Pell equation (alternatively called the Pell- Fermat equation) is a
type of a Diophantine equation of the form 2 -Dye 2 =1 for a natural number
D. If D is a perfect square, then pell equation can be rewritten as
y).(x+√y) = 1.similarly, the trivial solution (x,y) = (0,1)
is not very interesting. Therefore it is often assumed that D is not a square
and only nontrivial solution (non zero pairs of integers) are considered.
The present study is conducted to find the Economic Status Based on Data collection at Ariyalur District. Survey Method was used to collect data from 200 workers of Ariyalur District. The tools used were Economic Status by Investigator and Teacher made test. Product moment Co – efficient of Correlation ( r ) and t – test were used for data analysis. The results reveal that, there is a significant positive correlation of economic status based on data collection .
Graph representation in computers has always been a hot topic thanks to the amount of applications that directly enjoy graphs. Multiple methods have emerged in computing to represent graphs in numerical/logical formats; most current business applications also rely heavily on relational databases as a primary source of storing information.
We will study some of the basic concepts about vectors various operations on vectors, their algebraic and geometric properties. These two types of properties, when considered to gather give full realizations to the concepts of vectors, and lead to their vital applicability in various areas.
In mathematics, more specifically generally topology and related branches, a net or Moore-Smith sequence may be a generalization of the notion of sequence. In essence, a sequence may be a function with domain the natural numbers and within the context of topology, the co domain of this function is typically any mathematical space . However, within the context of topology, sequences don't fully encode all information a few function between topological spaces.
The four square theorem was proved by Lagrange in 1770; every positive integer is the sum of four squares. i.e, n=A2+B2+C2+D2, where, A,B,C,D ϵ z An interesting proof is presented here based on Hurwitz integers, a subset of Quarternions which act like integers in four dimension and have the prime divisor property
Topology is a beautiful science and forms a bridge between geometry and algebra.Topology means (Topo-place,logy-study) i.e.,study of place.One of the most wiedly used mathematical concepts in the study of place,optimization of any machinery parts such as mobiles,cycles,computers,cars,buses,trains and airplanes,etc.In this paper,the concept of a separation axioms considered.The separation axioms are only in the sense that when defining the notation of topological space.The separation axims are denoted with the letter “T” after the German Trennungsaxiom,which means “Separation Axioms”.In this paper proposed T0,T1,T2,T3 and T4 axioms with examples
Travelling salesman problem can be modeled as graph where as the cities are the graph vertices, path is graph edges and path distance is edge distance. Our goal is to seek out the shortest tour that visits each city during a given graph exactly ones then return to the starting city
We will study some of the basic concepts about vectors various operations on vectors, their algebraic and geometric properties. These two types of properties, when considered to gather give full realizations to the concepts of vectors, and lead to their vital applicability in various areas
The word topology is derived from Greek word “Topos” meaning “surface” and “Logos” meaning “Discourse” or “Study”. Topology thus literally means the Study of Surfaces. Its English form “Topology” was introduced in 1883 within the journal nature to differentiate . The term “net” was coined by John L. Kelly. Nets are one among the various tools utilized in topology to generalize certain concepts which will only be general enough within the context of metric spaces. In mathematics, more specifically in general topology and related branches, a net or Moore-Smith sequence is a generalization of the notion of sequence. In essence, a sequence is a function with domain, the natural numbers and within the context of topology, the co-domain of this function is usually any topological space. However, in the context of topology, seque
Seifert & van Kampen introduced the problem of describing the fundamental group of a space X in terms of the fundamental groups of the constituents xi of an open coveringIn mathematics, the Seifert-van Kampen theorem of Algebraic topology, sometimes it is called as van Kampen’s theorem. It expresses the structure of the fundamental group.
