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Approximation and moduli of continuity for a function belonging to Holder’s class Hα [0, 1) and solving Lane-Emden differential equation by Boubaker wavelet technique
Full text linkIn this paper, Boubaker wavelet is considered. The Boubaker wavelets are orthonormal. The series of this wavelet is verified for the function f(t) = t. The convergence analysis of solution function of Lane-Emden differential equation has been studied. New Boubaker wavelet estimator E2 k,M(f) for the approximation of solution function f belong to H¨older’s class Hα[0, 1) of order 0 < α ≤ 1, has been devloped. Furthermore, the moduli of continuity of solution function of Lane-Emden differential equation has been introduced and it has been estimated for solution function f∈ Hα[0, 1) class. These estimator and moduli of continuity are new and best possible in wavelet analysis. Boubaker wavelet collocation method has been proposed to solve Lane-Emden differential equations with unkown Boubaker coefficients. In this process, Lane-Emden differential equations are reduced into a system of algebraic equations and these equations are solved by collocation method. Three Lane-Emden type equations are solved to demonstrate the applicability of the proposed method. The solutions obtained by the proposed method are compared with their exact solutions. The absolute errors are negligible. Thus,this shows that the method described in this paper is applicable and accurate
Changing and Unchanging strong efficient edge domination number of some standard graphs when a vertex is removed or an edge is added
Full text linkLet G=(V,\ E) be a simple graph. A subset S of E(G) is a strong (weak) efficient edge dominating set of G if │Ns[e] S│ = 1 for all e E(G)(│Nw[e] S│ = 1 for all e E(G)) where Ns(e) ={f / f E(G), f is adjacent to e & deg f ≥ deg e}(Nw(e) ={f / f E(G), f is adjacent to e & deg f ≤ deg e}) and Ns[e]=Ns(e){e}(Nw[e] = Nw(e){e}). The minimum cardinality of a strong efficient edge dominating set of G (weak efficient edge dominating set of G) is called a strong efficient edge domination number of G and is denoted by {\gamma\prime}_{se}(G) ({\gamma^\prime}_{we}(G)).When a vertex is removed or an edge is added to the graph, the strong efficient edge domination number may or may not be changed. In this paper the change or unchanged of the strong efficient edge domination number of some standard graphs are determined, when a vertex is removed or an edge is added
Application Of Homotopy To The Ageing Process Of Human Bone
Full text linkThis article presents the ageing process of human bone which can play a major role in the structure of the human body from the concept of homotopy in algebraic topology. The structure of the human bone, which is precisely connected is consider here to be topologically equivalent to a cylinder. The elegant but complex skeletal shape of the human bone is described by the Cartesian functions of α = S1 X I and H, H' : α -> α. The bone shape of the human body at an early stage. That is the bone shape of the newborn is called α = S1 X I homotopy. The process of continuous ageing bone is considered to be family of homotopy based on its functions. The study discusses algebraic topology of homotopies through the homotopy of stable functions of the human bone from infancy to old age
Elongation of Sets in Soft Lattice Topological Spaces
Full text linkThe aim of this paper, we investigate some Lattice sets such as soft lattice exterior, soft lattice interior, soft lattice boundary and soft lattice border sets in soft lattice topological spaces which are defined over a soft lattice L with a fixed set of parameter A and it is also a generalization of soft topological spaces. Further, we develop and continue the initial views of some soft lattice sets, which are deep-seated for further research on soft lattice topology and will consolidate the origin of the theory of soft topological spaces
Topology via Graph Ideals
Full text linkThe study of ideal topological space has started since 1933 and till date it is being developed by several mathematicians. Various classes of open sets, different types of operators and exploration of elementary topological results in ideal topological spaces have been discussed in various research papers. Methods of generating topologies using various relations have been explored by many researchers. Many researchers explored the methods of inducing topologies via graphs. This paper, introduces the notions of graph ideals, graph local function and characterizes some of their properties. It also describes a method of generating a new graph topology on the vertex set of a graph from the graph adjacency topology using Kuratowski closure operator and depicts the nature of open sets with respect to the new topology. Further, it explores the condition for compatibility of the graph adjacency topology with graph ideal
