Research & Reviews: Discrete Mathematical Structures
http://computers.stmjournals.com/index.php?journal=RRDMS
<p><strong><span style="text-decoration: underline;">Research & Reviews: Discrete Mathematical Structures </span>(RRDMS) </strong>is a print and e-journal focused towards the rapid publication of fundamental research papers on all areas of Discrete Mathematical Structures.</p><p>Discrete mathematical structures journal deals with discrete objects. Discrete objects are those which are separated from each other like integers, rational numbers, automobiles, houses, peoples etc. are all discrete objects. Some of the major reasons that we adopt Discrete mathematics are. We can handle infinity or large quantity and indefiniteness with them which results from formal approaches are reusable.</p><p>eISSN- 2394-1979</p><p><strong><span style="text-decoration: underline;">Focus & Scope:</span></strong></p><ul><li>Mathematical induction</li><li>logic and Boolean algebra</li><li>set theory</li><li>relations and functions</li><li>sequences and series</li><li>algorithms and theory of computation</li><li>number theory</li><li>matrix theory</li><li>induction and recursion</li><li>counting and discrete probability</li><li>graph theory (trees)</li><li>Calculus of finite differences, discrete calculus or discrete analysis</li><li>Game theory, decision theory, utility theory, social choice theory</li><li>Discrete analogues of continuous mathematics</li><li>Hybrid discrete and continuous mathematics</li></ul>en-US<p align="center"><strong>Declaration and Copyright Transfer Form</strong></p><p align="center">(to be completed by authors)</p><p>I/ We, the undersigned author(s) of the submitted manuscript, hereby declare, that the above manuscript which is submitted for publication in the STM Journals(s), is <span>not</span> published already in part or whole (except in the form of abstract) in any journal or magazine for private or public circulation, and, is <strong><span>not</span></strong> under consideration of publication elsewhere.</p><ul><li>I/We will not withdraw the manuscript after 1 week of submission as I have read the Author Guidelines and will adhere to the guidelines.</li><li>I/We Author(s ) have niether given nor will give this manuscript elsewhere for publishing after submitting in STM Journal(s).</li><li>I/ We have read the original version of the manuscript and am/ are responsible for the thought contents embodied in it. The work dealt in the manuscript is my/ our own, and my/ our individual contribution to this work is significant enough to qualify for authorship.</li><li> I/We also agree to the authorship of the article in the following order:</li></ul><p>Author’s name </p><p> </p><p>1. ________________</p><p>2. ________________</p><p>3. ________________</p><p>4. ________________</p><table width="100%" border="0" cellpadding="0"><tbody><tr><td valign="top" width="5%"><p align="center"> </p></td><td valign="top" width="95%"><p>We Author(s) tick this box and would request you to consider it as our signature as we agree to the terms of this Copyright Notice, which will apply to this submission if and when it is published by this journal.</p></td></tr></tbody></table>computers@stmjournals.com (Editor in Chief)support@stmjournals.com (Administrator)Tue, 14 Nov 2017 03:21:02 -0700OJS 2.4.2.0http://blogs.law.harvard.edu/tech/rss60Self-Similarity Solution of Gravitating Cylindrical Shock Wave in the Theory of Flare-ups in Novae I
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1120
<p class="Normal13pt" align="center"><strong><span>Abstract</span></strong><strong></strong></p><p class="Normal13pt"><span>In this paper, the characteristics of the flow of a cylindrical shock wave are investigated where finite amount of energy in an infinitely concentrate form and total energy remain constant. The present paper deals with the problem in which a finite amount of energy in an infinitely concentrated form is suddenly released along a straight line in a conducting gas subjected to gravitational forces into account.</span></p><p class="Normal13pt"><strong>Keywords:</strong> Cylindrical shock; finite amount of energy, infinitely concentrate, Energy constant</p><p><strong>Cite this Article</strong></p><p>Jitendra Kumar Soni. Self-Similarity Solution of Gravitating Cylindrical Shock Wave in the Theory of Flare-ups in Novae I. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(3): <br /> 18–21p.<strong></strong></p>Jitendra Kumar Sonihttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1120Tue, 05 Dec 2017 04:17:31 -0700Intelligent Ranking Techniques for Software Reliability Growth Models
