https://maco.lu.ac.ir/ Mathematical Analysis and Convex Optimization en daily 1 Mon, 01 Dec 2025 00:00:00 +0330 Mon, 01 Dec 2025 00:00:00 +0330 https://maco.lu.ac.ir/article_731398.html There are some interesting Riemannian and non-Riemannian curvature in Riemann-Finsler geometry. Recently, the author introduced a new non-Riemannian quantity named mean stretch curvature. Taking trace with respect to fundamental tensor in first and second variables of stretch curvature gives rise the mean stretch curvature. A Finsler metric is said to be weakly stretch metric if has vanishing mean stretch curvature. In this paper, we are going to study the mean stretch curvature of 4-dimensional Finsler manifolds. First, we find the necessary and sufficient condition under which a 4-dimensional Finsler manifold is weakly stretch. Then, we show that the main scalars of a weakly stretch metric satisfies some certain PDEs. https://maco.lu.ac.ir/article_731479.html Finsler geometry is just Riemannian geometry without the quadratic restriction. In Riemannian geometry, the restriction of the metric to a tangent spaceis an inner product and hence tangent spaces at different points are linearlyisometric to each other.In this paper, we consider the special (α, β)-metric such that it is satisfyingF (α, β) = β + aα + βα2 , a ∈ R. We have investigate the geometric properties of this metric inhomogeneous spaces. We investigate the existence of invariant vector fields. Also, we obtainthe explicit formula for the S-curvature and mean Berwald curvature of homogeneous Finslerspace with this (α, β)-metric. Geodesics and geodesic vectors are other topics that we studyfor these spaces. https://maco.lu.ac.ir/article_731838.html This study presents a modified version of the Rohn iterative method to solve the absolute value equation in the form $Ax-|x|-b=0$, where $A$ is a matrix such that the norm of its inverse is less than $1$. The proposed method converges linearly to the unique solution of the absolute value equation. It offers a low computational cost algorithm that provides an approximate solution with acceptable accuracy after only a few iterations. Furthermore, this study compares the structure and convergence rates of the proposed method, the generalized Newton method, and the standard Rohn method. The potential applications of the proposed method are demonstrated through a comparison with the generalized Newton and Rohn methods, using $100$ randomly generated absolute value equations of various dimensions. In total, $900$ problems are solved. https://maco.lu.ac.ir/article_731844.html Let $S$ be a discrete semigroup and $T$ be a left multiplier operator on $S$. The semigroup $S$, equipped with the new operation defined by $T,(s\circ t:=sT(t))$,is called the induced semigroup and is denoted by $S _{T}$.We consider the semigroup algebras $ \ell^1({S}) $ and $ \ell^1({S_T}) $, as well as the triangular Banach algebras:\begin{equation*}\mathcal{T}=\Mat{\ell^1({S})}{M_{\delta_S}}{\ell^1({S})}\qquad \text{and} \qquad \mathcal{T}_T=\Mat{\ell^1({S_T})}{M_{\delta_{S_T}}}{\ell^1({S_T})}.\end{equation*} In this paper, we show that the first module cohomology groups of these triangular Banach algebras, $\HH^{1}_ \mathfrak{T}(\mathcal{T},\mathcal{T}^*) $ and $ \HH^{1}_{ \mathfrak{T}_{T}}(\mathcal{T}_T,\mathcal{T}_T^*)$, are equal, where\begin{equation*}\mathfrak{T}=\set{\Mat{\alpha}{}{\alpha},\alpha\in \ell^1({E})}\qquad \text{,} \qquad \mathfrak{T}_{T}=\set{\Mat{\beta}{}{\beta},\beta\in \ell^1({E_{T}})}.\end{equation*} Here, $ E $ and $ E_{T} $ denote the sets of idempotent elements in $ S $ and $ S_T $, respectively. This result implies that, in a particular case, $\mathcal{T}$ is weakly $ \mathfrak{T}$-module amenable if and only if $\mathcal{T}_T$ is weakly $\mathfrak{T}_{T}$-module amenable.Furthermore, $ M_{\delta_s} $ and $ M_{\delta_{S_T}} $ denote the canonical left modules over $ \ell^1({S}) $ and $ \ell^1({S_T}) $, respectively. https://maco.lu.ac.ir/article_731877.html In this paper, we consider $\alpha-$Chebyshev polynomials, $\alpha-$Chebyshev wavelet approximation and h$\ddot{o}$lder of order $l$. We estimate $\alpha-$Chebyshev-wavelet approximation of a function $f$ having satisfy condition h$\ddot{o}$lder where $f$ is expanded in terms of $\alpha-$Chebyshev wavelet polynomials. In this paper, we consider $\alpha-$Chebyshev polynomials, $\alpha-$Chebyshev wavelet approximation and h$\ddot{o}$lder of order $l$. We estimate $\alpha-$Chebyshev-wavelet approximation of a function $f$ having satisfy condition h$\ddot{o}$lder where $f$ is expanded in terms of $\alpha-$Chebyshev wavelet polynomials. In this paper, we consider $\alpha-$Chebyshev polynomials, $\alpha-$Chebyshev wavelet approximation and h$\ddot{o}$lder of order $l$. We estimate $\alpha-$Chebyshev-wavelet approximation of a function $f$ having satisfy condtion h$\ddot{o}$derl where $f$ is expanded in terms of $\alpha-$Chebyshev wavelet polynomials. https://maco.lu.ac.ir/article_731888.html ‎In this paper‎, ‎we study fuzzy stochastic differential equation initial value problems (IVPs)‎. ‎In modeling‎, ‎analyzing‎, ‎and predicting behaviors of physical and natural phenomena‎, ‎greater and greater emphasis has been placed upon fuzzy stochastic methods‎. ‎A large class of physically important problems is described by fuzzy stochastic differential systems‎.