483 results
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2. Applied Mathematics for Engineering Problems in Biomechanics and Robotics 2020.
- Author
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Llopis-Albert, Carlos, Rubio, Francisco, Zeng, Shouzhen, and Liao, Huchang
- Subjects
APPLIED mathematics ,BIOMECHANICS ,ROBOTICS ,ENGINEERING mathematics ,PARALLEL robots ,MANIPULATORS (Machinery) ,ASSEMBLY line balancing - Abstract
There is a disruptive impact of smart technologies in the 21st century, which is transforming the traditional industry and the healthcare sector into the Industry 5.0 and the Healthcare 5.0. Acknowledgments The Guest Editors would like to thank all authors and reviewers for their invaluable contributions towards the success of this special issue. [Extracted from the article]
- Published
- 2022
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3. Applied Mathematics for Engineering Problems in Biomechanics and Robotics.
- Author
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Llopis-Albert, Carlos, Rubio, Francisco, Zeng, Shouzhen, and Liao, Huchang
- Subjects
APPLIED mathematics ,MANIPULATORS (Machinery) ,ENGINEERING mathematics ,ROBOTICS ,BIOMECHANICS ,MULTIPLE criteria decision making ,GROUP decision making - Published
- 2019
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- View/download PDF
4. Inverse Problems: Theory and Application to Science and Engineering.
- Author
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Kunze, Herb, La Torre, Davide, Mendivil, Franklin, Galan, Manuel Ruiz, and Zaki, Rachad
- Subjects
INVERSE problems ,APPLIED mathematics ,MATHEMATICAL proofs ,MATHEMATICS theorems ,STATISTICAL models - Published
- 2014
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5. Inverse Problems: Theory and Application to Science and Engineering 2015.
- Author
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La Torre, Davide, Kunze, Herb, Mendivil, Franklin, Ruiz Galan, Manuel, and Zaki, Rachad
- Subjects
INVERSE problems ,APPLIED mathematics ,ESTIMATION theory ,PARAMETERS (Statistics) ,WAVE equation ,CONTROL theory (Engineering) - Published
- 2015
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6. A New Method Applied to the Quadrilateral Membrane Element with Vertex Rigid Rotational Freedom.
- Author
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Gao, Xiaowei, Liu, Yunfei, and Lv, Jun
- Subjects
- *
QUADRILATERALS , *APPLIED mathematics , *ROTATION groups , *CARTESIAN coordinates , *MATHEMATICAL functions - Abstract
In order to improve the performance of the membrane element with vertex rigid rotational freedom, a new method to establish the local Cartesian coordinate system and calculate the derivatives of the shape functions with respect to the local coordinates is introduced in this paper. The membrane elements with vertex rigid rotational freedom such as GQ12 and GQ12M based on this new method can achieve higher precision results than traditional methods. The numerical results demonstrate that the elements GQ12 and GQ12M with this new method can provide better membrane elements for flat shell elements. Furthermore, this new method presented in this paper offers a new approach for other membrane elements used in flat shell element to improve the computing accuracy. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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7. The Local and Parallel Finite Element Scheme for Electric Structure Eigenvalue Problems
- Author
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Fubiao Lin, Zhixin Liu, and Junying Cao
- Subjects
Article Subject ,Series (mathematics) ,Discretization ,Computer science ,General Mathematics ,Numerical analysis ,General Engineering ,Eigenfunction ,Engineering (General). Civil engineering (General) ,Finite element method ,Singularity ,QA1-939 ,Applied mathematics ,TA1-2040 ,Polar coordinate system ,Mathematics ,Eigenvalues and eigenvectors - Abstract
In this paper, an efficient multiscale finite element method via local defect-correction technique is developed. This method is used to solve the Schrödinger eigenvalue problem with three-dimensional domain. First, this paper considers a three-dimensional bounded spherical region, which is the truncation of a three-dimensional unbounded region. Using polar coordinate transformation, we successfully transform the three-dimensional problem into a series of one-dimensional eigenvalue problems. These one-dimensional eigenvalue problems also bring singularity. Second, using local refinement technique, we establish a new multiscale finite element discretization method. The scheme can correct the defects repeatedly on the local refinement grid, which can solve the singularity problem efficiently. Finally, the error estimates of eigenvalues and eigenfunctions are also proved. Numerical examples show that our numerical method can significantly improve the accuracy of eigenvalues.
- Published
- 2021
8. Convergence Analysis of Schwarz Waveform Relaxation for Nonlocal Diffusion Problems
- Author
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Ke Li, Yunxiang Zhao, and Dali Guo
- Subjects
Article Subject ,Discretization ,Differential equation ,General Mathematics ,General Engineering ,Relaxation (iterative method) ,010103 numerical & computational mathematics ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Convolution ,Fractional calculus ,Quadrature (mathematics) ,010101 applied mathematics ,Rate of convergence ,QA1-939 ,Applied mathematics ,TA1-2040 ,0101 mathematics ,Temporal discretization ,Mathematics - Abstract
Diffusion equations with Riemann–Liouville fractional derivatives are Volterra integro-partial differential equations with weakly singular kernels and present fundamental challenges for numerical computation. In this paper, we make a convergence analysis of the Schwarz waveform relaxation (SWR) algorithms with Robin transmission conditions (TCs) for these problems. We focus on deriving good choice of the parameter involved in the Robin TCs, at the continuous and fully discretized level. Particularly, at the space-time continuous level, we show that the derived Robin parameter is much better than the one predicted by the well-understood equioscillation principle. At the fully discretized level, the problem of determining a good Robin parameter is studied in the convolution quadrature framework, which permits us to precisely capture the effects of different temporal discretization methods on the convergence rate of the SWR algorithms. The results obtained in this paper will be preliminary preparations for our further study of the SWR algorithms for integro-partial differential equations.