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1177
<p align="center"><strong><em>Abstract</em></strong><em></em></p><p><em>Reliability is gaining a lot of importance in the modern society, be it gadgets, automation, hardware, software or any other application. We are getting dependent more on machines and so is the need for relives ability gaining more weightage. This paper focuses on software reliability and the complexity involved in the prediction of reliability of the developed software. The paper introduces various assumptions and pre-requisites for software reliability modeling. Different researchers have proposed various software reliability growth models to predict the reliability of software, but none of these models may fit for all software development scenarios. The paper explores the existing ranking and selection techniques for choosing the best model out of the available options.</em></p><p class="IndexTerms"><strong><em>Keywords: </em></strong><em>Software reliability, software quality, modeling, SRGM, failure data </em></p><p><strong>Cite this Article</strong><strong></strong></p><p>Archana Kumar, Abhinav Juneja. Intelligent Ranking Techniques for Software Reliability Growth Models. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(3): 22–29p.<strong></strong></p><p class="IndexTerms"><em><br /></em></p><p class="IndexTerms"> </p>Dr. Archana Kumar, Abhinav Junejahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1177Tue, 05 Dec 2017 03:43:17 -0700Topological Integer Additive Set-Valued Graphs: A Review
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1054
<p align="center"><strong><em><span style="font-family: Times New Roman; font-size: medium;">Abstract</span></em></strong></p><p><em><span style="font-family: Times New Roman;">Let </span></em> <em><span style="font-family: Times New Roman;"> denote a set of non-negative integers and </span></em> <em><span style="font-family: Times New Roman;"> be the collection of all non-empty subsets of </span></em> <em><span style="font-family: Times New Roman;">. An integer additive set-labeling (IASL) of a graph </span></em> <em><span style="font-family: Times New Roman;"> is an injective set-valued function </span></em> <em><span style="font-family: Times New Roman;"> where induced function </span></em> <em><span style="font-family: Times New Roman;"> is defined by</span></em> <em><span style="font-family: Times New Roman;">, where </span></em> <em><span style="font-family: Times New Roman;"> is the sumset of </span></em> <em><span style="font-family: Times New Roman;"> and </span></em> <em><span style="font-family: Times New Roman;">. A set-labeling </span></em> <em><span style="font-family: Times New Roman;"> is said to be a topological set-labeling if </span></em> <em><span style="font-family: Times New Roman;"> is a topology on the ground set </span></em> <em><span style="font-family: Times New Roman;"> and a set-labeling </span></em> <em><span style="font-family: Times New Roman;"> is said to be a topogenic set-labeling if </span></em> <em><span style="font-family: Times New Roman;"> is a topology on </span></em> <em><span style="font-family: Times New Roman;">. In this article, we critically review some interesting studies on the properties and characteristics of different topological and topogenic integer additive set-labeling of certain graphs.</span></em></p><p><span style="font-family: Times New Roman;"><strong><em>Keywords</em></strong><strong><em>:</em></strong><em> Integer additive set-labeled graphs, topological additive set-labeled graphs, topogenic integer additive set-labeled graphs, integer additive set-filter graphs</em></span></p><p> </p><p><strong><span style="font-family: Times New Roman; font-size: medium;">Cite this Article</span></strong></p><p><strong></strong><span style="font-family: Times New Roman;">Sudev NK, Chithra KP, Germina KA. Topological Integer Additive Set-Valued Graphs: A Review. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(3): 1–17p.</span></p><p><span style="font-family: Times New Roman;"><em><br /></em></span></p>N. K. Sudev, K. P. Chithra, K. A. Germinahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1054Tue, 14 Nov 2017 03:19:48 -0700Triple Dirichlet Average of New M-Function and Fractional Derivative