This “Introduction to vector- methods and their various applications to physics and mathematics” is an exposition of the late Willard Gibbs’ vector analysis. The author in his preface warns us that “no attempt at mathematical rigor is made” which perhaps explains the opening sentence of chapter “A vector is any quantity having direction as well as magnitude.” What of finite rotations? Are they not to be considered quantities having direction and magnitude? In an appendix the author compares notations, not always quite accurately. He believes Willard Gibbs’ notation to be the simplest and most symmetrical of any of the existing kinds. Burali-Forti and Marcolongo, who believe they have devised the perfect notation, object to Willard Gibbs’ “dot” in the scalar product, using a “cross” instead. As regards the question of symmetry, the truth is that the vector product is not symmetrical, for in Gibbs’s notation
In this paper we are deals that various type of index numbers and measured value an index number is a statistical value that measures the change in a variable with respect to time. Index numbers are meant to study changes in the effects of factors which cannot be measured directly
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
In mathematics, the Seifert-van Kampen theorem of Algebraic topology, sometimes it is called as van Kampen’s theorem. It expresses the structure of the fundamental group of a topological space X in terms of the fundamental groups of two open, path connected subspaces u and v that covers X is Abelian group.
In mathematics, the Seifert-van Kampen theorem of Algebraic topology, sometimes it is called as van Kampen’s theorem. It expresses the structure of the fundamental group of a topological space X in terms of the fundamental groups of two open, path connected subspaces u and v that covers X is Abelian group.
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
We will study some of the basic concepts about vectors various operations on vectors, their algebraic and geometric properties. These two types of properties, when considered to gather give full realizations to the concepts of vectors, and lead to their vital applicability in various areas.
A matrix x is a solvent of the matrix polynomials. f(x)=A o xm +…..+Am if f(x) = 0.Where A o, x, f are square matrices. In this paper we develop the linear algebra of matrix polynomials and solvents. we define division and interpolation the properties of matrices and define and study the existence of a complete set of solvents. we study the relation between the matrix polynomial problems and Theorems and lambda matrix problem, Which is to find scalar λ such that
A o λm+A1 λm-1+ ……. +Am is singular.
In a future paper we extend Cayley Hamilton Theorem for calculating of scalar polynomials to matrix polynomials. And lambda matrix for column and row Hermite calculating of lambda matrix.
The studies on the dynamics of particles have recently experienced advances in experimental technique, numerical simulations and theoretical advances in experimental techniques, numerical simulations and theoretical understandings. This focus on collection aims to provide a snapshot of this fast –evolving field. We attempt to collect the cutting –edge achievements from many branches in physics and engineering, among which dynamics of particles in turbulence is the common interest.
One can use van Kampen’s theorem to calculate fundamental groups for topological spaces that can be decomposed into simpler spaces. Thus we can see that there is a commutative diagram including A∩B into A and B and then another inclusion from A&B into s2 and that there is a corresponding diagram of homomorphism b/w the fundamental groups of each subspace. It is clear from this that the fundamental group of s2 is trivial.
In this paper we introduced what is meant by a permutation on a given set and showed how they form a group. We discussed the cycle notation of permutation and how it is useful in determining various properties of permutation groups. In fact it is shown that a permutation can be decomposed into disjoint cycles uniquely and that order of the permutation is the l.c.m of the lengths of the cycle in a decomposition of disjoint cycles.
wearepresentedwithtwospaceXandYtheproblemofdecidingwhetherornottheyarehomeomorphicisformidable.WehaveeithertoconstructahomeomorphismbetweenXandYor,worsestill,toprovethatnosuchhomeomorphismexists.Wetheretrytoreflecttheproblemalgebraically.
One can use van Kampen’s theorem to calculate fundamental groups for topological spaces that can be decomposed into simpler spaces. Thus we can see that there is a commutative diagram including A∩B into A and B and then another inclusion from A&B into s2 and that there is a corresponding diagram of homomorphism b/w the fundamental groups of each subspace. It is clear from this that the fundamental group of s2 is trivial.
In this paper we are learn with some definitions base shifting index numbers and we are proving some related index problems
The unique development of life on earth is human beings. Since their origin, their greater curiosity always encouraged them to speculate about the operation of the universe and to remain engaged in constant search of knowledge. Knowledge involves acquiring knowledge, facts, information, descriptions or abilities through experience or study. The argument provided deals with criticism of education as an academic subject with epistemological problems. The argument consists of a study that has classified the education field as based on three basic knowledge traditions. Contrasts with other disciplines, including mathematics and physics, are created to study the coherence of education as a field. The paper also examines the academic scholarship in regard to, and its significance to, the notion of near-practice education research as an academic field. The article concludes by suggesting a new model that shows the relationships between practical knowledge and academic knowledge that are an intrinsic part of education. There is also a stronger representation of education as an academic field.