- Published
- 2021
9. Solving Bisymmetric Solution of a Class of Matrix Equations Based on Linear Saturated System Model Neural Network
- Author
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Feng Zhang
- Subjects
Normalization (statistics) ,Class (set theory) ,Article Subject ,Artificial neural network ,Computer science ,General Mathematics ,010102 general mathematics ,General Engineering ,Process (computing) ,Structure (category theory) ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Backpropagation ,System model ,010101 applied mathematics ,Matrix (mathematics) ,QA1-939 ,Applied mathematics ,TA1-2040 ,0101 mathematics ,Mathematics - Abstract
In order to solve the complicated process and low efficiency and low accuracy of solving a class of matrix equations, this paper introduces the linear saturated system model neural network architecture to solve the bisymmetric solution of a class of matrix equations. Firstly, a class of matrix equations is constructed to determine the key problems of solving the equations. Secondly, the linear saturated system model neural network structure is constructed to determine the characteristic parameters in the process of bisymmetric solution. Then, the matrix equations is solved by using backpropagation neural network topology. Finally, the class normalization is realized by using the objective function of bisymmetric solution, and the bisymmetric solution of a class of matrix equations is realized. In order to verify the solving effect of the method in this paper, three indexes (accuracy, correction accuracy, and solving time) are designed in the experiment. The experimental results show that the proposed method can effectively reduce the solving time, can improve the accuracy and correction effect of the bisymmetric solution, and has high practicability.
- Published
- 2021
10. Stability Switches and Hopf Bifurcations in a Second-Order Complex Delay Equation.
- Author
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Roales, M. and Rodríguez, F.
- Subjects
- *
STABILITY theory , *HOPF bifurcations , *DELAY differential equations , *COEFFICIENTS (Statistics) , *APPLIED mathematics - Abstract
The existence of stability switches and Hopf bifurcations for the second-order delay differential equation x′′t+ax′t-τ+bxt=0, t>0, with complex coefficients, is studied in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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11. On Some Properties of the New Generalized Fractional Derivative with Non-Singular Kernel
- Author
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Khalid Hattaf
- Subjects
Lyapunov function ,Article Subject ,Non singular ,General Mathematics ,Science and engineering ,General Engineering ,Engineering (General). Civil engineering (General) ,01 natural sciences ,010305 fluids & plasmas ,Fractional calculus ,010101 applied mathematics ,symbols.namesake ,Exponential stability ,Kernel (statistics) ,0103 physical sciences ,QA1-939 ,symbols ,Applied mathematics ,TA1-2040 ,0101 mathematics ,Mathematics - Abstract
This paper presents some new formulas and properties of the generalized fractional derivative with non-singular kernel that covers various types of fractional derivatives such as the Caputo–Fabrizio fractional derivative, the Atangana–Baleanu fractional derivative, and the weighted Atangana–Baleanu fractional derivative. These new properties extend many recent results existing in the literature. Furthermore, the paper proposes some interesting inequalities that estimate the generalized fractional derivatives of some specific functions. These inequalities can be used to construct Lyapunov functions with the aim to study the global asymptotic stability of several fractional-order systems arising from diverse fields of science and engineering.
- Published
- 2021
12. Applied Mathematics and Algorithms for Cloud Computing and IoT.
- Author
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Yuxin Mao, Vijay Bhuse, Zhongmei Zhou, Pit Pichappan, Mahmoud Abdel-Aty, and Yoshinori Hayafuji
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APPLIED mathematics ,ALGORITHMS ,CLOUD computing ,INTERNET of things ,TECHNOLOGICAL revolution ,COMPUTER engineering - Abstract
Today's world is drifting in all new-fangled technology revolution due to the influence of cloud computing and Internet of Things (IoT) technologies. Currently, cloud computing and IoT are the hottest issues of future Internet. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
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13. A New Class of Difference Methods with Intrinsic Parallelism for Burgers–Fisher Equation
- Author
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Yueyue Pan, Lifei Wu, and Xiaozhong Yang
- Subjects
Article Subject ,General Mathematics ,General Engineering ,Fisher equation ,010103 numerical & computational mathematics ,Engineering (General). Civil engineering (General) ,01 natural sciences ,010101 applied mathematics ,Simple (abstract algebra) ,Scheme (mathematics) ,Convergence (routing) ,QA1-939 ,Parallelism (grammar) ,Applied mathematics ,Uniqueness ,TA1-2040 ,0101 mathematics ,Absolute stability ,Mathematics - Abstract
This paper proposes a new class of difference methods with intrinsic parallelism for solving the Burgers–Fisher equation. A new class of parallel difference schemes of pure alternating segment explicit-implicit (PASE-I) and pure alternating segment implicit-explicit (PASI-E) are constructed by taking simple classical explicit and implicit schemes, combined with the alternating segment technique. The existence, uniqueness, linear absolute stability, and convergence for the solutions of PASE-I and PASI-E schemes are well illustrated. Both theoretical analysis and numerical experiments show that PASE-I and PASI-E schemes are linearly absolute stable, with 2-order time accuracy and 2-order spatial accuracy. Compared with the implicit scheme and the Crank–Nicolson (C-N) scheme, the computational efficiency of the PASE-I (PASI-E) scheme is greatly improved. The PASE-I and PASI-E schemes have obvious parallel computing properties, which show that the difference methods with intrinsic parallelism in this paper are feasible to solve the Burgers–Fisher equation.
- Published
- 2020
14. Iterative Solution for Systems of a Class of Abstract Operator Equations in Banach Spaces and Application
- Author
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Hua Su
- Subjects
Class (set theory) ,Article Subject ,General Mathematics ,010102 general mathematics ,General Engineering ,Banach space ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Nonlinear differential equations ,010101 applied mathematics ,Operator (computer programming) ,QA1-939 ,Order (group theory) ,Applied mathematics ,Uniqueness ,TA1-2040 ,0101 mathematics ,Mathematics - Abstract
In this paper, by using the partial order method, the existence and uniqueness of a solution for systems of a class of abstract operator equations in Banach spaces are discussed. The result obtained in this paper improves and unifies many recent results. Two applications to the system of nonlinear differential equations and the systems of nonlinear differential equations in Banach spaces are given, and the unique solution and interactive sequences which converge the unique solution and the error estimation are obtained.
