In this section we introduce the Jones polynomial a link invariant found by Vaughan Jones in 1984.
Later on, Louis Kauffman expanded further Jones study of knot polynomials, allowing for a much simpler presentation of the Jones polynomial.
This article review on periodic function on cyclic groups.In group theory,a branch of mathematics ,a torsion group or a periodic group is a group in which every element has finite order.All finite groups are periodic.Every cyclic group is abelian.It states thet every finitely generated abelian group is a finite direct product of primary cyclic group.
In this chapter we shall apply the theory of derived functors to the important special case where the cochain complex, sequence of abelian, n – cochain, cyclic, Rham cohomology. This will lead cohomology group Hn(X, G). In developing the theory we shall attempt to deduce as much as possible form general properties of derived functors. Thus or example we shall give a proof of the fact that Hn(X, G).
A knot made out of a string are often deformed in space without cutting open the closed knot.The deformed knot is taken into account to be an equivalent because the original knot
Graph theory is one of the parts of current Mathshaving encountered a most noteworthy advancement lately. The theory of fuzzy graphs was created by in the year 1975. During a similarand have additionally presented different connectedness ideas in fuzzy graphs. Fuzzy set theory gives us not just an important and ground-breaking portrayal of measurement of vulnerabilities, yet an increasingly reasonable portrayal of dubious ideas communicated in natural languages. A few properties of unusual hubs, fringe hubs and focal hubs are gotten. The scientific implanting of ordinary set theory into fuzzy has become a natural marvel. Therefore the possibility of fluffiness is an improving one. This Research study analyzes the distancetotal conceptthat is a measurement, in a fuzzy graph is presented.
Point set topology are terse introduction to the topological concepts used in economic
theory. Topology is a basic mathematical field that deals with geometric properties,
continuity, and boundary in relation to subspaces. Tynchonoff’s theorem is classified as of
the topology theorem
The directed Zero divisor graph is a graph constructed out of a non-Commutative ring R and its non-zero divisors. In this paper we find various domination parameter for the zero-divisor graph. For all commutative rings provides characterization with unity of total perfect codes. In this paper we study the characterization of eigenvaluesand adjacency matrix. We find the numerical example of non-zero divisor graph
Mathematical studies of knots began within the 19
Cohomology is a general term for a sequence of abelian groups defined from a cochain complex. That is, cohomology is defined as the abstract study of cochains, cocycles and coboundaries. Cohomology can be viewed as a method of assigning algebraic invariants to a topological space that has a more refined algebraic structure than the homology
This article deals with Fuzzy matrix theory is a mathematical theory developed by Dr.W.B .Vasantha kandasamy , florentin smarandache ,k.ilantheral and others.The basic concept of the theory is that the mathematical matrices can be applied to social and natural situations to predict likely outcomes.The mathematics in fuzzy matrix theory is very simple and can be used to analyze a broad range of data.
The field of Maths assumes an indispensable job in different fields.Graph theory is asignificant zonein Maths, utilized for several models. An old style graph speaks to an old style connection among objects. The items are spoken to by vertices & relations by edges. Coloring of Graph is a considered issue of combinatorial streamlining. Theory of F-graphs has various applications in current science & innovation, particularly in neural networksfields, information theory, cluster analysis, expert systems, control theory, medical diagnosis, etc. In 1975Rosenfeldpresented the concept of F-graphs. The coloring of F-graphshas a few applications in reality. Graph coloring fills in as a model for compromise in issues of combinatorial improvement. F-graphsColoring has some genuine combinatorial streamlining applications issues as exam schedule, allocation registration, systemof traffic light, and so forth. The most significant issue in the coloring issue of the F-graphis to develop a strategy for finding F-graphschromatic numbers. In this Article, we analyzed Coloring Approach in Fuzzy Graph Theory.
This article reveals the basic techniques of fourier analysis on a finite abelian group .It may be used as to derive theorems in graph theory.The definition of fourier transform depend on the choice of Isomorphism but it is independent of this choice upto automorphism of R. Fourier transformation has been a rich source for applications in combinatories.
Our purpose is to give an overview of weak topologies in a fuzzy locally convex space. Firstly, we introduce locally convex spaces in fuzzy context. Furthermore fuzzy version of a semi - norm is obtained. Finally, we introduce a weak topology on a fuzzy locally convex space and the weak star topology on its dual as a generalization of usual weak topology. A special attention is also given to some properties of X- topology on X*, called fuzzy weak star topology.
Now we define hyper fuzzy set as a generalization of fuzzy sets and interval valued fuzzy sets. Then we introduce the notion of hyper fuzzy subgroups and study some of its important properties.
