Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

‎We say that a module $M$ is a emph{cms-module} if‎, ‎for every cofinite submodule $N$ of $M$‎, ‎there exist submodules $K$ and $K^{'}$ of $M$ such that $K$ is a supplement of $N$‎, ‎and $K$‎, ‎$K^{'}$ are mutual supplements in $M$‎. ‎In this article‎, ‎the various properties of cms-modules are given as a generalization of $oplus$-cofinitely supplemented modules‎. ‎In particular‎, ‎we prove tha...

It is proved that any non-normable Fréchet space with a semisymmetric absolute basis is isomorphic to the space ω of all scalar sequences. A similar result is shown for quasi-homogeneous absolute bases. It is also proved that any nuclear Fréchet space with a semi-subsymmetric basis is isomorphic to ω.

In this paper, we are focused upon the global uniqueness results for a stochastic integro-differential equation in Fréchet spaces. The main results are proved by using the resolvent operators combined with a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. As an application, a controllability result with one parameter is given to illustrate the theory.

Matching two geometric objects in two-dimensional (2D) and three-dimensional (3D) spaces is a central problem in computer vision, pattern recognition, and protein structure prediction. In particular, the problem of aligning two polygonal chains under translation and rotation to minimize their distance has been studied using various distance measures. It is well known that the Hausdorff distance...

We present a variant of the Fréchet distance (as well as geodesic and homotopic Fréchet distance) which forces the motion between the input objects to follow an ambient isotopy. This provides a measure of how much you need to continuously deform one shape into another while maintaining topologically equivalently shapes throughout the deformation.

The matrix exponential is a much-studied matrix function having many applications. The Fréchet derivative of the matrix exponential describes the first-order sensitivity of eA to perturbations in A and its norm determines a condition number for eA. Among the numerous methods for computing eA the scaling and squaring method is the most widely used. We show that the implementation of the method i...

We construct a Fréchet space as a subspace of Cω(Cn) where the Wick star product converges and is continuous. The resulting Fréchet algebra A~ is studied in detail including a ∗-representation of A~ in the Bargmann-Fock space and a discussion of star exponentials and coherent states.

We present shortest path maps that support min-link queries from any source point on a line segment to destination points in either a simple polygon or a polygonal domain (a polygon with holes). These structures are more versatile than the traditional shortest path map from a fixed source point, and we use them to compute the min-link Fréchet distance between two polygonal curves. In addition t...

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.