678 results
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2. Multivariate Tail Moments for Log-Elliptical Dependence Structures as Measures of Risks
- Author
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Tomer Shushi and Zinoviy Landsman
- Subjects
Multivariate statistics ,tail conditional expectation ,Physics and Astronomy (miscellaneous) ,log-skew-elliptical distributions ,General Mathematics ,Short paper ,Structure (category theory) ,Conditional expectation ,01 natural sciences ,Measure (mathematics) ,010104 statistics & probability ,log-elliptical distributions ,0502 economics and business ,Computer Science (miscellaneous) ,Econometrics ,multivariate tail covariance ,0101 mathematics ,Mathematics ,050208 finance ,lcsh:Mathematics ,05 social sciences ,Covariance ,lcsh:QA1-939 ,Chemistry (miscellaneous) ,Portfolio ,multivariate tail conditional expectation - Abstract
The class of log-elliptical distributions is well used and studied in risk measurement and actuarial science. The reason is that risks are often skewed and positive when they describe pure risks, i.e., risks in which there is no possibility of profit. In practice, risk managers confront a system of mutually dependent risks, not only one risk. Thus, it is important to measure risks while capturing their dependence structure. In this short paper, we compute the multivariate risk measures, multivariate tail conditional expectation, and multivariate tail covariance measure for the family of log-elliptical distributions, which captures the dependence structure of the risks while focusing on the tail of their distributions, i.e., on extreme loss events. We then study our result and examine special cases, as well as the optimal portfolio selection using such measures. Finally, we show how the given multivariate tail moments can also be computed for log-skew elliptical models based on similar approaches given for the log-elliptical case.
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- 2021
3. Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives
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Farid Nouioua, Nacereddine Hammami, Bilal Basti, Noureddine Benhamidouche, Rabah Djemiat, and Imadeddine Berrabah
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Physics and Astronomy (miscellaneous) ,Coronavirus disease 2019 (COVID-19) ,General Mathematics ,Population ,Fixed-point theorem ,0102 computer and information sciences ,Stability result ,system ,01 natural sciences ,Stability (probability) ,Hadamard transform ,QA1-939 ,Computer Science (miscellaneous) ,Applied mathematics ,Quantitative Biology::Populations and Evolution ,Uniqueness ,0101 mathematics ,education ,Mathematics ,education.field_of_study ,pandemic ,010102 general mathematics ,existence ,COVID-19 ,fractional derivative ,uniqueness ,Fractional calculus ,010201 computation theory & mathematics ,Chemistry (miscellaneous) ,SIRD model - Abstract
This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.
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- 2021
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4. Iterants, Majorana Fermions and the Majorana-Dirac Equation
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Louis H. Kauffman
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Physics and Astronomy (miscellaneous) ,complex number ,Majorana-Dirac equation ,General Mathematics ,Dirac (software) ,01 natural sciences ,010305 fluids & plasmas ,Schrödinger equation ,symbols.namesake ,iterant ,Spacetime algebra ,0103 physical sciences ,nilpotent ,QA1-939 ,Computer Science (miscellaneous) ,Dirac equation ,Clifford algebra ,010306 general physics ,Mathematical physics ,Physics ,Majorana fermion ,spacetime algebra ,Nilpotent ,MAJORANA ,Chemistry (miscellaneous) ,symbols ,discrete ,Mathematics - Abstract
This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algebras naturally give rise to the complex numbers, Clifford algebras and matrix algebras. The paper discusses the structure of the Schrödinger equation, the Dirac equation and the Majorana Dirac equations, finding solutions via the nilpotent method initiated by Peter Rowlands.
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- 2021
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5. Research on Path Planning Algorithm for Crowd Evacuation
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Zhenfei Wang, Lun Li, Zhiyun Zheng, Junfeng Wang, and Chuchu Zhang
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Physics and Astronomy (miscellaneous) ,Computer science ,ComputingMethodologies_SIMULATIONANDMODELING ,General Mathematics ,Population ,02 engineering and technology ,Pedestrian ,01 natural sciences ,Field (computer science) ,010305 fluids & plasmas ,0103 physical sciences ,QA1-939 ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Motion planning ,crowd evacuation ,education ,path planning ,Collision avoidance ,education.field_of_study ,collision handling ,agent-based model (ABM) ,Collision ,Chemistry (miscellaneous) ,Common cause and special cause ,Path (graph theory) ,020201 artificial intelligence & image processing ,Algorithm ,Mathematics - Abstract
In recent years, crowded stampede incidents have occurred frequently, resulting in more and more serious losses. The common cause of such incidents is that when large-scale populations gather in a limited area, the population is highly unstable. In emergency situations, only when the crowd reaches the safe exit as soon as possible within a limited evacuation time to complete evacuation can the loss and casualties be effectively reduced. Therefore, the safety evacuation management of people in public places in emergencies has become a hot topic in the field of public security. Based on the analysis of the factors affecting the crowd path selection, this paper proposes an improved path-planning algorithm based on BEME (Balanced Evacuation for Multiple Exits). And pedestrian evacuation simulation is carried out in multi-exit symmetrical facilities. First, this paper optimizes the update method of the GSDL list in the BEME algorithm as the basis for evacuating pedestrians to choose an exit. Second, the collision between pedestrians is solved by defining the movement rule and collision avoidance strategy. Finally, the algorithm is compared with BEME and traditional path-planning algorithms. The results show that the algorithm can further shorten the global evacuation distance of the symmetrical evacuation scene, effectively balance the number of pedestrians at each exit and reduce the evacuation time. In addition, this improved algorithm uses a collision avoidance strategy to solve the collision and congestion problems in path planning, which helps to maximize evacuation efficiency. Whether the setting of the scene or the setting of the exit, all studies are based on symmetric implementation. This is more in line with the crowd evacuation in the real scene, making the experimental results more meaningful.
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- 2021
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6. Quadruple Roman Domination in Trees
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Saeed Kosari, Jafar Amjadi, Nesa Khalili, Zheng Kou, and Guoliang Hao
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Vertex (graph theory) ,Physics and Astronomy (miscellaneous) ,Domination analysis ,General Mathematics ,Roman domination ,MathematicsofComputing_GENERAL ,Value (computer science) ,Minimum weight ,quadruple Roman domination ,0102 computer and information sciences ,01 natural sciences ,Upper and lower bounds ,Combinatorics ,Integer ,Computer Science (miscellaneous) ,QA1-939 ,0101 mathematics ,Mathematics ,010102 general mathematics ,Function (mathematics) ,trees ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,010201 computation theory & mathematics ,Chemistry (miscellaneous) ,Symmetry (geometry) - Abstract
This paper is devoted to the study of the quadruple Roman domination in trees, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. For any positive integer k, a [k]-Roman dominating function ([k]-RDF) of a simple graph G is a function from the vertex set V of G to the set {0,1,2,…,k+1} if for any vertex u∈V with f(u)<, k, ∑x∈N(u)∪{u}f(x)≥|{x∈N(u):f(x)≥1}|+k, where N(u) is the open neighborhood of u. The weight of a [k]-RDF is the value Σv∈Vf(v). The minimum weight of a [k]-RDF is called the [k]-Roman domination number γ[kR](G) of G. In this paper, we establish sharp upper and lower bounds on γ[4R](T) for nontrivial trees T and characterize extremal trees.
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- 2021
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7. Estimating the Variance of Estimator of the Latent Factor Linear Mixed Model Using Supplemented Expectation-Maximization Algorithm
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Khairil Anwar Notodiputro, Asep Saefuddin, Toni Toharudin, Henk Folmer, Yenni Angraini, and Urban and Regional Studies Institute
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Mixed model ,Physics and Astronomy (miscellaneous) ,General Mathematics ,longitudinal data analysis ,01 natural sciences ,Generalized linear mixed model ,010104 statistics & probability ,0504 sociology ,latent factor linear mixed model (LFLMM) ,Expectation–maximization algorithm ,Linear regression ,QA1-939 ,Computer Science (miscellaneous) ,Applied mathematics ,supplemented EM algorithm ,0101 mathematics ,Mathematics ,expectation-maximization (EM) algorithm ,Covariance matrix ,05 social sciences ,050401 social sciences methods ,Estimator ,Variance (accounting) ,Delta method ,Chemistry (miscellaneous) - Abstract
This paper deals with symmetrical data that can be modelled based on Gaussian distribution, such as linear mixed models for longitudinal data. The latent factor linear mixed model (LFLMM) is a method generally used for analysing changes in high-dimensional longitudinal data. It is usual that the model estimates are based on the expectation-maximization (EM) algorithm, but unfortunately, the algorithm does not produce the standard errors of the regression coefficients, which then hampers testing procedures. To fill in the gap, the Supplemented EM (SEM) algorithm for the case of fixed variables is proposed in this paper. The computational aspects of the SEM algorithm have been investigated by means of simulation. We also calculate the variance matrix of beta using the second moment as a benchmark to compare with the asymptotic variance matrix of beta of SEM. Both the second moment and SEM produce symmetrical results, the variance estimates of beta are getting smaller when number of subjects in the simulation increases. In addition, the practical usefulness of this work was illustrated using real data on political attitudes and behaviour in Flanders-Belgium.