- Published
- 2020
15. Linearization Method of Nonlinear Magnetic Levitation System
- Author
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Shengya Meng, Fanwei Meng, and Dini Wang
- Subjects
0209 industrial biotechnology ,Article Subject ,General Mathematics ,MathematicsofComputing_NUMERICALANALYSIS ,02 engineering and technology ,symbols.namesake ,020901 industrial engineering & automation ,Linearization ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,QA1-939 ,0202 electrical engineering, electronic engineering, information engineering ,Taylor series ,Applied mathematics ,Mathematics ,General Engineering ,Process (computing) ,Engineering (General). Civil engineering (General) ,Magnetic levitation system ,Nonlinear system ,Nonlinear model ,Maglev ,Control system ,symbols ,020201 artificial intelligence & image processing ,TA1-2040 - Abstract
Linearized model of the system is often used in control design. It is generally believed that we can obtain the linearized model as long as the Taylor expansion method is used for the nonlinear model. This paper points out that the Taylor expansion method is only applicable to the linearization of the original nonlinear function. If the Taylor expansion is used for the derived nonlinear equation, wrong results are often obtained. Taking the linearization model of the maglev system as an example, it is shown that the linearization should be carried out with the process of equation derivation. The model is verified by nonlinear system simulation in Simulink. The method in this paper is helpful to write the linearized equation of the control system correctly.
- Published
- 2020
16. Adaptive ADI Numerical Analysis of 2D Quenching-Type Reaction: Diffusion Equation with Convection Term
- Author
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Xiaoliang Zhu and Yongbin Ge
- Subjects
Article Subject ,Discretization ,General Mathematics ,Numerical analysis ,Degenerate energy levels ,General Engineering ,Finite difference ,Engineering (General). Civil engineering (General) ,01 natural sciences ,010305 fluids & plasmas ,010101 applied mathematics ,Nonlinear system ,symbols.namesake ,Alternating direction implicit method ,0103 physical sciences ,Reaction–diffusion system ,QA1-939 ,Taylor series ,symbols ,Applied mathematics ,TA1-2040 ,0101 mathematics ,Mathematics - Abstract
An adaptive high-order difference solution about a 2D nonlinear degenerate singular reaction-diffusion equation with a convection term is initially proposed in the paper. After the first and the second central difference operator approximating the first-order and the second-order spatial derivative, respectively, the higher-order spatial derivatives are discretized by applying the Taylor series rule and the temporal derivative is discretized by using the Crank–Nicolson (CN) difference scheme. An alternating direction implicit (ADI) scheme with a nonuniform grid is built in this way. Meanwhile, accuracy analysis declares the second order in time and the fourth order in space under certain conditions. Sequentially, the high-order scheme is performed on an adaptive mesh to demonstrate quenching behaviors of the singular parabolic equation and analyse the influence of combustion chamber size on quenching. The paper displays rationally that the proposed scheme is practicable for solving the 2D quenching-type problem.
- Published
- 2020
17. On Multiscale RBF Collocation Methods for Solving the Monge–Ampère Equation
- Author
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Qiuyan Xu and Zhiyong Liu
- Subjects
Collocation ,Article Subject ,General Mathematics ,Direct method ,General Engineering ,Boundary (topology) ,Monge–Ampère equation ,010103 numerical & computational mathematics ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Dirichlet distribution ,010101 applied mathematics ,Discrete system ,symbols.namesake ,Nonlinear system ,QA1-939 ,symbols ,Applied mathematics ,Radial basis function ,TA1-2040 ,0101 mathematics ,Mathematics - Abstract
This paper considers some multiscale radial basis function collocation methods for solving the two-dimensional Monge–Ampère equation with Dirichlet boundary. We discuss and study the performance of the three kinds of multiscale methods. The first method is the cascadic meshfree method, which was proposed by Liu and He (2013). The second method is the stationary multilevel method, which was proposed by Floater and Iske (1996), and is used to solve the fully nonlinear partial differential equation in the paper for the first time. The third is the hierarchical radial basis function method, which is constructed by employing successive refinement scattered data sets and scaled compactly supported radial basis functions with varying support radii. Compared with the first two methods, the hierarchical radial basis function method can not only solve the present problem on a single level with higher accuracy and lower computational cost but also produce highly sparse nonlinear discrete system. These observations are obtained by taking the direct approach of numerical experimentation.
- Published
- 2020
18. Coupled System of Nonlinear Fractional Langevin Equations with Multipoint and Nonlocal Integral Boundary Conditions
- Author
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Mohammad Alnegga, Faris Alzahrani, and Ahmed Salem
- Subjects
Article Subject ,General Mathematics ,General Engineering ,02 engineering and technology ,Engineering (General). Civil engineering (General) ,01 natural sciences ,010305 fluids & plasmas ,Fractional calculus ,Nonlinear system ,0103 physical sciences ,QA1-939 ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,Uniqueness ,Boundary value problem ,TA1-2040 ,Fractional differential ,Mathematics - Abstract
This research paper is about the existence and uniqueness of the coupled system of nonlinear fractional Langevin equations with multipoint and nonlocal integral boundary conditions. The Caputo fractional derivative is used to formulate the fractional differential equations, and the fractional integrals mentioned in the boundary conditions are due to Atangana–Baleanu and Katugampola. The existence of solution has been proven by two main fixed-point theorems: O’Regan’s fixed-point theorem and Krasnoselskii’s fixed-point theorem. By applying Banach’s fixed-point theorem, we proved the uniqueness result for the concerned problem. This research paper highlights the examples related with theorems that have already been proven.
- Published
- 2020
19. Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge
- Author
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G. R. Phaijoo, P. K. Santra, and G. S. Mahapatra
- Subjects
Equilibrium point ,Article Subject ,Phase portrait ,General Mathematics ,General Engineering ,Chaotic ,Fixed point ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Stability (probability) ,Domain (mathematical analysis) ,010305 fluids & plasmas ,Nonlinear Sciences::Chaotic Dynamics ,010101 applied mathematics ,0103 physical sciences ,QA1-939 ,Quantitative Biology::Populations and Evolution ,Applied mathematics ,TA1-2040 ,0101 mathematics ,Graphics ,Mathematics ,Bifurcation - Abstract
The paper investigates the dynamical behaviors of a two-species discrete predator-prey system with Crowley–Martin functional response incorporating prey refuge proportional to prey density. The existence of equilibrium points, stability of three fixed points, period-doubling bifurcation, Neimark–Sacker bifurcation, Marottos chaos, and Control Chaos are analyzed for the discrete-time domain. The time graphs, phase portraits, and bifurcation diagrams are obtained for different parameters of the model. Numerical simulations and graphics show that the discrete model exhibits rich dynamics, which also present that the system is a chaotic and complex one. This paper attempts to present a feedback control method which can stabilize chaotic orbits at an unstable equilibrium point.
