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 journal focused towards the rapid publication of fundamental research papers on all areas of Discrete Mathematical Structures. <span>It's a triannual journal, started in 2014.</span></p><p><strong>eISSN- 2394-1979</strong></p><p><strong><strong>Journal DOI no.: 10.37591/RRDMS</strong></strong></p><p><strong>Indexed In: <span>DRJI, Google Scholar</span></strong></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 analogs of continuous mathematics</li><li>Hybrid discrete and continuous mathematics</li></ul><div><span>All contributions to the journal are rigorously refereed and are selected on the basis of quality and originality of the work. The journal publishes the most significant new research papers or any other original contribution in the form of reviews and reports on new concepts in all areas pertaining to its scope and research being done in the world, thus ensuring its scientific priority and significance.</span></div><p><a title="EDITORIAL BOARD" href="/index.php?journal=RRDMS&page=about&op=editorialTeam" target="_blank">EDITORIAL BOARD</a></p>en-USResearch & Reviews: Discrete Mathematical Structures2394-1979<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>Prevention of Spreading COVID-19 by Using a Mathematical Expression and controlling suggestion A Review
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2490
<p>COVID-19 that is a strain of coronavirus first broke out in Wuhan, China in December 2019 and has since spreading in various countries.we observed that it is very tough time for everyone.COVID-19 is an infectious disease which is caused by a newly discovered coronavirus.It affects the people through different ways.COVID-19 is very risky for older age people and for pre-existing medical condition peoples. This review paper is prepared for the prediction of COVID-19 and for preventing.Main symptoms of COVID-19 are fever, dry cough and complexity in breathing. For stopping this virus we can follow the following precautions like wash your hands frequently, make social distance, do not touch your eyes and nose, and not visit anywhere without any emergency and cover your mouth by mask. In this review paper a mathematical expression is used for the obstruction of COVID-19 and the main goal of this paper is save yourself and protect others. It is very tough time for all because we fighting an invisible enemy.</p><p>Keywords: COVID-19,Mathematical expression, Probability, coronavirus, data set.</p>Manju RaniPuja Rani2020-07-032020-07-037Is the Universe an Illusion?: A review article shedding light upon one of the mind boggling paradoxes
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2467
We use the Russell’s paradox to dive into the philosophical aspect of life that mathematically supports the philosophical statement “We are all just a thought”. Just as the wind carries the fragrance of its source, so does this article. We mention how the Zermelo-Fraenkel Set Theory came into existence and also its axioms (two of them in detail). We have also mentioned two other paradoxes, which are similar to the Russell’s Paradox. These ‘simple-statement’ paradoxes provide a clear path to understand the Russell’s paradox. Though, they are not directly derived from the ‘most-argued’ Russell’s paradox, but are mere interpretations of the same. A view of these paradoxes provides clarity over the statement of the Russell’s Paradox.Parul KhannaDr. V. Vijai2020-06-292020-06-297Natural Frequency of Plate by Using Rayleigh Ritz Method with Varying Thickness and Thermal Effect
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2391