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- 2021
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8. Wilsonian Effective Action and Entanglement Entropy
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Takato Mori, Satoshi Iso, and Katsuta Sakai
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High Energy Physics - Theory ,Physics and Astronomy (miscellaneous) ,General Mathematics ,FOS: Physical sciences ,Quantum entanglement ,01 natural sciences ,symbols.namesake ,Theoretical physics ,entanglement entropy ,0103 physical sciences ,Computer Science (miscellaneous) ,QA1-939 ,Feynman diagram ,Gauge theory ,Quantum field theory ,010306 general physics ,interacting quantum field theory ,Effective action ,Physics ,Quantum Physics ,010308 nuclear & particles physics ,Mathematics::History and Overview ,Propagator ,Renormalization group ,Vertex (geometry) ,High Energy Physics - Theory (hep-th) ,Chemistry (miscellaneous) ,symbols ,Wilsonian effective action ,Quantum Physics (quant-ph) ,Mathematics - Abstract
This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In arXiv:2103.05303, we have proposed the notion of $\mathbb{Z}_M$ gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. As shown in the next paper arXiv:2105.02598, the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action., Comment: 29 pages, 10 figures; typos corrected, published version in Symmetry (v2)
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- 2021
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9. Estimation of Electricity Generation by an Electro-Technical Complex with Photoelectric Panels Using Statistical Methods
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Anna Turysheva, Irina Voytyuk, and Daniel Guerra
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Physics and Astronomy (miscellaneous) ,020209 energy ,General Mathematics ,solar power ,02 engineering and technology ,solar systems ,photovoltaic panel ,mathematical modeling ,statistics ,correlation ,skewness ,symmetry ,random variable distribution ,01 natural sciences ,010104 statistics & probability ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,QA1-939 ,Statistical physics ,0101 mathematics ,Solar power ,Mathematics ,business.industry ,Photovoltaic system ,Statistical model ,Symmetry (physics) ,Electricity generation ,Chemistry (miscellaneous) ,Skewness ,Probability distribution ,business ,Random variable - Abstract
This paper presents a computational tool for estimating energy generated by low-power photovoltaic systems based on the specific conditions of the study region since the characteristic energy equation can be obtained considering the main climatological factors affecting these systems in terms of the symmetry or skewness of the random distribution of the generated energy. Furthermore, this paper is aimed at determining any correlation that exists between meteorological variables with respect to the energy generated by 5-kW solar systems in the specific climatic conditions of the Republic of Cuba. The paper also presents the results of the influence of each climate factor on the distribution symmetry of the generated energy of the solar system. Studying symmetry in statistical models is important because they allow us to establish the degree of symmetry (or skewness), which is the probability distribution of a random variable, without having to make a graphical representation of it. Statistical skewness reports the degree to which observations are distributed evenly and proportionally above and below the center (highest) point of the distribution. In the case when the mentioned distribution is balanced, it is called symmetric.
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- 2021
10. Canonical Correlations and Nonlinear Dependencies
- Author
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Nicola Loperfido
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Multivariate statistics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,canonical correlations ,02 engineering and technology ,01 natural sciences ,010104 statistics & probability ,sign symmetry ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,QA1-939 ,Statistical physics ,0101 mathematics ,skew-symmetric distribution ,Independence (probability theory) ,Mathematics ,central symmetry ,Probabilistic logic ,Conditional probability distribution ,Semiparametric model ,Nonlinear system ,Distribution (mathematics) ,Chemistry (miscellaneous) ,020201 artificial intelligence & image processing ,Canonical correlation - Abstract
Canonical correlation analysis (CCA) is the default method for investigating the linear dependence structure between two random vectors, but it might not detect nonlinear dependencies. This paper models the nonlinear dependencies between two random vectors by the perturbed independence distribution, a multivariate semiparametric model where CCA provides an insight into their nonlinear dependence structure. The paper also investigates some of its probabilistic and inferential properties, including marginal and conditional distributions, nonlinear transformations, maximum likelihood estimation and independence testing. Perturbed independence distributions are closely related to skew-symmetric ones.
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- 2021
11. Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus
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Jessada Tariboon, Sotiris K. Ntouyas, Hüseyin Budak, Muhammad Ali, and [Belirlenecek]
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Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Quantum calculus ,co-ordinated convexity ,quantum calculus ,01 natural sciences ,Interval valued ,Hadamard transform ,(p ,Hermite–Hadamard inequality ,Hermite–Hadamard inclusion ,Computer Science (miscellaneous) ,QA1-939 ,0101 mathematics ,interval-valued functions ,Mathematics ,Hermite polynomials ,010102 general mathematics ,Regular polygon ,(p, q)-integral ,Convex ,010101 applied mathematics ,Hermite-Hadamard inequality ,Chemistry (miscellaneous) ,Hermite-Hadamard inclusion ,q)-integral ,Midpoint Type Inequalities ,Symmetry (geometry) - Abstract
In this paper, the notions of post-quantum integrals for two-variable interval-valued functions are presented. The newly described integrals are then used to prove some new Hermite-Hadamard inclusions for co-ordinated convex interval-valued functions. Many of the findings in this paper are important extensions of previous findings in the literature. Finally, we present a few examples of our new findings. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. WOS:000677046700001 2-s2.0-85110868353
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- 2021
12. On Coefficient Problems for Functions Connected with the Sine Function
- Author
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Katarzyna Tra̧bka-Wiȩcław
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Pure mathematics ,Class (set theory) ,functions starlike with respect to symmetric points ,Physics and Astronomy (miscellaneous) ,Logarithm ,Mathematics::Complex Variables ,General Mathematics ,010102 general mathematics ,01 natural sciences ,010101 applied mathematics ,generalized Zalcman coefficient functional ,Hankel determinant ,Chemistry (miscellaneous) ,coefficients of analytic functions ,Computer Science (miscellaneous) ,QA1-939 ,Sine ,0101 mathematics ,Mathematics ,Analytic function - Abstract
In this paper, some coefficient problems for starlike analytic functions with respect to symmetric points are considered. Bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates for the following: coefficients, logarithmic coefficients, some cases of the generalized Zalcman coefficient functional, and some cases of the Hankel determinant.
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- 2021
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13. General Summation Formulas Contiguous to the q-Kummer Summation Theorems and Their Applications
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Hari M. Srivastava, Kalpana Fatawat, Yashoverdhan Vyas, and Shivani Pathak
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Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Quantum calculus ,symmetric quantum calculus ,Mathematical proof ,01 natural sciences ,q-Kummer second and third summation theorems ,symbols.namesake ,Heine’s transformation ,QA1-939 ,Computer Science (miscellaneous) ,0101 mathematics ,Invariant (mathematics) ,Hypergeometric function ,Mathematics ,Series (mathematics) ,q-Kummer summation theorem ,010102 general mathematics ,Gauss ,Thomae’s q-integral representation ,010101 applied mathematics ,Number theory ,Chemistry (miscellaneous) ,symbols ,quantum or basic (or q-) hypergeometric series ,Jacobi polynomials ,q-Binomial theorem - Abstract
This paper provides three classes of q-summation formulas in the form of general contiguous extensions of the first q-Kummer summation theorem. Their derivations are presented by using three methods, which are along the lines of the three types of well-known proofs of the q-Kummer summation theorem with a key role of the q-binomial theorem. In addition to the q-binomial theorem, the first proof makes use of Thomae’s q-integral representation and the second proof needs Heine’s transformation. Whereas the third proof utilizes only the q-binomial theorem. Subsequently, the applications of these summation formulas in obtaining the general contiguous extensions of the second and the third q-Kummer summation theorems are also presented. Furthermore, the investigated results are specialized to give many of the known as well as presumably new q-summation theorems, which are contiguous to the three q-Kummer summation theorems. This work is motivated by the observation that the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) gamma and q-hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several diverse areas including Number Theory, Theory of Partitions and Combinatorial Analysis as well as in the study of Combinatorial Generating Functions. Just as it is known in the theory of the Gauss, Kummer (or confluent), Clausen and the generalized hypergeometric functions, the parameters in the corresponding basic or quantum (or q-) hypergeometric functions are symmetric in the sense that they remain invariant when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. A case has therefore been made for the symmetry possessed not only by hypergeometric functions and basic or quantum (or q-) hypergeometric functions, which are studied in this paper, but also by the symmetric quantum calculus itself.
