76 results
Search Results
2. On the r-dynamic coloring of the direct product of a path with either a complete graph or a wheel graph
- Author
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M. Venkatachalam, Raúl M. Falcón, T. Deepa, Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII), and Junta de Andalucía
- Subjects
Discrete mathematics ,direct product ,General Mathematics ,lcsh:Mathematics ,Complete graph ,path ,lcsh:QA1-939 ,wheel graph ,Path (graph theory) ,Wheel graph ,Chromatic scale ,r-dynamic coloring ,complete graph ,Direct product ,Mathematics ,MathematicsofComputing_DISCRETEMATHEMATICS - Abstract
In this paper, it is explicitly determined the r-dynamic chromatic number of the direct product of any given path with either a complete graph or a wheel graph. Illustrative examples are shown for each one of the cases that are studied throughout the paper. Junta de Andalucía FQM-016
- Published
- 2021
3. Error estimates of variational discretization for semilinear parabolic optimal control problems
- Author
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Zuliang Lu, Xuejiao Chen, Chunjuan Hou, and Fei Huang
- Subjects
Discretization ,General Mathematics ,lcsh:Mathematics ,Type (model theory) ,semilinear parabolic equations ,Residual ,Optimal control ,lcsh:QA1-939 ,Backward Euler method ,Omega ,Finite element method ,error estimates ,optimal control problems ,A priori and a posteriori ,Applied mathematics ,finite element methods ,Mathematics - Abstract
In this paper, variational discretization directed against the optimal control problem governed by nonlinear parabolic equations with control constraints is studied. It is known that the a priori error estimates is $|||u-u_h|||_{L^\infty(J; L^2(\Omega))} = O(h+k)$ using backward Euler method for standard finite element. In this paper, the better result $|||u-u_h|||_{L^\infty(J; L^2(\Omega))} = O(h^2+k)$ is gained. Beyond that, we get a posteriori error estimates of residual type.
- Published
- 2021
4. On the extinction of continuous-state branching processes in random environments
- Author
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Xiangqi Zheng
- Subjects
education.field_of_study ,Extinction ,extinction ,General Mathematics ,lcsh:Mathematics ,Population ,branching processes ,Asymptotic distribution ,State (functional analysis) ,virus ,lcsh:QA1-939 ,epidemic ,Branching (linguistics) ,Distribution (mathematics) ,Transformation (function) ,Quantitative Biology::Populations and Evolution ,Statistical physics ,asymptotic behavior ,time-space transformation ,education ,Epidemic model ,Mathematics - Abstract
This paper establishes a model of continuous-state branching processes with time inhomogeneous competition in Levy random environments. Some results on extinction are presented, including the distribution of the extinction time, the limiting distribution conditioned on large extinction times and the asymptotic behavior near extinction. This paper also provides a new time-space transformation which can be used for further exploration in similar models. The results are applied to an epidemic model to describe the dynamics of infectious population and a virus model to describe the dynamics of viral load.
- Published
- 2021
5. MQC-MB: Multiphoton Quantum Communication Using Multiple-Beam Concept in Free Space Optical Channel
- Author
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Zuriati Ahmad Zukarnain, Majed Khodr, Idawaty Ahmad, Zurina Mohd Hanapi, and Nur Ziadah Harun
- Subjects
Photon ,Physics and Astronomy (miscellaneous) ,mean photon number ,quantum key distribution ,General Mathematics ,Quantum key distribution ,Topology ,01 natural sciences ,010309 optics ,multiple-beam ,0103 physical sciences ,Computer Science (miscellaneous) ,Communication source ,010306 general physics ,Quantum information science ,Quantum ,single-beam ,Computer Science::Cryptography and Security ,Physics ,lcsh:Mathematics ,Transmitter ,atmospheric attenuation ,Quantum Physics ,Polarization (waves) ,lcsh:QA1-939 ,Chemistry (miscellaneous) ,geometrical loss ,Beam divergence - Abstract
Multiphoton Quantum Key Distribution (QKD) has recently been proposed to exchange the secret keys using the rotational of polarization over a multi-stage protocol. It has the ability to outperform the weaknesses of a single photon QKD by improving the generation of key rate and distance range. This paper investigates the theoretical aspects of multiphoton QKD protocol&rsquo, s performance over free space optic (FSO) networks. The most common setup for quantum communication is the single-beam approach. However, the single-beam setup has limitations in terms of high geometrical loss. In this paper, the symmetry multiple-beam for quantum communication which is called as Multiphoton Quantum Communication-Multiple Beam (MQC-MB) is proposed to transmit the multiphoton from the sender to the receiver in order to minimize the impact of geometrical loss that is faced by the single-beam setup. The analysis was carried out through mathematical analysis by establishing the FSO quantum model with the effects of atmospheric and geometrical loss as well as considering atmospheric turbulence modeled by log-normal distribution. The design criteria of FSO, such as the transmitter, receiver, beam divergence, and diameter of apertures, are analytically investigated. The numerical results demonstrate that the MQC-MB outperforms the single-beam in terms of reducing channel loss by about 8 dB and works well under strong turbulence channel. Furthermore, the MQC-MB reduces the quantum bit error rate (QBER) and improves the secret key rate (SKR) as compared to the single-beam system even though the distance between the sender and receiver increases.
- Published
- 2021
6. An Inertial Generalized Viscosity Approximation Method for Solving Multiple-Sets Split Feasibility Problems and Common Fixed Point of Strictly Pseudo-Nonspreading Mappings
- Author
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H. A. Abass and Lateef Olakunle Jolaoso
- Subjects
Logic ,Iterative method ,Computer science ,Computation ,strictly pseudocontractive mappings ,nonexpansive mappings ,01 natural sciences ,symbols.namesake ,Operator (computer programming) ,Convergence (routing) ,Applied mathematics ,0101 mathematics ,viscossity iterative scheme ,Mathematical Physics ,Sequence ,Algebra and Number Theory ,fixed point problem ,lcsh:Mathematics ,010102 general mathematics ,Hilbert space ,Lipschitz continuity ,multiple-sets split feasibility problem ,lcsh:QA1-939 ,010101 applied mathematics ,Viscosity (programming) ,symbols ,Geometry and Topology ,Analysis - Abstract
In this paper, we propose a generalized viscosity iterative algorithm which includes a sequence of contractions and a self adaptive step size for approximating a common solution of a multiple-set split feasibility problem and fixed point problem for countable families of k-strictly pseudononspeading mappings in the framework of real Hilbert spaces. The advantage of the step size introduced in our algorithm is that it does not require the computation of the Lipschitz constant of the gradient operator which is very difficult in practice. We also introduce an inertial process version of the generalize viscosity approximation method with self adaptive step size. We prove strong convergence results for the sequences generated by the algorithms for solving the aforementioned problems and present some numerical examples to show the efficiency and accuracy of our algorithm. The results presented in this paper extends and complements many recent results in the literature.
