Research & Reviews: Discrete Mathematical Structures
Research & Reviews: Discrete Mathematical Structures (RRDMS) ISSN: 2394-1979 Editor-in-Chief Dr. Engin Ozkan Professor, Professor, Department of Mathematics, Erzincan University, Erzincan, Turkey E-mail: eozkan@erzincan.edu.tr Click here for complete Editorial Board Scientific Journal Impact Factor (SJIF): 6.141 Research & Reviews: Discrete Mathematical Structures (RRDMS) 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. Journal DOI no.: 10.37591/ RRDMS Focus and Scope Cover Mathematical induction logic and Boolean algebra set theory relations and functions sequences and series algorithms and theory of computation number theory matrix theory induction and recursion counting and discrete probability graph theory (trees) Calculus of finite differences, discrete calculus or discrete analysis Game theory, decision theory, utility theory, social choice theory Discrete analogs of continuous mathematics Hybrid discrete and continuous mathematics Readership: Graduate, Postgraduate, Research Scholar, Faculties, Institutions, and in IT Companies. Indexing: The Journal is index in DRJI, Google Scholar Submission of Paper: 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. Manuscripts are invited from academicians, students, research scholars and faculties for publication consideration. Papers are accepted for editorial consideration through email info@stmjournals.com or nikita@stmjournals.com Abbreviation: RRDMS Frequency: Three issues per year Peer Reviewed Policy Editorial Board Instructions to Authors Publisher: STM Journals A division of: Consortium eLearning Network Private Ltd Address: A-118, 1st Floor, Sector-63, Noida, Uttar Pradesh-201301, India Phone no.: 0120-4746-214 Email: nikita@stmjournals.com
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A New Approach to Find Non-simple Zero’s of Functions
Finding acceptable approximation of zeros of even multiplicity of functions by the prevalent method of numerical analysis is impossible or difficult. In this paper we introduce the Intersecting Lines Method and its modified version applying to approximate zeros of even multiplicity of functions. We apply this method to approximate relative extremum points of differentiable functions.
On the Formula for Distribution of Prime Numbers
The detailed derivation of the distribution of prime numbers, the research result originally presented in the 2013’ monograph Study of Analytic Number Theory: Riemann’s Hypothesis and Prime Number Theorem with Addendum on Integer Partitions published with Cam- bridge International Science Publishing, is once again presented in this paper with the purpose to give an insight to unfamiliar authors.
Mass Transfer Process between The Fluid Flow and An Active Cylinder In Cross Flow
This paper presents a theoretical and numerical analysis applies to a cylinder in cross flow that is large in comparison with the inert particles, so that the bed may be treated as a continuum. Fluid flow in the packed bed around the cylinder in cross flow was assumed to follow Darcy’s law and the partial differential equation (PDE), resulting from a differential material balance on the solute, was analysed numerically over a large range of the relevant hydrodynamic and geometrical parameters, in order to obtain the concentration field near the soluble surface. A mathematical expression is proposed to describing the dependence between the value of the Sherwood number and the relevant variables analysed, numerically. This expression obtained is very useful for different physical situations of practical interest, such as to estimate the concentration contour plots or the contaminant distance given by the “continuous point source” solution for two-dimensional solute transport.
A Mathematical Approach to Represent Uncertain Data using Evidence and Possibility Theory
The uncertainty involved in any problem solving situation is a result of some information deficiency. Information may be incomplete, in precise, not fully reliable, and contradictory. In general, the lack of information may result in different types of uncertainty. In this paper we discuss the statistical approach for representing uncertain data using evidence theory and possibility theory and applications to the evidence and possibility approximation problems are briefly presented.
On The Pell Polynomıals Pn(x,s,q) and Tridiogonal Matrix
In this study, the Polynomial pn(x,s,q) in the real variables x and y , called q- Pell polynomials and its some properties are investigated. The some formulas for these polynomials are derivated by matrices. Tridiagonal determinant of the matrix is given by the relationship between the Polynomial pn(x,s,q).