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1103
<p><strong>Abstract</strong>:<strong></strong></p><p>The aim of present paper to establish some results of Triple Dirichlet average of <strong>M-Function</strong>, using fractional derivative. Fractional calculus is powerful branch of mathematics that has also sporadically been applied to structural dynamics problems. Indeed, it appears to us to be a solution in search of a good problem. In that sense, it has some of the character of the laser shortly after its development. Fractional calculus is also inherent in the physics of dynamic structural mechanics or whether it is a convenient mathematical tool for manipulating equations derived using more conventional arguments. It is generally known that integer-order derivatives and integrals have clear physical and geometric interpretations.</p><p><strong>Keywords and Phrases</strong>: Dirichlet average, <em>New </em><strong>M-Function </strong>fractional derivative and Fractional calculus operators.</p><p><strong>Cite this Article</strong></p><p><span style="font-size: medium;">Mohd. Farman Ali, Manoj Sharma, Renu Jain. Triple Dirichlet Average of New M-Function and Fractional Derivative. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(2): 37–41p.</span></p>Mohd. Farman Ali, Manoj Sharma, Renu Jainhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1103Thu, 12 Oct 2017 01:15:00 -0700Dirichlet Average of Extended Mainardi Function and Fractional Derivative
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1102
<p align="center"><strong><em>Abstract</em></strong></p><p><em>In this paper, we establish a relation of Dirichlet average of Extended Mainardi function, using fractional derivative. The fractional calculus deals with integrals and derivatives of arbitrary order. Special roles in the applications of fractional calculus operators are played by the transcendental function of the Mittag-Leffler, generalized M-series function, M-function Generalized Miller-Ross function, Wright’s functions and more generally by the Meijer’s G-functions, Fox’s H-functions and Saxena’s I-function. </em><strong><em> </em></strong></p><p><strong><em>Mathematics Subject Classification:</em></strong><em> 26A33, 33A30, 33A25 and 83C99</em></p><p><strong><em>Keywords: </em></strong><em>Dirichlet average, Mainardi function, Extended Mainardi function fractional derivative and Fractional calculus operators</em></p><p><em><br /></em></p>Santosh Verma, Manoj Sharmahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1102Thu, 12 Oct 2017 00:26:58 -0700Integral of Generalized M-Function Involving Product of Special Functions
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1100
<p align="center"><strong><em>Abstract</em></strong></p><p><em>In this paper, an attempt to be made for study about </em><em>integrals of generalized M-Function multiplied with Jacobi polynomial.</em></p><p><strong><em>Keywords: </em></strong><em>Generalized Mittag-Leffler function, Generalized M-Function.</em></p><p><strong>Cite this Article</strong></p><p><span style="font-size: medium;">Laxmi Morya, Manoj Sharma, Rajshree Mishra. Integral of Generalized M-Function Involving Product of Special Functions. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(2): 33–36p.</span></p><p><em><br /></em></p>Laxmi Morya, Manoj Sharma, Rajshree Mishrahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1100Thu, 12 Oct 2017 00:10:26 -0700Computable Extension of New Advanced Fractional Kinetic Equation
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1099
<p align="center"><strong><em>Abstract</em></strong><strong><em></em></strong></p><p><em>First, we obtain </em><em>computable extensions of advanced fractional kinetic equation. </em><em>The aim of this survey is to explore the behavior of physical and biological systems from the point of view of fractional calculus. Fractional calculus, integration and differentiation of an arbitrary or fractional order, provide new tools that expand the descriptive power of calculus beyond the familiar integer-order concepts of rates of change and area under a curve. Fractional calculus adds new functional relationships and new functions to the familiar family of exponentials and sinusoids that arise in the area of ordinary linear differential equations</em><em>. Among such functions that