- Published
- 2021
7. A Physical Layer Security Enhancement Scheme under the Ambient Backscatter System
- Author
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Jumin Zhao, Jianping Gong, and Pengfei Hou
- Subjects
passive tags ,ambient backscatter communication ,Physics and Astronomy (miscellaneous) ,Computer science ,General Mathematics ,02 engineering and technology ,0203 mechanical engineering ,Interference (communication) ,artificial noise ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Electronic engineering ,Radio-frequency identification ,business.industry ,lcsh:Mathematics ,Physical layer ,physical layer security ,020206 networking & telecommunications ,020302 automobile design & engineering ,lcsh:QA1-939 ,Noise ,Chemistry (miscellaneous) ,Modulation ,Artificial noise ,Radio frequency ,business ,Communication channel - Abstract
In this paper, we proposed a scheme that Injects artificial noise from the tag end (IANT) to enhance the physical layer security of the ambient backscatter communication (ABC) system. The difference between the ABC system and the traditional radio frequency identification system is whether it uses the radio frequency (RF) signals in the environment to supply energy and modulation information for passive tags. In the IANT scheme, we select the best tag to communicate with the reader according to the channel quality between tags and reader, and at the same time select another tag to generate artificial noise that affects the receiving effect of the eavesdropper. This paper uses the method of generating noise copies in the reader to reduce the interference of artificial noise on the signal received by the reader. The simulation results show that with the increase in channel quality between tags and reader and the increase in the number of tags, the proposed IANT scheme is significantly superior to the contrast scheme in terms of system achievable secrecy rate, effectively enhancing the physical layer security of the ABC system.
- Published
- 2021
8. Surrogate Modeling Approaches for Multiobjective Optimization: Methods, Taxonomy, and Results
- Author
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Proteek Chandan Roy, Rayan Hussein, and Kalyanmoy Deb
- Subjects
Mathematical optimization ,Adaptive strategies ,kriging method ,Optimization problem ,Adaptive algorithm ,Computer science ,Applied Mathematics ,lcsh:T57-57.97 ,lcsh:Mathematics ,General Engineering ,Evolutionary algorithm ,lcsh:QA1-939 ,Multi-objective optimization ,surrogate modeling ,lcsh:QA75.5-76.95 ,Metamodeling ,ensemble method ,Computational Mathematics ,Conflicting objectives ,adaptive algorithm ,lcsh:Applied mathematics. Quantitative methods ,Optimization methods ,multiobjective optimization ,lcsh:Electronic computers. Computer science ,evolutionary algorithms - Abstract
Most practical optimization problems are comprised of multiple conflicting objectives and constraints which involve time-consuming simulations. Construction of metamodels of objectives and constraints from a few high-fidelity solutions and a subsequent optimization of metamodels to find in-fill solutions in an iterative manner remain a common metamodeling based optimization strategy. The authors have previously proposed a taxonomy of 10 different metamodeling frameworks for multiobjective optimization problems, each of which constructs metamodels of objectives and constraints independently or in an aggregated manner. Of the 10 frameworks, five follow a generative approach in which a single Pareto-optimal solution is found at a time and other five frameworks were proposed to find multiple Pareto-optimal solutions simultaneously. Of the 10 frameworks, two frameworks (M3-2 and M4-2) are detailed here for the first time involving multimodal optimization methods. In this paper, we also propose an adaptive switching based metamodeling (ASM) approach by switching among all 10 frameworks in successive epochs using a statistical comparison of metamodeling accuracy of all 10 frameworks. On 18 problems from three to five objectives, the ASM approach performs better than the individual frameworks alone. Finally, the ASM approach is compared with three other recently proposed multiobjective metamodeling methods and superior performance of the ASM approach is observed. With growing interest in metamodeling approaches for multiobjective optimization, this paper evaluates existing strategies and proposes a viable adaptive strategy by portraying importance of using an ensemble of metamodeling frameworks for a more reliable multiobjective optimization for a limited budget of solution evaluations.
- Published
- 2021
9. 5 G Poor and Rich Novel Control Scheme Based Load Frequency Regulation of a Two-Area System with 100% Renewables in Africa
- Author
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Hady H. Fayek
- Subjects
Statistics and Probability ,0209 industrial biotechnology ,Computer science ,020209 energy ,Automatic frequency control ,PID controller ,02 engineering and technology ,lcsh:Analysis ,load frequency control ,lcsh:Thermodynamics ,Flywheel ,Automotive engineering ,Energy storage ,Electric power system ,020901 industrial engineering & automation ,Control theory ,Packet loss ,lcsh:QC310.15-319 ,0202 electrical engineering, electronic engineering, information engineering ,FOPID controller ,poor and rich optimization ,100% renewable power generation ,business.industry ,lcsh:Mathematics ,NFOPID controller ,lcsh:QA299.6-433 ,Statistical and Nonlinear Physics ,biodiesel generator ,lcsh:QA1-939 ,NPID controller ,Renewable energy ,biogas generator ,energy food nexus ,business ,Analysis - Abstract
Remote farms in Africa are cultivated lands planned for 100% sustainable energy and organic agriculture in the future. This paper presents the load frequency control of a two-area power system feeding those farms. The power system is supplied by renewable technologies and storage facilities only which are photovoltaics, biogas, biodiesel, solar thermal, battery storage and flywheel storage systems. Each of those facilities has 150-kW capacity. This paper presents a model for each renewable energy technology and energy storage facility. The frequency is controlled by using a novel non-linear fractional order proportional integral derivative control scheme (NFOPID). The novel scheme is compared to a non-linear PID controller (NPID), fractional order PID controller (FOPID), and conventional PID. The effect of the different degradation factors related to the communication infrastructure, such as the time delay and packet loss, are modeled and simulated to assess the controlled system performance. A new cost function is presented in this research. The four controllers are tuned by novel poor and rich optimization (PRO) algorithm at different operating conditions. PRO controller design is compared to other state of the art techniques in this paper. The results show that the PRO design for a novel NFOPID controller has a promising future in load frequency control considering communication delays and packet loss. The simulation and optimization are applied on MATLAB/SIMULINK 2017a environment.
- Published
- 2021
10. A systematic literature review on outlier detection in wireless sensor networks
- Author
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Abdullah Alsaeedi, Shahla Asadi, Rusli Abdullah, Mitra Safaei, Wadii Boulila, Mahmood Safaei, Hassan Chizari, and Maha Driss
- Subjects
QA75 ,Physics and Astronomy (miscellaneous) ,Computer science ,General Mathematics ,02 engineering and technology ,outlier detection ,computer.software_genre ,QA76 ,Set (abstract data type) ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,ComputerSystemsOrganization_SPECIAL-PURPOSEANDAPPLICATION-BASEDSYSTEMS ,Cluster analysis ,wireless sensor networks ,Data processing ,lcsh:Mathematics ,systematic literature review ,020206 networking & telecommunications ,lcsh:QA1-939 ,Identification (information) ,Systematic review ,Chemistry (miscellaneous) ,Outlier ,020201 artificial intelligence & image processing ,Anomaly detection ,Data mining ,Wireless sensor network ,computer - Abstract
A wireless sensor network (WSN) is defined as a set of spatially distributed and interconnected sensor nodes. WSNs allow one to monitor and recognize environmental phenomena such as soil moisture, air pollution, and health data. Because of the very limited resources available in sensors, the collected data from WSNs are often characterized as unreliable or uncertain. However, applications using WSNs demand precise readings, and uncertainty in data reading can cause serious damage (e.g., health monitoring data). Therefore, an efficient local/distributed data processing algorithm is needed to ensure: (1) the extraction of precise and reliable values from noisy readings, (2) the detection of anomalies from data reported by sensors, and (3) the identification of outlier sensors in a WSN. Several works have been conducted to achieve these objectives using several techniques such as machine learning algorithms, mathematical modeling, and clustering. The purpose of this paper is to conduct a systematic literature review to report the available works on outlier and anomaly detection in WSNs. The paper highlights works conducted from January 2004 to October 2018. A total of 3520 papers are reviewed in the initial search process. Later, these papers are filtered by title, abstract, and contents, and a total of 117 papers are selected. These papers are examined to answer the defined research questions. The current paper presents an improved taxonomy of outlier detection techniques. This will help researchers and practitioners to find the most relevant and recent studies related to outlier detection in WSNs. Finally, the paper identifies existing gaps that future studies can fill.