- Published
- 2020
20. Application of Adomian Decomposition Method to Bounded and Unbounded Stokes’ Problems
- Author
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Ray-Yeng Yang and Chi-Min Liu
- Subjects
Article Subject ,lcsh:Mathematics ,General Mathematics ,General Engineering ,02 engineering and technology ,Function (mathematics) ,lcsh:QA1-939 ,01 natural sciences ,010305 fluids & plasmas ,Exact solutions in general relativity ,Flow (mathematics) ,lcsh:TA1-2040 ,Bounded function ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Padé approximant ,020201 artificial intelligence & image processing ,Boundary value problem ,lcsh:Engineering (General). Civil engineering (General) ,Adomian decomposition method ,Variable (mathematics) ,Mathematics - Abstract
The well-known Stokes’ problems are reexamined by applying the Adomian decomposition method (ADM) associated with other mathematical techniques in this paper. Both the finite-depth (bounded) and infinite-depth (unbounded) cases are analyzed. The present paper raises and deals with two major concerns. The first one is that, for Stokes’ problems, it lacks one boundary condition at the expansion point to fully determine all coefficients of the ADM solution in which an unknown function appears. This unknown function which is dependent on the transformed variable will be determined by the boundary condition at the far end. The second concern is that the derived solution begins to deviate from the exact solution as the spatial variable grows for the unbounded problems. This can be greatly improved by introducing the Padé approximant to satisfy the boundary condition at the far end. For the second problems, the derived ADM solution can be easily separated into the steady-state and the transient parts for a deeper comprehension of the flow. The present result shows an excellent agreement with the exact solution. The ADM is therefore verified to be a reliable mathematical method to analyze Stokes’ problems of finite and infinite depths.
- Published
- 2018
21. Some Methods about Finding the Exact Solutions of Nonlinear Modified BBM Equation
- Author
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Zhiyong Zhou, Fan Niu, and Jianming Qi
- Subjects
Article Subject ,020209 energy ,General Mathematics ,General Engineering ,Elliptic function ,02 engineering and technology ,Rational function ,Engineering (General). Civil engineering (General) ,01 natural sciences ,010305 fluids & plasmas ,Nonlinear system ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,Applied mathematics ,TA1-2040 ,Nonlinear evolution ,Mathematics - Abstract
Finding exact solutions of nonlinear equations plays an important role in nonlinear science, especially in engineering and mathematical physics. In this paper, we employed the complex method to get eight exact solutions of the modified BBM equation for the first time, including two elliptic function solutions, two simply periodic solutions, and four rational function solutions. We used the exp − ϕ z -expansion methods to get fourteen forms of solutions of the modified BBM equation. We also used the sine-cosine method to obtain eight styles’ exact solutions of the modified BBM equation. Only the complex method can obtain elliptic function solutions. We believe that the complex method presented in this paper can be more effectively applied to seek solutions of other nonlinear evolution equations.
- Published
- 2021
- Full Text
- View/download PDF
22. A Nonconstant Shape Parameter-Dependent Competing Risks’ Model in Accelerate Life Test Based on Adaptive Type-II Progressive Hybrid Censoring
- Author
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Yan Wang, Yimin Shi, and Min Wu
- Subjects
Article Subject ,Scale (ratio) ,General Mathematics ,General Engineering ,010103 numerical & computational mathematics ,Bivariate analysis ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Censoring (statistics) ,Gompertz distribution ,Shape parameter ,Confidence interval ,010104 statistics & probability ,Bayes' theorem ,QA1-939 ,Applied mathematics ,Statistics::Methodology ,Uniqueness ,0101 mathematics ,TA1-2040 ,Mathematics - Abstract
In this paper, the dependent competing risks’ model is considered in the constant-stress accelerated life test under the adaptive type-II progressive hybrid-censored scheme. The dependency between failure causes is modeled by Marshall–Olkin bivariate Gompertz distribution. The scale and shape parameters in the model both change with the stress levels, and the failure causes of some test units are unknown. Then, the maximum likelihood estimations and approximation confidence intervals of the unknown parameters are considered. And, the necessary and sufficient condition is established for the existence and uniqueness of the maximum likelihood estimations for unknown parameters. The Bayes approach is also employed to estimate the unknown parameters under suitable prior distributions. The Bayes estimations and highest posterior credible intervals of the unknown parameters are obtained. Finally, a simulation experiment has been performed to illustrate the methods proposed in this paper.
- Published
- 2021
23. Existence and Uniqueness of Positive Solutions for a Class of Nonlinear Fractional Differential Equations with Singular Boundary Value Conditions
- Author
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Yan Debao
- Subjects
Class (set theory) ,Article Subject ,General Mathematics ,010102 general mathematics ,General Engineering ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Boundary values ,010101 applied mathematics ,Nonlinear fractional differential equations ,QA1-939 ,Applied mathematics ,Uniqueness ,0101 mathematics ,TA1-2040 ,Mathematics - Abstract
This paper focuses on a singular boundary value (SBV) problem of nonlinear fractional differential (NFD) equation defined as follows: D 0 + β υ τ + f τ , υ τ = 0 , τ ∈ 0,1 , υ 0 = υ ′ 0 = υ ″ 0 = υ ″ 1 = 0 , where 3 < β ≤ 4 , D 0 + β is the standard Riemann–Liouville fractional (RLF) derivative. The nonlinear function f τ , υ τ might be singular on the spatial and temporal variables. This paper proves that a positive solution to the SBV problem exists and is unique, taking advantage of Green’s function through a fixed-point (FP) theory on cones and mixed monotone operators.