play an important role, we have the Euler Gamma function, the Euler Beta function, the Mittag-Leffler functions, the Wright and Fox functions, M-Function, K-Function. </em><em>In late years, fractional kinetic equations are considered because of their helpfulness and significance in mathematical physics, particularly in astrophysical issues. In astrophysics, kinetic equations assign an arrangement of differential equations, portraying the rate of progress of chemical composition of a star for every species as far as the response rates for pulverization and creation of that species are concerned. Techniques for demonstrating procedures of pulverization and generation of stars have been created for bio-chemical reactions and their insecure harmony states and for concoction response systems with unstable states, oscillations and hysteresis. The point of present paper is to discover the arrangement of summed up fragmentary request motor condition, utilizing another exceptional capacity. The outcome got here is decently widespread in nature. Exceptional cases, identifying with the Mittag-Leffler work are additionally considered</em><em>.</em><em> </em></p><p><strong><em>Mathematics Subject Classification: </em></strong><em>33C60, 33E12, 82C31, 26A33</em></p><p><strong><em>Keywords: </em></strong><em>Fractional kinetic equation, </em><em>Generalized </em> <em>function</em><em>, Riemann-Liouville operator, Laplace transform</em><em>, modified Riemann-Liouville fractional derivative operator, differential equation</em></p><p><strong>Cite this Article</strong></p><p><span style="font-size: medium;">Manoj Sharma, Laxmi Morya, Rajshree Mishra. Computable Extension of New Advanced Fractional Kinetic Equation. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(2): 26–32p.</span></p><p><em><br /></em></p>Manoj Sharma, Laxmi Morya, Rajshree Mishrahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1099Wed, 11 Oct 2017 23:53:19 -0700Triple Dirichlet Average of M- Function and Fractional Derivative
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1060
<p align="center"><strong><em>Abstract</em></strong><strong><em></em></strong></p><p><em>The aim of present paper is to establish some results of triple Dirichlet average of </em> <strong><em> </em></strong><em>function, using fractional derivative.</em></p><p><strong><em>Keywords:</em></strong><em> Dirichlet average, </em> <em> function<strong> </strong>fractional derivative and Fractional calculus operators</em></p><p><strong>Cite this Article</strong><strong></strong></p><p>Manoj Sharma,Kiran Sharma, Susheel Dhanelia. Triple Dirichlet Average of M- Function and Fractional Derivative. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(2): 21–25p.</p>Manoj Sharma, Kiran Sharma, Susheel Dhaneliahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1060Fri, 01 Sep 2017 23:42:27 -0700Fractional Free Electron Laser Equation and K-Function
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1058
<p align="center"><strong><em>Abstract</em></strong><strong><em></em></strong></p><p><em>In this era, </em><em>fractional </em><em>free electron laser (FEL) </em><em>equations are studied due to their utility and importance in mathematical physics and engineering. The aim of present paper is to find the solution of generalized fractional order </em><em>free electron laser (FEL) </em><em>equation, using K-function. The results obtained here are moderately universal in nature. Special cases, relating to the exponential function are also considered. The special functions were introduced in 18th century to define solutions of differential equations emerging as mathematical models of certain problems in astronomy, physics and biological science. The adjective ‘special’ of this nomenclature can be attributed to the simple fact that these functions owed their origin to special circumstances. Here we present a brief survey of the hypergeometric functions and their generalized forms due to the prime importance of hypergeometric functions in the study of special functions.</em></p><p><strong><em>Keywords: </em></strong><em>Fractional </em><em>free electron laser (FEL) </em><em>equation, K-function, generalized </em><em>M-series</em><em>, Riemann-Liouville operator</em></p><p><strong>Cite this Article</strong><strong></strong></p><p>Manoj Sharma, Kishan Sharma. Fractional Free Electron Laser Equation and K-Function. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(2): 17–20p.</p>Manoj Sharma, Kishan Sharmahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1058Fri, 01 Sep 2017 23:20:21 -0700Asymptotically Double Lacunary Equivalent Sequences Defined by Ideals and Orlicz Functions