This article deals with the study of Algebra structures which will tend to finite free resolution of cyclic modules over an area noetherian ring. In recent years, a number of people exploited the unique algebric structure that can be put on a minimal finite free resolution of residue class field of local ring R.
Fuzzy soft set are presented by creator Molodtsov, which is tackle uncertain issues in the field of differentcultural, environment, economic and Medicinal studies. Graph theory fills in as a numerical framework to speak to double connection and Fuzzy set began with fundamental Article introduced by Zadeh in 1965. Theory of Fuzzy Graphs was presented by AzrielRosenfied in 1975. In spite of the fact that it is youthful it has been becoming quick and has humevous applications in fluctuates fields. The idea of in fuzzy graphs are presented by A. Somasundaram. The domination theoryhas been the core of research movement in graph theory as of late. The quickest developing zone inside graph theory is an investigation of and related subset issues such covering, independence, decomposition, marking and matching. This research Study gives the idea of Fuzzy graphs domination is presented in an alternate methodology.
We define hyper fuzzy set as a generalization of fuzzy sets and interval valued fuzzy sets. Then we introduce the notion of hyper fuzzy subgroups and study some of its important properties.
The concept of this research is introduced to interval-valued trapezoidal neutrosophic fuzzy graph which is combined to trapezoidal fuzzy numbers and interval-valued neutrosophic fuzzy graph. In this analysis, proposed algorithm finds source node and destination node because of the shortest path problem . In this research, we apply trapezoidal number with interval-valued neutrosophic fuzzy graph and finding their score function. Eventually an illustrative example to explain, to easy way of shortest path fuzzy graph.
So on handle inexact, tentative or partial information and knowledge circumstances in factual-life operational investigate predicaments dual-hesitant fuzzy set is applied. during this work a totally unique method called Allocation Table Method (ATM) for solving dual-hesitant fuzzy transportation problem is introduced. This method is explained with a numerical example and thus the result obtained through this method is compared with the prevailing method (VAM). This proposed method gives an optimum solution as compared with other method
In this paper it discuss about the partial differential equation of order two with variable coefficients. Here it explains how a large class of partial differential equations using Monge’s method. and the Monge’s method for solving some important type of second order partial differential equation.
Necessary and sufficient conditions are given for the regularity of block triangular matrices ..Equivalent condition for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived.Further fuzzy relational equations consistency is studied.As an application the existence of group inverse of a block triangular fuzzy matrix is discussed.
In this paper we are elaborate Electrostatics is based primarily inverse law. Then small volume distance between two forces. Also we solve the Uniqueness of the solution of an electrostatic problem .
For a mathematician it is natural to ask, since we have such a nice tool as the Seifert matrix, what matrix properties do we know that, via
This paper has two chapters, in chapter one, basic concepts about fuzzy matrices are introduced. Basic notations of matrices are given in section one in order to make the book self-contained. Section two gives the properties of fuzzy matrices. Since the data need to be transformed into fuzzy models, some elementary properties of graphs are given. Further, this section provides details of how to prepare in linguistic question to make use of in these fuzzy models when the data related with the problem is unsupervised
This paper tries to be an introductory text to spectral sequences, a useful technique in algebraic topology which has been frequently used in order to compute homology and homology group of spaces by means of some examples we show the utility of this construction and some of the problem thatdo often appear when dealing with spectral sequences
We introduce Soft ARS Closed on Soft topological Spaces and study some of their properties. We also investigate the concepts of Soft slightly ARS continuous functions
This paper proposes a simple and easy methods for determining the centre of gravity of a motionless object. A human’s Centre of gravity can change as he takes on different position, but in many other objects, it is a fixed location. Here the uniqueness of centre of gravity is discussed. Moreover,the general formula for determining the centre of gravity, centre of gravity by integration, centre of gravity of a compound body and remainder is also determined
In general, the demand rate and the unit cost of the items remains constant inspite of lot size in inventory models. But in reality,
the demand rate and the unit cost of the items are connected together. In this research, demand dependent unit cost inventory
model is considered where different cost parameters, maximum inventory and the lot size of the model are taken under fuzzy
environment. First an analytic solution of the crisp model is obtained by the method of calculus where the inventory parameters
are exact and deterministic. Later, the problem is developed with fuzzy parameters where inaccuracy has been introduced through
triangular membership function
A dominating set of a graph G = (V, E) may be a subset D of V. such every vertex not in D is adjacent to some vertex in D. The domatic number d(G) of G is that the maximum positive integer K. such V are often partitioned into K pairwise disjoint dominating sets. the aim of this paper is to review the domatic numbers and domination numbers of a graphs that are obtained from small graphs by performing graph operations.