- Published
- 2021
11. Uniqueness Theorems for Multiple Series by Vilenkin and Generalized Haar Systems
- Author
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Karen Navasardyan
- Subjects
Uniqueness Theorem ,Fourier Series ,Vilenkin System ,Haar System ,lcsh:Mathematics ,General Mathematics ,Summation Method ,lcsh:QA1-939 - Abstract
In this paper we discuss the uniqueness property of a summation method for multiple series with respect to Vilenkin and generalized Haar systems. It is proved that if the multiple series with respect to these systems is a.e. summable by that method to an integrable function on $[0,1)^d$ and satisfies an extra condition, then it is the Fourier series of this function.
- Published
- 2022
12. Hyperidentities and Related Concepts, II
- Author
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Yuri Movsisyan
- Subjects
Hypervariety ,Essential hyperidentity ,lcsh:Mathematics ,General Mathematics ,Hyperidentity ,Variety ,Termal Hyperidentity ,Bilattice, De Morgan algebra ,lcsh:QA1-939 - Abstract
This survey article illustrates many important current trends and perspectives for the field including classification of hyperidentities, characterizations of algebras with hyperidentities, functional representations of free algebras, structure results for bilattices, categorical questions and applications. However, the paper contains new results and open problems, too.
- Published
- 2022
13. On the democratic constant of Haar subsystems in $L_1 [0,1]^d$
- Author
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Nerses Srapionyan
- Subjects
Haar Subsystem ,Democratic Constant ,lcsh:Mathematics ,General Mathematics ,Greedy Algorithm in $L_1[0,1]^d$ ,lcsh:QA1-939 - Abstract
In this paper, we estimate the democratic constant for the democratic subsystems of the $d$-dimensional Haar system in $L_1[0,1]^d$.
- Published
- 2022
14. Fractional maximal and integral operators in variable exponent Morrey spaces
- Author
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Panwang Wang and Zongguang Liu
- Subjects
Mathematics::Functional Analysis ,fractional integral operator ,lcsh:Mathematics ,General Mathematics ,Mathematics::Classical Analysis and ODEs ,Morrey spaces ,lcsh:QA1-939 ,spaces of Homogeneous type - Abstract
In this paper, we study the boundedness of the fractional maximal operator and fractional integral operator on the variable exponent Morrey spaces defined over spaces $(X,d,\mu)$ of homogeneous type.
- Published
- 2022
15. On a Riemann boundary value problem for weighted spaces in the half-plane
- Author
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Hrachik Mergo Hayrapetyan and Smbat Ararat Aghekyan
- Subjects
factorization ,homogeneous problem ,lcsh:Mathematics ,General Mathematics ,Sokhotski-Plemelj formula ,weighted space ,Riemann boundary value problem ,lcsh:QA1-939 - Abstract
The paper considers the Riemann boundary value problem in the half-plane in the class of functions that are $C(\rho)$-continuous with respect to the weight $\rho(x)$, when the weight function has infinite number of zeros. Necessary and sufficient conditions for solvability of the problem are established. If the problem is solvable, solutions are represented in an explicit form.
- Published
- 2022
16. Enabling Symmetric Collaboration in Public Spaces through 3D Mobile Interaction
- Author
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Mayra Donaji Barrera Machuca, Winyu Chinthammit, Weidong Huang, Henry Been-Lirn Duh, and Rainer Wasinger
- Subjects
Activities of daily living ,3D user interfaces ,Physics and Astronomy (miscellaneous) ,Computer science ,General Mathematics ,cooperative application ,02 engineering and technology ,usability testing ,mobile devices ,Human–computer interaction ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Situational ethics ,3D mobile interaction ,Uncategorized ,business.industry ,lcsh:Mathematics ,Perspective (graphical) ,020207 software engineering ,Usability ,lcsh:QA1-939 ,Chemistry (miscellaneous) ,Order (business) ,020201 artificial intelligence & image processing ,Augmented reality ,business ,Mobile device ,Mobile interaction - Abstract
© 2018 by the authors. Collaboration has been common in workplaces in various engineering settings and in our daily activities. However, how to effectively engage collaborators with collaborative tasks has long been an issue due to various situational and technical constraints. The research in this paper addresses the issue in a specific scenario, which is how to enable users to interact with public information from their own perspective. We describe a 3D mobile interaction technique that allows users to collaborate with other people by creating a symmetric and collaborative ambience. This in turn can increase their engagement with public displays. In order to better understand the benefits and limitations of this technique, we conducted a usability study with a total of 40 participants. The results indicate that the 3D mobile interaction technique promotes collaboration between users and also improves their engagement with the public displays.
- Published
- 2023
- Full Text
- View/download PDF
17. The Meir-Keeler type contractions in extended modular b-metric spaces with an application
- Author
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Manuel De la Sen, Shaban Sedghi, Ozgur Ege, Abdolsattar Gholidahneh, Zoran D. Mitrović, and Ege Üniversitesi
- Subjects
Discrete mathematics ,extended modular metric space ,triangular fuzzy p-metric space ,business.industry ,General Mathematics ,lcsh:Mathematics ,Fixed-point theorem ,Mathematics::General Topology ,Fixed point ,Type (model theory) ,Modular design ,Space (mathematics) ,lcsh:QA1-939 ,Fuzzy logic ,alpha-nu-Meir-Keeler contraction ,Metric space ,$ \alpha $-$ \widehat{\nu} $-meir-keeler contraction ,integral equation ,fixed point ,Graph (abstract data type) ,business ,Mathematics - Abstract
In this paper, we introduce the notion of a modular p-metric space (an extended modular b-metric space) and establish some fixed point results for alpha-nu-Meir-Keeler contractions in this new space. Using these results, we deduce some new fixed point theorems in extended modular metric spaces endowed with a graph and in partially ordered extended modular metric spaces. Also, we develop an important relation between fuzzy-Meir-Keeler and extended fuzzy p-metric with modular p-metric and get certain new fixed point results in triangular fuzzy p-metric spaces. We provide an example and an application to support our results which generalize several well known results in the literature., Basque GovernmentBasque Government [IT1207-19]; Ege University Scientific Research Projects Coordination UnitEge University [FGA-2020-22080], The authors would like to thank the editor and the anonymous referees for their careful reading of our manuscript and their many insightful comments and suggestions. The authors thank the Basque Government for its support of this work through Grant IT1207-19. This study is supported by Ege University Scientific Research Projects Coordination Unit. Project Number FGA-2020-22080.
- Published
- 2021
18. An online conjugate gradient algorithm for large-scale data analysis in machine learning
- Author
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Tao Tao, Qiao Li, Pengcheng Wan, Ping Zhong, Wei Xue, and Gaohang Yu
- Subjects
Computer science ,business.industry ,General Mathematics ,lcsh:Mathematics ,online learning ,variance reduction ,stochastic optimization ,Machine learning ,computer.software_genre ,lcsh:QA1-939 ,Stochastic gradient descent ,machine learning ,Conjugate gradient method ,Convergence (routing) ,Benchmark (computing) ,Variance reduction ,Stochastic optimization ,conjugate gradient ,Artificial intelligence ,Online algorithm ,Convex function ,business ,Algorithm ,computer - Abstract
In recent years, the amount of available data is growing exponentially, and large-scale data is becoming ubiquitous. Machine learning is a key to deriving insight from this deluge of data. In this paper, we focus on the large-scale data analysis, especially classification data, and propose an online conjugate gradient (CG) descent algorithm. Our algorithm draws from a recent improved Fletcher-Reeves (IFR) CG method proposed in Jiang and Jian[13] as well as a recent approach to reduce variance for stochastic gradient descent from Johnson and Zhang [15]. In theory, we prove that the proposed online algorithm achieves a linear convergence rate under strong Wolfe line search when the objective function is smooth and strongly convex. Comparison results on several benchmark classification datasets demonstrate that our approach is promising in solving large-scale machine learning problems, viewed from the points of area under curve (AUC) value and convergence behavior.
