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.

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...

Advanced module systems like Standard ML's 13, 17] support structure generativity. Structure generativity denotes the mechanism that parameterized modules (functors) generate a "new" module instance (structure) for every application to a suitable argument. This operational behaviour is essentially a side eeect. Since interfaces in general depend on module instances, module instances are computa...

Advanced module systems like Standard ML's 13, 17] support structure generativity. Structure generativity denotes the mechanism that parameterized modules (functors) generate a "new" module instance (structure) for every application to a suitable argument. This operational behaviour is essentially a side eeect. Since interfaces in general depend on module instances, module instances are computa...

We introduce an MPI Python module, MYMPI, for parallel programming in Python using the Message Passing Interface (MPI). This is a true Python module which runs with a standard Python interpreter. In this paper we discuss the motivation for creating the MYMPI module, along with differences between MYMPI and pyMPI, another MPI Python interpreter. Additionally, we discuss three projects that have ...

for an $n$-gon with vertices at points $1,2,cdots,n$, the betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. in this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and betti numbers of the $s$-module $s/i$ where  $s=k[x_{1},cdots, x_{n}]$ and $i$ is the associated ideal to ...

A low-cost short-range K-band Doppler radar sensor for traffic control applications has been developed. The compact sensor, including a waveguide front-end module and a planar patch antenna, weighs only 0.1 lb. The module incorporates a Gunn oscillator, a mixer and a simple coupling/duplex configuration; the antenna is realized on a 0.031” thick Rogers 4003 laminate to allow its stand alone ope...