Research & Reviews: Discrete Mathematical Structures
https://computers.stmjournals.com/index.php?journal=RRDMS
<p align="center"><strong>Research & Reviews: Discrete Mathematical Structures (RRDMS)</strong></p><p align="center"><strong> </strong></p><p align="center"><strong>ISSN: 2394-1979</strong></p><p align="center"><strong> </strong></p><p align="center"><strong><em><span style="text-decoration: underline;">Editor-in-Chief</span></em></strong></p><p align="center"><strong>Dr. Engin Ozkan</strong></p><p align="center">Professor, <span>Professor, Department of Mathematics, </span></p><p align="center"><span>Erzincan University, Erzincan, Turkey</span></p><p align="center"><strong>E-mail: </strong>eozkan@erzincan.edu.tr</p><p align="center"> </p><p align="center"> </p><p align="center">Click <strong><a href="/index.php?journal=RRDMS&page=about&op=editorialTeam">here</a> </strong>for complete Editorial Board</p><p align="center"> </p><p align="center"><strong> </strong></p><p align="center"><strong><br /></strong></p><p align="center"><strong>Scientific Journal Impact Factor (SJIF):</strong> 6.141</p><p> </p><p><strong> </strong></p><p><strong>Research & Reviews: Discrete Mathematical Structures (RRDMS) </strong>is a journal focused towards the rapid publication of fundamental research papers on all areas of Discrete Mathematical Structures. It's a triannual journal, started in 2014.</p><p> </p><p align="center"> </p><p><strong> </strong></p><p><strong>Journal DOI no</strong>.: 10.37591/ RRDMS</p><p><strong> </strong></p><p><strong>Focus and Scope Cover</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<strong></strong></li></ul><p><strong> </strong></p><p><strong> </strong></p><p><strong><br /></strong></p><p><strong>Readership:</strong> Graduate, Postgraduate, Research Scholar, Faculties, Institutions, and in IT Companies.</p><p><strong> </strong></p><p><strong> </strong></p><p><strong><br /></strong></p><p><strong>Indexing: </strong>The Journal is index in DRJI, Google Scholar</p><p> </p><p> </p><p> </p><p><strong> </strong></p><p><strong>Submission of Paper: </strong></p><p><strong> </strong></p><p>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.</p><p> </p><p>Manuscripts are invited from academicians, students, research scholars and faculties for publication consideration.</p><p> </p><p>Papers are accepted for editorial consideration through email info@stmjournals.com or <span>deeksha.sharma</span>@celnet.in</p><p><strong> </strong></p><p><br /> <strong></strong></p><p><strong>Abbreviation: </strong><strong>RRDMS</strong><em></em></p><p><em><br /> <br /> </em><strong></strong></p><p><strong> </strong></p><p><strong>Frequency</strong>: Three issues per year</p><p> </p><p><strong> </strong></p><p><strong><a href="/index.php?journal=RRDMS&page=about&op=editorialPolicies#peerReviewProcess">Peer Reviewed Policy</a></strong></p><p> </p><p><strong><span style="text-decoration: underline;"><a href="/index.php?journal=RRDMS&page=about&op=editorialTeam">Editorial Board</a></span></strong><strong></strong></p><p> </p><p><strong><a href="http://stmjournals.com/pdf/Author-Guidelines-stmjournals.pdf">Instructions to Authors</a></strong></p><p> </p><p><strong>Publisher:</strong> STM Journals A division of: Consortium eLearning Network Private Ltd</p><p><strong>Address:</strong> A-118, 1<sup>st</sup> Floor, Sector-63, Noida, Uttar Pradesh-201301, India</p><p><strong>Phone no.:</strong> 0120-4746-214 Email: nikita@stmjournals.com</p><p> </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>Binary Shape Segmentation and Classification using Coordination Number (CN)*
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2711
<p><em>We proposed a novel, micro-structures, shape-preserving local descriptor for contour-segmentation- based binary object classification and recognition, named local coordination number count (LCNC). In this method, we formulate the problem by estimating the 8-neighbourof each binary object pixel. In the matching stage, we used Euclidean distance between eigenvalues corresponding to correlation coefficient and the dynamic programming to find out the optimal correspondence between boundary smoothness of two shapes. Experimental results obtained from shape data bases demonstrate that the proposed LCNC can achieve better classification rates compared to existing shape descriptors.It produces detailed data on the distributed coordination numbers that relate to various types of contacts between small, medium, and large components. The emphasis of the study is on the mean coordination numbers associated with these contacts. These partial mean coordination numbers differ with the volume fractions of the components, according to the findings, while the overall mean coordination numbers vary with the volume fractions of the components while the overall mean coordination number is essentially a constant and independent of particle size distribution.