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1036
<p align="center"><strong><em>Abstract</em></strong></p><p><em>In the present manuscript, we are going to introduce some new definitions that are a generalization of those given by Esi in 2014 about asymptotically equivalent and Orlicz function with respect to an ideal. We established some sequence spaces and studied some inclusion relations about them. The results obtained in this study are more than those obtained</em><em> by Esi in 2009 and 2014.</em></p><p><strong><em>Keywords: </em></strong><em>Pringsheim limit, </em><em>Orlicz functions, </em><em>equivalent sequences</em></p><p><strong>Cite this Article</strong></p><p>Ayhan Esi, M. Kemal Ozdemir. Asymptotically Double Lacunary Equivalent Sequences Defined by Ideals and Orlicz Functions. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(2): 7–16p.</p><p><em><br /></em></p>ayhan esi, M. Kemal Ozdemirhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1036Fri, 18 Aug 2017 22:16:13 -0700R-L-F Integral and Double Dirichlet Average of the R-Series
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1015
<p align="center"><strong><em>Abstract</em></strong></p><p><em>The object of the present paper is to establish a result of double Dirichlet average of the R-series by using Riemann-Liouville fractional integral. The R-series can be measured as a Dirichlet average and connected with fractional calculus. In this paper, the solution comes in compact form of double Dirichlet average of R-series. The special cases of our results are same as earlier obtained by Saxena et al, for double Dirichlet average of R-series [1].</em></p><p class="IEEEAbtract"><strong><em>Mathematics Subject Classification: </em></strong><em>26A33, 33A30, 33A25 and 83C99.</em></p><p><em></em><strong><em>Keywords:</em></strong><em> Dirichlet average, R-series, fractional derivative, fractional calculus operators</em></p><p><strong>Cite this Article</strong><strong></strong></p><p>Mohd. Farman Ali. R-L-F Integral and Double Dirichlet Average of the R-Series. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(2): 1–6p.</p><p><em><br /></em></p>Mohd. Farman Alihttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1015Tue, 18 Jul 2017 02:41:01 -0700Review Paper on Fundamental Soft Set Hypothesis
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1005
<p align="center"><strong><em>Abstract</em></strong></p><p><em>Soft set is a very the main level in practically every logical field. Soft set hypothesis is another scientific instrument for managing instabilities and is a set related with parameters and has been connected in a few headings. Since Molodtsov began the possibility of delicate sets, some exploration on delicate sets has been done in the writing. This hypothesis speaks to a promising procedure in blemished information examination which has discovered fascinating augmentations and different applications that handle defective learning, for example, Bayesian inference, fuzzy set and so forth. This paper characterizes the thought of soft sets, and the review that are fascinating and significant in the hypothesis of soft sets, which accentuation on a progression of utilizations particularly in basic leadership issues. Likewise displays far reaching study, advancement and review of its current writing. <br /></em></p><p><strong><em>Keywords: </em></strong><em>BCI, BCK, FCM, fuzzy set, fuzzy soft set, soft rough set, soft semi-rings, soft set,<strong> </strong>uncertainty</em></p><p><strong>Cite this Article</strong></p><p>Swadha Mishra. Review Paper on Fundamental Soft Set Hypothesis. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(1): 25–34p.</p><p><em><br /></em></p>Swadha Mishrahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1005Wed, 31 May 2017 22:26:00 -0700A Review of Discrete Mathematics Based on Different Researches
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1006