- Published
- 2021
- Full Text
- View/download PDF
24. An Integrated Genetic Algorithm and Homotopy Analysis Method to Solve Nonlinear Equation Systems
- Author
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Hala A. Omar
- Subjects
Article Subject ,Differential equation ,General Mathematics ,Homotopy ,General Engineering ,010103 numerical & computational mathematics ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Square (algebra) ,010101 applied mathematics ,Linear map ,Nonlinear system ,Genetic algorithm ,Convergence (routing) ,QA1-939 ,Applied mathematics ,0101 mathematics ,TA1-2040 ,Homotopy analysis method ,Mathematics - Abstract
Solving nonlinear equation systems for engineering applications is one of the broadest and most essential numerical studies. Several methods and combinations were developed to solve such problems by either finding their roots mathematically or formalizing such problems as an optimization task to obtain the optimal solution using a predetermined objective function. This paper proposes a new algorithm for solving square and nonsquare nonlinear systems combining the genetic algorithm (GA) and the homotopy analysis method (HAM). First, the GA is applied to find out the solution. If it is realized, the algorithm is terminated at this stage as the target solution is determined. Otherwise, the HAM is initiated based on the GA stage’s computed initial guess and linear operator. Moreover, the GA is utilized to calculate the optimum value of the convergence control parameter (h) algebraically without plotting the h-curves or identifying the valid region. Four test functions are examined in this paper to verify the proposed algorithm’s accuracy and efficiency. The results are compared to the Newton HAM (NHAM) and Newton homotopy differential equation (NHDE). The results corroborated the superiority of the proposed algorithm in solving nonlinear equation systems efficiently.
- Published
- 2021
25. Identification of Rational Systems with Logarithmic Quantized Data
- Author
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Shengchao Su and Mingming Ji
- Subjects
0209 industrial biotechnology ,Article Subject ,Logarithm ,Rational system ,General Mathematics ,020208 electrical & electronic engineering ,General Engineering ,Estimator ,02 engineering and technology ,Engineering (General). Civil engineering (General) ,Identification (information) ,020901 industrial engineering & automation ,Logarithmic quantizer ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,Applied mathematics ,Almost everywhere ,TA1-2040 ,Mathematics - Abstract
This paper is concerned with the quantized identification of rational systems, where the systems’ output is quantized by a logarithmic quantizer. Under the assumption that the systems’ input is periodic, the identification procedure is categorized into two steps. The first step is to identify the noise-free output of systems based on the quantized data. The second is to identify the unknown parameter based on the input and the estimation of the noise-free output. The identification algorithm is also summarized. Asymptotic convergence of the estimators is analyzed in detail, which shows that the estimators are convergent almost everywhere. A numerical example is given to illustrate the results obtained in this paper.
- Published
- 2021
26. Neural Network Method for Solving Time-Fractional Telegraph Equation
- Author
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Lelisa Kebena Bijiga and Wubshet Ibrahim
- Subjects
Optimization problem ,Artificial neural network ,Article Subject ,Differential equation ,General Mathematics ,General Engineering ,010103 numerical & computational mathematics ,Function (mathematics) ,Telegrapher's equations ,Engineering (General). Civil engineering (General) ,01 natural sciences ,010101 applied mathematics ,QA1-939 ,Applied mathematics ,Development (differential geometry) ,Boundary value problem ,0101 mathematics ,Fractional differential ,TA1-2040 ,Mathematics - Abstract
Recently, the development of neural network method for solving differential equations has made a remarkable progress for solving fractional differential equations. In this paper, a neural network method is employed to solve time-fractional telegraph equation. The loss function containing initial/boundary conditions with adjustable parameters (weights and biases) is constructed. Also, in this paper, a time-fractional telegraph equation was formulated as an optimization problem. Numerical examples with known analytic solutions including numerical results, their graphs, weights, and biases were also discussed to confirm the accuracy of the method used. Also, the graphical and tabular results were analyzed thoroughly. The mean square errors for different choices of neurons and epochs have been presented in tables along with graphical presentations.
- Published
- 2021
27. Monte Carlo Sampling Method for a Class of Box-Constrained Stochastic Variational Inequality Problems
- Author
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Pei-Yu Li
- Subjects
0209 industrial biotechnology ,Class (set theory) ,021103 operations research ,Optimization problem ,Article Subject ,General Mathematics ,Monte Carlo method ,0211 other engineering and technologies ,General Engineering ,02 engineering and technology ,Function (mathematics) ,Engineering (General). Civil engineering (General) ,020901 industrial engineering & automation ,Variational inequality ,Merit function ,Convergence (routing) ,QA1-939 ,Applied mathematics ,TA1-2040 ,Mathematics - Abstract
This paper uses a merit function derived from the Fishcher–Burmeister function and formulates box-constrained stochastic variational inequality problems as an optimization problem that minimizes this merit function. A sufficient condition for the existence of a solution to the optimization problem is suggested. Finally, this paper proposes a Monte Carlo sampling method for solving the problem. Under some moderate conditions, comprehensive convergence analysis is included as well.
- Published
- 2021
28. A Numerical Method for Compressible Model of Contamination from Nuclear Waste in Porous Media
- Author
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Zhifeng Wang
- Subjects
Article Subject ,General Mathematics ,Numerical analysis ,Linear system ,General Engineering ,010103 numerical & computational mathematics ,Mixed finite element method ,Grid ,Engineering (General). Civil engineering (General) ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Asymptotically optimal algorithm ,Compressibility ,QA1-939 ,Applied mathematics ,0101 mathematics ,TA1-2040 ,Porous medium ,Mathematics - Abstract
This paper studies and analyzes a model describing the flow of contaminated brines through the porous media under severe thermal conditions caused by the radioactive contaminants. The problem is approximated based on combining the mixed finite element method with the modified method of characteristics. In order to solve the resulting algebraic nonlinear equations efficiently, a two-grid method is presented and discussed in this paper. This approach includes a small nonlinear system on a coarse grid with size H and a linear system on a fine grid with size h . It follows from error estimates that asymptotically optimal accuracy can be obtained as long as the mesh sizes satisfy H = O h 1 / 3 .
