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>sugandha.mishra@celnet.in (Sugandha Mishra)info@stmjournals.com (Administrator)Wed, 23 Jan 2019 23:45:14 -0700OJS 2.4.2.0http://blogs.law.harvard.edu/tech/rss60Use of Matlab in Teaching The Fundamentals of Probability
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1870
<p align="center">The aim of this paper is to improve teaching efficiency with use of powerful educational software called 'MATLAB'. In this paper using the 'MATLAB' tool 'Makeshow' we attractively introduce normal probability distribution for the normally distributed random variables. Using these tool students can easily create interactive slideshows. Because of their rich library, available tools and demos matlab is easy to use for the students and so it provides option of self-study tool for them. This type of educational software allows the students to establish relationship between the problems solved in classroom and the reality that these problems refer to.<strong><em> </em></strong></p><p><strong>Cite this Article</strong></p><p>Bhavika M. Patel, Truptiben A. Desai. Use of Matlab in Teaching the Fundamentals of Probability. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3):<br /> 31–35p.<strong></strong></p><p align="center"><strong><em><br /></em></strong></p>Bhavika M Patel, Truptiben A Desaihttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1870Thu, 07 Feb 2019 02:21:10 -0700Degree and Distance in 2-cartesian Product of Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1868
<p class="CM17" align="center"><em>The cartesian product of two graphs is well-known graph product and studied in detail. This concept has been generalized by introducing 2-cartesian product of graphs. The connectedness of 2-cartesian product of graphs has been discussed earlier. In this paper, ﬁrst we obtain degree formula and discuss regularity of this product of graphs. Also, we have discuss distance between two vertices in this product.</em></p><p><strong>Cite this Article</strong></p><p>H.S. Mehta and U.P. Acharya. Degree and Distance in 2-Cartesian Product of Graphs. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3): 11–14p.</p>H.S. Mehta, U. P. Acharyahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1868Thu, 07 Feb 2019 02:21:05 -0700Solution of Solid Traveling Purchaser Problem Using Eﬃcient Genetic Algorithm with Probabilistic Selection and Multi-Parent Crossover Technique
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1865
<p>In this paper, I design a NP-hard optimization problem and solve this problem by developing a nature-based multi-parent crossover in genetic algorithm (GA). Initially, taking a set of markets, a depot and some products for each of which a positive demand is specified. Purchaser can purchase each product from a subset of markets only a given quantity, less than or equal to the required one, can be purchased at a given unit price. Traveling purchaser forms a cycle starting at and ending to the depot and visiting a subset of markets at a minimum traveling cost. Here, I consider multiple vehicle to visit different markets say solid TPP (STPP). The activeness of my model is illustrated by numerical examples.</p><p><strong>Cite this Article</strong></p><p>Arindam Roy. Solution of Solid Traveling Purchaser Problem Using Efficient Genetic Algorithm with Probabilistic Selection and Multi-Parent Crossover Technique. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3):<br /> 20–26p.</p>Arindam Royhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1865Thu, 07 Feb 2019 02:21:01 -0700Characterization of topologically 1-uniform dcsl graphs and learning graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1833
<p>A distance compatible set labeling (dcsl) of a connected graph $G$ is an injective set assignment $f : V(G) \rightarrow 2^{X},$ $X$ being a non empty ground set, such that the corresponding induced function $f^{\oplus} :E(G) \rightarrow 2^{X}\setminus \{\phi\}$ given by $f^{\oplus}(uv)= f(u)\oplus f(v)$ satisfies $ |f^{\oplus}(uv)| = k_{(u,v)}^{f}d_{G}(u,v) $ for every pair of distinct vertices $u, v \in V(G),$ where $d_{G}(u,v)$ denotes the path distance between $u$ and $v$ and $k_{(u,v)}^{f}$ is a constant, not necessarily an integer, depending on the pair of vertices $u,v$ chosen. A dcsl $f$ of $G$ is $k$-uniform if all the constants of proportionality with respect to $f$ are equal to $k,$ and if $G$ admits such a dcsl then $G$ is called a $k$-uniform dcsl graph. Let $\mathcal{F}$ be a family of subsets of a set $X.$ A graph $G$ is defined to be a learning graph, if it is a ${\mathcal{F}}$-induced graph of some learning space ${\mathcal{F}}.$ A graph $G$ is called a topologically $k$-uniform dcsl graph, if $\{f(V(G)\}$, the collection of vertex labeling of $G$ is a topology. In this paper, we characterize topologically $1$-uniform dcsl learning graphs.</p><p><strong>Cite this Article</strong></p><p>Gency Joseph, L. Benedict Michael Raj, Germina K. Augusthy. Characterization of Topologically 1-Uniform DCSL Graphs and Learning Graphs. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3): 6–10p.</p>Germina K. Augusthy, Gency Joseph, L Benedict Michael RAjhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1833Thu, 07 Feb 2019 02:14:56 -0700Control Chart for Attributes based on Inverse Rayleigh Distribution