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- 2021
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14. Generalized Variational Principle for the Fractal (2 + 1)-Dimensional Zakharov–Kuznetsov Equation in Quantum Magneto-Plasmas
- Author
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Yan-Hong Liang and Kang-Jia Wang
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Physics ,two-scale fractal theory ,Physics and Astronomy (miscellaneous) ,General Mathematics ,010102 general mathematics ,One-dimensional space ,Structure (category theory) ,Space (mathematics) ,01 natural sciences ,Symmetry (physics) ,010305 fluids & plasmas ,semi-inverse method ,Fractal ,Chemistry (miscellaneous) ,Variational principle ,Fractal derivative ,0103 physical sciences ,Computer Science (miscellaneous) ,QA1-939 ,fractal variational principle ,0101 mathematics ,Quantum ,Mathematics ,Mathematical physics ,symmetry - Abstract
In this paper, we propose the fractal (2 + 1)-dimensional Zakharov–Kuznetsov equation based on He’s fractal derivative for the first time. The fractal generalized variational formulation is established by using the semi-inverse method and two-scale fractal theory. The obtained fractal variational principle is important since it not only reveals the structure of the traveling wave solutions but also helps us study the symmetric theory. The finding of this paper will contribute to the study of symmetry in the fractal space.
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- 2021
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15. Explicit Solutions of Initial Value Problems for Fractional Generalized Proportional Differential Equations with and without Impulses
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Mohamed I. Abbas and Snezhana Hristova
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Physics and Astronomy (miscellaneous) ,Differential equation ,General Mathematics ,010102 general mathematics ,Scalar (physics) ,Function (mathematics) ,Type (model theory) ,01 natural sciences ,Symmetry (physics) ,010101 applied mathematics ,symbols.namesake ,Transformation (function) ,generalized proportional fractional derivatives ,Chemistry (miscellaneous) ,Mittag-Leffler function ,QA1-939 ,Computer Science (miscellaneous) ,symbols ,Initial value problem ,Applied mathematics ,Mittag–Leffler function ,0101 mathematics ,Mathematics - Abstract
The object of investigation in this paper is a scalar linear fractional differential equation with generalized proportional derivative of Riemann–Liouville type (LFDEGD). The main goal is the obtaining an explicit solution of the initial value problem of the studied equation. Note that the locally solvability, being the same as the existence of solutions to the initial value problem, is connected with the symmetry of a transformation of a system of differential equations. At the same time, several criteria for existence of the initial value problem for nonlinear fractional differential equations with generalized proportional derivative are connected with the linear ones. It leads to the necessity of obtaining an explicit solution of LFDEGD. In this paper two cases are studied: the case of no impulses in the differential equation are presented and the case when instantaneous impulses at initially given points are involved. All obtained formulas are based on the application of Mittag–Leffler function with two parameters. In the case of impulses, initially the appropriate impulsive conditions are set up and later the explicit solutions are obtained.
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- 2021
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16. Symmetric and Asymmetric Data in Solution Models
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Jurgita Antucheviciene, Zenonas Turskis, and Edmundas Kazimieras Zavadskas
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Physics and Astronomy (miscellaneous) ,Computer science ,General Mathematics ,media_common.quotation_subject ,Fuzzy set ,02 engineering and technology ,symmetric data ,01 natural sciences ,Asymmetry ,Data type ,neutrosophic sets ,asymmetric data ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,QA1-939 ,MCDM ,media_common ,Balance (metaphysics) ,Uncertain data ,010308 nuclear & particles physics ,Management science ,solution models ,Multiple-criteria decision analysis ,Symmetry (physics) ,fuzzy sets ,Chemistry (miscellaneous) ,020201 artificial intelligence & image processing ,Mathematics ,Economic problem - Abstract
This Special Issue covers symmetric and asymmetric data that occur in real-life problems. We invited authors to submit their theoretical or experimental research to present engineering and economic problem solution models that deal with symmetry or asymmetry of different data types. The Special Issue gained interest in the research community and received many submissions. After rigorous scientific evaluation by editors and reviewers, seventeen papers were accepted and published. The authors proposed different solution models, mainly covering uncertain data in multi-criteria decision-making problems as complex tools to balance the symmetry between goals, risks, and constraints to cope with the complicated problems in engineering or management. Therefore, we invite researchers interested in the topics to read the papers provided in the Special Issue.
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- 2021
17. Enhancing Ant-Based Algorithms for Medical Image Edge Detection by Admissible Perturbations of Demicontractive Mappings
- Author
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Vasile Berinde and Cristina Ţicală
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Physics and Astronomy (miscellaneous) ,Computer science ,General Mathematics ,Perturbation (astronomy) ,enriched demicontractive operator ,01 natural sciences ,Edge detection ,Brain ct ,QA1-939 ,Computer Science (miscellaneous) ,Numerical tests ,admissible perturbation ,ant-based algorithm ,0101 mathematics ,Complement (set theory) ,edge detection ,symmetric medical image ,010102 general mathematics ,Process (computing) ,test function ,010101 applied mathematics ,Image edge ,Chemistry (miscellaneous) ,Test functions for optimization ,Algorithm ,Mathematics ,asymmetric medical image - Abstract
The aim of this paper is to show analytically and empirically how ant-based algorithms for medical image edge detection can be enhanced by using an admissible perturbation of demicontractive operators. We thus complement the results reported in a recent paper by the second author and her collaborators, where they used admissible perturbations of demicontractive mappings as test functions. To illustrate this fact, we first consider some typical properties of demicontractive mappings and of their admissible perturbations and then present some appropriate numerical tests to illustrate the improvement brought by the admissible perturbations of demicontractive mappings when they are taken as test functions in ant-based algorithms for medical image edge detection. The edge detection process reported in our study considers both symmetric (Head CT and Brain CT) and asymmetric (Hand X-ray) medical images. The performance of the algorithm was tested visually with various images and empirically with evaluation of parameters.
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- 2021
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18. On Certain Differential Subordination of Harmonic Mean Related to a Linear Function
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Anna Dobosz, Piotr Jastrzębski, and Adam Lecko
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Subordination (linguistics) ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,Generalization ,General Mathematics ,Harmonic mean ,harmonic mean ,01 natural sciences ,arithmetic mean ,Mathematics::Probability ,Computer Science (miscellaneous) ,QA1-939 ,0101 mathematics ,Mathematics ,convex function ,Linear function (calculus) ,010102 general mathematics ,010101 applied mathematics ,geometric mean ,Chemistry (miscellaneous) ,Geometric mean ,Convex function ,differential subordination ,Differential (mathematics) ,Arithmetic mean - Abstract
In this paper we study a certain differential subordination related to the harmonic mean and its symmetry properties, in the case where a dominant is a linear function. In addition to the known general results for the differential subordinations of the harmonic mean in which the dominant was any convex function, one can study such differential subordinations for the selected convex function. In this case, a reasonable and difficult issue is to look for the best dominant or one that is close to it. This paper is devoted to this issue, in which the dominant is a linear function, and the differential subordination of the harmonic mean is a generalization of the Briot–Bouquet differential subordination.
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- 2021
19. A New Representation of Semiopenness of L-fuzzy Sets in RL-fuzzy Bitopological Spaces
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O. H. Khalil, Ibtesam Alshammari, and A. Ghareeb
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Physics and Astronomy (miscellaneous) ,Generalization ,Mathematics::General Mathematics ,General Mathematics ,Fuzzy set ,pairwise RL-fuzzy semicontinuous ,MathematicsofComputing_GENERAL ,Mathematics::General Topology ,02 engineering and technology ,01 natural sciences ,Fuzzy logic ,Set (abstract data type) ,(i,j)-RL-semiopen gradation ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,0101 mathematics ,Representation (mathematics) ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,Topology (chemistry) ,Mathematics ,RL-fuzzy bitopology ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,pairwise RL-fuzzy semi-compactness ,Algebra ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Chemistry (miscellaneous) ,pairwise RL-fuzzy irresolute ,020201 artificial intelligence & image processing ,Pairwise comparison - Abstract
In this paper, we introduce a new representation of semiopenness of L-fuzzy sets in RL-fuzzy bitopological spaces based on the concept of pseudo-complement. The concepts of pairwise RL-fuzzy semicontinuous and pairwise RL-fuzzy irresolute functions are extended and discussed based on the (i,j)-RL-semiopen gradation. Further, pairwise RL-fuzzy semi-compactness of an L-fuzzy set in RL-fuzzy bitopological spaces are given and characterized. As RL-fuzzy bitopology is a generalization of L-bitopology, RL-bitopology, L-fuzzy bitopology, and RL-fuzzy topology, the results of our paper are more general.
