Category: Issue 2

ABSTRACT:

The purpose of this study is to introduce, define and study several classes of nano quotient map in nano topological spaces. We have initiated the several types of mappings such as nano  -quotient map, nano strongly  – quotient map and nano *-quotient map in nano topological space and its properties are discussed. Also we have made comparisions among them.

KEYWORDS: Nano topology, nano quotient map, nano  -open, nano  -irresolute, nano  * -quotient map. 2010 Ams Subject Classification: 54B05,54CO8

ABSTRACT:

In this paper we propose a mathematical model of Friedreich’s Ataxia (FA) – a genetic neuro-muscular degenerative condition which causes imbalance, in-coordination and jerky limb movements. These continue to increase till patient loses independence and becomes wheelchair bound. Currently Friedreich’s Ataxia (FA) is not considered an important health problem because of its relatively low prevalence in the general population. However with improvement in health care diagnosis and delivery provisions, more and more people with Friedreich’s Ataxia (FA) are being diagnosed and surviving. This means that its incidence and prevalence is bound to change. We have used a mathematical model to estimate generational increase in the number of patients and carriers with FA. The results portray a scary picture and hence demand measures to take it more seriously by health care providers.

KEYWORDS: Friedreich’s Ataxia, Stochastic matrix, Probability vector, Fixed point

ABSTRACT:

In this work, we discuss the existence of fixed points of continuous contracting mappings defined on dislocated quasi-metric space. This work is a continuity of the previous works of Isufati.

KEYWORDS: Fixed point, dislocated quasi-metric space. AMS Subject Classification : 47H10, 54H25

ABSTRACT:

In this paper, we prove a fixed point theorem for self mappings satisfying a new contractive type condition in a compact metric space.

KEYWORDS: Fixed point, compact metric space, fixed point theorem

ABSTRACT:

In this paper we introduce and characterize -open sets and derive that this class of -open sets forms a topology on X. We also define the necessary and sufficient condition for a set to be -open set. Further we induce various kinds of spaces in N-topology and its applications.

KEYWORDS: N-topology, - closed, -closed, -closed, -closed. MSC 2010: 54A05,54A99, 54C10

ABSTRACT:

We define relation meet and relation join matrices on two different posets R and S of a lattice with respect to a complex-valued function f on P by (X,Y)f = (f(xi  yi)) and [X,Y]f = (f [xi  yi]) respectively. Also we present some examples for the determinant and inverse of(X, Y)f and [X,Y]f

KEYWORDS: Cartesian product, relations and its properties, posets, relation meet matrix, relation join matrix. Mathematics subject classification: 15A57, 11A57, 11C57, 06A57

ABSTRACT:

The Collatz conjecture is an open conjecture in mathematics named so after Lothar Collatz who proposed it in 1937. It is also known as 3n 1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutanis problem (after Shizuo Kakutani) and so on. Several various generalization of the Collatz conjecture has been carried. In this paper a new generalization of the Collatz conjecture called as the 3n  p conjecture; where p is a prime is proposed. It functions on 3n  p and 3n  p , and for any starting number n , its sequence eventually enters a finite cycle and there are finitely many such cycles. The 3n 1 conjecture, is a special case of the 3n  p conjecture when p is 1.

KEYWORDS: Collatz Conjecture; Kakutani’s Conjecture ; 3n 1 Conjecture; 3n  p Conjecture