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1854
<p>In this paper, a new attribute control chart based on inverse Rayleigh distribution is developed under a time truncated life test. The number of failures is observed from the life test and the fraction nonconforming is to be monitored by two pairs of lower and upper control limits. The simulation study shows the efficiency of the developed chart. An example is provided for illustrating the new control chart.</p><p><strong>Cite this Article</strong></p><p>Kowsalya K, Sathish Kumar K, Arul K. Control Chart for Attributes based on Inverse Rayleigh Distribution. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3): 1–5p.</p>K. Kowsalya, K. Sathish Kumar, K. Arulhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1854Thu, 07 Feb 2019 02:14:51 -0700Production Inventory Model for Deteriorating Products with Lifetime
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1867
<p>In this paper, an inventory model has been developed with production proportional to quadratic demand during life time and linear demand is taken during deterioration period. The deterioration rate is taken of power pattern form, i.e. 14 Î±Î²tÎ²-1"> . Shortage is not allowed.</p><p><strong>Cite this Article</strong></p><p>Rajender Kumar, Manju Pruthi, Gulshan Taneja. Production Inventory Model for Deteriorating Products with Lifetime. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3):<br /> 15–19p.</p>Rajender Kumar, Manju Pruthi, Gulshan Tanejahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1867Fri, 25 Jan 2019 04:37:37 -0700Some Algebraic Properties of me-homomorphism of Semi graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1936
<p>The theory of Semi graph was introduced by E. Sampat Kumar [6] which is analogous with theory of Hyper graph. Study of Homomorphism[4] is useful to prove numerous application of Graph theory, which is adjacency preserving mapping. In this Paper we have introduced me-homomorphism of Semi graphs and derived some of its algebraic properties [5]. We have also investigated nature of some parameters and its bounds under this mapping.</p><p><strong>Cite this Article</strong></p><p>P.D. Uchat, M.S. Sutaria. Some Algebraic Properties of me-homomorphism of Semi-Graphs. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3):<br /> 27–30p.</p>Paras Dineshchandra Uchat, Maitri Sutariahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1936Wed, 23 Jan 2019 23:45:50 -0700A Graph Theoretic Approach to quantify the Conflict of Traffic Streams in a Traffic Intersection
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1538
<p>A traffic intersection can be modelled by a graph by considering the streams as vertices and assigning an edge based on the mutually non-conflict streams. In this paper we propose a spectral approach to arrange the steams in order of their conflict and hence determine the most conflicted stream in a traffic intersection.<strong> </strong></p>Ankur Bharalihttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1538Fri, 21 Sep 2018 02:06:29 -0700FD and DDA of N2 Function
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1695
<p>The object of the present paper is to establish the results of Double Dirichlet average (DDA) of N<sub>2</sub> Function, using Riemann-Liouville Fractional derivative (FD). This function is a modified form of Mittag-Leffler function [15]. The author drives the results between N2-function and fractional operators. The N<sub>2 </sub>Function 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 N<sub>2 </sub>Function.</p>Mohd. Farman Ali, Manoj Sharmahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1695Fri, 21 Sep 2018 01:59:46 -0700Further Results on Some Degree Based Topological Indices of Sierpi´cski Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1486
Sierpi´cski graphs S(n, k) were defined originally in 1997 by Sandi Klavˇzar<br />and Uroˇs Milutinovi´c. In this paper, degree based topological indices of<br />Sierpi´cski graphs are considered. In particular M1(G), M2(G), M1(G, x), M2(G, x), R(G), (G), ABC(G), ABC4(G), GA(G), GA5(G), H(G), AZI(G), S(G) and F(G) of Sierpi´cski graphs are determined.Padmapriya Phttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1486Fri, 21 Sep 2018 01:37:17 -0700On Structure and Robustness of Airport Network of India
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1468
