The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

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 of...

Here we demonstrate the implementation of a single-molecule force clamp adapted for use with an atomic force microscope. We show that under force-clamp conditions, an engineered titin protein elongates in steps because of the unfolding of its modules and that the waiting times to unfold are exponentially distributed. Force-clamp measurements directly measure the force dependence of the unfoldin...

This article describes a set of modules for Max/MSP for real-time sound analysis and synthesis combining various models, representations and timing paradigms. Gabor provides a unified framework for granular synthesis, PSOLA, phase vocoder, additive synthesis and other STFT techniques. Gabor’s processing scheme allows for the treatment of atomic sound particles at arbitrary rates and instants. G...

The paper considers the application interface testing technology on the basis of probabilistic networks; it offers the criteria of reliability dependence measure for the different application modules sharing the same functionality; it proposes an expand criterion of the testing completeness by the measure of uncertainty of the modules reliability; it is shown how to use automated mechanism of t...

This paper explores the explanation of subsumption reasoning in Description Logics that are implemented using normalization methods, focusing on the perspective of knowledge en­ gineers. The notion of explanation is specified using a proof-theoretic framework for present­ ing the inferences supported in these systems. The problem of overly long explanations is ad­ dressed by decomposing them in...

bered that EUPHORIA is part of a distributed system; if the EUPHORIA module monopolizes the CPU, external modules will run slower which, in turn, will make EUPHORIA run slowly. Also, if other modules update their variables repeatedly at a rate faster than the update rate of EUPHORIA, time is still spent dealing with the intermediate values of the variables even though the values may be " skippe...

The Atomic Decomposition (AD) of an ontology O is a compact representation of all the modules of O. Besides its theoretical value, it has some practical applications, which include optimised reasoning techniques. In this paper we describe the existing programming APIs that allow for the use of the AD of an ontology in Java and C++ programs.

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...