- Published
- 2021
29. Analysis of Reliable Solutions to the Boundary Value Problems by Using Shooting Method.
- Author
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Arefin, Mohammad Asif, Nishu, Mahmuda Akhter, Dhali, Md Nayan, and Uddin, M. Hafiz
- Subjects
BOUNDARY value problems ,NUMERICAL solutions to boundary value problems ,MATHEMATICAL optimization ,ORDINARY differential equations ,APPLIED mathematics - Abstract
This research aims to use the shooting method (SM) to find numerical solutions to the boundary value problems of ordinary differential equations (ODEs). Applied mathematics, theoretical physics, engineering, control, and optimization theory all have two-point boundary value problems. If the two-point boundary value problem cannot be solved analytically, numerical approaches must be used. The scenario in the two-point boundary value issue for a single second-order differential equation with prescribed initial and final values of the solution gives rise to shooting method. Firstly, the method is discussed, and some boundary value problems of ODEs are solved by using the proposed method. Obtained results are compared with the exact solution for the validation of the proposed method and represented both in graphical and tabular form. It has been found that the convergence rate of the shooting method to the exact solution is so high. As a finding of this research, it has been determined that the shooting method produces the best-fit numerical results of boundary value problems. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
30. Mechanical Decoupling Algorithm Applied to Electric Drive Test Bed.
- Author
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Song Qiang and Luo Lin
- Subjects
- *
MATHEMATICAL decoupling , *ALGORITHMS , *APPLIED mathematics , *ELECTRIC drives , *DYNAMOMETER , *MATHEMATICAL models - Abstract
New approach and analysis are proposed in this paper to enhance the steady and rapidity of the electric drive test bed. Based on a basic drive motor dynamometer system (DMDS) test bed, detailed mathematical model and process control are established and analyzed. Relative gain array (RGA) method and diagonal matrix method are used to analyze the mechanical coupling caused by mechanical connection on the DMDS test bed, and the structure and algorithm of dynamic decoupling are proposed. Simulation and experiment all indicate that the designed decoupling method can efficiently improve the control accuracy and response speed. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
31. Wavelet Methods for Solving Fractional Order Differential Equations.
- Author
-
Gupta, A. K. and Ray, S. Saha
- Subjects
- *
FRACTIONAL differential equations , *APPLIED mathematics , *VISCOELASTICITY , *FRACTIONAL calculus , *ELECTROMAGNETISM , *NONLINEAR equations - Abstract
Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and manymore. In this paper, we review different wavelet methods for solving both linear and nonlinear fractional differential equations. Our goal is to analyze the selected wavelet methods and assess their accuracy and efficiency with regard to solving fractional differential equations. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study on various wavelets in order to solve differential equations of arbitrary order. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
32. A Smoothing Newton Method with a Mixed Line Search for Monotone Weighted Complementarity Problems
- Author
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Xiaoqin Jiang and He Huang
- Subjects
021103 operations research ,Line search ,Article Subject ,General Mathematics ,0211 other engineering and technologies ,General Engineering ,010103 numerical & computational mathematics ,02 engineering and technology ,Engineering (General). Civil engineering (General) ,System of linear equations ,01 natural sciences ,Complementarity (physics) ,symbols.namesake ,Monotone polygon ,Complementarity theory ,Robustness (computer science) ,QA1-939 ,symbols ,Applied mathematics ,TA1-2040 ,0101 mathematics ,Newton's method ,Mathematics ,Smoothing - Abstract
In this paper, we present a smoothing Newton method for solving the monotone weighted complementarity problem (WCP). In each iteration of our method, the iterative direction is achieved by solving a system of linear equations and the iterative step length is achieved by adopting a line search. A feature of the line search criteria used in this paper is that monotone and nonmonotone line search are mixed used. The proposed method is new even when the WCP reduces to the standard complementarity problem. Particularly, the proposed method is proved to possess the global convergence under a weak assumption. The preliminary experimental results show the effectiveness and robustness of the proposed method for solving the concerned WCP.
- Published
- 2020
- Full Text
- View/download PDF
33. On a System of k-Difference Equations of Order Three
- Author
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Ibrahim Yalcinkaya, Yong-Min Li, Hijaz Ahmad, and Durhasan Turgut Tollu
- Subjects
Article Subject ,General Mathematics ,General Engineering ,010103 numerical & computational mathematics ,Engineering (General). Civil engineering (General) ,01 natural sciences ,010101 applied mathematics ,Order (business) ,QA1-939 ,Applied mathematics ,0101 mathematics ,TA1-2040 ,Mathematics - Abstract
In this paper, we deal with the global behavior of the positive solutions of the system of k -difference equations u n + 1 1 = α 1 u n − 1 1 / β 1 + α 1 u n − 2 2 r 1 , u n + 1 2 = α 2 u n − 1 2 / β 2 + α 2 u n − 2 3 r 2 , … , u n + 1 k = α k u n − 1 k / β k + α k u n − 2 1 r k , n ∈ ℕ 0 , where the initial conditions u − l i l = 0,1,2 are nonnegative real numbers and the parameters α i , β i , γ i , and r i are positive real numbers for i = 1,2 , … , k , by extending some results in the literature. By the end of the paper, we give three numerical examples to support our theoretical results related to the system with some restrictions on the parameters.
- Published
- 2020
34. Turing Instability and Amplitude Equation of Reaction-Diffusion System with Multivariable
- Author
-
Qianqian Zheng and Jianwei Shen
- Subjects
Article Subject ,General Mathematics ,Multivariable calculus ,Dynamics (mechanics) ,General Engineering ,MathematicsofComputing_NUMERICALANALYSIS ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Stability (probability) ,010305 fluids & plasmas ,Amplitude ,0103 physical sciences ,Reaction–diffusion system ,QA1-939 ,Applied mathematics ,Matrix analysis ,TA1-2040 ,010301 acoustics ,Turing ,computer ,Bifurcation ,Mathematics ,computer.programming_language - Abstract
In this paper, we investigate pattern dynamics with multivariable by using the method of matrix analysis and obtain a condition under which the system loses stability and Turing bifurcation occurs. In addition, we also derive the amplitude equation with multivariable. This is an effective tool to investigate multivariate pattern dynamics. The example and simulation used in this paper validate our theoretical results. The method presented is a novel approach to the investigation of specific real systems based on the model developed in this paper.
- Published
- 2020
- Full Text
- View/download PDF
35. The Delayed Doubly Stochastic Linear Quadratic Optimal Control Problem
- Author
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Yan Chen and Jie Xu
- Subjects
Stochastic control ,0209 industrial biotechnology ,State variable ,Article Subject ,General Mathematics ,General Engineering ,Control variable ,MathematicsofComputing_NUMERICALANALYSIS ,02 engineering and technology ,Optimal control ,Engineering (General). Civil engineering (General) ,Matrix (mathematics) ,020901 industrial engineering & automation ,Bellman equation ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,0202 electrical engineering, electronic engineering, information engineering ,Riccati equation ,QA1-939 ,Applied mathematics ,020201 artificial intelligence & image processing ,Uniqueness ,TA1-2040 ,Mathematics - Abstract
In this paper, the delayed doubly stochastic linear quadratic optimal control problem is discussed. It deduces the expression of the optimal control for the general delayed doubly stochastic control system which contained time delay both in the state variable and in the control variable at the same time and proves its uniqueness by using the classical parallelogram rule. The paper is concerned with the generalized matrix value Riccati equation for a special delayed doubly stochastic linear quadratic control system and aims to give the expression of optimal control and value function by the solution of the Riccati equation.