</em></p>Ratnesh KumarKalyani Mali2021-06-122021-06-128Few Properties of REPRESENTED BY A DIRICHLET SERIES
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2713
<p><em>In this paper, we have discussed some properties of the mean values of an entire function represented by Dirichletseries in the usual notation. It is obvious that generally </em> <em>and </em> <em>, there are entire Dirichlet series for which </em> <em>and </em> <em>. Hence, we have generally to distinguish between the limits as well as types of </em> <em>belonging to the same order </em> <em>.In this paper, we obtain some result of </em> <em> for the mean value of an entire Dirichlet series. </em></p><p> </p>Praneeta Verma2021-06-122021-06-128Comparative Analysis of Distance Metrics using Face Recognition
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2712
<p><em>Researchers are using various distance metric standards in evaluation of face recognition methods. In past decades, the Eigenfaces and Fisherfaces face recognition methods were generally evaluated using the Euclidean distance (ED) metric that have shown better performance in cooperative environments, but poorly performed in non-cooperative environments. This paper presents a comparative analysis of distance metrics through face recognition methods i.e., Eigenfaces and Fisherfaces in both cooperative environments and non-cooperative environments. The recognition accuracies of these methods is critically evaluated using ED and Bray Curtis Dissimilarity (BCD) metrics in the face recognition under different conditions on publicly available face databases such as ORL and extended Yale B (EYB). The experimental results show significant improvement in recognition accuracies of Eigenfaces and Fisherfaces methods under BCD.</em></p>Radhey Shyam2021-06-122021-06-128Review on Fractional Order Sliding Mode Control of Nonlinear System
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2708
<p><em>This paper presents review fractional order sliding mode control of nonlinear system.Sliding mode control (SMC) may be a variable structure control (VSC). It is a nonlinear manipulates approach that approaches in supplied,an impact action andrestricts plant to manage to feature in accordance to some pre-defined ordinary dynamic. This desired dynamic is mentioned as sliding surface. When plant follows sliding surface, it is in sliding mode.Fractional sliding mode control (FSMC) is that use of SMC with fractional plants, or the utilization of sliding mode manages with a sliding surface like a fractional order dynamic, or both. Here, “fractional” refers to the inclusion of fractional derivatives within the equation leading the dynamic (that correspond to fractional powers of s when a Laplace seriously change is applied, or fractional powers of jω when a Fourier seriously change is applied). Forcing a plant to behave consistent with some pre-defined easy fractional dynamic may additionally be perfect once you consider that such a dynamical behavior has sizeable robustness properties.</em></p>Priyanka SinghL. B. Prasad2021-06-122021-06-128Simulation of Image Processing and Restoration Through A Base Image Using Matlab
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2690