- Published
- 2021
19. Closure properties of generalized λ-Hadamard product for a class of meromorphic Janowski functions
- Author
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Huo Tang, Tao He, Shu-Hai Li, and Lina Ma
- Subjects
Subordination (linguistics) ,Pure mathematics ,Class (set theory) ,Mathematics::Complex Variables ,General Mathematics ,lcsh:Mathematics ,hadamard product ,generalized λ-hadamard product ,janowski functions ,Function (mathematics) ,Lambda ,lcsh:QA1-939 ,closure property ,Closure (mathematics) ,Product (mathematics) ,Hadamard product ,meromorphic function ,Meromorphic function ,Mathematics - Abstract
In this paper, we introduce a class of meromorphic starlike function by subordination relationship and generalized $\lambda$-Hadamard product. We obtain the necessary and sufficient conditions and closure properties of the class. In addition, some new results of the class are given.
- Published
- 2021
20. On the stability of two functional equations for (S,N)-implications
- Author
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Dapeng Lang, Xinyu Han, Sizhao Li, and Songsong Dai
- Subjects
Stability study ,General Mathematics ,lcsh:Mathematics ,functional equations ,stability ,lcsh:QA1-939 ,Fuzzy logic ,Stability (probability) ,humanities ,Combinatorics ,(s,n)-implication ,law of importation ,iterative boolean-like law ,Product (mathematics) ,fuzzy implications ,Functional equation ,Beta (velocity) ,Law of importation ,Fuzzy negation ,Mathematics - Abstract
The iterative functional equation $ \alpha\rightarrow(\alpha\rightarrow \beta) = \alpha\rightarrow \beta $ and the law of importation $ (\alpha\wedge \beta)\rightarrow \gamma = \alpha\rightarrow (\beta\rightarrow \gamma) $ are two tautologies in classical logic. In fuzzy logics, they are two important properties, and are respectively formulated as $ I(\alpha, \beta) = I(\alpha, I(\alpha, \beta)) $ and $ I(T(\alpha, \beta), \gamma) = I(\alpha, I(\beta, \gamma)) $ where $ I $ is a fuzzy implication and $ T $ is a $ t $-norm. Over the past several years, solutions to these two functional equations involving different classes of fuzzy implications have been studied. However, there are no results about stability study of fuzzy functional equations involving fuzzy implication. This paper discusses fuzzy implications that do not strictly satisfying these equations, but approximately satisfy these equations. Then we establish the Hyers-Ulam stability of the iterative functional equation involving the $ (S, N) $-implication, where the $ (S, N) $-implication is a common class of fuzzy implications generated by a continuous $ t $-conorm $ S $ and a continuous fuzzy negation $ N $. Furthermore, given a fixed $ t $-norm (the minimum $ t $-norm or the product $ t $-norm) the Hyers-Ulam stability of the law of importation involving the $ (S, N) $-implication is studied.
- Published
- 2021
21. TLMPA: Teaching-learning-based Marine Predators algorithm
- Author
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Qifang Luo, Ming Jiang, Yongquan Zhou, and Keyu Zhong
- Subjects
marine predators algorithm ,Computer science ,General Mathematics ,lcsh:Mathematics ,Foraging ,Crossover ,lcsh:QA1-939 ,Hybrid algorithm ,ComputingMethodologies_ARTIFICIALINTELLIGENCE ,teaching-learning-based optimization ,Interactive Learning ,hybrid metaheuristic algorithm ,mutation and crossover ,Mutation (genetic algorithm) ,Benchmark (computing) ,Algorithm ,Metaheuristic ,Premature convergence - Abstract
Marine Predators algorithm (MPA) is a newly proposed nature-inspired metaheuristic algorithm. The main inspiration of this algorithm is based on the extensive foraging strategies of marine organisms, namely Lévy movement and Brownian movement, both of which are based on random strategies. In this paper, we combine the marine predator algorithm with Teaching-learning-based optimization algorithm, and propose a hybrid algorithm called Teaching-learning-based Marine Predator algorithm (TLMPA). Teaching-learning-based optimization (TLBO) algorithm consists of two phases: the teacher phase and the learner phase. Combining these two phases with the original MPA enables the predators to obtain prey information for foraging by learning from teachers and interactive learning, thus greatly increasing the encounter rate between predators and prey. In addition, effective mutation and crossover strategies were added to increase the diversity of predators and effectively avoid premature convergence. For performance evaluation TLMPA algorithm, it has been applied to IEEE CEC-2017 benchmark functions and four engineering design problems. The experimental results show that among the proposed TLMPA algorithm has the best comprehensive performance and has more outstanding performance than other the state-of-the-art metaheuristic algorithms in terms of the performance measures.
- Published
- 2021
22. Existence of nontrivial solutions for Schrödinger-Kirchhoff type equations involving the fractional p-Laplacian and local nonlinearity
- Author
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Liu Gao, Chunfang Chen, Jianhua Chen, and Chuanxi Zhu
- Subjects
moser iteration method ,truncation argument ,lcsh:Mathematics ,fractional p-laplacian ,kirchhoff equations ,local nonlinearity ,lcsh:QA1-939 - Abstract
In this paper, we deal with the existence of nontrivial solutions for the following Kirchhoff-type equation where $0 < s < 1 < p < \infty$, $sp < N$, $\lambda > 0$ is a real parameter, $(-\Delta)_{p}^{s}$ is the fractional $p$-Laplacian operator, $V:\mathbb{R}^N\rightarrow\mathbb{R}^N$ is a potential function, $M$ is a Kirchhoff function, the nonlinearity $f:\mathbb{R}^N\times\mathbb{R}\rightarrow\mathbb{R}$ is a continuous function and just super-linear in a neighborhood of $u = 0$. By using an appropriate truncation argument and the mountain pass theorem, we prove the existence of nontrivial solutions for the above equation, provided that $\lambda$ is sufficiently large. Our results extend and improve the previous ones in the literature.
- Published
- 2021
23. Interpolative Chatterjea and cyclic Chatterjea contraction on quasi-partial b-metric space
- Author
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Pragati Gautam, Vishnu Narayan Mishra, Swapnil Verma, and Rifaqat Ali
- Subjects
Pure mathematics ,quasi-partial b-metric space ,General Mathematics ,lcsh:Mathematics ,Fixed-point theorem ,qpb-cyclic chatterjea contraction mapping ,Fixed point ,cyclic mapping ,lcsh:QA1-939 ,Complete metric space ,interpolation ,Metric space ,chatterjea contraction ,fixed point ,Uniqueness ,Contraction (operator theory) ,Mathematics - Abstract
The fixed point results for Chatterjea type contraction in the setting of Complete metric space exists in literature. Taking this approach forward Karapinar gave the concept of cyclic Chatterjea contraction mappings. Fan also worked on these cyclic mappings in a new setting of quasi-partial b-metric space. Motivated by the work of these researchers, we have introduced the notion of $qp_{b}$-cyclic Chatterjea contractive mappings and established fixed point results on them. The aim of this paper is to use an interpolative approach in the framework of quasi-partial b-metric space and to prove existence and uniqueness of fixed point theorem for $qp_{b}$-interpolative Chatterjea contraction mappings. The results are affirmed with applications based on them.