A Discrete Gamma Lifetime Model and Its Reliability Applications
In this paper, we have first developed discrete gamma failure (dGam) lifetime model by discretizing the well-known gamma failure distribution. Thereafter, we have given a description of the distributional properties and reliability characteristics of dGam model. The next section consists of a few theorems on dGam and provides a basis for ML and Bayes estimation procedures are carried out in next sections along with a thorough simulation study depicting the behavior of these estimators. Finally, some real life situations have been discussed where dGam provides most plausible fitting.
Some I-Convergent Difference Sequence Spaces Defined by a Sequence of Orlicz Functions
In this paper, we introduce the di¤erence sequence spaces using a sequence of Orlicz functions. We study some properties of these sequence spaces like completeness, solidness, symmetricity, convergence free and some inclusion relations.
In a graph G = (V, E) P4 denotes a path of length 4 vertices <v1, v2, v3, v4> such that there is no edge between either <v1, v3> or <v2, v4>. This exists either in graph G = (V, E) or its complement or both for which both G and the complement Gc are connected. In this article we give a proof for this property.
Modified Riemann−Liouville Fractional Derivative and Differential Equation for a Class of New Levy-type Probabilities
The aim of the present paper to obtained the solution of differential equations involving Modified Riemann-Liouville fractional derivative in addition to it Levy-type one sided probability density function. Some scientist studied a small number of interesting problems regarding diffusing processes in media with fractal geometry, and formulated fractional diffusion.
Modified Riemann-Liouville fractional derivative operator
Dynamic Analysis of a Switched Boost Converter Singular System using Mehtod-Rachid Algorithm
Electronics technology is a very dynamically evolving technology as compared to any other domains. The advent of these changes is forcing us to relook at the conventional physics, and mathematical models related to switching systems in particular or singular systems in general. Mostly we always drive system characteristics assuming a singular system to be linear. Singular systems are those the dynamics of which are governed by a mixture of algebraic and differential equations. Switched linear systems of the form
On the Riemann Hypothesis in The Light of The Littlewood Criterion of Equivalence
In 1859, Riemann extended the Euler study onto the case of a complex variable according to then new Cauchy's complex analysis. According to his point of view, all non-trivial zeros of the Riemann zeta function are located on the critical line s=1/2+it, where t is a real number. In 1912, Littlewood presented the equivalence criterion for the Riemann Hypothesis based on the Mertens function. In this paper, the Riemann Hypothesis is discussed and this is shown that the Littlewood criterion can be immediately applied for proving the Riemann Hypothesis, according to the analytic number theory.
Origin of Modern Mathematical Numeral – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9: the Hindu-Indian-Brahmagubta, The Islamo-Arabic or the West?
The aim of this paper is to examine, analyze and ascertain the root of the modern mathematical numeral system between the Indian-Hindu Brahmagubta, Islamo-Arabic and the Western numeral systems. The paper utilized secondary source of data. The methodology adopted by the paper is content analysis. The findings of the paper revealed that the origin of the shapes of our ten modern numerals do not concern the Indian mathematics history, as Hindus do not have full-fledged mathematical numeral system before the development of Arabic Numerals between 8th-15th Centuries. The character of Hindu-Indian numerals in whatever form and categories it belongs- Brahmagubta or anyone else, does not have any genealogical affiliations to the present modern mathematical numeral versions, as well the same thing applies to the Western mathematical systems. The paper argued that, the root/origin of the modern Arabic numeral is traced to its original and independent Arabic character versions, which transmuted from one stage to another with some state of galvanization - from Abjadi, Mashriki to Ghubari. The paper argued that apart from the non-reliability of the thesis of disparity in characters or shapes of the Arabic numerals compare to that of the Hindu-Indian Brahmagubta, there is also that of philosophical caricature fiction of genealogical linkage as well as the phonological misplacement of language or terms. The paper also argued that during the Golden-Age of Islam between 7th and 15th centuries, European arithmeticians especially in the eleventh, twelfth and part of thirteenth centuries, knew nothing about Arabic numerals; it was incredibly absent, they knew only the use of antiquated Roman numerals and Abacus in counting. In that regard, the Arabic numeral symbols (or system) were developed by Islamo-Arabic mathematicians, learned by Indians and some Europeans who cares about knowledge. In the east, the numeral system attracted the Indian mathematicians, while in Europe, the numeral system was first employed in Italy, then later France for practical purposes after the translation of the work of Al-Khwarizmi Mohammed Ibn Musa (Latin Algorithm) in 12th century into Latin by Gerard of Cremona, also known as Leonardo Fibonacci.