<p><em>Basically, in image processing the main work is done on pixels and its value. Basically, an image is a two-dimensional function f(x, y), where x and y are spatial coordinates. Here, in the present study geometrical transformation is being used for image restoration and processing. Steps are carried some for the result outcome. First the image is read in the algorithm, further the coordinates and pixels are being specified, and then it is geometrically transformed at a 31 degree. Further the inliers and outliers are being matched and a restored image is obtained. The mean square error (MSE) and Peak square noise ratio (PSNR) will also be studied. The study is based on Matlab algorithm m-file. The imaging systems have wide use among number of applications, including commercial photography, microscopy, aerial photography, astronomical and space imaging, etc. Many a times the output images or a video suffers from blur due to lenses, transmission medium, algorithms or a camera/person motion. The amount of blur can be measured and it’s an important issue. Image processing and restoration is a technique to enhance the quality of an image or a video, using some methods and processes.</em></p>Deepshikha SahuAnkita Sharma2021-06-092021-06-098Research Frame work of Missing Data Analysis using Mathematical Models
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2617
<p align="center"><strong><em>Abstract</em></strong><em></em></p><p><em>This article deals with providing an overall framework of missing data analysis using mathematical models. Mathematical models serves at large for missing data imputation. Several algorithms in machine learning techniques like Mean, Median, Standard Deviation, Regression and Naïve Bayesian classifier use Mathematical models for analysis. The performance of above mathematical models has been compared by using correlation statistics analysis gives the imputed values are positively related or negatively related or not related with each other. To evaluate the performance of missing values can be measured by using nonparametric approach to inference on multivariate categorical data, which set the bounds to the data imputation. Based upon the performance of nonparametric approach to inference on multivariate categorical data, the imputed missing values are increasing or decreasing or a bounded monotonic sequence of finite limit and also analyzing that every bounded sequence of missing values has a convergent subsequence. Recognizing the above as a specific Poisson process probability gives an easy and exact way of constructing a practical decision indicator. This comes at the cost of requiring the appropriate boundedness conditions. To evaluate the performance, the standard machine learning repository dataset can be used. This article focuses primarily on how to implement Mathematical models to perform imputation of missing values.</em></p><p><strong><em> </em></strong></p><p><strong><em>Keywords:</em></strong><em> Imputation, Knowledge Transfer, missing data, Mathematical Models, Boundedness conditions, data patterns, multivariate data, multiple imputation.</em></p>A. Finny BelwinA. Linda Sherin2021-01-182021-01-188Downhill Zagreb Polynomials of Graphs
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2586
<p align="center"><strong><em>Abstract</em></strong></p><p><em>In a number of applied and theoretical environments, graph polynomials and their roots have emerged. To deeply explore counting sequences connected to different graph parameters, graph polynomials have been introduced as generating polynomials. In addition, there has been a great deal of recent interest in graph polynomials. The first, second and forgotten downhill Zagreb indices are defined as </em><em>and </em><em>.</em><em> In this paper, we define and study the first, second and forgotten downhill Zagreb polynomials, we compute the exact values of some standard families of graphs. Finally, the first, second and forgotten Zagreb polynomials for firefly graph, Graphene and honeycomb network are obtained with 3D graphical representation.</em></p><p><em> </em></p><p><strong><em>AMS Subject Classification:</em></strong><em> 2010: 05C07, 05C30, 05C76.</em></p><p><strong><em>Keywords:</em></strong><em> Zagreb downhill polynomial, Downhill Zagreb indices.</em></p>Bashair Al- AhmadiAnwar SalehWafa Al- Shammakh2021-01-182021-01-188New Number Sequences Obtained with Grouping of Fibonacci Numbers
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2594