<p>Plate systems had been intensively used in a diffusion of engineering disciplines concerning civil engineering, aerospace, construction zone, nuclear flowers, electricity flora, marine engineering. It may additionally use for production of wings and tails of the plane, rockets and missiles etc. A through expertise of their vibrational characteristics in conjunction with specific thermal conditions is of extremely good significance to engineers and architects ensuring reliability in layout procedure. In this paper, the elliptical plate fabric is believed to be homogeneous, additionally temperature and thickness in x and y guidelines. To discover the result as frequency parameter, Rayleigh Ritz method is implemented. Frequency is calculated for 2 modes exclusive set of cost of thermal gradient and taper constant.</p><p>Keywords: Vibration, visco-elastic, elliptical plate, taper constant, Rayleigh Ritz</p><p>Cite this Article Preeti Prashar, Ashish Kumar Sharma. Natural Frequency of Plate by Using Rayleigh Ritz Method with Varying Thickness and Thermal Effect. Research & Reviews: Discrete Mathematical Structures. 2020; 7(1): 28–33p.</p>Preeti PrasharAshish Kumar Sharma2020-05-042020-05-047Continuity
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2454
<p><em>Let us assume there exists a Clairaut function. K.O. Harris (2005) and Z.N. Gauss et al. (2002) address the connectedness of globally admissible equations under the additional assumption that |</em><em>ƴ</em><em>|</em><em>⊂</em><em>D. We show that</em> <em>λ</em><em> is geometric. Unfortunately, we cannot assume that |L|<</em><em>ε</em><em>. It is not yet known whether Dirichlet's conjecture is false in the context of Hippocrates, j-embedded algebras, although K.O. Harris (2005) and C. Anderson (2001) does address the issue of admissibility.</em></p><p><em>Keywords:</em><em> </em><em>Boolean, Unbounded, Limit, Lp, Separability, Housdorrf, Indivisibility, Tensor</em></p><p>Cite this Article</p><p>Olcay Akman, Z. Landau. Continuity. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2020; 7(1): 23–27p.</p>Olcay AkmanZ. Landau2020-05-042020-05-047Common Fixed-Point Theorems Satisfying Integral Type Contractive Conditions
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2455
<p>In this paper, we establish common fixed-point theorems using a contractive condition of integral type. Also, we prove common fixed-point theorems, from a smaller class of compatible continuous mappings to larger class of weakly compatible mappings without using continuity. In the present paper, we establish common fixed-point result for four mappings satisfying a more general contractive condition of integral type and using the recent concept of weak compatible maps.</p><p>Keywords: compatible mapping, weakly compatible mappings, Fuzzy metric space, fixed point</p><p>Cite this Article Sandeep Kumar, Mohd. Nafees Siddiqui. Common Fixed-Point Theorems Satisfying Integral Type Contractive Conditions. Research & Reviews: Discrete Mathematical Structures. 2020; 7(1): 16–22p.</p>Sandeep KumarMohd. Nafees Siddiqui2020-05-042020-05-047Certain Results Involving Ramanujan’s Theta Functions
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2390
<p>In this present work, our main aim is to obtain “certain results involving Ramanujan’s theta functions”. In this paper, we have evaluated Ramanujan’s theta functions by making use of certain modular equations due to Ramanujan. Using these values of theta functions, we have also evaluated Ramanujan’s cubic continued fraction and Ramanujan–Weber class invariants Gn and gn.</p><p>Keywords: Ramanujan’s theta functions, modular equations, Ramanujan–Weber class invariants, Ramanujan’s cubic continued fraction, Modular identities</p><p>Cite this Article Mohd. Nafees Siddiqui, Sandeep Kumar. Certain Results Involving Ramanujan’s Theta Functions. Research & Reviews: Discrete Mathematical Structures. 2020; 7(1): 6–15p.</p>Mohd. Nafees SiddiquiSandeep Kumar2020-05-042020-05-047A Study on the Derivations of Two-dimensional Geometry
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2452
<p>Two-dimensional geometry is the study of conic sections. The conic section includes figures like circle, hyperbola, ellipse, parabola, semi circles etc. The study of two-dimensional geometry has many formulas related to Area, perimeter. However, the derivation of the particular geometrical figures are not studied due to their complexity. This paper focuses on how to reduce the complex nature of derivations and provides them in new and easy form. In addition, this paper explores how to use trigonometrical concepts in easy form for the derivation of any particular two-dimensional figure.</p><p>Keywords: Two-dimensional geometry, trigonometrical concept, conic section, equilateral triangle, curves</p><p>Cite this Article Khushboo Malhotra, Shallu Gupta. A Study on the Derivations of Two-dimensional Geometry. Research & Reviews: Discrete Mathematical Structures. 2020; 7(1): 1–5p.</p>Khushboo MalhotraShallu Gupta2020-05-042020-05-047Dirichlet Average of Hyper-geometric Kiran Function and Fractional Derivative