- Published
- 2021
24. Derivation of some integrals in Gradshteyn and Ryzhik
- Author
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Robert Reynolds and Allan Stauffer
- Subjects
Physics ,Combinatorics ,entries of gradshteyn and ryzhik ,General Mathematics ,lcsh:Mathematics ,hyperbolic integrals ,Definite integrals ,lerch function ,hypergeometric function ,Function (mathematics) ,Hypergeometric function ,lcsh:QA1-939 ,Complex number - Abstract
In this work we present derivations of the formula listed in entry 4.113 in the sixth edition of Gradshteyn and Rhyzik's table of integrals. We evaluate two definite integrals of the form $ \begin{equation*} \int_{0}^{\infty}\frac{e^{-iay}(-iy+\log(z))^k+e^{iay}(iy+\log(z))^k}{\cosh(by)}dy \end{equation*} $ and $ \begin{equation*} \int_{0}^{\infty}\frac{e^{iay}(iy+\log(z))^k-e^{-iay}(-iy+\log(z))^k}{\sinh(b y)}dy \end{equation*} $ in terms of the Lerch function where $ k $, $ a $, $ z $ and $ b $ are arbitrary complex numbers. The entries in the table(s) are obtained as special cases in the paper below.
- Published
- 2021
25. New iterative approach for the solutions of fractional order inhomogeneous partial differential equations
- Author
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Rashid Nawaz, Sumbal Ahsan, Kottakkaran Sooppy Nisar, Dumitru Baleanu, and Laiq Zada
- Subjects
Partial differential equation ,Laplace transform ,Iterative method ,General Mathematics ,lcsh:Mathematics ,fractional order inhomogeneous system ,Interval (mathematics) ,fractional calculus ,lcsh:QA1-939 ,approximate solutions ,Fractional calculus ,Transformation (function) ,Integer ,fractional order roseau-hyman equation ,Applied mathematics ,Decomposition method (constraint satisfaction) ,new iterative method ,Mathematics - Abstract
In this paper, the study of fractional order partial differential equations is made by using the reliable algorithm of the new iterative method (NIM). The fractional derivatives are considered in the Caputo sense whose order belongs to the closed interval [0, 1]. The proposed method is directly extended to study the fractional-order Roseau-Hyman and fractional order inhomogeneous partial differential equations without any transformation to convert the given problem into integer order. The obtained results are compared with those obtained by Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Laplace Variational Iteration Method (LVIM) and the Laplace Adominan Decomposition Method (LADM). The results obtained by NIM, show higher accuracy than HPM, LVIM and LADM. The accuracy of the proposed method improves by taking more iterations.
- Published
- 2021
26. Error bounds for generalized vector inverse quasi-variational inequality Problems with point to set mappings
- Author
-
J. F. Tang, X. R. Wang, M. Liu, S. S. Chang, and Salahuddin
- Subjects
residual gap function ,General Mathematics ,lcsh:Mathematics ,Hausdorff space ,Solution set ,Inverse ,hausdorff lipschitz continuity ,Monotonic function ,Function (mathematics) ,error bounds ,Lipschitz continuity ,Residual ,relaxed monotonicity ,lcsh:QA1-939 ,generalized f-projection operator ,regularized gap function ,Variational inequality ,Applied mathematics ,generalized vector inverse quasi-variational inequality problems ,global gap function ,bi-mapping ,Mathematics ,strong monotonicity - Abstract
The goal of this paper is further to study a kind of generalized vector inverse quasi-variational inequality problems and to obtain error bounds in terms of the residual gap function, the regularized gap function, and the global gap function by utilizing the relaxed monotonicity and Hausdorff Lipschitz continuity. These error bounds provide effective estimated distances between an arbitrary feasible point and the solution set of generalized vector inverse quasi-variational inequality problems.
- Published
- 2021
27. Mathematical modeling of HIV/HTLV co-infection with CTL-mediated immunity
- Author
-
N. H. AlShamrani, Ahmed M. Elaiw, and A. D. Hobiny
- Subjects
Lyapunov function ,Physics ,General Mathematics ,lcsh:Mathematics ,virus diseases ,hiv/htlv-i co-infection ,lcsh:QA1-939 ,global stability ,symbols.namesake ,CTL ,Immune system ,Exponential stability ,Immunity ,Bounded function ,symbols ,Applied mathematics ,Cytotoxic T cell ,Latency (engineering) ,lyapunov function ,ctl-mediated immune response - Abstract
In the literature, a great number of HIV and HTLV-I mono-infection models has been formulated and analyzed. However, the within-host dynamics of HIV/HTLV-I co-infection has not been modeled. In the present paper we formulate and analyze a new HIV/HTLV-I co-infection model with latency and Cytotoxic T lymphocytes (CTLs) immune response. The model describes the interaction between susceptible CD$4^{+}$T cells, latently HIV-infected cells, actively HIV-infected cells, latently HTLV-infected cells, Tax-expressing HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. The HIV can spread by virus-to-cell and cell-to-cell transmissions, while the HTLV-I can only spread via cell-to-cell transmission. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We derive the threshold parameters which govern the existence and stability of all equilibria of the model. We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and Lyapunov-LaSalle asymptotic stability theorem. We have presented numerical simulations to illustrate the effectiveness of our main results. In addition, we have discussed the effect of HTLV-I infection on the HIV-infected patients and vice versa. We have pointed out the influence of CTL immune response on the co-infection dynamics.
- Published
- 2021
28. Generating bicubic B-spline surfaces by a sixth order PDE
- Author
-
Yan Wu and Chun-Gang Zhu
- Subjects
Surface (mathematics) ,Partial differential equation ,bicubic b-spline surfaces ,Basis (linear algebra) ,General Mathematics ,B-spline ,pde surfaces ,lcsh:Mathematics ,Mathematical analysis ,sixth order pde ,lcsh:QA1-939 ,Mathematics::Numerical Analysis ,PDE surface ,Computer Science::Graphics ,Bicubic interpolation ,Boundary value problem ,Representation (mathematics) ,Mathematics - Abstract
As the solutions of partial differential equations (PDEs), PDE surfaces provide an effective way for physical-based surface design in surface modeling. The bicubic B-spline surface is a useful tool for surface modeling in computer aided geometric design (CAGD). In this paper, we present a method for generating bicubic B-spline surfaces with the uniform knots and the quasi-uniform knots from the sixth order PDEs. From the given boundary condition, based on the cubic B-spline basis representation and the PDE mask, the resulting bicubic B-spline surface can be generated uniquely. The boundary condition is more flexible and can be applied for curvature-continuous surface design, surface blending and hole filling. Some representative examples show the effectiveness of the presented method.
- Published
- 2021
29. The stationary distribution of a stochastic rumor spreading model
- Author
-
Dapeng Gao, Peng Guo, and Chaodong Chen
- Subjects
Lyapunov function ,Stationary distribution ,Stochastic modelling ,General Mathematics ,lcsh:Mathematics ,White noise ,Rumor ,lcsh:QA1-939 ,stationary distribution ,symbols.namesake ,rumor spreading ,symbols ,threshold ,Applied mathematics ,Ergodic theory ,Uniqueness ,Persistence (discontinuity) ,Mathematics - Abstract
In this paper, we develop a rumor spreading model by introducing white noise into the model. We establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the stochastic model by constructing a suitable stochastic Lyapunov function, which provides us a good description of persistence. Finally, we provide some numerical simulations to illustrate the analytical results.