This paper uses a complex network approach to study the structure and robustness of Airport Network of India (ANI). The ANI displays small-world (SW) network properties with an average path length of 2.262 and a clustering coefficient of 0.605, and it also exhibits disassortative mixing on degree of nodes, that means the high-degree nodes in the network tend to have connections with low-degree nodes. Being a disassortative network, ANI doesn’t percolate more easily and less robust to node removal. A study of the robustness of ANI is also carried out for targeted node removal.Ankur Bharali, Dimpee Baruahhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1468Sat, 01 Sep 2018 10:30:58 -0700Vertex Odd Divisor Cordial Labeling of Ring Sum of Different Graphs With star Graph
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1696
<p>A graph <em>tt </em>= (<em>V,</em><em> </em><em>E</em>) is said to have a vertex odd divisor cordial labeling if there is a bijection <em>f </em>: <em>{</em>1<em>, </em>3<em>, </em><em>. . . , </em>2<em>n </em><em>− </em>1<em>} </em>such that each edge <em>e </em>= <em>uv </em>is assigned the label 1 if <em>f </em>(<em>u</em>)<em>|</em><em>f </em>(<em>v</em>) or <em>f </em>(<em>v</em>)<em>|</em><em>f </em>(<em>u</em>) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph admits a vertex odd divisor cordial labeling, then it is called vertex odd divisor cordial graph. In this paper we have derived vertex odd divisor cordial labeling of ring sum of different graphs.</p>D. G. Adalja, G. V. Ghodasarahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1696Fri, 31 Aug 2018 03:36:36 -0700Difference Cordial Labeling in context of Joint sum of Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1570
<p>Suppose G be a (p, q) graph. Suppose f be a map from f(G) to {1,2,...,p}. For each edge xy assign, the label |f(x) – f(y)|. f is difference cordial if f is 1-1 and |e<sub>f</sub>(0) – e<sub>f</sub>(1)| <!--?mso-application progid="Word.Document"?--> 14â‰¤"> 1, where e<sub>f</sub>(1) and e<sub>f</sub>(0) denote the number of edges with labeled 1 except labeled with 1 respectively. A graph which admit difference cordial labeling is called a difference cordial graph.</p><p> In this paper I prove the following results.</p><ol><li>The joint sum of two copies of wheel graph is difference cordial.</li><li>The joint sum of two copies of shell graph is difference cordial.</li><li>The joint sum of two copies of double wheel graph is difference cordial.</li><li>The joint sum of two copies of Petersen graph is difference cordial.</li><li>The joint sum of two copies of coconut tree is difference cordial.</li></ol>amit himmatbhai rokadhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1570Tue, 26 Jun 2018 23:40:43 -0700E-Cordial Labeling for Theta Graph
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1463
<strong><em> </em></strong>A binary vertex labeling <em>f </em>:<em> E</em>(<em>G</em>)<em> → </em>{0,1} with induced labeling <em>f <sup>* </sup></em>:<em> V</em>(<em>G</em>)<em> → </em>{0,1} defined by <em>f <sup>*</sup></em>(<em>v</em>) = ∑ { <em>f </em>(<em>uv</em>) : <em>uv </em>ϵ <em>E</em>(<em>G</em>)}(<em>mod 2</em>) is called an E-cordial labeling of graph <em>G</em> if the number of vertices labeled 0 and number of vertices labeled 1 differ by at most 1and the number of edges labeled 0 and number of edges labeled 1 differ by at most 1. A graph which admits E-cordial labeling is called an E-cordial graph. We prove that the graphs obtained by duplication, switching, fusion and open star of theta graph <em>T<sub>α</sub></em> are E-cordial graphs.vishnu prakashhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1463Sun, 24 Jun 2018 22:38:39 -0700Analysis of Numerical and Categorical Prediction Algorithms : A Case Study of Hypertension
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1558
<strong>An extremely wide variety and volume of data are generated by the healthcare industries which can be effectively utilized by applying data mining techniques so as to attain significant knowledge that can aid the process of decision making. In this paper an analysis of Prediction Algorithms is performed using clinical data of hypertension patients. Data mining techniques are effectively employed to estimate systolic and diastolic blood pressure of patients and categorize the risk level for each patient.</strong>Ashwini Menonhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1558Tue, 19 Jun 2018 23:29:49 -0700Chromatic Curling Number of Certain Derived Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1229
<p>The curling number of a graph G is dened as the number of times an element in the degree sequence of G appears the maximum number of times. Graph colouring is an assignment of colours, labels or weights to the vertices or edges of a graph. A colouring C of colours c1, c2,..., cl is said to be a minimum parameter colouring if C consists of minimum number of colours with smallest subscripts. In this paper, we study the chromatic colouring version of curling number of certain derived graphs, with respect to their minimum parameter colourings.</p>Susanth Chandoor, Sudev Naduvath, Sunny Joseph Kalayathankalhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1229Mon, 28 May 2018 04:40:27 -0700Fibonacci Cordial Labeling of Some Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1416