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- 2021
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20. On the Generalized Laplace Transform
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Paul Bosch, Héctor José Carmenate García, José M. Rodríguez, José M. Sigarreta, Comunidad de Madrid, and Ministerio de Ciencia, Innovación y Universidades (España)
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Work (thermodynamics) ,Physics and Astronomy (miscellaneous) ,Matemáticas ,General Mathematics ,Inverse ,010103 numerical & computational mathematics ,01 natural sciences ,Convolution ,Computer Science (miscellaneous) ,Applied mathematics ,convolution ,0101 mathematics ,Harmonic oscillator ,Mathematics ,Laplace transform ,lcsh:Mathematics ,010102 general mathematics ,Order (ring theory) ,fractional derivative ,Fractional derivative ,lcsh:QA1-939 ,Generalized Laplace transform ,Fractional calculus ,generalized Laplace transform ,Chemistry (miscellaneous) ,Fractional differential - Abstract
This article belongs to the Special Issue Discrete and Fractional Mathematics: Symmetry and Applications. In this paper we introduce a generalized Laplace transform in order to work with a very general fractional derivative, and we obtain the properties of this new transform. We also include the corresponding convolution and inverse formula. In particular, the definition of convolution for this generalized Laplace transform improves previous results. Additionally, we deal with the generalized harmonic oscillator equation, showing that this transform and its properties allow one to solve fractional differential equations. We would like to thank the referees for their comments, which have improved the paper. The research of José M. Rodríguez and José M. Sigarreta was supported by a grant from Agencia Estatal de Investigación (PID2019-106433GB-I00/AEI/10.13039/501100011033), Spain. The research of José M. Rodríguez is supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation).
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- 2021
21. New Applications of the Fractional Integral on Analytic Functions
- Author
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Alina Alb Lupaş
- Subjects
fractional integral ,Physics and Astronomy (miscellaneous) ,Confluent hypergeometric function ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,02 engineering and technology ,Function (mathematics) ,differential superordination ,lcsh:QA1-939 ,01 natural sciences ,confluent hypergeometric function ,Dual (category theory) ,Chemistry (miscellaneous) ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Applied mathematics ,020201 artificial intelligence & image processing ,0101 mathematics ,differential subordination ,Differential (mathematics) ,Analytic function ,Mathematics - Abstract
The fractional integral is a function known for the elegant results obtained when introducing new operators, it has proved to have interesting applications. In the present paper, differential subordinations and superodinations for the fractional integral of the confluent hypergeometric function introduced in a previously published paper are presented. A sandwich-type theorem at the end of the original part of the paper connects the outcomes of the studies done using the dual theories.
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- 2021
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22. Differential Subordination and Superordination Results Using Fractional Integral of Confluent Hypergeometric Function
- Author
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Alina Alb Lupaş and Georgia Irina Oros
- Subjects
Subordination (linguistics) ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,subordinant ,02 engineering and technology ,univalent function ,01 natural sciences ,analytic function ,best subordinant ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,0101 mathematics ,dominant ,Mathematics ,best dominant ,Confluent hypergeometric function ,lcsh:Mathematics ,010102 general mathematics ,differential superordination ,Differential operator ,lcsh:QA1-939 ,Dual (category theory) ,Chemistry (miscellaneous) ,differential operator ,020201 artificial intelligence & image processing ,differential subordination ,Differential (mathematics) ,Analytic function ,Univalent function - Abstract
Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories.
- Published
- 2021
23. Applications of Inequalities in the Complex Plane Associated with Confluent Hypergeometric Function
- Author
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Georgia Irina Oros
- Subjects
Subordination (linguistics) ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,subordinant ,02 engineering and technology ,univalent function ,01 natural sciences ,analytic function ,best subordinant ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,0101 mathematics ,Hypergeometric function ,Mathematics ,convex function ,Conjecture ,Confluent hypergeometric function ,lcsh:Mathematics ,010102 general mathematics ,differential superordination ,lcsh:QA1-939 ,confluent hypergeometric function ,Chemistry (miscellaneous) ,020201 artificial intelligence & image processing ,Complex plane ,Differential (mathematics) ,Analytic function ,Univalent function - Abstract
The idea of inequality has been extended from the real plane to the complex plane through the notion of subordination introduced by Professors Miller and Mocanu in two papers published in 1978 and 1981. With this notion came a whole new theory called the theory of differential subordination or admissible functions theory. Later, in 2003, a particular form of inequality in the complex plane was also defined by them as dual notion for subordination, the notion of differential superordination and with it, the theory of differential superordination appeared. In this paper, the theory of differential superordination is applied to confluent hypergeometric function. Hypergeometric functions are intensely studied nowadays, the interest on the applications of those functions in complex analysis being renewed by their use in the proof of Bieberbach’s conjecture given by de Branges in 1985. Using the theory of differential superodination, best subordinants of certain differential superordinations involving confluent (Kummer) hypergeometric function are stated in the theorems and relation with previously obtained results are highlighted in corollaries using particular functions and in a sandwich-type theorem. An example is also enclosed in order to show how the theoretical findings can be applied.
- Published
- 2021
24. Some Gronwall–Bellman Inequalities on Time Scales and Their Continuous Forms: A Survey
- Author
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Francesca Barich
- Subjects
0209 industrial biotechnology ,Physics and Astronomy (miscellaneous) ,Inequality ,nonlinear inequalities ,General Mathematics ,media_common.quotation_subject ,linear inequalities ,02 engineering and technology ,Type (model theory) ,01 natural sciences ,020901 industrial engineering & automation ,Computer Science (miscellaneous) ,Applied mathematics ,integral inequalities ,0101 mathematics ,Mathematics ,media_common ,lcsh:Mathematics ,time scales ,010102 general mathematics ,lcsh:QA1-939 ,Connection (mathematics) ,Linear inequality ,Nonlinear system ,Chemistry (miscellaneous) ,Gronwall-Bellman inequality - Abstract
Some generalizations of the Gronwall&ndash, Bellman (G&ndash, B) inequality are presented in this paper in continuous form and on time scales. After S. Hilger introduced the time scales theory in 1988, over the years many mathematicians have studied new versions of this inequality according to new results, the purpose of this paper is to present some of them. Therefore, in the Introduction, some generalizations of G&ndash, B inequality in continuous forms, linear and nonlinear are presented. In the second section, some important and interesting results on time scales theory are given. In the third and main part of our paper, G&ndash, B inequalities on time scales and their possible connection with G&ndash, B inequalities presented in the introduction are investigated. In particular, in the third section of this work, more attention is given to G&ndash, B type inequalities on time scales discussed in the last four years.
- Published
- 2021
- Full Text
- View/download PDF
25. A Type of Time-Symmetric Stochastic System and Related Games
- Author
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Yufeng Shi, Hui Zhang, Jiaqiang Wen, and Qingfeng Zhu
- Subjects
0209 industrial biotechnology ,Current (mathematics) ,Physics and Astronomy (miscellaneous) ,General Mathematics ,backward doubly stochastic differential equations ,Monotonic function ,02 engineering and technology ,time-delayed generator ,01 natural sciences ,Stochastic differential equation ,symbols.namesake ,020901 industrial engineering & automation ,Maximum principle ,Differential game ,Computer Science (miscellaneous) ,Applied mathematics ,Uniqueness ,0101 mathematics ,Differential (infinitesimal) ,Mathematics ,Nash equilibrium point ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,maximum principle ,Chemistry (miscellaneous) ,Nash equilibrium ,symbols ,stochastic differential game - Abstract
This paper is concerned with a type of time-symmetric stochastic system, namely the so-called forward&ndash, backward doubly stochastic differential equations (FBDSDEs), in which the forward equations are delayed doubly stochastic differential equations (SDEs) and the backward equations are anticipated backward doubly SDEs. Under some monotonicity assumptions, the existence and uniqueness of measurable solutions to FBDSDEs are obtained. The future development of many processes depends on both their current state and historical state, and these processes can usually be represented by stochastic differential systems with time delay. Therefore, a class of nonzero sum differential game for doubly stochastic systems with time delay is studied in this paper. A necessary condition for the open-loop Nash equilibrium point of the Pontriagin-type maximum principle are established, and a sufficient condition for the Nash equilibrium point is obtained. Furthermore, the above results are applied to the study of nonzero sum differential games for linear quadratic backward doubly stochastic systems with delay. Based on the solution of FBDSDEs, an explicit expression of Nash equilibrium points for such game problems is established.
