Open Access Method Article

Bayesian Approach to Predict Offender’s Probable Anchor Point Using Geographic Profiling System in Akure, Nigeria

B. O. Afeni, O. Olabode, N. O. Oluwaniyi

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/22192

One of the vital clues offenders leave behind when they commit crime is the crime location.  In recent years, several algorithms have been used to forecast the home site of unknown serial offenders on the basis of crime locations that have been linked to one offender. These have developed from spatial typologies to softwares that can provide direct support to crime investigations. Geographic profiling is an investigative methodology used in criminology that analyses the locations of a linked series of crimes to decide the most probable location for where the offender lives. This work establishes Bayesian Dirichlet Process Mixture Model (DPM) for crime hotspots analysis and as a geographic profiling system. It expands physiological profiling approach by integrating the idea of distance decay and buffer zone. The model was then implemented and tested with 119 spatial data of report serial theft cases in Akure, Nigeria. GPS Garmin was used to collect the data. The reported crime locations were visited to gather the data and were pre-processed by converting it into the machine readable format. The final output of the analysis (geoprofile) using the model was developed that depicts the most probable area of criminal(s) anchor point. A probability score was calculated for every point within the study area to indicate the likelihood that it contained the offender’s residence. The model was implemented in R. The model provides a practical tool for criminologist in targeting interventions and a more efficient use of resources for serial crime investigation. It can assist law enforcement agencies in decisions and policies making.

Open Access Original Research Article

Combined Solitary Wave Solutions in Higher-order Effects Optical Fibers

J. R. Bogning, C. T. Djeumen Tchaho, H. M. Omanda

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/10620

We construct in this manuscript, the combined solitary wave solutions of nonlinear Schrödinger equation that governs the dynamics of propagation of waves in optical fibers with higher-order effects. We base our survey on the sum of two analytic shapes of the solitary waves of bright and dark type to form a resulting solitary wave to determine.

Open Access Original Research Article

Theory of Approximative Relative Retracts and Its Applications

Mirosław Ślosarski

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/BJMCS/2016/22694

In the article a simpler and more generalized perspective of approximative multiretracts is presented (see [1]). This perspective allows for new results and applications. In order to reach it, a class of approximative relative retracts will be de ned with the use of single-valued mappings only. Their properties will be studied and some applications to fixed point theory, the theory of the extension of multivalued mappings, to graph-approximation theory and to the theory of approximative retracts will be given.

Open Access Original Research Article

On k-cordial Labeling of Some Graphs

M. V. Modha, K. K. Kanani

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/BJMCS/2016/21768

In this paper we present k-cordiality of one point union of some path, cycle and star related graphs. We prove that bistar graph Bm,n is k-cordial for all k, restricted square graph B2n,n of Bistar is k-cordial for all k. We also prove that one point union of cycle C3 with star graph K1,n and one point union of path Pn with K1 are k-cordial for all k.

Open Access Original Research Article

Moments of Truncated Skew-t Distribution and Graph Theory Applied to the Shortest Path Problem

C. José A. González, Julián A. A. Collazos

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/BJMCS/2016/22577

In the shortest path problem most approaches has been proposed over the last twenty years are focused to deterministic approaches. Stochastic approaches that include theory of truncated asymmetric probability distributions have not been tackled in the literature of optimal paths. Since, in practice, the paths are distances that must be traveled in finite times which are not always fixed, the stochasticity of the time has to be considered into the problem. In this paper, we consider using the moments of the truncated skew-t distribution to the problem of finding the shortest path between two locations with minimum distance by the transition times. The skew-tand truncated skew-t distributions are described explicitly to show the moments and their existence by the convergence of the hypergeometric series. An application to optimal paths using the moments of the truncated skew-t distribution and the graph theory illustrates the shortest path by the minimum average transition time.

Open Access Original Research Article

A Block Hybrid Implicit Algorithms for Solution of First Order Differential Equations

Y. A. Yahaya, Asabe A. Tijjani

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2016/19682

The paper consider the derivation of block hybrid algorithms , with k=4 for solution of first order ordinary differential equations, we adopted the method  of interpolation and collocation of power series approximation to generate  the continuous formula, which  was evaluated at off grid and some grid points within the  step length to generate the proposed  block schemes. Also the schemes obtained were investigated and found to be consistent and zero stable. Finally the method is tested with numerical experiments to ascertain their level of accuracy.

Open Access Original Research Article