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This paper introduces the research on the inductance‐capacitor‐capacitor‐inductance grid‐connected inverter using active disturbance rejection and grid voltage feedforward coordinated control technology. The pade approximation is performed on the inductance‐capacitor‐capacitor‐inductance filter to derive the first‐order discretization mathematical...
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We extend the bijective correspondence between finite semimodular lattices and Faigle geometries to an analogous correspondence between semimodular lattices of finite lengths and a larger class of geometries. As the main application, we prove that if e is a join-irreducible element of a semimodular lattice L of finite length and h < e in L such tha...
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Let $G=(V, E)$ be a graph, where $V$ and $E$ are the vertex and edge sets, respectively. For two disjoint subsets $A$ and $B$ of $V$, we say $A$ \textit{dominates} $B$ if every vertex of $B$ is adjacent to at least one vertex of $A$ in $G$. A vertex partition $\pi = \{V_1, V_2, \ldots, V_k\}$ of $G$ is called a \emph{transitive $k$-partition} if $V... Article Full-text available In this study, we provide a discrete mathematical SEIR model that depicts the evolution of an infectious disease while introducing the novel idea of taking regional infection spread into account. To reduce the disease's ability to spread among people and places, we suggest three control measures. The optimal controls are defined using the Pontryagi... Preprint Full-text available A vertex g v in a connected graph G is said to distinguish two distinct elements p, q ∈ V (G) E(G) if d G (p, g v) = d G (q, g v). A subset W ⊆ V (G) is a mixed metric generator of G if every two distinct elements from V (G) E(G) are distinguished by W. The mixed metric dimension of G, denoted by β m (G), is the minimum cardinality of mixed metric... Preprint Full-text available Blood components are a perishable resource that play a crucial role in clinical medicine. The blood component inventory is managed by transfusion services, who ultimately aim to balance supply with demand so as to ensure availability whilst minimising waste. Whilst the blood component inventory problem has been the focus of theoretical approaches f... Article Full-text available Se argumenta que, en barrios periurbanos de producción Estatal, las propiedades espaciales del entorno construido y la forma física de lo edificado, no son suficientes para comprender la complejidad de la concentración de delitos y la formación de barrios seguros. Cuando se trata de barrios de producción estatal localizados en áreas desprovistas de... Preprint Full-text available In an attempt to understanding the complexity of the independent set problem, Chv{\'a}tal defined t-perfect graphs. While a full characterization of this class is still at large, progress has been achieved for claw-free graphs [Bruhn and Stein, Math.\ Program.\ 2012] and$P_{5}$-free graphs [Bruhn and Fuchs, SIAM J.\ Discrete Math.\ 2017]. We take... Article Full-text available The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete Fourier transforms due to their high computational efficiency. However, the mathematics underpinning these al... Article Full-text available For local exhaust ventilation systems to be capable of removing contaminants reliably, accurate data on the velocity field around local exhaust devices is needed. The boundaries of the separation airflow at its inlet must be determined as a prerequisite for shaping leading edges of the exhaust hood. This shaping technique makes it possible to reduc... Preprint Full-text available We consider the computational problem of finding short paths in the skeleton of the perfect matching polytope of a bipartite graph. We prove that unless$P=NP$, there is no polynomial-time algorithm that computes a path of constant length between two vertices at distance two of the perfect matching polytope of a bipartite graph. Conditioned on$P\n...
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Cyclic codes have many applications in consumer electronics, communication and data storage systems due to their efficient encoding and decoding algorithms. An efficient approach to constructing cyclic codes is the sequence approach. In their articles [Discrete Math. 321, 2014] and [SIAM J. Discrete Math. 27(4), 2013], Ding and Zhou constructed sev...
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Normalization is believed to be one of the most important parts of numerical computation in discrete mathematics. This process aims to transform a wide numerical range into a narrower one. Hence, in a number of fields of study, numerous distribution functions (DF) have been extended based on their applications, one of which is drought calculation....
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For an integer ℓ≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell \ge 2$$\end{document}, a P≥ℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysy...
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It is well-known that eigenvalues of graphs can be used to describe structural properties and parameters of graphs. A theorem of Nosal and Nikiforov states that if $G$ is a triangle-free graph with $m$ edges, then $\lambda (G)\le \sqrt{m}$, equality holds if and only if $G$ is a complete bipartite graph. Recently, Lin, Ning and Wu [Combin. Probab....