- Published
- 2021
- Full Text
- View/download PDF
26. Stability Analysis and Cauchy Matrix of a Mathematical Model of Hepatitis B Virus with Control on Immune System near Neighborhood of Equilibrium Free Point
- Author
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Salvo Danilo Lombardo, Irina Volinsky, and Paz Cheredman
- Subjects
Physics and Astronomy (miscellaneous) ,exponential stability ,General Mathematics ,medicine.disease_cause ,integro-differential systems ,01 natural sciences ,Stability (probability) ,03 medical and health sciences ,0302 clinical medicine ,Exponential stability ,Computer Science (miscellaneous) ,medicine ,Applied mathematics ,0101 mathematics ,Mathematics ,Hepatitis B virus ,Mathematical model ,lcsh:Mathematics ,010102 general mathematics ,Cauchy distribution ,Hepatitis B ,medicine.disease ,lcsh:QA1-939 ,Cauchy matrix ,feedback control ,immune system ,CTL ,functional differential equations ,Chemistry (miscellaneous) ,030211 gastroenterology & hepatology ,hepatitis B - Abstract
Mathematical models are useful tools to describe the dynamics of infection and predict the role of possible drug combinations. In this paper, we present an analysis of a hepatitis B virus (HBV) model including cytotoxic T lymphocytes (CTL) and antibody responses, under distributed feedback control, expressed as an integral form to predict the effect of a combination treatment with interleukin-2 (IL-2). The method presented in this paper is based on the symmetry properties of Cauchy matrices C(t,s), which allow us to construct and analyze the stability of corresponding integro-differential systems.
- Published
- 2021
27. Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions
- Author
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Daliang Zhao and Juan Mao
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,Banach space ,Fixed-point theorem ,fixed point theorem ,01 natural sciences ,Computer Science::Digital Libraries ,Singularity ,Computer Science (miscellaneous) ,Boundary value problem ,0101 mathematics ,Mathematics ,Variable (mathematics) ,lcsh:Mathematics ,010102 general mathematics ,Mathematical analysis ,Riemann–Stieltjes integral ,fractional differential equations ,cone ,lcsh:QA1-939 ,singularity ,010101 applied mathematics ,Nonlinear system ,Cone (topology) ,Chemistry (miscellaneous) ,Computer Science::Programming Languages ,coupled integral boundary value conditions - Abstract
In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann&ndash, Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions f(t,u,v) and g(t,u,v) in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann&ndash, Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green&rsquo, s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.
- Published
- 2021
28. Secure w-Domination in Graphs
- Author
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Juan A. Rodríguez-Velázquez, Alejandro Estrada-Moreno, and Abel Cabrera Martínez
- Subjects
Physics and Astronomy (miscellaneous) ,lcsh:Mathematics ,General Mathematics ,0102 computer and information sciences ,02 engineering and technology ,w-domination ,lcsh:QA1-939 ,01 natural sciences ,Graph ,Vertex (geometry) ,Combinatorics ,secure Italian domination ,weak roman domination ,010201 computation theory & mathematics ,Chemistry (miscellaneous) ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,020201 artificial intelligence & image processing ,secure domination ,Mathematics ,MathematicsofComputing_DISCRETEMATHEMATICS ,Computer Science::Cryptography and Security - Abstract
This paper introduces a general approach to the idea of protection of graphs, which encompasses the known variants of secure domination and introduces new ones. Specifically, we introduce the study of secure w-domination in graphs, where w=(w0,w1,⋯,wl) is a vector of nonnegative integers such that w0&ge, 1. The secure w-domination number is defined as follows. Let G be a graph and N(v) the open neighborhood of v&isin, V(G). We say that a function f:V(G)⟶{0,1,⋯,l} is a w-dominating function if f(N(v))=&sum, u&isin, N(v)f(u)&ge, wi for every vertex v with f(v)=i. The weight of f is defined to be &omega, (f)=&sum, v&isin, V(G)f(v). Given a w-dominating function f and any pair of adjacent vertices v,u&isin, V(G) with f(v)=0 and f(u)>, 0, the function fu&rarr, v is defined by fu&rarr, v(v)=1, fu&rarr, v(u)=f(u)&minus, 1 and fu&rarr, v(x)=f(x) for every x&isin, V(G)∖{u,v}. We say that a w-dominating function f is a secure w-dominating function if for every v with f(v)=0, there exists u&isin, N(v) such that f(u)>, 0 and fu&rarr, v is a w-dominating function as well. The secure w-domination number of G, denoted by &gamma, ws(G), is the minimum weight among all secure w-dominating functions. This paper provides fundamental results on &gamma, ws(G) and raises the challenge of conducting a detailed study of the topic.
- Published
- 2020
- Full Text
- View/download PDF
29. Total Domination in Rooted Product Graphs
- Author
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Juan A. Rodríguez-Velázquez and Abel Cabrera Martínez
- Subjects
Discrete mathematics ,Physics and Astronomy (miscellaneous) ,Domination analysis ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Graph theory ,010103 numerical & computational mathematics ,lcsh:QA1-939 ,01 natural sciences ,Graph ,rooted product graph ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,total domination ,0101 mathematics ,Mathematics ,domination - Abstract
During the last few decades, domination theory has been one of the most active areas of research within graph theory. Currently, there are more than 4400 published papers on domination and related parameters. In the case of total domination, there are over 580 published papers, and 50 of them concern the case of product graphs. However, none of these papers discusses the case of rooted product graphs. Precisely, the present paper covers this gap in the theory. Our goal is to provide closed formulas for the total domination number of rooted product graphs. In particular, we show that there are four possible expressions for the total domination number of a rooted product graph, and we characterize the graphs reaching these expressions.
- Published
- 2020
- Full Text
- View/download PDF
30. Optimal and Nonoptimal Gronwall Lemmas
- Author
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Daniela Marian, Sorina Anamaria Ciplea, and Nicolaie Lungu
- Subjects
Discrete mathematics ,Physics and Astronomy (miscellaneous) ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,Type (model theory) ,lcsh:QA1-939 ,optimal Bihari type inequality ,01 natural sciences ,Upper and lower bounds ,abstract Gronwall lemma ,Picard operators ,010101 applied mathematics ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,optimal Gronwall lemma ,Wendorf type inequality ,0101 mathematics ,optimal Riccati type inequality ,Mathematics - Abstract
In this paper, we study some optimal inequalities of the Riccati type and of the Bihari type. We also consider nonoptimal inequalities of the Wendorf type. At the same time, we get a partial answer to Problems 5 and 9, formulated by I. A. Rus. This paper is also motivated by the fact that, in many inequalities, the upper bound is not an optimal one.
- Published
- 2020
- Full Text
- View/download PDF
31. Symmetric Identities for Carlitz’s Type Higher-Order (p,q)-Genocchi Polynomials
- Author
-
Ahyun Kim and Cheon Seoung Ryoo
- Subjects
Physics and Astronomy (miscellaneous) ,Distribution (number theory) ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,02 engineering and technology ,Type (model theory) ,lcsh:QA1-939 ,01 natural sciences ,Combinatorics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Chemistry (miscellaneous) ,symmetric identities ,alternating power sums ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Order (group theory) ,020201 artificial intelligence & image processing ,higher-order (p,q)-Genocchi polynomials ,0101 mathematics ,Mathematics - Abstract
In this paper, we study Carlitz&rsquo, s type higher-order (p,q)-Genocchi polynomials. To be specific, we define Carlitz&rsquo, s type higher-order (p,q)-Genocchi polynomials and Carlitz&rsquo, s type higher-order (h,p,q)-Genocchi polynomials. This paper also explores properties including distribution relation and symmetric identities. In addition, we find alternating (p,q)-power sums. We identify symmetric identities using Carlitz&rsquo, s type higher-order (h,p,q)-Genocchi polynomials and alternating (p,q)-power sums.
- Published
- 2020
- Full Text
- View/download PDF
32. Estimates of Coefficient Functionals for Functions Convex in the Imaginary-Axis Direction
- Author
-
Paweł Zaprawa and Katarzyna Tra̧bka-Wiȩcław
- Subjects
Pure mathematics ,Class (set theory) ,convexity in imaginary-axis direction ,coefficient problems ,Physics and Astronomy (miscellaneous) ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Regular polygon ,close-to-convex functions ,typically real functions ,lcsh:QA1-939 ,01 natural sciences ,Unit disk ,010101 applied mathematics ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,successive coefficients ,0101 mathematics ,Mathematics - Abstract
Let C0(h) be a subclass of analytic and close-to-convex functions defined in the open unit disk by the formula ()(1&minus, z2)f&prime, (z)}>, 0. In this paper, some coefficient problems for C0(h) are considered. Some properties and bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates of the difference and of sum of successive coefficients, bounds of the sum of the first n coefficients and bounds of the n-th coefficient. The obtained results are used to determine coefficient estimates for both functions convex in the imaginary-axis direction with real coefficients and typically real functions. Moreover, the sum of the first initial coefficients for functions with a positive real part and with a fixed second coefficient is estimated.
- Published
- 2020
33. D-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations
- Author
-
Michal Fečkan, Natalia Dilna, and Mykola Solovyov
- Subjects
Cauchy problem ,Physics and Astronomy (miscellaneous) ,Differential equation ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Mathematical analysis ,Scalar (mathematics) ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Symmetric property ,Chemistry (miscellaneous) ,symmetric solution ,Computer Science (miscellaneous) ,Symmetric solution ,Initial value problem ,unique solution ,0101 mathematics ,D stability ,D-stability ,Mathematics - Abstract
This paper presents a method of establishing the D-stability terms of the symmetric solution of scalar symmetric linear and nonlinear functional differential equations. We determine the general conditions of the unique solvability of the initial value problem for symmetric functional differential equations. Here, we show the conditions of the symmetric property of the unique solution of symmetric functional differential equations. Furthermore, in this paper, an illustration of a particular symmetric equation is presented. In this example, all theoretical investigations referred to earlier are demonstrated. In addition, we graphically demonstrate two possible linear functions with the required symmetry properties.