<p align="center"><strong><em>Abstract</em></strong></p><p><em>This paper describes an extensive specimen of distributions on the educating of discrete structures and discrete mathematics in software engineering educational module. The approach is deliberate, in that an organized inquiry of electronic assets has been directed, and the outcomes are displayed and quantitatively dissected. Various wide subjects in discrete structures training are recognized identifying with course content, showing procedures and the methods for assessing the accomplishment of a course.</em><em></em></p><p><em></em><strong><em>Keywords: </em></strong><em>Computing curriculum, discrete structures, discrete mathematics</em></p><p><strong>Cite this Article</strong><strong></strong></p><p>Swadha Mishra, Krti Singh. A Review of Discrete Mathematics Based on Different Researches. <em>Research & Reviews: Discrete Mathematical Structures.</em> 2017; 4(1): 18–24p.</p><p><em><br /></em></p>Swadha Mishra, Kirti Singhhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1006Fri, 12 May 2017 02:08:56 -0700Fractional Integral and Dirichlet Average of the R-Series
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=927
<p align="center"><strong><em>Abstract</em></strong></p><p><em>The aim of the present paper is to investigate the results of Dirichlet average of a new special R-Series, using Riemann-Liouville Fractional derivative. The R-Series can be measured as a Dirichlet average and connected with fractional calculus. </em></p><p><strong><em>Keywords:</em></strong><em> Dirichlet average, R-series, fractional derivative, Fractional calculus operators</em></p><p><strong>Cite this Article</strong></p><p>Mohd. Farman Ali. Fractional Integral and Dirichlet Average of the R-Series. <em>Research & Reviews: Discrete Mathematical Structures.</em> 2017; 4(1): 1–4p.</p><p><em><br /></em></p>Mohd. Farman Alihttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=927Fri, 12 May 2017 01:49:57 -0700Fractional q-calculus of the R-Series
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=929
<p align="center"><strong><em>Abstract</em></strong></p><p><em>In this present paper we introduce a new special function, called as R-series given by the author. This function is a special case of H-function given by Inayat Hussain. This paper is devoted to fractional q-derivative of special function. To begin with the theorem on term by term q-fractional differentiation has been derived. Fractional q-differentiation of R-series has been obtained. </em></p><p><strong><em>Keywords and Phrases</em></strong><em>: Fractional integral and derivative operators, Fractional q-derivative, R-series and Special functions</em></p><p><strong>Cite this Article</strong></p><p>Mohd. Farman Ali. Fractional q-calculus of the R-Series. <em>Research & Reviews: Discrete Mathematical Structures.</em> 2017; 4(1): 5–7p.</p>Mohd. Farman Alihttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=929Fri, 12 May 2017 01:29:08 -0700Edge Domination Number on Cartesian product of Simple Fuzzy Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=936
<p align="center"><strong><em>Abstract</em></strong></p><p><em>In this paper, we define the concept of edge domination number on Cartesian product of simple fuzzy graphs (G&H). Some results and bounds on edge domination number are derived in fuzzy graph (G×H). We prove some theorems that relate the parameters </em><em>g</em><em>(G×H), </em><em>g</em><em><sub>cd</sub></em><em>(G×H) and </em><em>g</em><em>¢</em><em>(G×H). Finally, the relationship between the fuzzy dominator chromatic number and edge domination number on Cartesian product of simple fuzzy graphs are discussed.</em></p><p><strong><em>Keywords:</em></strong><em> Dominating set, edge dominating set, Cartesian product of fuzzy graphs, connected dominating set, fuzzy dominator chromatic number</em></p><p><strong>Cite this Article</strong></p><p>Muthuraj R, Sasireka A. Edge Domination Number on Cartesian Product of Simple Fuzzy Graphs. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(1): 8–17p.</p>R. Muthuraj, A. Sasirekahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=936Wed, 10 May 2017 01:22:13 -0700Research and Industrial Insight: Discrete Mathematics
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=911
<p>Mazes are in vogue right now, from NBO's West world, to the arrival of the British faction TV arrangement, The Crystal Maze. Be that as it may, labyrinths have been around for centuries and a standout amongst the most acclaimed labyrinths, the Labyrinth home of the Minotaur, assumes a featuring part in Greek mythology.</p>Sugandha Mishrahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=911Mon, 20 Feb 2017 01:26:22 -0700A Brief Review on Algorithms for Finding Shortest Path of Knapsack Problem
