one of the most practical routine tests for convergence of a positive series makes use of the ratio test. if this test fails, we can use rabbe's test. when rabbe's test fails the next sharper criteria which may sometimes be used is the bertrand's test. if this test fails, we can use a generalization of bertrand's test and such tests can be continued innitely. for simplicity...

<abstract><p>Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact triangulated categories. In this paper, we first introduce the concept left Frobenius pairs on an extriangulated category $ \mathcal{C} $, then establish bijective correspondence between certain cotorsion in $. As application, some new admissible model structures are ...

We consider a generalization of spatial branching coalescing processes in which the behaviour individuals is not (necessarily) independent, on contrary, tend to take simultaneous actions. show that these have moment duals, happen be multidimensional diffusions with jumps. Moment duality provides general framework study structural properties this class. present some conditions under expectation ...

in this paper the class of n-ary hypergroups is introduced and several properties are found andexamples are presented. n-ary hypergroups are a generalization of hypergroups in the sense of marty. on theother hand, we can consider n-ary hypergroups as a good generalization of n-ary groups. we define thefundamental relation β* on an n-ary hypergroup h as the smallest equivalence relation such tha...

In this paper, pretopological and topological operators are introduced based on partially continuous linear transformations of the membership and non-membership functions for intuitionistic fuzzy sets. They turn out to be a generalization of the topological operators for intuitionistic fuzzy sets.On the other hand it is a generalization of the fuzzy set pretopological operators introduced...

The concept of algebraic hyperstructures introduced by Marty as a generalization of ordinary algebraic structures. In an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. The concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper‌rings and a generalizat...

We introduce the notion of integrality Grothendieck categories as a simultaneous generalization primeness noncommutative noetherian rings and locally schemes. Two different spaces associated to category yield respective definitions integrality, we prove equivalence these using Grothendieck-categorical version Gabriel's correspondence, which originally related indecomposable injective modules pr...

Nuclear magnetic resonance microscopy poses fundamental as well as practical challenges. The Torrey–Bloch equation obeyed by the magnetization density is basic to this field. We discuss exact solutions of the equation from a generalization that addresses the motion of the nuclear spins towards an attractive center with an arbitrary time dependence in the attractive (harmonic) potential. The sol...