- Published
- 2020
34. Analysis of Homotopy Decomposition Varieties in Quotient Topological Spaces
- Author
-
Susmit Bagchi and Gyeongsang National University
- Subjects
Pure mathematics ,Connected space ,Fundamental group ,Physics and Astronomy (miscellaneous) ,General Mathematics ,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] ,Topological space ,01 natural sciences ,Mathematics::Algebraic Topology ,Separable space ,0103 physical sciences ,Computer Science (miscellaneous) ,[MATH]Mathematics [math] ,0101 mathematics ,010306 general physics ,Quotient ,Mathematics ,fundamental groups ,Homotopy ,lcsh:Mathematics ,010102 general mathematics ,homotopy ,Quotient space (topology) ,lcsh:QA1-939 ,topological spaces ,Sierpiński space ,Chemistry (miscellaneous) ,[MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT] ,quotient topology ,embeddings - Abstract
The fundamental groups and homotopy decompositions of algebraic topology have applications in systems involving symmetry breaking with topological excitations. The main aim of this paper is to analyze the properties of homotopy decompositions in quotient topological spaces depending on the connectedness of the space and the fundamental groups. This paper presents constructions and analysis of two varieties of homotopy decompositions depending on the variations in topological connectedness of decomposed subspaces. The proposed homotopy decomposition considers connected fundamental groups, where the homotopy equivalences are relaxed and the homeomorphisms between the fundamental groups are maintained. It is considered that one fundamental group is strictly homotopy equivalent to a set of 1-spheres on a plane and as a result it is homotopy rigid. The other fundamental group is topologically homeomorphic to the first one within the connected space and it is not homotopy rigid. The homotopy decompositions are analyzed in quotient topological spaces, where the base space and the quotient space are separable topological spaces. In specific cases, the decomposed quotient space symmetrically extends Sierpinski space with respect to origin. The connectedness of fundamental groups in the topological space is maintained by open curve embeddings without enforcing the conditions of homotopy classes on it. The extended decomposed quotient topological space preserves the trivial group structure of Sierpinski space.
- Published
- 2020
35. The Sequential and Contractible Topological Embeddings of Functional Groups
- Author
-
Susmit Bagchi
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,Topological space ,Topology ,01 natural sciences ,Contractible space ,group decomposition ,Separable space ,Computer Science (miscellaneous) ,0601 history and archaeology ,0101 mathematics ,Mathematics ,homeomorphism ,lcsh:Mathematics ,010102 general mathematics ,Hausdorff space ,Schoenflies embeddings ,06 humanities and the arts ,sequence ,lcsh:QA1-939 ,Circle group ,topological spaces ,060105 history of science, technology & medicine ,Chemistry (miscellaneous) ,Embedding ,Subspace topology ,Normal space - Abstract
The continuous and injective embeddings of closed curves in Hausdorff topological spaces maintain isometry in subspaces generating components. An embedding of a circle group within a topological space creates isometric subspace with rotational symmetry. This paper introduces the generalized algebraic construction of functional groups and its topological embeddings into normal spaces maintaining homeomorphism of functional groups. The proposed algebraic construction of functional groups maintains homeomorphism to rotationally symmetric circle groups. The embeddings of functional groups are constructed in a sequence in the normal topological spaces. First, the topological decomposition and associated embeddings of a generalized group algebraic structure in the lower dimensional space is presented. It is shown that the one-point compactification property of topological space containing the decomposed group embeddings can be identified. Second, the sequential topological embeddings of functional groups are formulated. The proposed sequential embeddings follow Schoenflies property within the normal topological space. The preservation of homeomorphism between disjoint functional group embeddings under Banach-type contraction is analyzed taking into consideration that the underlying topological space is Hausdorff and the embeddings are in a monotone class. It is shown that components in a monotone class of isometry are not separable, whereas the multiple disjoint monotone class of embeddings are separable. A comparative analysis of the proposed concepts and formulations with respect to the existing structures is included in the paper.
- Published
- 2020
- Full Text
- View/download PDF
36. Fixed Point Problems on Generalized Metric Spaces in Perov’s Sense
- Author
-
Liliana Guran, Asim Naseem, and Monica-Felicia Bota
- Subjects
Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Data dependence ,Stability (learning theory) ,Type (model theory) ,Fixed point ,Ulam–Hyers stability ,01 natural sciences ,coupled fixed points ,well-posedness ,Computer Science (miscellaneous) ,0101 mathematics ,Mathematics ,lcsh:Mathematics ,data dependence ,010102 general mathematics ,Perov space ,Sense (electronics) ,generalized w-distance ,lcsh:QA1-939 ,010101 applied mathematics ,Metric space ,fixed point ,Chemistry (miscellaneous) ,Metric (mathematics) ,Symmetry (geometry) - Abstract
The aim of this paper is to give some fixed point results in generalized metric spaces in Perov&rsquo, s sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy&ndash, Rogers type. The second part of the paper is devoted to the study of the data dependence, the well-posedness, and the Ulam&ndash, Hyers stability of the fixed point problem. An example is also given to sustain the presented results.
- Published
- 2020
37. On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks
- Author
-
Marco Menale, Carlo Bianca, Bruno Carbonaro, Bianca, Carlo, Carbonaro, Bruno, and Menale, Marco
- Subjects
State variable ,Physics and Astronomy (miscellaneous) ,integro-differential equation ,General Mathematics ,Complex system ,010103 numerical & computational mathematics ,complexity ,kinetic theory ,Cauchy problem ,nonlinearity ,Mathematical models, Boltzmann equation, Vlasov equation, Kinetic Theory for Active Particles, well-posedness problems ,01 natural sciences ,Quadratic equation ,Computer Science (miscellaneous) ,Applied mathematics ,Initial value problem ,Uniqueness ,0101 mathematics ,Mathematics ,Variable (mathematics) ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,Nonlinear system ,Chemistry (miscellaneous) - Abstract
This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic theory frameworks for the modeling of nonequilibrium complex systems composed by particles whose microscopic state includes a vectorial state variable. The mathematical analysis refers to the global existence and uniqueness of the solution of the related Cauchy problem. Specifically, the paper is divided in two parts. In the first part the thermostatted framework with a continuous vectorial variable is proposed and analyzed. The framework consists of a system of partial integro-differential equations with quadratic type nonlinearities. In the second part the thermostatted framework with a discrete vectorial variable is investigated. Real world applications, such as social systems and crowd dynamics, and future research directions are outlined in the paper.
- Published
- 2020
38. Oscillatory Behavior of Fourth-Order Differential Equations with Neutral Delay
- Author
-
Rami Ahmad El-Nabulsi, Osama Moaaz, and Omar Bazighifan
- Subjects
fourth-order differential equations ,Physics and Astronomy (miscellaneous) ,Differential equation ,General Mathematics ,lcsh:Mathematics ,Mathematical analysis ,neutral delay ,02 engineering and technology ,oscillation ,lcsh:QA1-939 ,01 natural sciences ,Symmetry (physics) ,Complement (complexity) ,010101 applied mathematics ,Fourth order ,Chemistry (miscellaneous) ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Oscillation (cell signaling) ,020201 artificial intelligence & image processing ,0101 mathematics ,Neutral differential equations ,Mathematics - Abstract
In this paper, new sufficient conditions for oscillation of fourth-order neutral differential equations are established. One objective of our paper is to further improve and complement some well-known results which were published recently in the literature. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. An example is given to illustrate the importance of our results.
- Published
- 2020
- Full Text
- View/download PDF
39. Exceptional Set for Sums of Symmetric Mixed Powers of Primes
- Author
-
Min Zhang, Jinjiang Li, Zhuo Zhang, and Chao Liu
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,Mathematics::Number Theory ,Mathematics::Classical Analysis and ODEs ,0102 computer and information sciences ,01 natural sciences ,Upper and lower bounds ,Prime (order theory) ,Square (algebra) ,circle method ,Set (abstract data type) ,Combinatorics ,Computer Science (miscellaneous) ,0101 mathematics ,Representation (mathematics) ,Mathematics ,Mathematics::Functional Analysis ,Mathematics::Complex Variables ,lcsh:Mathematics ,010102 general mathematics ,Waring–Goldbach problem ,Cube (algebra) ,Mathematics::Spectral Theory ,exceptional set ,lcsh:QA1-939 ,symmetric form ,010201 computation theory & mathematics ,Chemistry (miscellaneous) - Abstract
The main purpose of this paper is to use the Hardy&ndash, Littlewood method to study the solvability of mixed powers of primes. To be specific, we consider the even integers represented as the sum of one prime, one square of prime, one cube of prime, and one biquadrate of prime. However, this representation can not be realized for all even integers. In this paper, we establish the exceptional set of this kind of representation and give an upper bound estimate.