Fuzzy soft set connected mappings
Full text linkIn this paper, the concepts of fuzzy soft connectedness between fuzzy soft sets and fuzzy soft set connected mappings in fuzzy soft topological spaces has been introduced. It is shown that a fuzzy soft topological space is fuzzy soft connected if and only if it is fuzzy soft connected between every pair of its nonempty fuzzy soft sets. Every fuzzy soft continuous mapping is fuzzy soft set-connected a counter example is given to show the converse may not be true. Several properties of fuzzy soft set-connected mappings in fuzzy soft topological spaces have been studied
Stability of Domination in Graphs
Full text linkThe stability of dominating sets in Graphs is introduced and studied,in this paper. Here D is a dominating set of Graph G. In thispaper the vertices of D and vertices of are called donorsand acceptors respectively. For a vertex u in D, let denotethe number d^{D}_{inst}(e)\|\psi_{D}(u)-\psi_{D}(v)\|\psi_{d}(D) is the sum ofd-instabilities of all edges connecting vertices in D. For a vertex unot in D, let \|N(u)\cap D\|. The Acceptor Instabilityor simply a-instability of an edge e connecting twoacceptor vertices u and v is . The a-instability of D, is the sum of a-instabilities of all edges connecting vertices in. The dominating set D is d-stable if and a-stableif . D is stable, if and . Given anon negative integer #\alpha\alpha-d-stabled^{D}_{inst}(e)\leq\alpha\alpha-a-stablea^{D}_{inst}(e)\leq\alpha\alpha\alpha$
Analytical Study of Mixed Convective Flow and Heat Transfer in Vertical Channel Filled with Immiscible Viscous Fluids
Full text linkIn this paper investigation of mixed convective flow and heat transfer in vertical channel filled with immiscible viscous fluids has been carried out. The governing differential equations are solved analytically by regular perturbation method. The impact of governing parameters on velocity and temperature fields namely Grashof number, Brinkman number, perturbation parameter, viscosity ratio, width ratio, conductivity ratio, Nusselt number are investigated and represented graphically
Radio Heronian Mean k-Graceful Labeling on Degree Splitting of Graphs
Full text linkA mapping g:V\left(G\right)\rightarrow{k,k+1,\ldots,k+N-1} is a radio heronian mean k-labeling such that if for any two distinct vertices s and t of G, d\left(s,t\right)+\left\lceil\frac{g\left(s\right)+g\left(t\right)+\sqrt{g\left(s\right)g\left(t\right)}}{3}\right\rceil\geq1+D,for every s,t\in\ V(G), where D is the diameter of G. The radio heronian mean k-number of g, {rrhmn}_k(g), is the maximum number assigned to any vertex of G. The radio heronian mean number of G, {rhmn}_k(g), is the minimum value of {rhmn}_k(g) taken overall radio heronian mean labelings g of G. If {rhmn}_k(g)=\left|V\left(G\right)\right|+k-1, we call such graphs as radio heronian mean k-graceful graphs. In this paper, we investigate the radio heronian mean k-graceful labeling on degree splitting of graphs such as comb graph P_n\bigodot K_1, rooted tree graph {RT}_{n,n} hurdle graph {Hd}_n and twig graph\ {TW}_n.A mapping is a radio heronian mean k-labeling such that if for any two distinct vertices and of , ,for every V(G), where is the diameter of . The radio heronian mean k-number of g, , is the maximum number assigned to any vertex of . The radio heronian mean number of , , is the minimum value of taken overall radio heronian mean labelings of . If , we call such graphs as radio heronian mean k-graceful graphs. In this paper, we investigate the radio heronian mean k-graceful labeling on degree splitting of graphs such as comb graph , rooted tree graph hurdle graph and twig graph
Common fixed points of self-maps over the generalized cone b-metric spaces
Full text linkThe main aim of this research paper is to establish the most generalized common fixed-point theorem for two self-maps that are commuting to each other under \mathbf{T}-Kannan type contractive condition over a generalized cone \mathbb{b}-metric spaces. The novelty of this research paper is to find a common fixed point of two weekly compatible self-maps over a generalized cone \mathbb{b}-metric spaces without assuming the normality condition of a cone. We illustrate our main result with a suitable example