- Published
- 2021
30. On Janowski type p-harmonic functions associated with generalized Sǎlǎgean operator
- Author
-
Shuhai Li, Lina Ma, and Huo Tang
- Subjects
p-harmonic function ,lcsh:Mathematics ,janowski function ,sǎlǎgean operator ,convolution ,subordination ,extreme point ,lcsh:QA1-939 - Abstract
In this paper, some classes of Janowski type p-harmonic functions associated with the generalized Sǎlǎgean operator are introduced. Further, coefficient conditions, distortion estimates and the other properties of the classes are obtained. On the one hand, the results presented here generalize the results of Yaşar and Yalçin [8]. On the other hand, we obtain some new results on sufficient convolution condition of the classes.
- Published
- 2021
31. Embedding of Qp spaces into tent spaces and Volterra integral operator
- Author
-
Ruishen Qian and Xiangling Zhu
- Subjects
qp space ,lcsh:Mathematics ,volterra integral operator ,tent space ,lcsh:QA1-939 ,carleson measure - Abstract
In this paper, the boundedness and compactness of the inclusion mapping from $Q_p$ spaces into tent spaces $\mathcal{T}_{\frac{qp}{2},s}^{q}$ are completely characterized when $q>2$. As an application, the boundedness of the Volterra integral operator $T_g$ from $Q_p$ to the space $\mathcal{LF}(q,q-2,\frac{qp}{2})$ is obtained. Moreover, the essential norm and compactness of $T_g$ are also investigated.
- Published
- 2021
32. On the first general Zagreb eccentricity index
- Author
-
Aisha Javed, Muhammad Imran, Muhammad Jamil, and Roslan Hasni
- Subjects
Combinatorics ,eccentricity of vertices ,first general zagreb eccentricity index ,General Mathematics ,extremal graphs ,lcsh:Mathematics ,Shortest path problem ,Bipartite graph ,lcsh:QA1-939 ,Upper and lower bounds ,Graph ,Vertex (geometry) ,Mathematics - Abstract
In a graph G, the distance between two vertices is the length of the shortest path between them. The maximum distance between a vertex to any other vertex is considered as the eccentricity of the vertex. In this paper, we introduce the first general Zagreb eccentricity index and found upper and lower bounds on this index in terms of order, size and diameter. Moreover, we characterize the extremal graphs in the class of trees, trees with pendant vertices and bipartite graphs. Results on some famous topological indices can be presented as the corollaries of our main results.
- Published
- 2021
33. Acceleration of an adaptive generalized Arnoldi method for computing PageRank
- Author
-
Bing-Yuan Pu, Yu-Yun Huang, Qian-Ying Hu, and Chun Wen
- Subjects
Trace (linear algebra) ,Google matrix ,Computer science ,General Mathematics ,lcsh:Mathematics ,Extrapolation ,Process (computing) ,extrapolation ,lcsh:QA1-939 ,law.invention ,generalized arnoldi method ,power method ,Acceleration ,PageRank ,Power iteration ,law ,Convergence (routing) ,pagerank ,Algorithm - Abstract
By considering a weighted inner product, an adaptive generalized Arnoldi (GArnoldi) method was constructed by [ 13 ] for computing PageRank. In order to accelerate the adaptive GArnoldi method, this paper proposes a new method by using the power method with extrapolation process based on Google matrix's trace (PET) as an accelerated technique of the adaptive GArnoldi method. The new method is called as GArnoldi-PET method, whose implementation and convergence analysis are discussed in detail. Numerical experiments are used to illustrate the effectiveness of our proposed method.
- Published
- 2021
34. Inertial projection methods for solving general quasi-variational inequalities
- Author
-
Khalida Inayat Noor, Saudia Jabeen, Muhammad Aslam Noor, and Bandar Bin-Mohsin
- Subjects
Optimization problem ,Inertial frame of reference ,convergence ,Computer science ,General Mathematics ,lcsh:Mathematics ,inertial methods ,Fixed point ,lcsh:QA1-939 ,Projection (linear algebra) ,inertial term ,Complementarity (molecular biology) ,quasi-variational inequality ,Variational inequality ,Convergence (routing) ,Applied mathematics ,projection operator ,Equivalence (measure theory) - Abstract
In this paper, we consider a new class of quasi-variational inequalities, which is called the general quasi-variational inequality. Using the projection operator technique, we establish the equivalence between the general quasi-variational inequalities and the fixed point problems. We use this alternate formulation to propose some new inertial iterative schemes for solving the general quasi-variational inequalities. The convergence criteria of the new inertial projection methods under some appropriate conditions is investigated. Since the general quasi-variational inequalities include the quasi-variational inequalities, variational inequalities, complementarity problems and the related optimization problems as special cases, our results continue to hold for these problems. It is an interesting problem to compare the efficiency of the proposed methods with other known methods.
- Published
- 2021
35. Ordering results of extreme order statistics from dependent and heterogeneous modified proportional (reversed) hazard variables
- Author
-
Rongfang Yan, Bin Lu, and Miaomiao Zhang
- Subjects
Hazard (logic) ,General Mathematics ,lcsh:Mathematics ,Hazard ratio ,Order statistic ,archimedean copula ,Sample (statistics) ,stochastic orders ,lcsh:QA1-939 ,Stochastic ordering ,Statistics ,majorization ,Majorization ,mphr and mprhr models ,Mathematics - Abstract
In this paper, we carry out stochastic comparisons on extreme order statistics (i.e. smallest and largest order statistics) from dependent and heterogeneous samples following modified proportional hazard rates (MPHR) and modified proportional reversed hazard rates (MPRHR) models. We build the usual stochastic order for sample minimums and maximums, and the hazard rate order on minimums of sample and the reversed hazard rate order on maximums of sample are also derived, respectively. Finally, some examples are given to illustrate the theoretical results.
- Published
- 2021
36. Sign-changing solutions for a class of fractional Kirchhoff-type problem with logarithmic nonlinearity
- Author
-
Chuanzhi Bai and Qing Yang
- Subjects
Physics ,fractional kirchhoff-schrodinger-type equation ,Class (set theory) ,Logarithm ,General Mathematics ,variation methods ,lcsh:Mathematics ,sign-changing solutions ,lcsh:QA1-939 ,Omega ,Combinatorics ,Nonlinear system ,Variational method ,Bounded function ,Domain (ring theory) ,Ground state ,logarithmic nonlinearity - Abstract
In this paper, we are interested the following fractional Kirchhoff-type problem with logarithmic nonlinearity \begin{equation*} \left\{ \begin{array} {ll} \left(a+b \iint_{\Omega^2} \frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}} dxdy\right)(-\Delta)^s u + V(x)u = Q(x) |u|^{p-2}u \ln u^2, & {\rm in } \ \Omega, \\ u=0, & {\rm in } \ \mathbb{R}^N \setminus \Omega, \end{array} \right. \end{equation*} where $\Omega \subset \mathbb{R}^N$ is a smooth bounded domain, $N > 2s$ ($0 < s < 1$), $(-\Delta)^s$ is the fractional Laplacian, $V, Q$ are continuous, $V, Q \ge 0$. $a, b > 0$ are constants, $4 < p < 2_s^* := \frac{2N}{N-2s}$. By using constraint variational method, a quantitative deformation lemma and some analysis techniques, we obtain the existence of ground state sign-changing solutions for above problem.