- Published
- 2020
- Full Text
- View/download PDF
40. Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space
- Author
-
Amelia Bucur
- Subjects
Pure mathematics ,Physics and Astronomy (miscellaneous) ,multivalued left-weighted mean contraction ,General Mathematics ,lcsh:Mathematics ,fixed points ,010102 general mathematics ,Function (mathematics) ,Fixed point ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Metric space ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,In real life ,Order (group theory) ,0101 mathematics ,Equilibrium solution ,Weighted arithmetic mean ,multivalued right-weighted mean contraction ,regular-global-inf function ,Mathematics - Abstract
This paper defines two new concepts: the concept of multivalued left-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space and the concept of multivalued right-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space, and demonstrates fixed-point theorems for them. For these, we demonstrated two fixed-point existence theorems and their corollaries, by using the properties of the regular-global-inf function and the properties of symmetric generalized metric spaces, respectively. Moreover, we demonstrated that the theorems can be applied in particular cases of inclusion systems. This article contains not only an example of application in science, but also an example of application in real life, in biology, in order to find an equilibrium solution to a prey&ndash, predator-type problem. The results of this paper extend theorems for multivalued left-weighted mean contractions in the generalized sense of Nadler, demonstrating that some of the results given by Rus (2008), Mureșan (2002), and Nadler (1969) in metric spaces can also be proved in symmetric generalized metric spaces.
- Published
- 2020
- Full Text
- View/download PDF
41. CARS Algorithm-Based Detection of Wheat Moisture Content before Harvest
- Author
-
Chong Dongfeng, Wanzhang Wang, Zhang Boyang, and Hong Ji
- Subjects
panicle moisture content (pmc) ,Physics and Astronomy (miscellaneous) ,Logarithm ,Correlation coefficient ,Mean squared error ,wheat moisture content (wmc) ,cars algorithm ,General Mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,Approximation error ,wheat ,Partial least squares regression ,Computer Science (miscellaneous) ,Range (statistics) ,0101 mathematics ,Mathematics ,lcsh:Mathematics ,spectral detection ,0402 animal and dairy science ,Univariate ,Regression analysis ,04 agricultural and veterinary sciences ,lcsh:QA1-939 ,040201 dairy & animal science ,Chemistry (miscellaneous) ,Algorithm - Abstract
To rapidly detect the wheat moisture content (WMC) without harm to the wheat and before harvest, this paper measured wheat and panicle moisture content (PMC) and the corresponding spectral reflectance of panicle before harvest at the Beijing Tongzhou experimental station of China Agricultural University. Firstly, we used correlation analysis to determine the optimal regression model of WMC and PMC. Secondly, we derived the spectral sensitive band of PMC before filtering the redundant variables competitive adaptive reweighted sampling (CARS) to select the variable subset with the least error. Finally, partial least squares regression (PLSR) was used to build and analyze the prediction model of PMC. At the early stage of wheat harvest, a high correlation existed between WMC and PMC. Among all regression models such as exponential, univariate linear, polynomial models, and the power function regression model, the logarithm regression model was the best. The determination coefficients of the modeling sample were: R2 = 0.9284, the significance F = 362.957, the determination coefficient of calibration sample R2v = 0.987, the root mean square error RMSEv = 3.859, and the relative error REv = 7.532. Within the range of 350&ndash, 2500 nm, bands of 728&ndash, 907 nm, 1407&ndash, 1809 nm, and 1940&ndash, 2459 nm had a correlation coefficient of PMC and wavelength reflectivity higher than 0.6. This paper used the CARS algorithm to optimize the variables and obtained the best variable subset, which included 30 wavelength variables. The PLSR model was established based on 30 variables optimized by the CARS algorithm. Compared with the all-sensitive band, which had 1103 variables, the PLSR model not only reduced the number of variables by 1073, but also had a higher accuracy in terms of prediction. The results showed that: RMSEC = 0.9301, R2c = 0.995, RMSEP = 2.676, R2p = 0.945, and RPD = 3.362, indicating that the CARS algorithm could effectively remove the variables of spectral redundant information. The CARS algorithm provided a new way of thinking for the non-destructive and rapid detection of WMC before harvest.
- Published
- 2020
42. Certain Results for the Twice-Iterated 2D q-Appell Polynomials
- Author
-
Hari M. Srivastava, Abdulghani Muhyi, Ghazala Yasmin, Serkan Araci, and HKÜ, İktisadi, İdari ve Sosyal Bilimler Fakültesi, İktisat Bölümü
- Subjects
Surface (mathematics) ,Class (set theory) ,Polynomial ,Pure mathematics ,recurrence relations ,Physics and Astronomy (miscellaneous) ,General Mathematics ,apostol type bernoulli ,01 natural sciences ,twice-iterated 2D q-Appell polynomials ,2D q-Genocchi polynomials ,Computer Science (miscellaneous) ,2d q-bernoulli polynomials ,0101 mathematics ,2d q-genocchi polynomials ,Mathematics ,2D q-Euler polynomials ,Recurrence relation ,Series (mathematics) ,2d q-euler polynomials ,lcsh:Mathematics ,010102 general mathematics ,2D q-Appell polynomials ,determinant expressions ,Generating function ,2d q-appell polynomials ,lcsh:QA1-939 ,Expression (mathematics) ,010101 applied mathematics ,euler and genocchi polynomials ,Chemistry (miscellaneous) ,Iterated function ,twice-iterated 2d q-appell polynomials - Abstract
In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of this polynomial class are established. The determinant expression for the twice-iterated 2D q-Appell polynomials is also derived. Further, certain twice-iterated 2D q-Appell and mixed type special q-polynomials are considered as members of this polynomial class. The determinant expressions and some other properties of these associated members are also obtained. The graphs and surface plots of some twice-iterated 2D q-Appell and mixed type 2D q-Appell polynomials are presented for different values of indices by using Matlab. Moreover, some areas of potential applications of the subject matter of, and the results derived in, this paper are indicated.
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- 2019
43. Hankel Determinants for Univalent Functions Related to the Exponential Function
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Paweł Zaprawa
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Pure mathematics ,Class (set theory) ,starlike functions ,convex functions ,Physics and Astronomy (miscellaneous) ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,exponential function ,02 engineering and technology ,Function (mathematics) ,lcsh:QA1-939 ,01 natural sciences ,Unit disk ,Exponential function ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Chemistry (miscellaneous) ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,020201 artificial intelligence & image processing ,0101 mathematics ,Invariant (mathematics) ,Convex function ,Mathematics ,hankel determinant - Abstract
Recently, two classes of univalent functions S e * and K e were introduced and studied. A function f is in S e * if it is analytic in the unit disk, f ( 0 ) = f &prime, ( 0 ) - 1 = 0 and z f &prime, ( z ) f ( z ) ≺ e z . On the other hand, g &isin, K e if and only if z g &prime, &isin, S e * . Both classes are symmetric, or invariant, under rotations. In this paper, we solve a few problems connected with the coefficients of functions in these classes. We find, among other things, the estimates of Hankel determinants: H 2 , 1 , H 2 , 2 , H 3 , 1 . All these estimates improve the known results. Moreover, almost all new bounds are sharp. The main idea used in the paper is based on expressing the discussed functionals depending on the fixed second coefficient of a function in a given class.
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- 2019
44. On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations
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Sanda Micula
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fixed-point theory ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Numerical analysis ,lcsh:Mathematics ,Fixed-point theorem ,010103 numerical & computational mathematics ,Fixed point ,lcsh:QA1-939 ,01 natural sciences ,Integral equation ,010101 applied mathematics ,mixed Volterra–Fredholm integral equations ,cubature formulas ,Chemistry (miscellaneous) ,Fixed-point iteration ,Convergence (routing) ,Picard iteration ,Computer Science (miscellaneous) ,Applied mathematics ,Uniqueness ,0101 mathematics ,Trapezoidal rule ,numerical approximation ,Mathematics - Abstract
In this paper, we propose a class of simple numerical methods for approximating solutions of one-dimensional mixed Volterra&ndash, Fredholm integral equations of the second kind. These methods are based on fixed point results for the existence and uniqueness of the solution (results which also provide successive iterations of the solution) and suitable cubature formulas for the numerical approximations. We discuss in detail a method using Picard iteration and the two-dimensional composite trapezoidal rule, giving convergence conditions and error estimates. The paper concludes with numerical experiments and a discussion of the methods proposed.
