Bulletin of Mathematical Sciences and Applications最新文献

{"title":"On the Line Degree Splitting Graph of a Graph","authors":"B. Basavanagoud, Roopa S. Kusugal","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.18.1","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.18.1","url":null,"abstract":"In this paper, we introduce the concept of the line degree splitting graph of a graph. We obtain some properties of this graph. We find the girth of the line degree splitting graphs. Further, we establish the characterization of graphs whose line degree splitting graphs are eulerian, complete bipartite graphs and complete graphs.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134339940","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":"Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations Using Haar Wavelet Collocation Method","authors":"S. Shiralashetti, R. Mundewadi","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.18.50","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.18.50","url":null,"abstract":"In this paper, we present a numerical solution of nonlinear Volterra-Fredholm integral equations using Haar wavelet collocation method. Properties of Haar wavelet and its operational matrices are utilized to convert the integral equation into a system of algebraic equations, solving these equations using MATLAB to compute the Haar coefficients. The numerical results are compared with exact and existing method through error analysis, which shows the efficiency of the technique.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129532890","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":"Operations on Semigraphs","authors":"P. R. Hampiholi, Meenal M. Kaliwal","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.18.11","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.18.11","url":null,"abstract":"In this paper the structural equivalence of union, intersection ring sum and decomposition of semigraphs are explored by using the various types of isomorphisms such as isomorphism, evisomorphism, a-isomorphism and eisomorphism for Ge, Ga and Gca. We establish various types of binary operations in semigraphs.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116383373","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":"On Enumeration of some Non-Isomorphic Dendroids","authors":"P. R. Hampiholi, Jotiba P. Kitturkar","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.18.40","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.18.40","url":null,"abstract":"A dendroid is a connected semigraph without a strong cycle. In this paper, we obtain the various results on the enumeration of the non-isomorphic dendroids containing two edges and the dendroids with three edges.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122599137","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":"Upper Bounds for the Modified Second Multiplicative Zagreb Index of Graph Operations","authors":"B. Basavanagoud, Shreekant Patil","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.17.10","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.17.10","url":null,"abstract":"The modified second multiplicative Zagreb index of a connected graph G, denoted by ∏ ‍ 2 (G), is defined as ∏ ‍ ∗ 2 (G) = ∏ ‍ uv∈E(G) [dG(u) + dG(v)] [dG(u)+dG(v)] where dG(z) is the degree of a vertex z in G . In this paper, we present some upper bounds for the modified second multiplicative Zagreb index of graph operations such as union, join, Cartesian product, composition and corona product of graphs are derived.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"90 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":"128633980","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":"Wavelet Transform as an Alternative to Power Transformation in Time Series Analysis","authors":"C. Ogbonna, C. Nweke, Eleazer C. Nwogu, I. Iwueze","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.17.57","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.17.57","url":null,"abstract":"This study examines the discrete wavelet transform as a transformation technique in the analysis of non-stationary time series while comparing it with power transformation. A test for constant variance and choice of appropriate transformation is made using Bartlett’s test for constant variance while the Daubechies 4 (D4) Maximal Overlap Discrete Wavelet Transform (DWT) is used for wavelet transform. The stationarity of the transformed (power and wavelet) series is examined with Augmented Dickey-Fuller Unit Root Test (ADF). The stationary series is modeled with Autoregressive Moving Average (ARMA) Model technique. The model precision in terms of goodness of fit is ascertained using information criteria (AIC, BIC and SBC) while the forecast performance is evaluated with RMSE, MAD, and MAPE. The study data are the Nigeria Exchange Rate (2004-2014) and the Nigeria External Reserve (1995-2010). The results of the analysis show that the power transformed series of the exchange rate data admits a random walk (ARIMA (0, 1, 0)) model while its wavelet equivalent is adequately fitted to ARIMA (1,1,0). Similarly, the power transformed version of the External Reserve is adequately fitted to ARIMA (3, 1, 0) while its wavelet transform equivalent is adequately fitted to ARIMA (0, 1, 3). In terms of model precision (goodness of fit), the model for the power transformed series is found to have better fit for exchange rate data while model for wavelet transformed series is found to have better fit for external reserve data. In forecast performance, the model for wavelet transformed series outperformed the model for power transformed series. Therefore, we recommend that wavelet transform be used when time series data is non-stationary in variance and our interest is majorly on forecast. 1.0 Introduction In several organizations, managerial decisions are largely based on the available information of the past and present observations and possibly on the process that generate such observations. A time series data provides such information. Time series is used to represent the characterized time course of behavior of wide range of several systems which could be biological, physical or economical. The utility of the time series data lies in the result of the time series analysis. Such analysis will be helpful in achieving the aim for collection of such data which could be for description (exposing the main properties of a series), explanation (revealing the relationship between variables of a series especially when observations are taken on two or more variables), forecasting (prediction of the future values of a series) and control (taking appropriate corrective actions) [1]. To analyze any time series data, time series analysis techniques are adopted. The commonly used techniques are: descriptive technique, probability models technique and spectral density analysis technique. The inference based on the descriptive method and probability models is often referred to as","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"33 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":"122400493","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":"Stochastic Analysis of the Effect of Asset Prices to a Single Economic Investor","authors":"E. Ekuma-Okereke, J. T. Eghwerido, E. Efe-Eyefia, S. Zelibe","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.17.33","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.17.33","url":null,"abstract":"In this paper, we propose a single economic investor whose asset follows a geometric Brownian motion process. Our objective therefore is to obtain