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=880
<p align="center"><strong><em>Abstract</em></strong></p><p><em>The gathering knapsack and knapsack problems are summed up to briefest way issue in a class of graphs. An effective calculation is used for finding briefest ways that bend lengths are non-negative. A more effective calculation is portrayed for the non-cyclic which incorporates the knapsack issue. </em></p><p><em> </em></p><p><strong><em>Keywords:</em></strong><em> knapsack problem, rucksack problem</em></p><br /><p><strong>Cite this Article</strong><strong></strong></p><p>Swadha Mishra. A Brief Review on Algorithms for Finding Shortest Path of Knapsack Problem. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2016; 3(3): 17–19p.</p>Swadha Mishrahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=880Mon, 20 Feb 2017 01:21:10 -0700R-L F Integral and Triple Dirichlet Average of the R-Series
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=867
<p align="center"><strong><em>Abstract</em></strong></p><p><em>In this article, we establish the relation between some results of triple Dirichlet average of the R-series and fractional operators. We use a new special function called as R-series, which is a special case of H-function given by Inayat Hussain. In this article, the solution is obtained in compact form of triple Dirichlet average of R-series as well as conversion into single Dirichlet average of R-series, using fractional integral.</em></p><p><em> </em></p><p><strong><em>Keywords:</em></strong><em> Dirichlet averages, special functions, R-series and Riemann-Liouville fractional integral</em></p><p><strong>Cite this Article</strong></p><p>Mohd. Farman Ali. R-L F Integral and Triple Dirichlet Average of the R-Series. <em>Research & Reviews: Discrete Mathematical Structures.</em> 2016; 3(3): 6–12p.</p>Mohd. Farman Alihttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=867Wed, 01 Feb 2017 21:28:49 -0700Dirichlet Average of New Generalized M-series and Fractional Calculus
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=866
<p align="center"><strong><em>Abstract</em></strong></p><p><em>We know that every analytic function can be measured as a Dirichlet average and connected with fractional calculus. In this note, we set up a relation between Dirichlet average of </em><em>new generalized M-series</em><em>, and fractional derivative. Fractional derivative is a derivative of arbitrary order i.e. may be real, complex, integer or fractional order.</em></p><p><strong><em>Keywords</em></strong><em>: Dirichlet average</em><em> new generalized M-series</em><em>, fractional derivative, fractional calculus operators</em></p><p><strong>Cite this Article</strong></p><p>Manoj Sharma. Dirichlet Average of New Generalized M-series and Fractional Calculus. <em>Research & Reviews: Discrete Mathematical Structures.</em> 2016; 3(3): 13–16p.</p>Manoj Sharmahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=866Wed, 01 Feb 2017 21:13:21 -0700Fractional Calculus of the R-Series
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=815
<p class="IEEEAbtract"><span>The present paper creates a special function called as R-series. This is a special case of H-function given by Inayat Hussain. The Hypergeometric function, Mainardi function and M-series follow R-series and these functions have recently found essential applications in solving problems in physics, biology, bio-science, engineering and applied science etc. </span></p><p class="IEEEAbtract"><span><br /></span></p><p class="IEEETitle"><strong>Cite this Article</strong></p><p>Mohd. Farman Ali, Manoj Sharma. Fractional calculus of the R-Series. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2016; 3(3): 1–5p.</p><p class="IEEEAbtract"><span><br /></span></p>Mohd. Farman Ali, Manoj Sharmahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=815Thu, 29 Dec 2016 04:03:18 -0700Homogeneous geodesics on the solvable homogeneous principal bundles
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=739
