We study multiplication modules. The rings are not assumed to be commutative. Several criteria with some applications given for a direct sum of modules module.

We provide an asymptotically tight, computationally efficient approximation of the joint spectral radius of a set of matrices using sum of squares (SOS) programming. The approach is based on a search for a SOS polynomial that proves simultaneous contractibility of a finite set of matrices. We provide a bound on the quality of the approximation that unifies several earlier results and is indepen...

A technique to prove the termination of a given term rewriting system (TRS, for short) is presented. We propose tree lifting orderings by which from a given TRS R candidates for the termination of R can be obtained|the termination of (at least) one of these candidates guarantees the termination ofR. It should be remarked that for a given nite TRS all its candidates can be computed automatically...

Stratified fault sampling is used in RTL fault simulation to estimate the gate-level fault coverage of given test patterns. RTL fault modeling and fault injection algorithm are developed such that the RTL fault list of a module can be treated as a representative fault sample of the collapsed stuck-at fault set of the module. The RTL coverage for the module is experimentally found to track the g...

The purpose of this paper is to introduce a new concept in module M over ring R, called e∗-essential submodule, which generalization an essential submodule. We will some examples and properties about such that, what the inverse image intersection submodules direct sum submodules. show relationship between submodule Noetherian R-module. Also we define e∗-closed with

This paper establishes a functional law of large numbers and central limit theorem for marked Hawkes point measures their corresponding shot noise processes. We prove that the normalized random measure can be approximated in distribution by sum Gaussian white process plus an appropriate lifting map correlated one-dimensional Brownian motion. The motion results from self-exciting arrivals events...

Let E be a cyclic algebraic number eld of a prime degree. We prove an identity which lifts an exponential sum similar to the Kloosterman sum to an exponential sum taken over certain algebraic integers in E.

Let E be a cyclic algebraic number field of prime degree. We prove an identity which lifts an exponential sum similar to the Kloosterman sum to an exponential sum taken over certain algebraic integers in E.