- Published
- 2020
- Full Text
- View/download PDF
36. Synchronized Chaos of a Three-Dimensional System with Quadratic Terms
- Author
-
Ali Allahem
- Subjects
Computer simulation ,Phase portrait ,Article Subject ,General Mathematics ,General Engineering ,Chaotic ,Lyapunov exponent ,Bifurcation diagram ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Synchronization ,010101 applied mathematics ,Nonlinear Sciences::Chaotic Dynamics ,Nonlinear system ,symbols.namesake ,Quadratic equation ,0103 physical sciences ,symbols ,QA1-939 ,Applied mathematics ,0101 mathematics ,TA1-2040 ,010301 acoustics ,Mathematics - Abstract
In this paper, a novel chaotic new three-dimensional system has been studied by Zhang et al. in 2012. In the system, there are three control parameters and three different nonlinear terms which governed equations. Zhang et al. studied elementary (preliminary) dynamic properties of the chaotic new three-dimensional system by means of bifurcation diagram, maximum Lyapunov exponent, phase portraits, dynamics behaviors by changing some parameters etc., using all possible theoretical analysis and numerical simulation. In this paper, we have demonstrated its complete synchronization. The proposed results are verified by numerical simulations.
- Published
- 2020
- Full Text
- View/download PDF
37. The Limit Theorems for Function of Markov Chains in the Environment of Single Infinite Markovian Systems
- Author
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Xiangyu Ge, Zhanfeng Li, Min Huang, and Xiaohua Meng
- Subjects
Article Subject ,Markov chain ,General Mathematics ,010102 general mathematics ,General Engineering ,Markov process ,Engineering (General). Civil engineering (General) ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,Law of large numbers ,symbols ,QA1-939 ,Applied mathematics ,Even and odd functions ,Finite state ,0101 mathematics ,TA1-2040 ,Martingale (probability theory) ,Mathematics - Abstract
This paper is intended to study the limit theorem of Markov chain function in the environment of single infinite Markovian systems. Moreover, the problem of the strong law of large numbers in the infinite environment is presented by means of constructing martingale differential sequence for the measurement under some different sufficient conditions. If the sequence of even functions gnx,n≥0 satisfies different conditions when the value ranges of x are different, we have obtained SLLN for function of Markov chain in the environment of single infinite Markovian systems. In addition, the paper studies the strong convergence of the weighted sums of function for finite state Markov Chains in single infinitely Markovian environments. Although the similar conclusions have been carried out, the difference results performed by previous scholars are that we give weaker different sufficient conditions of the strong convergence of weighted sums compared with the previous conclusions.
- Published
- 2020
38. Novel Two-Stage Method for Low-Order Polynomial Model
- Author
-
Xiuli Shen, Cheng Yan, and Fushui Guo
- Subjects
Surface (mathematics) ,Polynomial ,Article Subject ,lcsh:Mathematics ,General Mathematics ,0211 other engineering and technologies ,General Engineering ,Sampling (statistics) ,Statistical model ,02 engineering and technology ,lcsh:QA1-939 ,Nonlinear system ,020303 mechanical engineering & transports ,Polynomial and rational function modeling ,0203 mechanical engineering ,lcsh:TA1-2040 ,Applied mathematics ,Response surface methodology ,lcsh:Engineering (General). Civil engineering (General) ,Engineering design process ,021106 design practice & management ,Mathematics - Abstract
One of the most popular statistical models is a low-order polynomial response surface model, i.e., a polynomial of first order or second order. These polynomials can be used for global metamodels in weakly nonlinear simulation to approximate their global tendency and local metamodels in response surface methodology (RSM), which has been studied in various applications in engineering design and analysis. The order of the selected polynomial determines the number of sampling points (input combinations) and the resulting accuracy (validity, adequacy). This paper derives a novel method to obtain an accurate high-order polynomial while requiring fewer sampling points. This method uses a two-stage procedure such that the second stage modifies the low-order polynomial estimated in the first stage; this second stage does not require new points. This paper evaluates the performance of the method numerically by using several test functions. These numerical results show that the proposed method can provide more accurate predictions than the traditional method.
- Published
- 2018
39. Inverse Problem Solution and Regularization Parameter Selection for Current Distribution Reconstruction in Switching Arcs by Inverting Magnetic Fields
- Author
-
Zhiqiang Zhang, Yingsan Geng, Jinlong Dong, Jianhua Wang, and Guogang Zhang
- Subjects
010302 applied physics ,Article Subject ,Computer science ,lcsh:Mathematics ,General Mathematics ,General Engineering ,Inverse problem ,lcsh:QA1-939 ,01 natural sciences ,Regularization (mathematics) ,010305 fluids & plasmas ,Magnetic field ,Tikhonov regularization ,Sensor array ,lcsh:TA1-2040 ,Robustness (computer science) ,0103 physical sciences ,Applied mathematics ,lcsh:Engineering (General). Civil engineering (General) - Abstract
Current density distribution in electric arcs inside low voltage circuit breakers is a crucial parameter for us to understand the complex physical behavior during the arcing process. In this paper, we investigate the inverse problem of reconstructing the current density distribution in arcs by inverting the magnetic fields. A simplified 2D arc chamber is considered. The aim of this paper is the computational side of the regularization method, regularization parameter selection strategies, and the estimation of systematic error. To address the ill-posedness of the inverse problem, Tikhonov regularization is analyzed, with the regularization parameter chosen by Morozov’s discrepancy principle, the L-curve, the generalized cross-validation, and the quasi-optimality criteria. The provided range of regularization parameter selection strategies is much wider than in the previous works. Effects of several features on the performance of these criteria have been investigated, including the signal-to-noise ratio, dimension of measurement space, and the measurement distance. The numerical simulations show that the generalized cross-validation and quasi-optimality criteria provide a more satisfactory performance on the robustness and accuracy. Moreover, an optimal measurement distance can be expected when using a planner sensor array to perform magnetic measurements.