- Published
- 2021
37. Applications of higher-order q-derivatives to the subclass of q-starlike functions associated with the Janowski functions
- Author
-
Muhammad Sabil Ur Rehman, Qazi Zahoor Ahmad, H. M. Srivastava, Nazar Khan, Maslina Darus, and Bilal Khan
- Subjects
univalent functions ,Mathematics::Complex Variables ,lcsh:Mathematics ,starlike and q-starlike functions ,lcsh:QA1-939 ,q-derivative operator ,multivalent functions ,convex and q-convex functions - Abstract
In this paper, we first investigate some subclasses of q-starlike functions. We then apply higher-order q-derivative operators to introduce and study a new subclass of q-starlike functions, which involves the Janowski functions. Several coefficient inequalities and a sufficient condition are derived. Relevant connections with a number of earlier works on this subject are also pointed out.
- Published
- 2021
38. Lie symmetry reductions and exact solutions to a generalized two-component Hunter-Saxton system
- Author
-
Yunmei Zhao, Huizhang Yang, and Wei Liu
- Subjects
generalized two-component hunter-saxton system ,Pure mathematics ,Conservation law ,Similarity (geometry) ,lie symmetry analysis ,General Mathematics ,Computation ,Infinitesimal ,lcsh:Mathematics ,Mathematics::Analysis of PDEs ,Lie group ,exact solutions ,lcsh:QA1-939 ,Symmetry (physics) ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,symmetry reductions ,Lie algebra ,conservation law ,Vector field ,Mathematics - Abstract
Based on the classical Lie group method, a generalized two-component Hunter-Saxton system is studied in this paper. All of the its geometric vector fields, infinitesimal generators and the commutation relations of Lie algebra are derived. Furthermore, the similarity variables and symmetry reductions of this new generalized two-component Hunter-Saxton system are derived. Under these Lie symmetry reductions, some exact solutions are obtained by using the symbolic computation. Moreover, a conservation law of this system is presented by using the multiplier approach.
- Published
- 2021
39. More on proper nonnegative splittings of rectangular matrices
- Author
-
Shu-Xin Miao and Ting Huang
- Subjects
Pure mathematics ,convergence ,General Mathematics ,lcsh:Mathematics ,Comparison results ,rectangular matrix ,lcsh:QA1-939 ,Matrix (mathematics) ,Convergence (routing) ,proper nonnegative splitting ,comparison theorems ,moore-penrose inverse ,Moore–Penrose pseudoinverse ,Mathematics - Abstract
In this paper, we further investigate the single proper nonnegative splittings and double proper nonnegative splittings of rectangular matrices. Two convergence theorems for the single proper nonnegative splitting of a semimonotone matrix are derived, and more comparison results for the spectral radii of matrices arising from the single proper nonnegative splittings and double proper nonnegative splittings of different rectangular matrices are presented. The obtained results generalize the previous ones, and it can be regarded as the useful supplement of the results in [Comput. Math. Appl., 67: 136–144, 2014] and [Results. Math., 71: 93–109, 2017].
- Published
- 2021
40. On the characterization of Pythagorean fuzzy subgroups
- Author
-
Supriya Bhunia, Ganesh Ghorai, and Qin Xin
- Subjects
Normal subgroup ,Generalization ,Mathematics::General Mathematics ,General Mathematics ,lcsh:Mathematics ,Pythagorean theorem ,Mathematics::History and Overview ,pythagorean fuzzy coset ,pythagorean fuzzy subgroup ,Intuitionistic fuzzy ,Characterization (mathematics) ,lcsh:QA1-939 ,Fuzzy logic ,Algebra ,Physics::Popular Physics ,Mathematics::Group Theory ,pythagorean fuzzy set ,Coset ,Group homomorphism ,pythagorean fuzzy level subgroup ,pythagorean fuzzy normal subgroup ,Mathematics - Abstract
Pythagorean fuzzy environment is the modern tool for handling uncertainty in many decisions making problems. In this paper, we represent the notion of Pythagorean fuzzy subgroup (PFSG) as a generalization of intuitionistic fuzzy subgroup. We investigate various properties of our proposed fuzzy subgroup. Also, we introduce Pythagorean fuzzy coset and Pythagorean fuzzy normal subgroup (PFNSG) with their properties. Further, we define the notion of Pythagorean fuzzy level subgroup and establish related properties of it. Finally, we discuss the effect of group homomorphism on Pythagorean fuzzy subgroup.
- Published
- 2021
41. Bifurcation for a fractional-order Lotka-Volterra predator–prey model with delay feedback control
- Author
-
Zhouhong Li, Wei Zhang, Chengdai Huang, and Jianwen Zhou
- Subjects
Nonlinear Sciences::Chaotic Dynamics ,bifurcation control ,lcsh:Mathematics ,lotka-volterra predator–prey system ,Quantitative Biology::Populations and Evolution ,lcsh:QA1-939 ,Nonlinear Sciences::Pattern Formation and Solitons ,fractional-order ,delay feedback control - Abstract
This paper addresses the bifurcation control of a fractional-order Lokta-Volterra predator– prey model by using delay feedback control. By employing time delay as a bifurcation parameter, the conditions of bifurcation are gained for controlled systems. Then, it indications that the onset of bifurcation can be postponed as feedback gain decreases. An example numerical results are ultimately exploited to validate the correctness of the the proposed scheme.
- Published
- 2021
42. Finite element approximation of time fractional optimal control problem with integral state constraint
- Author
-
Jie Liu and Zhaojie Zhou
- Subjects
Discretization ,General Mathematics ,lcsh:Mathematics ,a priori error estimate ,space time finite element method ,Optimal control ,lcsh:QA1-939 ,integral state constraint ,Finite element method ,Piecewise linear function ,Scheme (mathematics) ,Piecewise ,A priori and a posteriori ,Applied mathematics ,time fractional optimal control problem ,Constant (mathematics) ,Mathematics - Abstract
In this paper we investigate the finite element approximation of time fractional optimal control problem with integral state constraint. A space-time finite element scheme for the control problem is developed with piecewise constant time discretization and piecewise linear spatial discretization for the state equation. A priori error estimate for the space-time discrete scheme is derived. Projected gradient algorithm is used to solve the discrete optimal control problem. Numerical experiments are carried out to illustrate the theoretical findings.
- Published
- 2021
43. Geometric behavior of a class of algebraic differential equations in a complex domain using a majorization concept
- Author
-
Dumitru Baleanu and Rabha W. Ibrahim
- Subjects
Physics ,Pure mathematics ,Mathematics::Functional Analysis ,General Mathematics ,lcsh:Mathematics ,Physics::Medical Physics ,univalent function ,lcsh:QA1-939 ,Unit disk ,analytic function ,subordination and superordination ,Connection (algebraic framework) ,Algebraic number ,Convex function ,Majorization ,Bernoulli number ,majorization method ,open unit disk ,algebraic differential equations ,Univalent function ,Analytic function - Abstract
In this paper, a type of complex algebraic differential equations (CADEs) is considered formulating by $ \alpha [\varphi(z) \varphi" (z) +(\varphi' (z))^2]+ a_m \varphi^m(z)+a_{m-1} \varphi^{m-1}(z)+...+ a_1 \varphi(z)+ a_0 = 0. $ The conformal analysis (angle-preserving) of the CADEs is investigated. We present sufficient conditions to obtain analytic solutions of the CADEs. We show that these solutions are subordinated to analytic convex functions in terms of $e^z.$ Moreover, we investigate the connection estimates (coefficient bounds) of CADEs by employing the majorization method. We achieve that the coefficients bound are optimized by Bernoulli numbers.
