Bulletin of Mathematical Sciences and Applications最新文献

{"title":"Haar Wavelet Collocation Method for Solving Riccati and Fractional Riccati Differential Equations","authors":"S. Shiralashetti, A. Deshi","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.17.46","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.17.46","url":null,"abstract":"In this paper, numerical solutions of Riccati and fractional Riccati differential equations are obtained by the Haar wavelet collocation method. An operational matrix of integration based on the Haar wavelet is established, and the procedure for applying the matrix to solve these equations. The fundamental idea of Haar wavelet method is to convert the proposed differential equations into a group of non-linear algebraic equations. The accuracy of approximate solution can be further improved by increasing the level of resolution and an error analysis is computed. The examples are given to demonstrate the fast and flexibility of the method. The results obtained are in good agreement with the exact in comparison with existing ones and it is shown that the technique introduced here is robust, easy to apply and is not only enough accurate but also quite stable.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130508812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric","authors":"Mokaedi V. Lekgari","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.17.40","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.17.40","url":null,"abstract":"We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metric and show that the finiteness of the expectation E(i,j)[ ∑τ△−1 k=0 r(k)], where τ△ is the hitting time on the coupling set △ and r is a subgeometric rate function, is equivalent to a sequence of Foster-Lyapunov drift conditions which imply subgeometric convergence in the Wassertein distance. We give an example for a ’family of nested drift conditions’. Introduction and Notations We start with a brief review of ergodicity. Let Z+ = {0, 1, 2, ...}, N+ = {1, 2, ...}, and R+ = [0,∞). Let (Φn)n∈Z+ denote a Markov chain with transition kernel P on a countably generated state space denoted by (X ,B(X )). P (i, j) = Pi(Φn=j) = Ei[1Φn=j ], where Pi and Ei respectively denote the probability and expectation of the chain under the condition that its initial state Φ0 = i, and 1A is the indicator function of set A. According to Markov’s theorem, a Markov chain (Φn)n∈Z+ is ergodic if there’s positive probability to pass from any state, say i ∈ X to any other state, say · ∈ X in one step. That is, for states i, · ∈ X then chain (Φn)n∈Z+ is ergodic if P (i, ·) > 0. Also the chain (Φn)n∈Z+ is said to be (ordinary) ergodic if ∀ i, · ∈ X then P (i, ·) → π(·) as n → ∞, where the σ-finite measure π is the invariant limit distribution of the chain. Chain (Φn)n∈Z+ is referred to as geometrically ergodic if there exists some measurable function V : X → (0,∞), and constants β < 1 andM < ∞ such that ||P (i, ·)− π(·)|| ≤ MV (i)β, ∀ n ∈ N+, where here and hereafter for the (signed) measure μwe define μ(f) = ∫ μ(dj)f(j), and the norm ||μ|| is defined by sup|g|≤f |μ(g)|, whereas the total variation norm is defined similarly but with f ≡ 1. Markov chain (Φn)n∈Z+ is strongly ergodic if lim n→∞ sup i∈X ||P (i, ·)− π(·)|| = 0. Loosely speaking subgeometric ergodicity, which we define next, is a kind of convergence that’s faster than ordinary ergodicity but slower than geometric ergodicity. Let function r ∈ Λ0 where Λ0 is the family of measurable increasing functions r : R+ → [1,∞) satisfying log r(t) t ↓ 0 as t ↑ ∞. Let Λ denote the class of positive functions r : R+ → (0,∞) such that for some r ∈ Λ0 we have; 0 < lim n inf r(n) r(n) ≤ lim n sup r(n) r(n) < ∞. (1) Indeed (1) implies the equivalence of the class of functionsΛ0 with the class of functions Λ. Examples of functions in the class r ∈ Λ is the rate r(n) = exp(sn), α > 0, s > 0. Without loss to Bulletin of Mathematical Sciences and Applications Submitted: 2016-08-30 ISSN: 2278-9634, Vol. 17, pp 40-45 Revised: 2016-10-10 doi:10.18052/www.scipress.com/BMSA.17.40 Accepted: 2016-10-17 2016 SciPress Ltd, Switzerland Online: 2016-11-01 SciPress applies the CC-BY 4.0 license to works we publish: https://creativecommons.org/licenses/by/4.0/ generality we suppose that r(0) = 1 whenever r ∈ Λ. The properties of r ∈ Λ0 which follow from (1) and are to be used frequently in this study are; r(x+ y) ≤ r(x)r(y) ∀ x, y ∈ R+ (2) r(x+ a) r(x) → 1 as x → ","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"197 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131661077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linear Hypergraph Edge Coloring - Generalizations of the EFL Conjecture","authors":"V. Faber","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.17.1","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.17.1","url":null,"abstract":"Motivated by the Erdos-Faber-Lovász (EFL) conjecture for hypergraphs, we consider the edge coloring of linear hypergraphs. We discuss several conjectures for coloring linear hypergraphs that generalize both EFL and Vizing's theorem for graphs. For example, we conjecture