<p align="center"><strong><em>Abstract</em></strong><em></em></p><p><em>The relations of the sum and difference of two Fibonacci numbers, in which the difference of subscripts is even, was given by Koshy. In this study, the relations of the sum and difference of two Fibonacci numbers, in which is the difference of subscripts is odd, is introduced by using the generating functions. Similar results are given for Lucas numbers. Also, two new family of Fibonacci numbers are obtained.</em></p><p><strong><em> </em></strong></p><p><strong><em>Keywords:</em></strong><em> Binet Formula, Fibonacci sequence, the generalized Fibonacci sequence, Generating functions, Lucas sequence.</em></p>İnan DurukanEngin Özkan2021-01-162021-01-168An Atlas of Vertex Degree Polynomials of Graphs of Order at Most Six
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2580
<p align="center"><strong><em>Abstract</em></strong></p><p><em>The vertex degree polynomial of a graph G of order n is defined as V D(G, x) = </em><em> </em><em>å</em><em><sub>uv</sub></em><em><sub>∈</sub></em><em><sub>E(G)</sub></em><em> d(u)x<sup>d(v)</sup> where d(u) is the degree of the vertex u [5]. We call the roots of a vertex degree polynomial of a graph the vertex degree roots of that graph. In this article, we compute the vertex degree polynomial of all graphs of order less than or equal six and their roots and present them in tables.</em></p><p><strong><em> </em></strong></p><p><strong><em>Keywords: </em></strong><em>Adjacent vertex, Vertex degree polynomial, Vertex degree root. Mathematics Subject Classification:</em></p>Hanan AhmedAnwar AlwardiRuby Salestina M.2021-01-162021-01-168New Recurrence Relations for Tribonacci Sequence and Generalized Tribonacci Sequence
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2616
<p align="center"><strong><em>Abstract</em></strong><em></em></p><p><em>Tribonacci numbers are placed on the corners of polygons clockwise with each corner receiving a term. Then, it is argued whether there is a relationship among the numbers in the same corners. It is shown to be able to find m<sup>th </sup>term corresponding to the corner A<sub>k </sub>in an n-gon by a relation:</em></p><p><em>where, </em> <em> is a Tribonaccisequence and </em> <em> is a Tribonacci- Lucas sequence. The relation is proved by using a binet formula obtained for </em> <em>. It is also argued whether the relation corrects all Generalized Tribonacci sequences by changing the beginning terms. Moreover, it is shown that m<sup>th</sup> term corresponding to the corner A<sub>k</sub> in an n-gon can be found by using the following relation:</em></p><p align="center"><strong><em> </em></strong></p><p><strong><em>Keywords: </em></strong><em>Binet formula, Fibonacci Sequences,<strong> </strong>n-gon, Tribonacci Numbers, Tribonacci-Lucas Numbers </em></p>Engin ÖZKANSongül ÇELİKİnan DURUKAN2021-01-162021-01-168Abstract Fuzzy Function
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2579
<p>The grading of the set is studied by L. A. Zadeh in 1965. The set is defined by the membership function. Fuzzy set and fuzzy logic are the two domain defined as the discrete mathematical structure. Its discreteness is associated with the fundamental axioms of the classical set theory and its operation. This paper defines the fuzzy function and its applications.</p><p>Keywords: Fuzzy Set, Fuzzy Logic, Fuzzy Function, Set Theory, Membership Function.</p><p>Cite this Article: Amita Telang, Sunil Kumar Kashyap. Abstract Fuzzy Function. Research & Reviews: Discrete Mathematical Structures. 2020; 7(2): 10–13p.</p>Amita TelangSunil Kumar Kashyap2020-08-212020-08-218An Application of Fractional Calculus in L-R and C-R Circuit
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2536
<p>In this paper, we proposed a Fractional differential equation for the electrical L-R and C-R Circuit and obtained the solution in the form of Mittag-Leffler function.</p><p>Keywords: Circuit analysis, L-R and C-R circuit, Fractional differential equation, Riemann-Liouville Fractional derivative, Laplace transform, Inverse Laplace transform.</p><p>Mathematical Subject Classification: -26A33, 33E12, 44A10</p><p>Cite this Article: Laxmi Morya, Manoj Sharma, Rajshree Mishra. An Application of Fractional Calculus in L-R andC-R Circuit. Research & Reviews: Discrete Mathematical Structures. 2020; 7(2): 14–17p.</p>Laxmi MoryaManoj SharmaRajshree Mishra2020-08-212020-08-218An Ecology Equation
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2534