<p>Let $M=G/K$ be a homogeneous differentiable manifold .We consider the<br /> homogeneous bundle $\Im=(G,\pi,G/K,K)$<br /> and the tangent bundle $\tau_{G/K}$ of $M=G/K$. Let $G$ be a connected Lie group and $K$<br />a closed subgroup of $G$. We take the Lie algebras $\cal{G}$ and<br />$\cal{K}$ of $G$ and $K$ respectively and define $\xi=(G\times_{K}<br />\cal{ G} / \cal {K}, \rho_{\xi}, \emph{G} / \emph{K},\cal {G} /<br />\cal {K})$ to be the bundle associated with $\Im$. We consider<br />that $ \xi$ is strongly isomorphic to tangent bundle<br />$\tau_{G/K}=(T_{G/K},\pi_{G/K},G/K, {\textbf{R}}^{m})$ .\\</p><p>In this paper we take $G$ be a solvable Lie group and prove some<br />results about the existence of homogeneous geodesics and geodesic<br />vectors on the fiber</p>Dr. Reza Chavosh Khatamyhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=739Thu, 08 Sep 2016 04:13:39 -0700Enhanced Association Rule Mining Algorithm (EARMA) for Reducing Computational Time on Large Data Set
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=797
<p>Association rule learning is a trendy process for discovering exciting relationships between variables in big database. It is frequently used in market basket analysis field e.g. if a buyer buys onions and potatoes then he also purchases beef. But, in fact, it can be implemented in different application area where we want to determine the association among variables. The APRIORI method is definitely the trendiest. But, even with its good quality property, this procedure has a drawback: the number of obtained rules can be very high. The capabilities to highlight the most exciting rules, those which are related, become a major challenge.</p><p><strong>Cite this Article</strong><br />Priyanka Rana, Jaspreet Singh, Shashi Bhushan. Enhanced Association Rule Mining Algorithm (EARMA) for Reducing Computational Time on Large Data Set. Research & Reviews: Discrete Mathematical Structures. 2016; 3(2): 20–25p.</p>priyanka rana, Jaspreet Singh, Dr. Shashi Bhushanhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=797Tue, 06 Sep 2016 01:13:06 -0700A Statistical Approach Noise Tolerant Texture Classification
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=790
<p>A simple, efficient, yet robust multi resolution approach to texture classification binary rotation invariant and noise tolerant. The proposed approach is very fast to build and very compact while remaining robust to illumination variations, rotation changes, and noise. We have developed a novel and simple strategy to compute a local binary descriptor based on the conventional local binary pattern (LBP) approach, preserving the advantageous characteristics of uniform LBP. Points are sampled in a circular neighborhood, but keeping the number of bins in a single-scale LBP histogram constant and small, such that arbitrarily large circular neighborhoods can be sampled and compactly encoded over a number of scales. There is no necessity to learn a texton dictionary, as in methods based on clustering, and no tuning of parameters is required to deal with different data sets. This noise robustness characteristic of the proposed binary rotation invariant and noise tolerant is evaluated quantitatively with different artificially generated types and levels of noise including Gaussian, salt, pepper and speckle noise in natural texture images.</p><p><strong>Cite this Article</strong><br />Raparthi Shilpa, Satish Chandra B. A Statistical Approach Noise Tolerant<br />Texture Classification. Research & Reviews: Discrete Mathematical<br />Structures. 2016; 3(2): 14–19p.</p>Raparthi Shilpa, B. Satish Chandrahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=790Tue, 06 Sep 2016 00:02:13 -0700Laceability in Line Graphs and Jump Graphs of Petersen Graph
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=808
<p>A simple connected graph is Hamiltonian laceable if there exists a Hamiltonian path between every pair of distinct vertices at an odd distance in it. is Hamiltonian-t-laceable (t*-laceable) if there exists a Hamiltonian path in between every pair (at least one pair) of vertices u and v in with the property Manjunath et al. obtained Hamiltonian laceability properties in line graphs and jump graphs of some graphs. In this paper we explore laceabilty properties in Petersen graphs and also explore the laceability properties of line graphs and jump graphs [1, 2].</p><p><strong>Cite this Article</strong><br />Manjunath G, Murali R. Laceability in Line Graphs and Jump Graphs of Petersen Graph. Research & Reviews: Discrete Mathematical Structures. 2016; 3(2): 5–13p.</p>Manjunath g, Murali Rhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=808Mon, 05 Sep 2016 23:44:54 -0700