A Study on the Sparing Number of the Corona of Certain Graphs
Let be the set of all non-negative integers and be its the power set. An integer additive set-indexer (IASI) is defined as an injective function such that the induced function defined by is also injective, where is the sum set of and . If , then is said to be a -uniform integer additive set-indexer. An integer additive set-indexer is said to be a weak integer additive set-indexer if . We have some characteristics of the graphs which admit weak integer additive set-indexers. In this paper, we study about the sparing number of the corona of two graphs.
On Some Triple Almost Lacunary Sequence Spaces Defined by Orlicz Functions
In this paper we introduce the concept of almost lacunary strong convergent triple sequences with respect to an Orlicz function and examine some properties of these sequence spaces. We also introduce and study almost lacunary statistical convergence for triple sequences and also present some inclusion relations.
On Symmetry Preserving Diffeomorphisms of Generalized Symmetric Finsler Spaces
In this paper, we study generalized symmetric Finsler spaces. We first study symmetry preserving diffeomorphisms, then we show that the group of symmetry preserving diffeomorphisms is a transitive Lie transformation group. Finally we give some existence theorems. MSC: 53C60, 53C30
Review on Fractional Order Sliding Mode Control of Nonlinear System
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.
Binary Shape Segmentation and Classification using Coordination Number (CN)*
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.
Comparative Analysis of Distance Metrics using Face Recognition
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.
Few Properties of REPRESENTED BY A DIRICHLET SERIES
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 and , there are entire Dirichlet series for which and . Hence, we have generally to distinguish between the limits as well as types of belonging to the same order .In this paper, we obtain some result of for the mean value of an entire Dirichlet series.
Simulation of Image Processing and Restoration Through A Base Image Using Matlab
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.
Abstract 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 and . 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. AMS Subject Classification: 2010: 05C07, 05C30, 05C76. Keywords: Zagreb downhill polynomial, Downhill Zagreb indices.
An Atlas of Vertex Degree Polynomials of Graphs of Order at Most Six
Abstract The vertex degree polynomial of a graph G of order n is defined as V D(G, x) = åuv∈E(G) d(u)xd(v) 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. Keywords: Adjacent vertex, Vertex degree polynomial, Vertex degree root. Mathematics Subject Classification:
Research Frame work of Missing Data Analysis using Mathematical Models
Abstract 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. Keywords: Imputation, Knowledge Transfer, missing data, Mathematical Models, Boundedness conditions, data patterns, multivariate data, multiple imputation.
New Number Sequences Obtained with Grouping of Fibonacci Numbers
Abstract 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. Keywords: Binet Formula, Fibonacci sequence, the generalized Fibonacci sequence, Generating functions, Lucas sequence.
New Recurrence Relations for Tribonacci Sequence and Generalized Tribonacci Sequence
Abstract 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 mth term corresponding to the corner Ak in an n-gon by a relation: where, is a Tribonaccisequence and is a Tribonacci- Lucas sequence. The relation is proved by using a binet formula obtained for . It is also argued whether the relation corrects all Generalized Tribonacci sequences by changing the beginning terms. Moreover, it is shown that mth term corresponding to the corner Ak in an n-gon can be found by using the following relation: Keywords: Binet formula, Fibonacci Sequences, n-gon, Tribonacci Numbers, Tribonacci-Lucas Numbers