that in a linear hypergraph of rank 3, the edge chromatic number is at most 2 times the maximum degree unless the hypergraph is the Fano plane where the number is 7. We show that for sufficiently large fixed rank and sufficiently large degree, the conjectures are true. Introduction In 1972, a three week conference on hypergraphs was held at The Ohio State University. It was during this conference that the seeds of EFL were planted. In particular, in Problem 18 (see below and [1]) we asked for bounds on edge coloring. Later, we added the condition that the hypergraph be linear which modified the conjectured bounds in Problem 18 and when we couldn’t prove or disprove that we added the additional constraints that created EFL. In this paper, I go back to the precursor of EFL and show that some of the facts we know about EFL from [2] apply equally well to the precursor. Generalizations Preliminaries. Before we can discuss extensions to EFL, we need to give a short list of the concepts involved. Notation. Let ) , ( E V H  be a hypergraph (see, for example [3]): a set of subsets E of the set V . We call the elements of V the vertices and the elements of E the edges. We often write | |V n  and | | E m  . The degree of a vertex x is the number of edges ) (x d which include it. We let the minimum degree be  and the maximum degree be  . If all vertices have the same degree, we say the hypergraph is regular. The rank of an edge e is the cardinality ) (e r of e . We let the minimum rank be  and the maximum rank be  . If all edges have the same rank, we say the hypergraph is uniform. If 2 ) (  e r for every edge then H is a graph. If the intersection of any two edges has at most one vertex, we call the hypergraph linear. Incidence matrix formulation. An equivalent formulation for a hypergraph is to consider H to be the incidence matrix of the hypergaph. In this case, H is an m n matrix: a row of H is the transpose of the characteristic vector of a vertex and a column of H is the characteristic vector of a edge. We use these two formulations interchangeably. It is often easier to understand a fact in one formulation or the other. For example, a fundamental theorem for a hypergraph is that the sum of the ranks is equal to the sum of the degrees. This is trivial to see in the matrix formulation because both sides of the equality are clearly equal to the number of non-zero entries in the matrix H . In this formulation, an edge e is a column vector and a vertex x is a row vector. Two vertices x and y are independent if and only if they are orthogonal, that is, the inner product 0 ) , (      y x xy . Two edges are independent if and only if they are orthogonal, that is 0 ) , (    f e","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130177031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A New Numerical Scheme for the Generalized Huxley Equation","authors":"B. Inan","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.16.105","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.16.105","url":null,"abstract":"In this paper, an implicit exponential finite difference method is applied to compute the numerical solutions of the nonlinear generalized Huxley equation. The numerical solutions obtained by the present method are compared with the exact solutions and obtained by other methods to show the efficiency of the method. The comparisons showed that proposed scheme is reliable, precise and convenient alternative method for solution of the generalized Huxley equation.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122990789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical Behaviour in Two Prey-Predator System with Persistence","authors":"V. Madhusudanan, S. Vijaya","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.16.20","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.16.20","url":null,"abstract":"In this work, the dynamical behavior of the system with two preys and one predator popu- lation is investigated. The predator exhibits a Holling type II response to one prey which is harvested and a Beddington-DeAngelis functional response to the other prey. The boundedness of the system is analyzed. We examine the occurrence of positive equilibrium points and stability of the system at those points. At trivial equilibrium E 0 and axial equilibrium ( E 1) ; the system is found to be unstable. Also we obtain the necessary and sufficient conditions for existence of interior equilibrium point ( E 6) and local and global stability of the system at the interior equilibrium ( E 6) : Depending upon the exis- tence of limit cycle, the persistence condition is established for the system. The numerical simulation infer that varying the parameters such as e and � 1 it is possible to change the dynamical behavior of the system from limit cycle to stable spiral. It is also observed that the harvesting rate plays a crucial role in stabilizing the system.