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2371
<p>Abstract: In this paper, first of all define a new function namely Hyper-geometric Kiran Function which is generalization of Hyper-geometric Function then a relation between Dirichlet average of Hyper-geometric Kiran function and fractional derivative is established.</p><p>Mathematics Subject Classification: 26A33, 33A30, 33A25 and 83C99.</p><p>Keywords and Phrases: Dirichlet average, Hyper-geometric Kiran function Hyper-geometric function, fractional derivative and Fractional calculus operators</p><p>Cite this Article: Manoj Sharma, Kiran Sharma. Dirichlet Average of Hyper-geometric Kiran Function and Fractional Derivative. Research & Reviews: Discrete Mathematical Structures. 2019; 6(3): 29–31p.</p>Manoj SharmaKiran Sharma2020-01-102020-01-107Subtract Divisor Cordial Labeling of Ring Sum of a Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2351
<p>Abstract: A subtract divisor cordial labeling of a graph G with vertex set is a bijection f from V to {1, 2,…, |V|} such that an edge is assigned the label 1 if 2 divides (f(u) – f(v)) and 0 otherwise, then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a subtract divisor cordial labeling is called a subtract divisor cordial graph. In this paper, I have Proved that ring sum of cycle with star graph, cycle with one chord with star graph, cycle with twin chords with star graph and cycle with triangle with star graphs are subtract divisor cordial graph. I also proved that ring sum of wheel with star graph, flower graph with star graph, gear graph with star graph and path graph with star graph are subtract divisor cordial graphs. Further I proved that shell graph with star graph are subtract divisor cordial graphs. And in last I proved that double fan with star graphs are subtract divisor cordial graph.</p><p>AMS Subject classification number: 05C78</p><p>Keywords: Subtract divisor cordial labeling, ring sum, shell graph, double fan, gear graph</p><p>Cite this Article: A. H. Rokad. Subtract Divisor Cordial Labeling of Ring Sum of a Graphs. Research & Reviews: Discrete Mathematical Structures. 2019; 6(3): 23–28p.</p>A H Rokad2020-01-102020-01-107k-Fibonacci Polynomials in The Family of Fibonacci Numbers
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2347
<p>Abstract: In this study, we define k-Fibonacci Polynomials by using terms of a new family of Fibonacci numbers given by Mikkawy and Sogabe. We compare the polynomials with known Fibonacci polynomial. Furthermore, we show the relationship between Pascal’s triangle and the coefficient of the k-Fibonacci polynomials. We give some important properties of the polynomial.</p><p>2010 Mathematics Subject Classification: 11B39.</p><p>Keywords: Fibonacci Numbers, Fibonacci Polynomials, Pascal’s triangle, k-Fibonacci polynomials, The derivative of the k-Fibonacci polynomial</p><p>Cite this Article: Engin Özkan, Merve Taştan, k-Fibonacci Polynomials in The Family of Fibonacci Numbers. Research & Reviews: Discrete Mathematical Structures. 2019; 6(3): 19–22p.</p>Engin ÖzkanMerve Taştan2020-01-102020-01-107Generalized Yang-Fourier Transforms by using K-Function to Heat Conduction in a Semi-infinite Fractal Bar
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2361
<p>The main objective of present research paper to solve one-dimensional fractal heat-conduction differential equation problem in a fractal semi-infinite bar has been developed by local fractional calculus employing the analytical Generalized Yang-Fourier transforms method.</p><p><strong>Keywords</strong>: Fractal bar, heat-conduction equation, Generalized Yang-Fourier transforms, Yang-Fourier transforms, local fractional calculus, K-Function</p><p><strong>Cite this Article</strong></p><p>Manoj Sharma, Kiran Sharma. Generalized Yang-Fourier Transforms by using K-Function to Heat Conduction in a Semi-Infinite Fractal Bar. Research<em> & Reviews: Discrete Mathematical Structures</em>. 2019; 6(3): 13–18p.<strong></strong></p>Manoj SharmaKiran Sharma2020-01-092020-01-097Coxeter Dihedral Symmetric Tetrahedrons with Triangle Groups: Euclidean, Spherical and Hyperbolic
