In this paper, we discuss on the existence of filtrations of modules having good properties. In particular, we focus on filtered homomorphisms called strict, and show that there exists a filtration which makes a filtered homomorphism a strict filtered homomorphism. Moreover, by using this result, we study purity for filtered modules over a Gorenstein filtered ring.

Objective(s): Predegeneration is a standard technique to obtain mitotically activated and enriched cultures of Schwann cells (SCs). This study, for the first time, evaluated the impact of various duration of predegeneration on cell yield and enrichment of SCs from dog peripheral nerve. Materials and Methods: Dog sural nerves were subjected to 5, 10, 15 day-long in vitro predegeneration. The tot...

Restricting destructive update to values of a distinguished reference type prevents functions from being polymorphic in the mutability of their arguments. This restriction makes it easier to reason about program behaviour during transformation, but the lack of polymorphism reduces the expressiveness of the language. We present a System-F style core language that uses dependently kinded proof wi...

We emphasize the role of the choice of vocabulary in formalization of a mathematical area and remark that this is a particular preoccupation of logicians. We use this framework to discuss Kennedy’s notion of ‘formalism freeness’ in the context of various schools in model theory. Then we clarify some of the mathematical issues in recent discussions of purity in the proof of the Desargues proposi...

Logical inferentialism claims that the meaning of the logical constants should be given, not model-theoretically, but by the rules of inference of a suitable calculus. It has been claimed that certain proof-theoretical systems, most particularly, labelled deductive systems for modal logic, are unsuitable, on the grounds that they are semantically polluted and suffer from an untoward intrusion o...

the question of the purity or impurity of non-muslims has always attracted the attention of the islamic jurists. the importance of this question has been due to the fact that the social and political interactions between muslims and non-muslims were quite inevitable. the present article is concerned first to examine the notion of purity and impurity as viewed by the sunni and shiite jurists and...