the fair price and the present market value of the asset with an infinitely horizon expected discounted investment output. We apply dynamic programming principle to derive the Hamilton Jacobi Bellman (HJB)-equation associated with the problem which is found to be equivalent to the famous Black-Scholes Model under no risk neutrality. In addition, for a complete market under equilibrium, we obtained the value of the present asset with risk neutrality and its fair price. Introduction The study that Asset Prices follow a simple diffusion process was first proposed in the historical work of Bachelier in 1900. His work is rather remarkable in that it addressed the problem of option pricing and his main aim was to actually provide a fair price for the European call option [3]. Bachelier assumed stock price dynamics with a Brownian motion without drift (resulting in a normal distribution for the stock prices), and no time-value of money. The formula provided may be used to valuate a European style call option [10]. Later on, [4] obtained the same results as Bachelier. As pointed out by [5] and [9], this approach allows negative realizations for both stock and option prices. Moreover, the option price may exceed the price of its underlying asset. According to [10], Black – Scholes Model is often regarded as either the end or the beginning of the option valuation history. Using two different approaches for the valuation of European style options, they present a general equilibrium solution that is a function of “observable” variables only, making therefore the model subject to direct empirical tests. The stock price dynamics is described by a geometric Brownian motion with drift as a more refined market model for which prices cannot be negative, the volatility can be viewed as the diffusion coefficient of this random walk [7]. The manifest characteristic of the final valuation formula is the parameters it does not depend on. The option price does not depend on the expected return rate of the stock or the risk preferences of the investors. It is not assumed that the investors agree on the expected return rate of the stock. It is expected that investors may have quite different estimates for current and future returns. However, the option price depends on the risk-free interest rate and on the variance of the return rate of the stock. To make simplier normally distributed financial asset returns, on assumption that its distribution is difficult, [11] concludes that for a distribution model to reproduce the properties of empirical evidence it must possess certain parameters as: a location parameter; a scale parameter; an asymmetry parameter and a parameter describing the decay of the distribution since financial returns distribution is difficult to determine since normally distributed financial asset returns is not","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"198 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":"132584453","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":"Harmonic Status Index of Graphs","authors":"H. Ramane, B. Basavanagoud, A. Yalnaik","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.17.24","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.17.24","url":null,"abstract":"The status of a vertex u is defined as the sum of the distances between u and all other vertices of a graph G. In this paper we have defined the harmonic status index of a graph and obtained the bounds for it. Further the harmonic status indices of some graphs are obtained.","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":"130323820","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":"Qlick Graphs with Crossing Number One","authors":"B. Basavanagoud, V. Kulli","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.17.75","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.17.75","url":null,"abstract":"In this paper, we deduce a necessary and sufficient condition for graphs whose qlick graphs have crossing number one. We also obtain a necessary and sufficient condition for qlick graphs to have crossing number one in terms of forbidden subgraphs.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"50 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":"122172829","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":"Homotopy Analysis Method for Conformable Burgers-Korteweg-de Vries Equation","authors":"A. Kurt, O. Tasbozan, Yücel Çenesiz","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.17.17","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.17.17","url":null,"abstract":"The main goal of this paper is finding the approximate analytical solution of BurgersKorteweg-de Vries with newly defined conformable derivative by using homotopy analysis method (HAM). Then the approximate analytical solution is compared with the exact solution and comparative tables are given. Introduction The adventure of fractional calculus started with the L’Hospital’s letter to Leibnitz in 1695. In this letter the original question which caused the name fractional question was: Can a derivative of integer order dy dxn be extended to have the meaning when n is a fractional number? This question has a golden value for the development of fractional calculus. After that time fractional calculus has been a valuable tool for expressing the nonlinear phenomenons in the nature. Thus scientists presented various applications of fractional derivatives and integrals for the physical interpretation the real world circumstances. For this interpretation most of scientists use popular and known derivative formulas such as Riemann-Liouville, Caputo [1, 2, 3]. As time progressed researchers found some insufficiencies at these definitions. It is understood that these definitions do not satisfy basic properties of the Newtonian concept, for instance the product, quotient, the Chain rules and etc. Researchers who study in the field of fractional calculus has been worried about these problems. To overcome this issue, R. Khalil et al. [4] introduced a new derivative and its anti-derivative called ’conformable derivative and integral’. Definition. Let f : [0,∞) → R be a function. The α order ”conformable derivative” of f is defined by, Tα(f)(t) = lim ε→0 f(t+ εt1−α)− f(t) ε , for all t > 0, α ∈ (0, 1). If f is α-differentiable in some (0, a), a > 0 and lim t→0+ f (t) exists then define f (0) = lim t→0+ f (t) and the ”conformable integral” of a function f starting from a ≥ 0 is defined as: I α(f)(t) = t ˆ a f(x) x1−α dx where the integral is the usual Riemann improper integral, and α ∈ (0, 1]. To test the efficiency and the accuracy of the conformable derivative, researchers made huge number of scientific articles on it. For example T. Abdeljawad [5] has presented conformable versions of the chain rule, exponential functions, Gronwalls inequality, integration by parts, Taylor power series expansions and Laplace transform. Iyiola et al. [6] expressed the analytical solution of space-time fractional Fornberg-Whitham equation, Hesameddini et al. [7] demonstrated the numerical solution Bulletin of Mathematical Sciences and Applications Submitted: 2016-08-11 ISSN: 2278-9634, Vol. 17, pp 17-23 Revised: 2016-10-21 doi:10.18052/www.scipress.com/BMSA.17.17 Accepted: 2016-10-24 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/ of multi-order fractional differential equations via the sinc collocation method and K. R. Prasad et al. [8] discussed prove the existence of mult","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"10 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":"131982891","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}