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2127
<p>Abstract: In this article, we have classified the Coxeter Dihedral Symmetric (CDS) tetrahedrons with triangle groups: Euclidean, Spherical and Hyperbolic. We have calculated the gram spectrums of these CDS tetrahedrons with triangle groups: Euclidean, spherical and hyperbolic, and finally studied their existence in the spaces: Euclidean, spherical and hyperbolic.</p><p>MSC 2010 Codes: 51M05, 05C50, 15A45, 15A42, 05C69.</p><p>Keywords: Coxeter Dihedral Symmetric Tetrahedrons, Triangle groups, gram matrix, spectrum, Euclidean, eigen values</p><p>Cite this Article: Pranab Kalita. Coxeter Dihedral Symmetric Tetrahedrons with Triangle Groups: Euclidean, Spherical and Hyperbolic. Research & Reviews Discrete Mathematical Structures. 2019; 6(3): 1–12p.</p>Pranab Kalita2020-01-092020-01-097Zagreb Degree Eccentricity Indices of Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2019
<p align="center"><strong><em>Abstract</em></strong></p><p><em>Let G be a connected graph, the first Zagreb index M<sub>1</sub>(G) of G is defined as </em><em></em><em>The second Zagreb index M<sub>2</sub>(G) of G is defined as In this paper we introduce first and second Zagreb degree eccentricity indices. Further, the first Zagreb degree eccentricity index of join, Cartesian product, tensor product, corona product of two graphs are computed.</em></p><p><em> </em></p><p><strong><em>Keywords</em></strong><em>: Zagreb indices, Eccentricity, Degree, Zagreb degree eccentricity indices.</em></p><p> </p><p><strong>Cite this Article</strong></p><p>Padmapriya P., Veena Mathad. Zagreb Degree Eccentricity Indices of Graphs. <em>Research & Reviews Discrete Mathematical Structures<strong>.</strong></em><strong> </strong><strong>2019; 6(2): 59–69p.</strong><strong></strong></p>Padmapriya P.Veena Mathad2019-08-192019-08-197Primitive Idempotents and Weight Distributions of Irreducible Cyclic Codes of Length 5l^m
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2125
<p align="center"><strong><em>Abstract</em></strong></p><p><em>Let </em> <em>be a finite field with q elements such that</em> <em>and </em><em>gcd </em> <em> = </em><em>1</em><em>, where</em> <em> is a prime. In this paper, we give all primitive idempotents in a ring</em> <em>[x]</em> <em>. </em><em>We give the weight distributions of all irreducible cyclic codes of length </em> <em>over</em> <em>.</em></p><p><em> </em></p><p class="Style"><strong><em>Keywords: </em></strong><em>Primitive Idempotents, Cyclotomic Cosets, Cyclic Codes.</em></p><p class="Style"> </p><p><strong>Cite this Article</strong></p><p>Sunil Kumar, Manju Pruthi, Rahul. Primitive Idempotents and Weight Distributions of Irreducible Cyclic Codes of Length . <em>Research & Reviews Discrete Mathematical Structures<strong>.</strong></em><strong> 2019; 6(2): 49–58p.</strong><strong></strong></p>Sunil KumarManju PruthiRahul .2019-08-192019-08-197On b-Coloring Parameters of Some Classes of Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2042
<p align="center"><strong><em>Abstract</em></strong></p><p><em>Vertex coloring has always been a topic of interest. Motivated by the studies on </em><em>-chromatic mean and variance of some standard graphs, in this paper, we obtain few results for </em><em>-chromatic and </em><em>-chromatic mean and variance of some cycle related graph classes. Here, Vertex coloring of a graph </em><em> is taken to be the random experiment. Discrete random variable </em><em> for this random experiment is the color of randomly chosen vertex of </em><em>. </em></p><p><strong><em>Mathematics Subject Classification</em></strong><em>: 05C15, 05C75. </em></p><p> </p><p><strong><em>Keywords</em></strong><em>: </em><em>-coloring, coloring mean, coloring variance, </em><em>-chromatic mean, </em><em>-chromatic variance.</em></p><p><strong>Cite this Article</strong></p><p>M R Raksha, P Hithavarshini, N K Sudev, C. Dominic. On -Coloring Parameters of Some Classes of Graphs. <em>Research & Reviews Discrete Mathematical Structures</em><strong><em>.</em></strong><strong> 2019; 6(2): 41–48p.</strong><strong></strong></p>M R RakshaP HithavarshiniN K SudevC. Dominic2019-08-192019-08-197Injective Coloring Parameters of Some Special Classes of Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2263
