in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

in this paper we introduce the concept of dirac structures on (hermitian) modules and vectorbundles and deduce some of their properties. among other things we prove that there is a one to onecorrespondence between the set of all dirac structures on a (hermitian) module and the group of allautomorphisms of the module. this correspondence enables us to represent dirac structures on (hermitian)mod...

Let  be a commutative ring and  be a unitary  module. We define a semi prime sub module of a module and consider various properties of it. Also we define semi-radical of a sub module of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.

Understanding how biological systems transduce dynamic, soluble chemical cues into physiological processes requires robust experimental tools for generating diverse temporal chemical patterns. The advent of microfluidics has seen the development of platforms for rapid fluid exchange allowing ease of changes in the cellular microenvironment and precise cell handling. Rapid exchange is important ...

The dispersion of torsional wave in transverse and layered one-dimensional component of infinite length is investigated. The study is carried out by treating the one-dimensional component as a cylinder of infinite length firstly, Then put forward a way that the component is divided into a multilayer to analyze torsional wave propagation, the model is constructed in cylindrical coordinates for h...

Most learning systems applied to problem solving have the goal of learning knowledge for solving problems more eeciently. However, very few systems have focused on the acquisition of planning operator descriptions. In this paper, we present a system that learns operator deenitions from the interaction with a completely unknown environment. In order to achieve better learning convergence, severa...

Most learning systems applied to problem solving have the goal of learning knowledge for solving problems more eeciently. However, very few systems have focused on the acquisition of planning operator descriptions. In this paper, we present a system that learns operator deenitions from the interaction with a completely unknown environment. In order to achieve better learning convergence, severa...

In order to understand the mechanisms involved in the forming step of LCM processes and provide validation data to numerical models, a specific experimental device has been designed in collaboration between PRISME Institute and EADS. This toot also makes it possible to test the feasibility to obtain specific double curved shape constituted with dry fabric reinforcement. It contains one mechanic...

The state of melt viscosity in injection process is significantly influenced by the setting parameters due to that the shear rate of injection process is higher than other processes. How to determine plastic melt viscosity during injection process is important to understand the influence of setting parameters on the melt viscosity. An apparatus named as pressure sensor bushing (PSB) module that...