<p>The conservation of ecology is reviewed by an equation. Ecology is studied in this paper via mathematics. This paper presents an equation of ecology. The objective of this paper is to solve the problems of nature by the mathematical concept. The mathematical transformation of natural phenomenon for analyzing the hidden rules of the nature is the key objective of this paper. The theory of sets, function and its application based results are presented in this paper.</p><p>Keywords: Nature, Conservation, Equation, Ecology, Function, Set, Transformation.</p><p>Cite this Article: Sunil Kumar Kashyap. An Ecology Equation. Research & Reviews: Discrete Mathematical Structures. 2020; 7(2): 18–20p.</p>Sunil Kumar Kashyap2020-08-212020-08-218PKC based on DLP
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2535
<p>We propose a new representation of Discrete Logarithm Problem (DLP) as and use this to design a Public Key Cryptosystem (PKC). The problem to find the index of the primitive element of the cyclic group is referred as the DLP. This paper sets the discrete structure of the finite field for introducing the securer PKC than the existed.</p><p>Key Words: DLP, PKC, Cyclic Group, Primitive Element, Finite Field.</p><p>Cite this Article: Sunil Kumar Kashyap, Birendra Kumar Sharma, Amitabh Banerjee. PKC based on DLP: Research & Reviews: Discrete Mathematical Structures. 2020; 7(2): 28–30p.</p>Sunil Kumar KashyapBirendra Kumar SharmaAmitabh Banerjee2020-08-212020-08-218On Searching the New Chemical Element by Prime Numbers
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2533
<p>This paper presents a direction for searching the new chemical element by prime number. Every chemical element is defined by atomic number and weight. These comprised with the set of natural numbers. The prime number is the subset of natural number. We define the new mapping for chemical element and prime number in this paper. Beryllium is taken as an example to prove the proposed theory.</p><p>Keywords: Chemical Element, Prime Number, Natural Number, Atomic Number, Atomic Weight, Beryllium.</p><p>Cite this Article: Sunil Kumar Kashyap, Vikas Kumar Jain. On Searching the New Chemical Element by Prime Numbers. Research & Reviews: Discrete Mathematical Structures. 2020; 7(2):21–23p.</p>Sunil Kumar KashyapVikas Kumar Jain2020-07-312020-07-318Prevention of Spreading COVID-19 by Using a Mathematical Expression and controlling suggestion A Review
https://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><p>Cite this Article: Manju Rani, Puja Rani. Prevention of Spreading COVID-19 by Using a Mathematical Expression and Controlling Suggestion A Review. Research& Reviews: Discrete Mathematical Structures. 2020; 7(2): 6–9p.</p>Manju RaniPuja Rani2020-07-032020-07-038Is the Universe an Illusion?: A review article shedding light upon one of the mind boggling paradoxes
https://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2467
<p>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.</p><p>Keywords: Paradox, Zermelo-Fraenkel Set Theory, Axiom of Extension, Axiom of Specification, Principle of Bivalence.</p><p>Cite this Article: Parul Khanna, V. Vijai. Is the Universe an Illusion?: A Review Article Shedding light Upon one of the Mind Boggling Paradoxes. Research & Reviews: Discrete Mathematical Structures. 2020; 7(2): 1–5p.</p>Parul KhannaDr. V. Vijai2020-06-292020-06-298Natural Frequency of Plate by Using Rayleigh Ritz Method with Varying Thickness and Thermal Effect
https://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 Sharma2020-05-042020-05-048Continuity
https://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. Landau2020-05-042020-05-048Common Fixed-Point Theorems Satisfying Integral Type Contractive Conditions
https://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 Siddiqui2020-05-042020-05-048Certain Results Involving Ramanujan’s Theta Functions
https://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 Kumar2020-05-042020-05-048A Study on the Derivations of Two-dimensional Geometry
https://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 Gupta2020-05-042020-05-048Dirichlet Average of Hyper-geometric Kiran Function and Fractional Derivative
https://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 Sharma2020-01-102020-01-108Subtract Divisor Cordial Labeling of Ring Sum of a Graphs
https://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 Rokad2020-01-102020-01-108k-Fibonacci Polynomials in The Family of Fibonacci Numbers
https://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 Taştan2020-01-102020-01-108