<p align="center"><strong><em>Abstract</em></strong></p><p><em>The vertex coloring of a graph can be viewed as a random experiment and with respect to this experiment, a random variable </em><em> can be defined such that </em><em> denotes the color of an arbitrarily chosen vertex. In this paper, we broaden the ideas of coloring mean and variance of graphs with respect to a particular type of proper injective coloring and determine these parameters for some standard graph classes.</em></p><p><strong><em>MSC2010:</em></strong><em> 05C15, 05C38. </em></p><p><em> </em></p><p><strong><em>Keywords</em></strong><em>: Coloring mean; coloring variance; </em><em>-chromatic mean; </em><em>-chromatic variance; </em><em>-chromatic mean; </em><em>-chromatic variance. </em></p><p> </p><p><strong>Cite this Article</strong></p><p>V. Santhosh Priya, N.K. Sudev<em>.</em> Injective Coloring Parameters of Some Special Classes of Graphs.<em> Discrete Mathematical Structures</em><strong><em>.</em></strong><strong> 2019; 6(2): 30–40p.</strong><strong></strong></p>V. Santhosh PriyaN. K. Sudev2019-08-192019-08-197Contra Harmonic Mean Labeling for Some Tree and Corona Related Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2128
<p align="center"><strong><em>Abstract</em></strong></p><p><em>A graph G (V,E) is called a Contra Harmonic mean graph with p vertices and q edges, if it is possible to label the vertices x</em><em>Î</em><em>V with distinct element f(x) from 0, 1,…,q in such a way that when each edge e = uv is labeled with f(e=uv) = </em><em> <!--?mso-application progid="Word.Document"?--> 16f(u)2+f(v)2f(u)+f(v)"> </em><em> or </em><em> <!--?mso-application progid="Word.Document"?--> 16f(u)2+f(v)2f(u)+f(v)"> </em><em> with distinct edge labels. The mapping f is called </em><em>Contra Harmonic </em><em>mean labeling of G.</em></p><p><em> </em></p><p><strong><em>Keywords: </em></strong><em>Graph, </em><em>Contra Harmonic mean graph, </em><em>Triangular snake, Quadrilateral snake, Step Ladder, Flower graph.</em></p><p><strong>Cite this Article</strong></p><p>J. Rajeshni Golda, S. S. Sandhya. Contra Harmonic Mean Labeling for Some Tree and Corona Related Graphs. <em>Research & Reviews Discrete Mathematical Structures</em><strong><em>.</em></strong><strong> 2019; 6(2): 24–29p.</strong><strong></strong></p>J. Rajeshni GoldaS. S. Sandhya2019-08-192019-08-197Common Fixed-Point Results for Weakly Increasing Dominating Maps on Vector b-Metric Spaces
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2124
<p align="center"><strong><em>Abstract</em></strong></p><p><em>In this paper, we consider E-b-metric space, which is a generalized vector metric space. This is a Riesz space valued metric space. Here, we prove some results concerning common fixed point for four mappings on E-b-metric space. This generalizes the results of Rahimi, Abbas and Rad [16].</em></p><p><strong><em> </em></strong></p><p><strong><em>Keywords: </em></strong><em>Dominating map, E-b-metric space, Weak annihilators, Weakly compatible, Weakly increasing</em></p><p><strong> </strong></p><p><strong>Cite this Article</strong></p><p>Mamta Kamra, Kumari Sarita, Renu Chugh. Common Fixed-Point Results for Weakly Increasing Dominating Maps on Vector b-Metric Spaces. <em>Research & Reviews Discrete Mathematical Structures<strong>.</strong></em><strong> 2019; 6(2): 7–23p.</strong><strong></strong></p>Mamta KamraKumari SaritaRenu Chugh2019-08-192019-08-197Codes Over Frobenius Groups
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2132
