Open Access Others

Corrigendum: Covering of Line Graph of Zero Divisor Graph over Ring Zn

S. Suthar, O. Prakash, R. Kumar

Journal of Advances in Mathematics and Computer Science, Page 1-4
DOI: 10.9734/BJMCS/2017/14436

Corrigendum for  British Journal of Mathematics & Computer Science 5(6), 728-734, 2015


It has been drawn to the journal's attention that there is a corrigendum of the published paper.


Therefore, following the 'SDI Correction and retraction policy' this Corrigendum was processed and approved. Link of the 'Previously Published Paper'  is available here.

Open Access Short Research Article

Solving the System of Two Nonlinear Voltera Intehral Equations of the Second Kind Using the Trapezoidal Predictor – Corrector Method

Borhan F. Jumaa

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2017/31131

In this paper, we consider the system of two nonlinear Volterra integral equations of the second kind (SNLVIE-2). We proposed method of Trapezoidal Predictor-Corrector (TRP-PCR) to solve SNLVIE-2. In addition, new algorithm IS introduced. The method is supported by numerical examples and simulations using Matlab. The results are reasonably good when compared with the exact solution.

Open Access Original Research Article

Oscillating Solutions of the Lane-Emden Equation for Polytropic Indices m = 0 and 1

Tanfer Tanriverdi

Journal of Advances in Mathematics and Computer Science, Page 1-5
DOI: 10.9734/BJMCS/2017/30543

With new approach, trigonometric solutions of the well-known Lane-Emden equation for m = 0, 1 are derived. To the best of author's knowledge these trigonometric solutions oscillating are not reported in the existing literature yet. New solutions are compared with the classical ones.

Open Access Original Research Article

The Impulse Interactive Cuts of Entropy Functional Measure on Trajectories of Markov Diffusion Process, Integrating in Information Path Functional, Encoding and Applications

Vladimir S. Lerner

Journal of Advances in Mathematics and Computer Science, Page 1-35
DOI: 10.9734/BJMCS/2017/30359

The introduced entropy integral measure on random trajectories (EF) is defined by the process additive functional with functions drift and diffusion reducing this functional on trajectories to a regular integral functional. This functional evaluates the cutting process impulses imposed through an impulse control.

The impulse control cuts the process EF on elementary information impulse  which the introduced information path functional (IPF) integrates in a bit composing an information process.

Compared to Shannon entropy measure of a random state, cutting the process on separated states decreases quantity of process information by the amount, concealed in correlation connections between these states, which hold a hidden process information infinite.

The impulse elementary interactive cutting action provides both reduction of the observing process entropy and discrete unit of the cutting entropy memorized as an information Bit.

That defines information as memorized entropy cutting in random observations which process interactions.

Cutting maximum of minimal impulse information and transferring minimal entropy between impulses implement the paper maxmin-minimax principle of converting process entropy to information. Each cutoff sequentially and automatically converts entropy to information, naturally encoding information Bit from random process, which connects the Bits sequences in the IPF, and the EF predicts next cut.

The impulse curvature, enclosing the entropy of interacting impulses, enables converting inner energy of an external (natural) process to bit of the interacting process which memorizes the bit by delivering the Landauer energy. It allows encoding the IPF information in evolving natural code.

We found the conditions creating a natural bit memorized in interacting curved impulse and the conditions generating a code of the interacting information process which assembles the natural bits.

The natural encoding satisfied Landauer’s principle and compensates for the cost of Maxwell’s Demon.

The energy of a specific interaction limits the universal code length and density.

It is shown that each IPF dimensional cut measures Feller kernel information.

The n -dimensional process cutoff generates a finite information measure, integrated in the IPF whose information approaches the EF measure at n→∞, restricting maximal information of the Markov diffusion process.

Estimation extracting information confirms non-additivity of the EF measured fractions.

The multiple applications validate the results.

Open Access Original Research Article

Support Theorem for Random Evolution Equations in Hölderian Norm

J. H. Andriatahina, R. N. B. Rakotoarisoa, T. J. Rabeherimanana

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2017/29942

In this paper, we purpose to prove the support theorem of the random evolution equation 16.PNGwhere 22.PNG  is the solution of (E) considered as which a random-variable to value in 42.PNG The coefficients σ and b satisfied Lipschitz condition and linear growth and depend to31.PNG and W is a d-dimensional brownian motion. For this, we use the method of approximations of the solution of random evolution equations and extend the results well-known of diffusion processes.

Open Access Original Research Article

Analysis of a Repairable k-out-of-n:G System with Expert Repairman's Multiple Vacations and Shut off Rule

Yuanyuan Zhang, Wenqing Wu, Yinghui Tang

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/BJMCS/2017/30869

This paper investigates an k-out-of-n:G repairable system with expert repairman’s multiple vacations and continuous operation rule where the operating times and the repair times of components follow exponential distributions. When there is no failed component in the system, the expert repairman leaves for a vacation, the duration of which is governed by a phase type distribution. Once an operating component fails during his/her vacation period, it is repaired by an ordinary repairman. The ordinary repairman becomes inactivated when there is no failed component or the expert repairman returns from the vacation. Employing the matrix analytical method, we obtain the transient system availability, the rate of occurrence of failures at time t, the system reliability, the stationary availability, the stationary rate of occurrence of failures, and the mean time to failure of the system. Further, we discuss the time-dependent behaviour of the system reliability measures under different initial system states. Finally, special cases of the system are given to show the correctness of our results.

Open Access Original Research Article

The Domination Number of Pm x Pn

Ramy Shaheen, Mohammad Assaad

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2017/31051

A mixed graph GM(V, E, A) is a graph containing unoriented edges (set E) as well as oriented edges (set A), referred to as arcs. In this paper we calculate the domination number of the Cartesian product of a path Pm with directed path  (mixed-grid graph (  ) for 8 ≤ m ≤ 10 and arbitrary n.

Open Access Original Research Article

Generation of Checkered Patterns and Their Variations by Making Use of Eulerian Graph Features

Tomio Kurokawa

Journal of Advances in Mathematics and Computer Science, Page 1-29
DOI: 10.9734/BJMCS/2017/30783

A variety of pictures of checkered pattern graphics appear on the Internet. However, rarely seen is how those graphics were produced. This paper shows various checkered patterns and their variations generated automatically by a computer program, making use of features of Eulerian Graph. Given a line drawing of binary images, the procedure extracts contours of the line figures. The contours in turn form a set of contour cycles of the regions surrounded by the original lines of the figures, which are supposed to form an Eulerian Circuit. The drawing can be various combinations of closed lines -- circles, rectangles, ellipses, any of closed drawings. Bi-partitioning the contours into partitions (X, Y), filling inside the regions of X and Y, the procedure outputs the checkered patterns or their likes. Various patterns were successfully produced in a number of experiments as well as demonstrating that the algorithm is very robust and that some of the patterns are aesthetic. Since the checkered patterns are used in the Emblem of Tokyo Olympic 2020, it is timely to do the demonstration about the design of checkered patterns and their relations with computer programs and mathematics.