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124564518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Seidel Equienergetic Graphs","authors":"H. Ramane, Mahadevappa M. Gundloor, S. Hosamani","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.16.62","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.16.62","url":null,"abstract":"The Seidel matrix S(G) of a graph G is the square matrix with diagonal entries zeroes and off diagonal entries are - 1 or 1 corresponding to the adjacency and non-adjacency. The Seidel energy SE (G) of G is defined as the sum of the absolute values of the eigenvalues of S(G). Two graphs G1 and G2 are said to be Seidel equienergetic if SE (G1) = SE (G2). We establish an expression for the characteristic polynomial of the Seidel matrix and for the Seidel energy of the join of regular graphs. Thereby construct Seidel non cospectral, Seidel equienergetic graphs on n vertices, for all n ≥ 12.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130931862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Sum Degree Distance and the Product Degree Distance of Generalized Transformation Graphs G ab","authors":"K. G. Mirajkar, Y. Priyanka","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.16.76","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.16.76","url":null,"abstract":"In this contribution, we consider line splitting graph ) (G Ls of a graph G as transformation graph   G of ab G . We investigate the sum degree distance ) (G DD and product degree distance ) ( * G DD of transformation graph ab G , which are weighted version of Wiener index. The Transformation graphs of ab G are   G ,   G ,   G and   G .","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133961603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Optimal Investment Returns with N-Step Utility Functions","authors":"J. T. Eghwerido, T. Obilade","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.16.96","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.16.96","url":null,"abstract":"In this paper, we shall validate the optimal payoff of an investment with an N-step utility function, (6, 7), such that H* is the payoff at time N in every possible state say 2n; in an N period market setting. Negative exponential, logarithm, square root and power utility functions were considered as the market structures change according to a Markov chain. These models were used to predict the performances of some selected companies in the Nigeria Capital Market. The estimates for models design parameters p, q, p', q' correspond to halving or doubling of investment. The performance of any utility function is determined by the ratio q: q' of the probability of rising to falling as well as the ratio p: p' of the risk neutral probability measure of rising to the falling.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"44 7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123732901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Data Envelopment Analysis as a Kaizen Tool: SBM Variations Revisited","authors":"K. Tone","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.16.49","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.16.49","url":null,"abstract":"Slacks-based measure (SBM) (Tone (2001), Pastor et al. (1999)) has been widely utilized as a representative non-radial DEA model. In Tone (2010), I developed four variants of the SBM model where main concerns are to search the nearest point on the efficient frontiers of the production possibility set. However, in the worst case, a massive enumeration of facets of polyhedron associated with the production possibility set is required. In this paper, I will present a new scheme, called SBM-Max , for this purpose which requires a limited number of additional linear program solutions for each inefficient DMU. Although the point thus obtained is not always the nearest point, it is acceptable for practical purposes and from the point of computational loads. Inefficient DMUs can be improved to the efficient status with less input- reductions and less output-enlargement. Thus, this model proposes a Kaizen (improvement) tool by DEA.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"2015 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127782620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Transformed Tree-Structured Regression Method","authors":"Gloria Gheno","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.16.70","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.16.70","url":null,"abstract":"Many times the response variable is linked linearly to the function of the regressors and to the error term through its function g(Y). For this reason the traditional tree-structured regression methods do not understand the real relationship between the regressors and the dependent variable. I derive a modified version of the most popular tree-structured regression methods to consider this situation of nonlinearity. My simulation results show that my method with regression tree is better than the tree-based regression methods proposed in literature because it understands the true relationship between the regressors and the dependent variable also when it is not possible to divide exactly the error part from the regressors part.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132785704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}