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The Kirchhoff index of graphs, introduced by Klein and Randi\'{c} in 1993, has been known useful in the study of computer science, complex network and quantum chemistry. The Kirchhoff index of a graph $G$ is defined as $Kf(G)=\sum\limits_{\{u,v\}\subseteq V(G)}\Omega_{G}(u,v)$, where $\Omega_{G}(u,v)$ denotes the resistance distance between $u$ and...
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Introduction. The complexity of computational algorithms for solving typical problems of computational, applied, and discrete mathematics is analyzed from the perspective of the theory of computation, depending on the computer architecture and the used computing model: single-processor, multiprocessor, and quantum. The following classes of problems...
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Today, the Internet of Things (IoT), often referred to as smart home technology, is used by many individuals in their daily life. The majority of IoT devices include a companion mobile application that consumers must install on their tablet or smartphone to operate, configure, and interface with the IoT device. Multiple kinds of IoT systems have gr...
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Self-testing is a technology to certify states and measurements using only the statistics of the experiment. Self-testing is possible if some extremal points in the set BQ of quantum correlations for a Bell experiment are achieved, up to isometries, with specific states and measurements. However, BQ is difficult to characterize, so it is also diffi...
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Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical and computational equations for solving today's scientific problems and challenges. This paper presents combinatorial geometric series, innovative binomial coefficients, combinatorial equations, binomial expansions, calculus with comb...
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La Matemática Discreta se ha constituido en la base de una buena parte del conocimiento humano en la actualidad, fundamental para la informática, una de las ciencias cuyo basamento matemático es muy fuerte, combinando en ella pensamiento algorítmico y pensamiento matemático, en una simbiosis que se reconoce hoy en la literatura como pensamiento...
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The aim of this paper is to study a discrete mathematical model of panic spreading on an airplane inspired by SIRS model, and the optimal control strategies, applied to reduce the number of panicked passengers during the flight. The population is divided into three compartments: Panic-prone panicked, and recovered passengers. Two control strategies...
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The results presented in this paper are obtained as part of the continued development and research of clustering algorithms based on the discrete mathematical analysis. The article briefly describes the theory of Discrete Perfect Sets (DPS-sets) that is the basis for the construction of DPS-clustering algorithms. The main task of the previously con...
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In this paper, we study the convexity (concavity) of the function $$x\mapsto {{\,\mathrm{{{{\textsf {\textit{K}}}}}}\,}}_a(\sqrt{x})-\log \left( 1+c/\sqrt{1-x}\right)$$ on (0, 1) for $$a\in (0,1/2]$$ and $$c\in (0,\infty )$$, where $${{\,\mathrm{{{{\textsf {\textit{K}}}}}}\,}}_a(r)$$ is the generalized complete elliptic integral of the first kind....
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An antimagic labeling for a graph $G$ with $m$ edges is a bijection $f: E(G) \to \{1, 2, \dots, m\}$ so that $\phi_f(u) \neq \phi_f(v)$ holds for any pair of distinct vertices $u, v \in V(G)$, where $\phi_f(x) = \sum_{x \in e} f(e)$. A strongly antimagic labeling is an antimagic labeling with an additional condition: For any $u, v \in V(G)$, if $\d... Article Full-text available The presence of Covid-19 was a game-changer in all the sectors that traditional learning, working, selling even living methods have changed from basic methods to something else to curb Covid-19. The impact was huge on most sectors due to the lack of experience in overcoming pandemics. One of the sectors that face the most struggle was educational i... Article Full-text available An H-graph is one representable as the intersection graph of connected subgraphs of a suitable subdivision of a fixed graph H, introduced by Biró et al. (Discrete Mathematics 100:267–279, 1992). An H-graph is proper if the representing subgraphs of H can be chosen incomparable by the inclusion. In this paper, we focus on the isomorphism problem for... Article Full-text available Graph theory is a delightful playground for the exploration of proof techniques in discrete mathematics and its results have applications in many areas of the computing, social, and natural sciences. The fastest growing area within graph theory is the study of domination and Independence numbers. Domination number is the cardinality of a minimum do... Article Full-text available There used to be journal by the name Publications of the Faculty Electrical Engineering - Series Mathematics (Publikacije Elektrotehniˇckog Fakulteta - Serija Matematika) which had a problem section, popular among the problem-solving community. In 2007, it rebranded itself into a fully-research journal, Applicable Analysis and Discrete Mathematics... Cover Page Full-text available The aim of this Special Issue is to attract leading researchers in different areas of discrete mathematics and theoretical computer science. To this end, it is intended to involve in this Special Issue new high-quality results on discrete mathematics including (but not limited to) graph theory, coding theory, cryptography, algorithms and complexity... Article Full-text available Altshuler (Discrete Math 4(3):201–217, 1973) characterized the 6-regular triangulations on the torus to be precisely those that are obtained from a regular triangulation of the r×s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{u... Article Full-text available Binge drinking is a multi-factorial problem where peer influence in the immediate environment has a key role in the appearance of the first episode and the recurrence. However, information regarding the interaction of variables that mediate the influence among people is limited. Binge drinking pattern is generally derived from interrelationships wi... Article Full-text available With the improvement of people’s living standards, people’s pursuit of art is also getting higher and higher. Ceramic products are artistic works whose meanings contain thousands of stories including mountains, waters, and rivers. Ceramic products include vases, tea sets, flower pots, plates, and rice bowls. A vase is a vessel, mostly made of ceram... Article Full-text available The main goal of this research is to identify the impact of COVID-19 on online final exam scores among Computer Science students. The correlation matrix we used indicates the interrelationships among learning outcomes and student profile, type of classes, and student online behaviour. Six courses were taken under consideration: Practical Algorithms... Article Full-text available Predicting student’s successful completion of academic programs and the features that influence their performance can have a significant effect on improving students’ completion, and graduation rates and reduce attrition rates. Therefore, identifying students are at risk, and the courses where improvements in content, delivery mode, pedagogy, and a... Preprint Full-text available Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical and computational equations for solving today’s scientific problems and challenges. This paper presents combinatorial geometric series, innovative binomial coefficients, combinatorial equations, binomial expansions, calculus with comb... Article Full-text available The objective of this work is to show an educational path for combinatorics and graph theory that has the aim, on one hand, of helping students understand some discrete mathematics properties, and on the other, of developing modelling skills through a robust understanding. In particular, for the path proposed to middle-school students, we used a co... Article Full-text available In (QSAR)/(QSPR) studies, topological indices play an essential role, as a molecular descriptor. For measuring the structural information of chemical graphs and complex networks, the graph entropies with topological indices take the help of Shannon’s entropy concept, which now become the information-theoretic quantities. In discrete mathematics,... Article Full-text available The Maximum Weight Independent Set Problem (WIS) is a well-known NP-hard problem. A popular way to study WIS is to detect graph classes for which WIS is solvable in polynomial time, with particular reference to hereditary graph classes, i.e., defined by a hereditary graph property or equivalently by forbidding one or more induced subgraphs. For any... Article Full-text available A 3-way $$(v,k,t)$$ trade $$T$$ of volume $$m$$ consists of three pairwise disjoint collections $$T_{1}$$, $$T_{2}$$ and $$T_{3}$$, each of $$m$$ blocks of size $$k$$, such that for every $$t$$-subset of $$v$$-set $$V$$, the number of blocks containing this $$t$$-subset is the same in each $$T_{i}$$ for $$1\leq i\leq 3$$. If any $$t$$-subset of fou... Article Full-text available An edge-colored graph G is a graph with an edge coloring. We say G is properly colored if any two adjacent edges of G have distinct colors, and G is rainbow if any two edges of G have distinct colors. For a vertex $$v \in V(G)$$, the color degree $$d_G^{col}(v)$$ of v is the number of distinct colors appearing on edges incident with v. The minimum... Article Full-text available A set S⊆V is independent in a graph G=V,E if no two vertices from S are adjacent. The independence numberα(G) is the cardinality of a maximum independent set, while μ(G) is the size of a maximum matching in G. If α(G)+μ(G) equals the order of G, then G is called a König–Egerváry graph (Deming in Discrete Math 27:23–33, 1979; Sterboul in J Combin Th... Preprint Full-text available The growing complexity of mathematical and computational modelling demands the simplicity of mathematical and computational equations for solving today’s scientific problems and challenges. This paper presents combinatorial