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- 2019
45. The Existence of Two Homogeneous Geodesics in Finsler Geometry
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Zdeněk Dušek
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Pure mathematics ,homogeneous Finsler space ,Physics and Astronomy (miscellaneous) ,Geodesic ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,homogeneous manifold ,lcsh:QA1-939 ,01 natural sciences ,Chemistry (miscellaneous) ,Homogeneous ,homogeneous geodesic ,0103 physical sciences ,Computer Science (miscellaneous) ,Mathematics::Metric Geometry ,010307 mathematical physics ,Finsler manifold ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
The existence of a homogeneous geodesic in homogeneous Finsler manifolds was positively answered in previous papers. However, the result is not optimal. In the present paper, this result is refined and the existence of at least two homogeneous geodesics in any homogeneous Finsler manifold is proved. In a previous paper, examples of Randers metrics which admit just two homogeneous geodesics were constructed, which shows that the present result is the best possible.
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- 2019
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46. On Invariant Subspaces for the Shift Operator
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Junfeng Liu
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Physics and Astronomy (miscellaneous) ,Function space ,General Mathematics ,reducing subspace ,Shift operator ,01 natural sciences ,hyperinvariant subspace ,Combinatorics ,symbols.namesake ,invariant subspace ,0103 physical sciences ,Computer Science (miscellaneous) ,0101 mathematics ,Invariant (mathematics) ,Mathematics ,Mathematics::Functional Analysis ,shift operator ,lcsh:Mathematics ,010102 general mathematics ,Invariant subspace ,Hardy space ,lcsh:QA1-939 ,Linear subspace ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Chemistry (miscellaneous) ,Bergman space ,lebesgue space ,symbols ,Standard probability space ,010307 mathematical physics ,hardy space - Abstract
In this paper, we improve two known invariant subspace theorems. More specifically, we show that a closed linear subspace M in the Hardy space H p ( D ) ( 1 &le, p <, &infin, ) is invariant under the shift operator M z on H p ( D ) if and only if it is hyperinvariant under M z , and that a closed linear subspace M in the Lebesgue space L 2 ( &part, D ) is reducing under the shift operator M e i &theta, on L 2 ( &part, D ) if and only if it is hyperinvariant under M e i &theta, At the same time, we show that there are two large classes of invariant subspaces for M e i &theta, that are not hyperinvariant subspaces for M e i &theta, and are also not reducing subspaces for M e i &theta, Moreover,we still show that there is a large class of hyperinvariant subspaces for M z that are not reducing subspaces for M z . Furthermore, we gave two new versions of the formula of the reproducing function in the Hardy space H 2 ( D ) , which are the analogue of the formula of the reproducing function in the Bergman space A 2 ( D ) . In addition, the conclusions in this paper are interesting now, or later if they are written into the literature of invariant subspaces and function spaces.
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- 2019
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- View/download PDF
47. Relations among the Riemann Zeta and Hurwitz Zeta Functions, as Well as Their Products
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Athanassios S. Fokas and A. C. L. Ashton
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Mean square ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,Mathematics::General Mathematics ,Mathematics::Number Theory ,General Mathematics ,01 natural sciences ,Hurwitz zeta function ,symbols.namesake ,Simple (abstract algebra) ,FOS: Mathematics ,Computer Science (miscellaneous) ,Riemann zeta function ,Number Theory (math.NT) ,Complex Variables (math.CV) ,0101 mathematics ,Mathematics ,Lindelöf hypothesis ,Mathematics - Number Theory ,Series (mathematics) ,Mathematics - Complex Variables ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,010101 applied mathematics ,11M35, 11L07 ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,asymptotics ,Chemistry (miscellaneous) ,symbols - Abstract
In this paper, several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation of the important results of Katsurada and Matsumoto on the mean square of the Hurwitz zeta function. Also, a relation derived here provides the starting point of a novel approach which, in a series of companion papers, yields a formal proof of the Lindelö, f hypothesis. Some of the above relations motivate the need for analysing the large &alpha, behaviour of the modified Hurwitz zeta function &zeta, 1 ( s , &alpha, ) , s &isin, C , &alpha, &isin, ( 0 , &infin, ) , which is also presented here.
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- 2019
48. Optimal Trajectory Synthesis for Spacecraft Asteroid Rendezvous
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Ranjan Vepa and M. Hasan Shaheed
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asteroids ,Physics and Astronomy (miscellaneous) ,General Mathematics ,02 engineering and technology ,01 natural sciences ,optimal trajectory synthesis ,0203 mechanical engineering ,0103 physical sciences ,QA1-939 ,Computer Science (miscellaneous) ,State space ,Aerospace engineering ,010303 astronomy & astrophysics ,Physics ,020301 aerospace & aeronautics ,Spacecraft ,State-space representation ,business.industry ,Rendezvous ,dynamic modelling of satellite relative motion ,simulation ,optimal control of relative motion ,Orbit ,Chemistry (miscellaneous) ,Asteroid ,Physics::Space Physics ,Trajectory ,Satellite ,Astrophysics::Earth and Planetary Astrophysics ,business ,Mathematics - Abstract
Several researchers are considering the plausibility of being able to rapidly launch a mission to an asteroid, which would fly in close proximity of the asteroid to deliver an impulse in a particular direction so as to deflect the asteroid from its current orbit. Planetary motion, in general, and the motion of asteroids, in particular, are subject to planetary influences that are characterised by a kind of natural symmetry, which results in an asteroid orbiting in a stable and periodic or almost periodic orbit exhibiting a number of natural orbital symmetries. Tracking and following an asteroid, in close proximity, is the subject of this paper. In this paper, the problem of synthesizing an optimal trajectory to a NEO such as an asteroid is considered. A particular strategy involving the optimization of a co-planar trajectory segment that permits the satellite to approach and fly alongside the asteroid is chosen. Two different state space representations of the Hill–Clohessy–Wiltshire (HCW) linearized equations of relative motion are used to obtain optimal trajectories for a spacecraft approaching an asteroid. It is shown that by using a state space representation of HCW equations where the secular states are explicitly represented, the optimal trajectories are not only synthesized rapidly but also result in lower magnitudes of control inputs which must be applied continuously over extended periods of time. Thus, the solutions obtained are particularly suitable for low thrust control of the satellites orbit which can be realized by electric thrusters.
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- 2021
49. Well-Posedness and Porosity for Symmetric Optimization Problems
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Alexander J. Zaslavski
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Work (thermodynamics) ,Optimization problem ,Physics and Astronomy (miscellaneous) ,General Mathematics ,0211 other engineering and technologies ,02 engineering and technology ,porous set ,01 natural sciences ,Complete metric space ,Set (abstract data type) ,QA1-939 ,Computer Science (miscellaneous) ,generic element ,Applied mathematics ,Porous set ,0101 mathematics ,Complement (set theory) ,Mathematics ,021103 operations research ,010102 general mathematics ,Chemistry (miscellaneous) ,complete metric space ,Bounded function ,Computer Science::Programming Languages ,Minification ,lower semi-continuous function - Abstract
In the present work, we investigate a collection of symmetric minimization problems, which is identified with a complete metric space of lower semi-continuous and bounded from below functions. In our recent paper, we showed that for a generic objective function, the corresponding symmetric optimization problem possesses two solutions. In this paper, we strengthen this result using a porosity notion. We investigate the collection of all functions such that the corresponding optimization problem is well-posed and prove that its complement is a σ-porous set.
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- 2021
50. Newton’s Third Law in the Framework of Special Relativity for Charged Bodies
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Shailendra Rajput and Asher Yahalom
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Physics ,relativity ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Newton’s third law ,electromagnetism ,Energy–momentum relation ,02 engineering and technology ,Special relativity ,021001 nanoscience & nanotechnology ,01 natural sciences ,Relativity of simultaneity ,Action (physics) ,Momentum ,Theory of relativity ,Classical mechanics ,Chemistry (miscellaneous) ,Electromagnetism ,0103 physical sciences ,QA1-939 ,Computer Science (miscellaneous) ,Speed of light ,010306 general physics ,0210 nano-technology ,Mathematics - Abstract
Newton’s third law states that any action is countered by a reaction of equal magnitude but opposite direction. The total force in a system not affected by external forces is, therefore, zero. However, according to the principles of relativity, a signal cannot propagate at speeds exceeding the speed of light. Hence, the action and reaction cannot be generated at the same time due to the relativity of simultaneity. Thus, the total force cannot be null at a given time. In a previous paper, we showed that Newton’s third law cannot strictly hold in a distributed system where the different parts are at a finite distance from each other. This analysis led to the suggestion of a relativistic engine. As the system is affected by a total force for a finite period, the system acquires mechanical momentum and energy. The subject of momentum conversation was discussed in another previous paper, while energy conservation was discussed in additional previous papers. In those works, we relied on the fact that the bodies were macroscopically natural. Here, we relax this assumption and study charged bodies, thus analyzing the consequences on a possible electric relativistic engine.
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- 2021
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