<p align="center"><strong><em>Abstract</em></strong></p><p><em>In this paper we consider the group algebra FG where G is Frobenius group </em> <em> </em><em>of order </em> <em>, where </em> <em> and char(F) does not divide order of G. We find the generating idempotents in the group algebra of Frobenius group by using character theory. We also find the minimum distance and dimension of the codes generated by these idempotents.</em></p><p class="MTDisplayEquation"><em>2010 Mathematics Subject Classification: 20G05, 20E45, 94B60</em></p><p><strong><em>Keywords: </em></strong><em>Group algebra, linear and non-linear characters,<strong> </strong>idempotents, Frobenius group.</em></p><p><em><strong>Cite this Article</strong></em></p><p><em>Sudesh Sehrawat, Manju Pruthi. Codes over Frobenius Groups. Research & Reviews Discrete Mathematical Structures<strong>.</strong> 2019; 6(2): 1–6p.</em><strong></strong></p><p><em><br /></em></p>Sudesh SehrawatManju Pruthi2019-08-192019-08-197Fractional q-Derivative and N2 Function
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2037
<p align="center"><strong><em>Abstract</em></strong><em></em></p><p><em>The study of fractional q-calculus in this paper serves as a bridge between the fractional q-calculus in the literature and the fractional q-calculus of Special Functions. This paper is devoted to fractional q-derivative of special functions. Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, physics, or other applications in engineering .To begin with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav and Purohit and Sharma, Jain and Ali. As a special case, of fractional q-differentiation of N<sub>2</sub> Function has been obtained.</em></p><p><strong><em>Keywords: </em></strong><em>Fractional integral and derivative operators, Fractional q-derivative, N2 Function and Special functions</em></p><p><em><strong>Mathematics Subject Classification:</strong> </em><em>Primary 33A30, Secondary 33A25, 83C99</em></p><p><em><strong>Cite this Article</strong></em></p><p>Manoj Sharma, Mohd. Farman Ali. Fractional q-Derivative and N2 Function. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2019; 6(1): 41–43p.</p><p><em><br /></em></p>Manoj SharmaMohd. Farman Ali2019-06-232019-06-237Fractional q-Derivative and Generalized N2 Function
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2036
<p align="center"><strong><em>Abstract</em></strong><em></em></p><p><em>This paper is devoted to fractional q-derivative of special functions. To begin with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav and Purohit and Sharma, Jain and Ali. As a special case, of fractional q-differentiation of N<sub>2</sub> Function has been obtained.</em></p><p><strong><em>Keywords: </em></strong><em>Fractional integral and derivative operators, Fractional q-derivative, N2 Function and Special functions</em></p><p><em><strong>Mathematics Subject Classification:</strong> </em><em>Primary 33A30, Secondary 33A25, 83C99</em></p><p><em><strong>Cite this Article</strong></em></p><p>Manoj Sharma, Mohd. Farman Ali. Fractional Q-Derivative and Generalized N2 Function. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2019; 6(1): 38–40p.</p><p><em><br /></em></p>Manoj SharmaMohd. Farman Ali2019-06-232019-06-237FRACTIONAL q-DERIVATIVE AND GENERALIZED K-FUNCTION
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2043
<p align="center"><strong><em>Abstract</em></strong><em></em></p><p><em>This investigation is basically intended to fractional q-derivative of special functions. In this article we drive the results on term by term q-fractional differentiation of a generalized k-Series. As particular case we will obtain the fractional q-differentiation of the power series and exponential series. To start with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav and Purohit (2004) and Sharma, Jain and Ali (2009). As a special case, of fractional q-differentiation of generalized K-series has been obtained.</em></p><p><strong><em> </em></strong><em><strong>Mathematics Subject Classification—</strong></em><em>Primary 33A30, Secondary 33A25, 83C99</em></p><p><em> </em><strong><em>Keywords: </em></strong><em>Fractional integral and derivative operators, fractional q-derivative, generalized K-series and special functions</em></p><p><strong>Cite this Article</strong></p><p>Manoj Sharma, Laxmimorya, Rajshree Mishra. Fractional q-Derivative and Generalized K-Function. <em>Research & Reviews: Discrete Mathematical Structures.</em> 2019; 6(1): 6–9p.<strong></strong></p><p><em><br /></em></p>Manoj SharmaLaxmimorya .Rajshree Mishra2019-05-172019-05-177On Generalized fractional Integral Operators
