Iranian Journal of Science and Technology, Transactions A: Science最新文献

Optimization problems on curved spaces such as Hadamard manifolds arise in machine learning, computer vision, and data analysis. Motivated by these applications, this paper studies the interplay between nonsmooth vector variational inequality problems (NVVIP), their Minty-type counterparts (MNVVIP), and nonsmooth vector optimization problems (NVOP) on Hadamard manifolds. Using vector-valued bifunctions as the main tool, we develop a framework for generalized geodesic convexity, introducing geodesic h-convexity, h-pseudoconvexity, and h-quasiconvexity for vector-valued functions, and illustrate their structure through a non-trivial example. Relying on bifunctional methods and generalized convexity techniques, we prove uniqueness results for NVVIP and establish characterizations linking NVVIP with MNVVIP. We also derive conditions under which solutions of NVVIP, MNVVIP, and NVOP coincide, providing a unified theoretical perspective. These results not only extend the theory of vector variational inequalities and optimization on manifolds but also offer foundational tools for applications in optimization over non-Euclidean spaces.

Let G be a finite group. A subset X of G is called a trivial intersection set if for every (gin G), either (X^{g} = X) or (X^{g}cap X subseteq {1}). A subgroup S of G is called a TI-subgroup if S is a trivial intersection set. Also, a subgroup K of G is termed an H-subgroup if (N_{G}(K) cap K^xle K) for all (xin G). In this paper, we introduce the concept of HI-subgroups. A subgroup T of G is said to be an HI-subgroup if (N_{G}(T) cap T^xle T) and (N_{G}(T) cap T^xne {1}) for every (xin Gsetminus N_{G}(T)). We describe the structure of finite groups G in which every subgroup is either a TI-subgroup or an HI-subgroup. We demonstrate that if G is a nilpotent TH-group, then it is either a Dedekind group or a p-group in which all non-normal subgroups of G have the same prime order p. Furthermore, we show that if G is a TH-group and every subgroup of order two in a non-abelian Sylow 2-subgroup P of G is normal in the normalizer of P in G, then G is 2-nilpotent.

In this paper, we characterize the skew constacyclic codes of length ( p^s ) over ( R_3= mathbb {F}_{p^m}+umathbb {F}_{p^m}+{u^2}mathbb {F}_{p^m}) for special automorphisms, where p is a prime, m is a positive integer, ( mathbb {F}_{p^m} ) is a finite field of cardinality ( p^m) and ( u^3=0. ) First, we classify all skew constacyclic codes of length ( p^s ) over ( R_3) and obtain the torsion codes of them.

The zero forcing number of a graph (G) is defined as the smallest number of vertices initially colored black, such that all other vertices are colored white and can iteratively turn black if they are the only white neighbor of a black vertex. In quantum systems, the concept of zero forcing can model the propagation of control or influence through a network, reflecting the ability to achieve desired states or behaviors through a minimal set of control points. Toeplitz graphs form a special class of graphs which are constructed based on Toeplitz matrices, which are matrices where each descending diagonal from left to right is constant. In this paper, we provide a comprehensive analysis of the zero forcing numbers for various families of Toeplitz graphs. We identify specific values for which the zero forcing number remains invariant under increases in the generator values and present generalized findings for the zero forcing numbers across these graph families.

In this paper, we introduce generalized formulae for well-known polynomials such as Chebyshev polynomials. We define ((beta ,gamma ))-Chebyshev polynomial, ((beta ,gamma ))-pseudo-Chebyshev wavelet approximation and ((beta ,gamma ))-pseudo Chebyshev wavelet coapproximation. We show if for (f in L^2([-1,1])) is a uniformly bounded function and (f (t) =sum _{n=0}^{2^k}sum _{m=0}^{infty }t_{n,m}Psi _{n,m}^{beta ,gamma }(t)) be expanded in terms of ((beta ,gamma ))-Chebyshev wavelets (((beta ,gamma ))-pseudo Chebyshev wavelets). Then wavelets Chebyshev approximation (wavelets Chebyshev coapproximation) exist.

In this essay, a new numerical method for solving linear Lane–Emden differential equations arising in astrophysics is proposed. The method begins by approximating the second derivative in the equation using a finite series of the Boubaker polynomials, which is then expressed in matrix form. By integrating this approximation and applying the derivative condition, the expression for the first derivative term is obtained. A second integration, along with the other boundary condition, yields the Boubaker series representation of the unknown function. Using this matrix formulation and associated operations, the problem is reduced to a system of linear algebraic equations. Furthermore, an error estimation and improvement technique are introduced and applied, along with the proposed method, to numerical examples. The results demonstrate the effectiveness of the new method, showing improved accuracy compared with other standard polynomial approaches. This is evident from the tables and graphs presented in the numerical examples.

In our study, we examine a mathematical model that characterizes the dynamic Coulomb’s frictional contact between a thermo-viscoelastic body and a thermally conductive rigid foundation. This model incorporates a nonlinear constitutive viscoelastic law with long-term memory and thermal effects. The contact condition on the contact surface is modeled using Signorini’s boundary condition, expressed through Clarke subdifferential. By formulating the problem’s weak form as a system combining variational–hemivariational inequalities, we establish the existence and uniqueness of a weak solution to the model, leveraging recent advances in the theory of variational–hemivariational inequalities.