<p><em>An injective function f: V (G) → {F0, F1, F2, . . . , Fn+1}, where Fj is the j<sup>th</sup> Fibonacci number (j = 0, 1, . . . , n+1), is said to be Fibonacci cordial labeling if the induced function f </em><em>∗</em><em> </em><em>: E(G) → {0, 1} defined by f </em><em>∗</em><em>(uv)</em><em> </em><em>= (f (u) + f (v))(mod2) satisfies the condition |e<sub>f </sub>(0) − e<sub>f</sub> (1)| ≤ 1. A graph which admits Fibonacci cordial labeling is called Fibonacci cordial graph. In this paper, the author investigated the existence of Fibonacci Cordial Labeling of some Graphs.<strong></strong></em></p>amit himmatbhai rokadhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1416Mon, 09 Apr 2018 21:27:20 -0700INTEGRAL REPRESENTATION OF K-FUNCTION
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1266
<p><strong>Abstract: </strong>In this article, an attempt to be made to introduce the four-different integral representation of Extended K-function and special cases have also been discussed [1, 2]. The Extended K Function which is introduced by the authors first time in this work is extended version of earlier K-Function of Sharma [3]. We will use Riemann-Liouville fractional calculus operator in finding the integral representation of this extended K- Function. Fractional Calculus operators means calculus operators of arbitrary order (real, complex), So, these operators are useful in finding Integral representations of special functions of fractional calculus.</p><p><strong>Mathematics Subject Classification</strong>: 33C60, 33E12, 82C31, 26A33 </p><p><strong>Keywords</strong>: Riemann-Liouville fractional derivative operator, K-function, Gamma and Beta Function, M-Function.</p><p><strong>Cite this Article</strong></p><p><span style="font-size: medium;">Manoj Sharma, Laxmi Morya, Rajshree Mishra. Integral Representation of K-Function</span><span style="font-size: medium;">. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(3):<br /> 81–88p.</span></p>Manoj Sharma, Laxmi Morya, Rajshree Mishrahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1266Mon, 22 Jan 2018 03:42:03 -0700Advanced Computable Extension of New Fractional Kinetic Equation
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1265
<p class="Standard" align="center"><strong><em>Abstract</em></strong><strong><em></em></strong></p><p class="Standard"><em>The aim of this work is to find</em><em> advanced computable extension of kinetic equation with fractional calculus approach. Fractional calculus originated in 1695, shortly after the inversion of classical calculus. The pioneer researchers who studied it were Liouville, Riemann, Leibniz, etc. For a long time, fractional calculus has been regarded as a pure mathematical area without applications. But, in recent decades, such type of synergism has been changed. It has been found that fractional calculus can be useful and even a powerful tool and a précis of the simple information about fractional calculus and its applications can be found in literature. The first use of a derivative of non-integer order is credited to the French mathematician S. F. Lacroix in 1819 who expressed the derivative of non-integer order </em> <em>in terms of Legendre’s factorial symbol </em><em>G</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>new modified 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;">Sharma M, Tyagi A. Advanced Computable Extension of New Fractional Kinetic Equation. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(3): 74–80p.</span></p><p><em><br /></em></p>Manoj Sharma, A. Tyagihttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1265Mon, 22 Jan 2018 03:36:10 -0700Triple Dirichlet Average of New Generalized M-Function and Fractional Derivative
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1267
<p><strong>Abstract</strong></p><p>The aim of present work to establish some results of Triple Dirichlet average of New Generalized M-Function, using fractional derivative.</p><p><strong>Keywords and Phrases</strong>: Dirichlet average, New Generalized M-Function fractional derivative and Fractional calculus operators.</p><p class="IEEEAbtract"><strong>Mathematics Subject Classification:</strong> 26A33, 33A30, 33A25 and 83C99.</p><p> </p><p><strong><span style="font-size: medium;">Cite this Article</span></strong></p><p> </p><p>Manoj Sharma. Triple Dirichlet Average of New Generalized M-Function and Fractional Derivative. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(3): 89–93p.</p><p><span style="font-size: medium;">.</span></p>Manoj Sharmahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1267Mon, 22 Jan 2018 03:32:05 -0700Reliability Analysis of an Infinite Range Failure Model under Different Prior Distributions