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1997
<h4><em>Abstract</em></h4><p><em>In this paper, different integral operators for functions of two variables namely fractional</em><em> integral operator and generalized fractional integral operator</em><em> have been defined</em><em>. Also defined the different spaces for functions of two variables and</em><em> studied defined the operators on these spaces. Finally, proved the</em><em> generalized fractional integral operators for function of two variables that are </em><em>bounded from a generalized Morrey space of functions of two variables to another.</em></p><p><strong>Keywords</strong>: fractional integral operator, function space, generalized fractional integral operator, Morrey spaces.</p><p><strong>Cite this Article</strong></p><p>T.G. Thange. On Generalized Fractional Integral Operators. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2019; 6(1): 10–14p.<strong></strong></p>T. G. Thange2019-05-162019-05-167Resolving Travelling Salesman Problem Using Modified Clustering Technique
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1996
<p align="center"><strong><em>Abstract</em></strong></p><p><em>Travelling Salesman Problem (TSP) is a quotidian stumbling block in the field of Computer Science and operation research designed to seek out the shortest pathway amid the given targets viz. cities where each target is considered only once. Many solutions to this setback like Ant Colony Optimization. Brute-Force approach, Genetic Algorithm, Fruit Fly Optimization etc. are available in literature. The main objective of these solutions is to minimize the time complexity and to search an optimized path that covers the entire region; however the urge of finding shortest path in minimum time still persists. This research work is an attempt to solve the above problem using clustering technique. Generally, for N cities the number of permutations conventionally considered are (N-1); for the proposed research work the permutations contemplated are reduced by the factor m. The results exhibit that the proposed method can effectively improve time complexity and search ability for achieving higher accuracy and optimal results. TSP discerns its application in X-Ray crystallography, the order-picking problem in warehouses, drilling of Printed Circuit Boards (PCB), mission planning problem etc. so an exigency for an optimum solution is requisite.</em></p><p><strong><em>Keywords: </em></strong><em>Brute-Force, lexicographic ordering, non-deterministic polynomial (NP) hard problem</em></p><p><strong>Cite this Article</strong></p><p>Hardik Dhingra, Gagan Deep Dhand, Rashmi Chawla, Shailende Gupta, Samarth Mittal. Resolving Travelling Salesman Problem Using Modified Clustering Technique. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2019; 6(1):<br /> 22–31p.<strong></strong></p><p><em><br /></em></p>Hardik DhingraGagan Deep DhandRashmi ChawlaShailender GuptaSamarth Mittal2019-05-162019-05-167n-Dimensional Eigenfunction Wavelet Transform
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1995
<h4><em>Abstract</em></h4><p><em>In this paper, Eigenfunction transform defined for single variable is extended for functions of n variables. Translation, convolution and dilation associated with n dimensional Eigenfunction transform are defined. Also, we define Eigenfunction wavelet for n variables. Eigenfunction wavelet transform (EWT) for n variables is introduced. Inversion formula for n dimensional EWT is also derived. </em></p><p><strong>Keywords:</strong> Eigenfunction transform Eigenfunction wavelet transform, translation, convolution, dilation</p><p><strong>Cite this Article</strong></p><p>T.G. Thange, R.D. Swami, A.M.Alure. n-Dimensional Eigenfunction Wavelet Transform. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2019; 6(1):<br /> 32–37p.</p>T. G. ThangeR. D. SwamiA. M. Alure2019-05-162019-05-167