geometric series, innovative binomial coefficients, combinatorial equations, binomial expansions, calculus with combinatorial... Article Full-text available A graph G is $$(s_1,s_2,\ldots ,s_k)$$-linked, if for any k disjoint vertex sets $$S_1,S_2,\ldots ,S_k$$ with $$|S_i|\le s_i$$, G has k vertex-disjoint connected subgraphs $$G_1,G_2,\ldots ,G_k$$ such that $$S_i\subseteq V(G_i)$$ for all $$1\le i \le k$$. The main purpose of this paper is to characterize $$(s_1,s_2,\ldots ,s_k)$$-linked planar grap... Article Full-text available The main purpose of this work is, first, a construction of the indirect Hamilton’s variational principle for the problem of motion of a pendulum with a vibration suspension with friction, oscillating along a straight line making a small angle with the vertical line. Second, the construction on its basis of the difference scheme. Third, to carry out... Article Full-text available How to cite this article: Lomngam Kamga Victor and Ebodé Atangana Pie Désire, 2-distance vertex distinguishing index of sparse graphs, Advances and Applications in Discrete Mathematics 33 (2022), 1-18. http://dx. Abstract The 2-distance vertex distinguishing index () Preprint Full-text available Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical and computational equations for solving today’s scientific problems and challenges. This paper presents combinatorial geometric series, innovative binomial coefficients, combinatorial equations, binomial expansions, calculus with comb... Preprint Full-text available In today’s world, the growing complexity of mathematical modelling demands the simplicity of mathematical and numerical equations for solving today’s scientific problems and challenges. This paper presents combinatorial geometric series, innovative binomial coefficients, combinatorial equations, binomial expansions, calculus with combinatorial geom... Preprint Full-text available Nowadays, the growing complexity of mathematical modelling demands the simplicity of mathematical equations for solving today's scientific problems and challenges. This paper presents combinatorial geometric series, innovative binomial coefficients, combinatorial equations, binomial expansions, calculus with combinatorial geometric series, and its... Article Full-text available In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes, topics,... Article Full-text available The$n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of$n$in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration system with a regular numeration language, we consider those built on languages associated with trees having per... Article Full-text available Mathematical models are efficient tools of modelling of different phenomena. In the modelling process we formulate these phenomena in the language of mathematics. Typically, the construction of the models is realized with the modelling chain physical / biological model → continuous model → discrete (numerical) model. In order to have an adequate mo... Preprint Full-text available Bollob\'{a}s, Erd\H{o}s, and Szemer\'{e}di [Discrete Math 13 (1975), 97--107] investigated a tripartite generalization of the Zarankiewicz problem: what minimum degree forces a tripartite graph with$n$vertices in each part to contain an octahedral graph$K_3(2)$? They proved that$n+2^{-1/2}n^{3/4}$suffices and suggested it could be weakened to... Preprint Full-text available In today’s world, the growing complexity of computational and mathematical modelling demands the simplicity of mathematical equations for solving today’s scientific problems and challenges. This paper presents combinatorial geometric series, innovative binomial coefficients, combinatorial equations, binomial expansions, calculus with combinatorial... Article Full-text available In this paper we apply multistep recurrence relations, as one of very simple and useful mathematical models. It is an efficient tool for solving many problems in mathematics, science, and technics. We also use generating functions, as a connection between real number sequences and real functions, and as a very smooth and efficient connection betwee... Preprint Full-text available This paper presents a technique to compute the sum of Annamalai’s binomial expansions. This computing technique is a sort of methodological advance which is used for researchers working in computational science, computation, cryptography, combinatorics, discrete mathematics, and theoretical computer science. Preprint Full-text available The$\!{}\bmod k$chromatic index of a graph$G$is the minimum number of colors needed to color the edges of$G$in a way that the subgraph spanned by the edges of each color has all degrees congruent to$1\!\!\pmod k$. Recently, the authors proved that the$\!{}\bmod k$chromatic index of every graph is at most$198k-101$, improving, for large$k...
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Dear Colleagues, Research in discrete mathematics in theoretical and application aspects has significantly increased in recent decades. The first aim of this Special Issue is to encourage new theoretical results in discrete mathematics, such as results related to graph theory, theoretical computer science, and combinatorial optimization. The secon...