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1219
<p align="center"><strong><em>Abstract</em></strong><strong><em></em></strong></p><p><em>A failure rate model has been selected for the present study and Bayesian estimates of reliability and hazard rate functions of that model have been obtained. The prior distributions considered for this study are, uniform and inverted gamma distributions. Since, the same mathematics is required for the study of survival analysis that is why the estimate of survival function has also been obtained in this paper.</em></p><p><strong><em>Keywords:</em></strong><em> Reliability function, hazard function, maximum likelihood estimate, inverted gamma distribution, survival function, conception rate function</em></p><p><strong>Cite this Article</strong><strong></strong></p><p>Dev Singh. Reliability Analysis of an Infinite Range Failure Model under Different Prior Distributions. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(3): 51–73p.<strong></strong></p><p><em><br /></em></p>Dev Singhhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1219Thu, 11 Jan 2018 03:48:02 -0700Vector of Auto-Regressive Modeling for Agricultural Crop Production
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1210
<p align="center"><strong><em>Abstract</em></strong><strong><em></em></strong></p><p><em>The present investigation was carried out to study the trends in area and production of paddy crop, grown in Tamil Nadu during the period 1950–51 to 2009–10, using the multivariate time series modeling. The multivariate time-series model, VAR (p) model of order 1 was found suitable to study the trends in area as well as production of these crops. Decreasing trends in area as well production of these crops have been observed.</em></p><p><strong><em>Keywords: </em></strong><em>Cross correlation, partial canonical correlations<strong>,</strong> vector of auto-regression,</em><em> Portmanteau test, Jarque-Bera normality test</em></p><p><strong>Cite this Article</strong></p><p>Vetriselvi R, Rajarathinam A. Vector of Auto-Regressive Modeling for Agricultural Crop Production. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(3): 42–50p.<strong></strong></p><p><em><br /></em></p>R. Vetriselvi, Rajarathinam Arunachalamhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1210Thu, 11 Jan 2018 03:36:26 -0700Cointegration and Error Correaction Modeling for BSE and NSE Stock Prices Time Series Data
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1198
<p class="Sous-auteur1" align="center"><strong><span lang="EN-GB">Abstract</span></strong></p><p class="Sous-auteur1"><span lang="FR">Econometrician always have been observed that most of the economics time series are non-stationary. The ordinary least square technique could be applied to estimate the model parameters only if the variables have been found to be stationary, i.e., they do not have unit roots. Otherwise, an alternative approach has to be followed, which is ‘co-integration’. Co-integration is a method of finding out the long-term relationship between economic variables under consideration. In the present study, it is necessary to know whether National Stock Exchange (NSE) and Bombay Stock Exchange (BSE) daily closing stock prices time séries data will have a long-term movements or relationship between them for which the co-integration analysis is being proposed. The error correction model (ECM) captures the impact of long-run equilibrium on the short run dynamics, provided that the variables are co-integrated. The ECM developed by Engle and Granger reconciles the short run behavior of an economic variable with its log run behavior. The ECM results showed that the coefficient of the error correction term ONELAGU, of about -0.020 suggests that only about 2% of the discrepancy between long-term and short-term LOGNSE is corrected, suggesting a slow rate of adjustment to equilibrium. Further, the validity of ECM showed that all three tests conducted through spurious of the model and serial correlation of residual and normality of residual are in favour of the model. Since, all tests in favour of ECM, the results of the model can be used for policy decisions.</span> </p><p class="Sous-auteur1"><strong><span lang="EN-GB">Keywords:</span></strong><span lang="EN-GB">Stationarity, co-integration, error correction model, </span><span lang="FR">breusch-godfrey test, granger representation theorem</span></p><p><strong>Cite this Article</strong><strong></strong></p><p>Rajarathinam A, Balamurugan D. Cointegration and Error Correaction Modeling for BSE and NSE Stock Prices Time Series Data. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(3): 30–41p.<strong></strong></p><p class="Sous-auteur1"><span lang="FR"><br /></span></p>Rajarathinam Arunachalam, Balamurugan D.http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1198Thu, 11 Jan 2018 03:15:15 -0700Self-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 -0700