‎We obtain the existence and‎‎uniqueness theorem for a solution of the fuzzy stochastic differential equation (FSDE) under the Lipschitz condition‎. ‎We‎‎present characterization theorems for the solution of a FSDE under the m.s‎. ‎derivative-based interpretation‎, ‎by the solution of a system of ODEs‎. ‎Numerical examples are provided which connect the new results with previous findings‎. ‎ https://maco.lu.ac.ir/article_731889.html In this paper, as using T-norms, we introduce and analyze the new classes of BCC-algebras as fuzzy subalgebras, fuzzy ideals, fuzzy left derivation ideals, fuzzy right derivationideals and fuzzy derivation ideals and we obtain the relationships between them and classicalconcepts of BCC-algebras such that every fuzzy subalgebras, fuzzy ideals, fuzzy left derivation ideals, fuzzy right derivation ideals and fuzzy derivation ideals will be subalgebras, ideals, left derivation ideals, right derivation ideals and derivation ideals of BCC-algebras, respectively.Next we investigate the intersection and direct product of them andprove the algebraic structures of them. Finally, we investigate image and pre-image of themunder homomorphisms of BCC-algebras. https://maco.lu.ac.ir/article_731999.html In this paper, we investigate partition regularity of matrices over vector spaces where the matrix entries consist of linear transformations on the vector space. The paper also examines the existence of monochromatic solutions for matrix entries of linear transformations, which generalizes Rado's theorem.Our main results establish that matrices satisfying these conditions are not only partition regular but also preserve solutions within large combinatorial sets, such as central sets. Furthermore, we present a counterexample involving affine maps, demonstrating a limitation of these results and highlighting the necessity of the linearity assumption. This work bridges combinatorial number theory and linear algebra, offering a functional-analytic perspective on Ramsey-type problems. https://maco.lu.ac.ir/article_732065.html The invariance of frames and their extensions under the operator perturbation is one of the most important problems in frame theory.In this paper, we focus on the stabilities of scalable K-frames under the operator perturbation and thenwe construct new scalable K-frames for Hilbert spaces by some operator theory tools.More precisely, we investigate several sufficient and/or conditionsof the operator perturbation for a scalable K-frame by using certain operators with specific properties.Finally, since the finite sum of scalable K-frames may not be a scalable K-frames forthe Hilbert space, we demonstrate that under some special conditions, the sum of two scalable K-frames remains a scalable K-frame. https://maco.lu.ac.ir/article_732718.html In this article, we obtain algebraic versions of algorithms NGHK and KL (two geometric methods for solving systemsof linear equations), that is, we show that in these two algorithms,the vector sequences that converge to the solution of the system oflinear equations are located in the row space of the coefficients matrix of system. In the following, we will compare these algorithmswith the Gauss-Seidel method by providing a few examples.In this article, we obtain algebraic versions of algorithms NGHK and KL (two geometric methods for solving systemsof linear equations), that is, we show that in these two algorithms,the vector sequences that converge to the solution of the system oflinear equations are located in the row space of the coefficients matrix of system. In the following, we will compare these algorithmswith the Gauss-Seidel method by providing a few examples. https://maco.lu.ac.ir/article_733206.html Type 3 sum of squares (T3SS) is used to test model comparisons that violate the marginality principle when testing main effects and are not dependent on the order of the model terms, and also, the sum of the individual effect SS is not equal to the total effect SS. This paper presents a new method to obtain T3SSs based on projection (P) matrices in two-way fixed effects (T-WFE) model. Previous research has shown that in analysis of variance (ANOVA) for unbalanced data, the total SS is not obtained by summing the T3SSs of the components considered as factors of variation. In fact, in such a case, there is a significant difference between the values of these two quantities. The method proposed in this paper uses P matrices to identify where differences occur and the magnitude of their differences, while the traditional ANOVA method cannot clearly explain these. This paper also discusses how to use the eigenvalues and eigenvectors of P matrices to obtain T3SSs. Then, a study was conducted on a real dataset based on an unbalanced dataset for the proposed model fitting method to calculate TESSs based on P matrices. https://maco.lu.ac.ir/article_733583.html In uniformly smooth Banach spaces, we prove a dual ergodic theorem for an almost-orbit of a sequence of nonexpansive mappings. We also present a new definition of almost-orbit for a sequence of nonexpansive mappings and prove the dual ergodic theorem for this sequence. This results extend the dual ergodic theorem established by Bruck and Reich for iterations of nonexpansive mappings as well as ergodic theorems for a sequence of nonexpansive mappings from Hilbert spaces to Banach spaces. Finally, some applications to fixed point iterative methods for nonexpansive mappings and the proximal point algorithm for m-accretive operators to approximate a zero of the operator are presented. https://maco.lu.ac.ir/article_735081.html This paper introduces and rigorously analyzes the concept of parallel dynamical systems, a novel framework for understanding and achieving synchronizationin chaotic systems. For any given dynamical system defined by ordinary differentialequations, we construct a corresponding parallel system through a scaling transformation of phase space variables. We prove rigorously that the parallel systempreserves all fundamental chaotic properties of the original system, including sensitive dependence on initial conditions, topological transitivity, and density of periodicorbits. This theoretical foundation enables a controller-free synchronization methodwhere systems naturally synchronize through appropriate initial condition scaling.Numerical simulations of the Lorenz system validate our theoretical predictions,demonstrating perfect synchronization and practical applicability