore systems and highlights the value of qualitative analysis in comprehending intricate ecological systems. PubDate: 2024-04-01
Abstract: Abstract In this work, we consider fractional variational problems depending on higher order fractional derivatives. We obtain optimality conditions for such problems and we present and discuss some examples. We conclude with possible research directions. PubDate: 2024-04-01
Abstract: Abstract This paper attempts to prove the Lipschitz continuity of the resolvent operator associated with a \((P,\eta )\) -accretive mapping and compute an estimate of its Lipschitz constant. This is done under some new appropriate conditions that are imposed on the parameter and mappings involved in it; with the goal of approximating a common element of the solution set of a system of generalized variational-like inclusions and the fixed point set of a total asymptotically nonexpansive mapping in the framework of real Banach spaces. A new iterative algorithm based on the resolvent operator technique is proposed. Under suitable conditions, we prove the strong convergence of the sequence generated by our proposed iterative algorithm to a common element of the two sets mentioned above. The final section is dedicated to investigating and analyzing the notion of a generalized H(., .)-accretive mapping introduced and studied by Kazmi et al. (Appl Math Comput 217:9679–9688, 2011). In this section, we provide some comments based on the relevant results presented in their work. PubDate: 2024-04-01
Abstract: Abstract The purpose of this article is to obtain appropriate tools for solving fractional differential equations that are flexible enough to adapt to different purposes. We thus look for a very general fractional Fourier transform with a phase function which can be appropriately chosen according to the problem you want to face. PubDate: 2024-04-01
Abstract: Abstract We focus on two-phase problems with singular and superlinear parametric terms on the right-hand side. Using fibering maps and the Nehari manifold method, we prove that there are at least two non-trivial positive solutions in a geometric setting that is locally similar to Euclidean spaces but has different global properties for all except the smallest values of parameter \(\mu > 0.\) Singularities may appear at discrete locations in the manifold, which is a challenge for the work due to the unpredictable behavior of the solution. The findings presented here generalize some known results. PubDate: 2024-04-01
Abstract: Abstract The objective of this research is to prove that an additive mapping \(\Delta :{\mathcal {A}}\rightarrow {\mathcal {A}}\) will be a generalized derivation associated with a derivation \(\partial :{\mathcal {A}}\rightarrow {\mathcal {A}}\) if it satisfies the following identity \(\Delta (r^{m+n+p})=\Delta (r^m)r^{n+p}+r^m\partial (r^{n})r^p+r^{m+n}\partial (r^p)\) for all \(r\in {\mathcal {A}}\) , where \(m, n\ge 1\) and \(p\ge 0\) are fixed integers and \({\mathcal {A}}\) is a semiprime ring. Another analogous has been done where an additive mapping behaves like a generalized left derivation associated with a left derivation on \({\mathcal {A}}\) satisfying certain algebraic identity. The proofs of these advancements are derived employing algebraic concepts. These theorems have been validated by offering an example that shows they are not insignificant. Furthermore, we provide an application in the framework of Banach algebra. PubDate: 2024-04-01
Abstract: Abstract In this work, we obtain fixed point theorems and convergence theorems for Suzuki-generalized nonexpansive mappings in complete \(CAT_p(0)\) metric spaces for \(p\ge 2\) . Our results extend and improve many results in the literature. PubDate: 2024-02-22
Abstract: Abstract In this article, we employ the group-theoretic methods to explore the Lie symmetries of the Klein–Gordon–Zakharov equations, which include time-dependent coefficients. We obtain the Lie point symmetries admitted by the Klein–Gordon–Zakharov equations along with the forms of variable coefficients. From the resulting symmetries, we construct similarity reductions.The similarity reductions are further analyzed using the power series method/approach and furnished the series solutions. Additionally, the convergence of the series solutions has been reported. PubDate: 2024-01-23
Abstract: Abstract Of concern is a Cohen–Grossberg neural network (CGNNs) system taking into account distributed and discrete delays. The class of delay kernels ensuring exponential stability existing in the previous papers is enlarged to an extended class of functions guaranteeing more general types of stability. The exponential and polynomial (or power type) type stabilities becomes particular cases of our result. This is achieved using appropriate Lyapunov-type functionals and the characteristics of the considered class. PubDate: 2023-12-15
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