- Published
- 2021
44. A relaxed generalized Newton iteration method for generalized absolute value equations
- Author
-
Senlai Zhu, Yang Cao, and Shi Quan
- Subjects
Generalized Jacobian ,Iterative method ,General Mathematics ,lcsh:Mathematics ,Positive-definite matrix ,globally convergence ,lcsh:QA1-939 ,symbols.namesake ,generalized absolute value equations ,relaxation ,Fixed-point iteration ,Absolute value equation ,symbols ,newton method ,Applied mathematics ,Well-defined ,Coefficient matrix ,Newton's method ,Mathematics - Abstract
To avoid singular generalized Jacobian matrix and further accelerate the convergence of the generalized Newton (GN) iteration method for solving generalized absolute value equations Ax - B|x| = b, in this paper we propose a new relaxed generalized Newton (RGN) iteration method by introducing a relaxation iteration parameter. The new RGN iteration method involves the well-known GN iteration method and the Picard iteration method as special cases. Theoretical analyses show that the RGN iteration method is well defined and globally linearly convergent under suitable conditions. In addition, a specific sufficient condition is studied when the coefficient matrix A is symmetric positive definite. Finally, two numerical experiments arising from the linear complementarity problems are used to illustrate the effectiveness of the new RGN iteration method.
- Published
- 2021
45. Effect of edge and vertex addition on Albertson and Bell indices
- Author
-
Ismail Naci Cangul and Sadik Delen
- Subjects
Vertex (graph theory) ,Vertex deletion ,General Mathematics ,lcsh:Mathematics ,omega invariant ,Topological graph ,vertex addition ,lcsh:QA1-939 ,albertson index ,Graph ,Combinatorics ,bell index ,Computer Science::Discrete Mathematics ,edge addition ,Mathematics ,irregularity index - Abstract
Topological graph indices have been of great interest in the research of several properties of chemical substances as it is possible to obtain these properties only by using mathematical calculations. The irregularity indices are the ones to determine the degree of irregularity of a graph. Albertson and Bell indices are two of them. Edge and vertex deletion and addition are important and useful methods in calculating several properties of a given graph. In this paper, the effects of adding a new edge or a new vertex to a graph on the Albertson and Bell indices are determined.
- Published
- 2021
46. Admissible multivalued hybrid $\mathcal{Z}$-contractions with applications
- Author
-
Monairah Alansari, Mohammed Shehu Shagari, Akbar Azam, and Nawab Hussain
- Subjects
simulation function ,Pure mathematics ,$\mathcal{z}$-contraction ,General Mathematics ,hybrid contraction ,lcsh:Mathematics ,multivalued contraction ,Fixed-point theorem ,Fixed point ,lcsh:QA1-939 ,Nonlinear system ,Matrix (mathematics) ,$b$-metric space ,matrix equation ,fixed point ,Graph (abstract data type) ,Point (geometry) ,Partially ordered set ,Complement (set theory) ,Mathematics - Abstract
In this paper, we introduce new concepts, admissible multivalued hybrid $\mathcal{Z}$-contractions and multivalued hybrid $\mathcal{Z}$-contractions in the framework of $b$-metric spaces and establish sufficient conditions for existence of fixed points for such contractions. A few consequences of our main theorem involving linear and nonlinear contractions are pointed out and discussed by using variants of simulation functions. In the case where our notions are reduced to their single-valued counterparts, the results presented herein complement, unify and generalize a number of significant fixed point theorems due to Branciari, Czerwik, Jachymski, Karapinar and Argawal, Khojasteh, Rhoades, among others. Nontrivial illustrative examples are provided to support the assertions of the obtained results. From application point of view, some fixed point theorems of $b$-metric spaces endowed with partial ordering and graph are deduced and solvability conditions of nonlinear matrix equations are investigated.
- Published
- 2021
47. Some (p, q)-Hardy type inequalities for (p, q)-integrable functions
- Author
-
Suriyakamol Thongjob, Kamsing Nonlaopon, and Sortiris K. Ntouyas
- Subjects
(p ,hardy type inequalities ,lcsh:Mathematics ,minkowski integral inequality ,q)-calculus ,lcsh:QA1-939 ,q)-integrable function - Abstract
In this paper, we study some $(p,q)$-Hardy type inequalities for $(p,q)$-integrable functions. Moreover, we also study $(p,q)$-Hölder integral inequality and $(p,q)$-Minkowski integral inequality for two variables. By taking $p=1$ and $q\to 1$, our results reduce to classical results on Hardy type inequalities, Hölder integral inequality and Minkowski integral inequality for two variables.
- Published
- 2021
48. A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five
- Author
-
Raúl M. Falcón, Laura Johnson, Stephanie Perkins, Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII), and Junta de Andalucía
- Subjects
Class (set theory) ,critical set ,Enumeration ,Mathematics::General Mathematics ,General Mathematics ,Order up to ,Structure (category theory) ,enumeration ,Combinatorics ,Set (abstract data type) ,cycle structure ,Latin square ,Mathematics ,Autotopism ,Mathematics::Combinatorics ,Group (mathematics) ,Cycle structure ,lcsh:Mathematics ,Mathematics::History and Overview ,Census ,lcsh:QA1-939 ,autotopism ,latin square ,Critical set - Abstract
This paper delves into the study of critical sets of Latin squares having a given isotopism in their autotopism group. Particularly, we prove that the sizes of these critical sets only depend on both the main class of the Latin square and the cycle structure of the isotopism under consideration. Keeping then in mind that the autotopism group of a Latin square acts faithfully on the set of entries of the latter, we enumerate all the critical sets based on autotopisms of Latin squares of order up to five. Junta de Andalucía FQM-016
- Published
- 2021
49. eromorphic harmonic univalent functions related with generalized (p,q)-post quantum calculus operators
- Author
-
Shuhai Li, Huo Tang, and Lina Ma
- Subjects
Subordination (linguistics) ,Pure mathematics ,Mathematics::Complex Variables ,General Mathematics ,lcsh:Mathematics ,Harmonic (mathematics) ,meromorphic harmonic univalent function ,subordination ,Quantum calculus ,lcsh:QA1-939 ,Convolution ,generalized (p ,Distortion ,convolution ,q)-post quantum calculus operator ,Extreme point ,Mathematics ,Meromorphic function - Abstract
In this paper, we introduce certain subclasses of meromorphic harmonic univalent functions, which are defined by using generalized (p, q)-post quantum calculus operators as well as subordination relationship. Sufficient coefficient conditions, extreme points, distortion bounds and convolution properties for functions belonging to the subclasses are obtained.
- Published
- 2021
50. An averaging principle for stochastic evolution equations with jumps and random time delays
- Author
-
Min Han and Bin Pei
- Subjects
Time delays ,Markov chain ,averaging principle ,General Mathematics ,lcsh:Mathematics ,jumps ,Process (computing) ,Stochastic evolution ,stochastic evolution equations ,lcsh:QA1-939 ,random time delays ,two-time-scale markov switching processes ,Statistical physics ,Limit (mathematics) ,Mathematics - Abstract
This paper investigates an averaging principle for stochastic evolution equations with jumps and random time delays modulated by two-time-scale Markov switching processes in which both fast and slow components co-exist. We prove that there exists a limit process (averaged equation) being substantially simpler than that of the original one.
- Published
- 2021
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