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The bare rudiments of the principle of mathematical induction as a method of proof date back to ancient times. In the contemporary university milieu, the demonstrative scheme is taught as part of a course in discrete mathematics, set theory, number theory, graph theory, group theory, game theory, linear algebra, logic, and combinatorics. In theoret...
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A graph G is k-edge-Hamiltonian if any collection of vertex-disjoint paths with at most k edges altogether belong to a Hamiltonian cycle in G. A graph G is k-Hamiltonian if for all S⊆V(G) with |S|≤k, the subgraph induced by V(G)∖S has a Hamiltonian cycle. These two concepts are classical extensions of the usual Hamiltonian graphs. In this paper, we...
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After the pandemic, people began to adjust to the changes during the pandemic. The rapid progress and development of information and technology are now entering the world of education. Information technology has begun to be widely used to support the smooth running of the teaching and learning process, one of which is to support student learning ou...
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We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics of randomly growing permutations. Permutations connect total orders on a finite set, which leads to the use of...
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Huemer et al. (Discrete Mathematics, 2019) proved that for any two point sets R and B with $$|R|=|B|$$ | R | = | B | , the perfect matching that matches points of R with points of B , and maximizes the total squared Euclidean distance of the matched pairs, has the property that all the disks induced by the matching have a common point. Each pair of...
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The paper describes and analyzes a discrete mathematical model of the variable state of the pandemic, which is important for determining production quantities of vaccines and antiviral drugs, predicting the number of infected persons, and the intensity of the process of disseminating information or new ideas to the public. According to the system o...
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The aim of this work is to propose a discrete mathematical model to study the behavioral dynamics of a population affected by the disease of obesity. Thus, the population under study is divided into six compartments: susceptible (S), exposed (E), slightly obese (I1), moderately obese (I2), very obese (I3), and recovered (R). To fight this disease,...
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In this paper the term translation structure will denote any geometric object canonically constructed from an elementary abelian group. Hence, translation weak affine spaces, translation planes, linear sets, translation ovoids of polar spaces, translation generalized quadrangles and linear MRD-codes are examples of translation structures. I will pr...
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In this paper, we employ the optimal control theory, using a discrete mathematical model to mitigate the risk posed by bird strikes to flying aircraft. The aim of this study is to assess the performance of different strategies in reducing bird strike incidents and ultimately adopt the best performing strategy. The model used in this research is set...
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In this paper, we give a series of counterexamples to negate a conjecture and answer an open question on the k-power domination of regular graphs [see Dorbec et al. (SIAM J Discrete Math 27:1559–1574, 2013)]. Furthermore, we focus on the study of k-power domination of claw-free graphs. We show that for l∈{2,3}\documentclass[12pt]{minimal} \usepacka...
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.Let G = (V (G), E(G)) be a connected graph. A restrained weakly connected 2-dominating set in G is a set D of vertices in G such that every vertex in V (G)\D is dominated by at least two vertices in D and is adjacent to at least one vertex in V (G)\D and that the subgraph _w weakly induced by D is connected. The restrained weakly connected 2-d...
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Kemampuan mahasiswa dalam memecahkan masalah masih sangat kurang. Tujuan penelitian ini untuk meningkatkan kemampuan pemecahan masalah (KPM) mahasiswa melalui pembelajaran berbasis masalah dengan bantuan lembar kerja mahasiswa (LKM). Jenis penelitian yang digunakan melalui pendekatan yakni penelitian tindakan kelas dengan 2 siklus. Objek penelitian...
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This paper presents a theorem based on the summation of Annamalai’s binomial expansions with the binomial coefficient and binomial identity. This theorem is a sort of methodological advance that will help to the researchers who are working in computational science, computation, cryptography, combinatorics, discrete mathematics and theoretical compu...
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We report on our experience using ACL2 in the classroom to teach students about software testing. The course COSC2300 at the University of Wyoming is a mostly traditional Discrete Mathematics course, but with a clear focus on computer science applications. For instance, the section on logic and proofs is motivated by the desire to write proofs abou...
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We leverage an algorithm of Deming [R.W. Deming, Independence numbers of graphs -- an extension of the Koenig-Egervary theorem, Discrete Math., 27(1979), no. 1, 23--33; MR534950] to decompose a matchable graph into subgraphs with a precise structure: they are either spanning even subdivisions of blossom pairs, spanning even subdivisions of the comp...