- Published
- 2018
40. Stability of Fractional Order Systems.
- Author
-
Rivero, Margarita, Rogosin, Sergei V., Machado, José A. Tenreiro, and Trujillo, Juan J.
- Subjects
- *
STABILITY theory , *FRACTIONAL calculus , *APPLIED mathematics , *PROBLEM solving , *DYNAMICAL systems - Abstract
The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, fromthemathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
41. Stability Analysis of a Variant of the Prony Method.
- Author
-
Jaramillo, Rodney and Lentini, Marianela
- Subjects
- *
STRUCTURAL analysis (Engineering) , *PRONY analysis , *APPLIED mathematics , *LINEAR algebra , *POLYNOMIALS - Abstract
Prony type methods are used in many engineering applications to determine the exponential fit corresponding to a dataset. In this paper we study a variant of Prony's method that was used by Martfn-Landrove et al., in a process of segmentation of T2-weighted MRI brain images. We show the equivalence between that method and the classical Prony method and study the stability of the computed solutions with respect to noise in the data set. In particular, we show that the relative error in the calculation of the exponential fit parameters is linear with respect to noise in the data. Our analysis is based on classical results from linear algebra, matrix computation theory, and the theory of stability for roots of polynomials. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
42. Combined Energy Minimization for Image Reconstruction from Few Views.
- Author
-
Wei Wei, Xiao-Lin Yang, Bin Zhou, Jun Feng, and Pei-Yi Shen
- Subjects
- *
IMAGE reconstruction , *APPLIED mathematics , *CONJUGATE gradient methods , *APPROXIMATION theory , *IMAGE processing , *DIAGNOSTIC imaging - Abstract
Reconstruction from few views is an important problem in medical imaging and applied mathematics. In this paper, a combined energy minimization is proposed for image reconstruction. l2 energy of the image gradient is introduced in the lower density region, and it can accelerate the reconstruction speed and improve the results. Total variation of the image is introduced in the higher density region, and the image features can be preserved well. Nonlinear conjugate gradient method is introduced to solve the problem. The efficiency and accuracy of our method are shown in several numerical experiments. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
43. Stochastic Dynamics of Discrete-Time Fuzzy Random BAM Neural Networks with Time Delays
- Author
-
Sufang Han, Guoxin Liu, and Tianwei Zhang
- Subjects
0209 industrial biotechnology ,Artificial neural network ,Article Subject ,lcsh:Mathematics ,General Mathematics ,General Engineering ,Fixed-point theorem ,Periodic sequence ,02 engineering and technology ,lcsh:QA1-939 ,Fuzzy logic ,Moment (mathematics) ,020901 industrial engineering & automation ,Exponential stability ,Discrete time and continuous time ,lcsh:TA1-2040 ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,lcsh:Engineering (General). Civil engineering (General) ,Stochastic neural network ,Mathematics - Abstract
By using the semidiscrete method of differential equations, a new version of discrete analogue of stochastic fuzzy BAM neural networks was formulated, which gives a more accurate characterization for continuous-time stochastic neural networks than that by the Euler scheme. Firstly, the existence of the 2p-th mean almost periodic sequence solution of the discrete-time stochastic fuzzy BAM neural networks is investigated with the help of Minkowski inequality, Hölder inequality, and Krasnoselskii’s fixed point theorem. Secondly, the 2p-th moment global exponential stability of the discrete-time stochastic fuzzy BAM neural networks is also studied by using some analytical skills in stochastic theory. Finally, two examples with computer simulations are given to demonstrate that our results are feasible. The main results obtained in this paper are completely new, and the methods used in this paper provide a possible technique to study 2p-th mean almost periodic sequence solution and 2p-th moment global exponential stability of semidiscrete stochastic fuzzy models.
- Published
- 2019
- Full Text
- View/download PDF
44. A New Stability Analysis of Uncertain Delay Differential Equations
- Author
-
Yufu Ning and Xiao Wang
- Subjects
0209 industrial biotechnology ,Article Subject ,General Mathematics ,lcsh:Mathematics ,General Engineering ,02 engineering and technology ,Delay differential equation ,lcsh:QA1-939 ,Stability (probability) ,Measure (mathematics) ,020901 industrial engineering & automation ,lcsh:TA1-2040 ,0202 electrical engineering, electronic engineering, information engineering ,sort ,Applied mathematics ,020201 artificial intelligence & image processing ,Almost surely ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
This paper first provides a concept of almost sure stability for uncertain delay differential equations and analyzes this new sort of stability. In addition, this paper derives three sufficient conditions for uncertain delay differential equations being stable almost surely. Finally, the relationship between almost sure stability and stability in measure for uncertain delay differential equations is discussed.
- Published
- 2019
45. The Behavior of Weighted Graph's Orbit and Its Energy.
- Author
-
Shukur, Ali A., Jahanbani, Akbar, and Shelash, Haider
- Subjects
WEIGHTED graphs ,APPLIED mathematics ,DYNAMICAL systems ,DISCRETE systems - Abstract
Studying the orbit of an element in a discrete dynamical system is one of the most important areas in pure and applied mathematics. It is well known that each graph contains a finite (or infinite) number of elements. In this work, we introduce a new analytical phenomenon to the weighted graphs by studying the orbit of their elements. Studying the weighted graph's orbit allows us to have a better understanding to the behaviour of the systems (graphs) during determined time and environment. Moreover, the energy of the graph's orbit is given. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
46. A Modified Precise Integration Method for Long-Time Duration Dynamic Analysis
- Author
-
Minghui Fu and Ce Huang
- Subjects
Article Subject ,Computer science ,General Mathematics ,lcsh:Mathematics ,General Engineering ,Inversion (meteorology) ,02 engineering and technology ,Time duration ,Dissipation ,lcsh:QA1-939 ,01 natural sciences ,Numerical integration ,010101 applied mathematics ,Method of undetermined coefficients ,Matrix (mathematics) ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Homogeneous ,lcsh:TA1-2040 ,Fundamental solution ,Applied mathematics ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) - Abstract
This paper presents a modified Precise Integration Method (PIM) for long-time duration dynamic analysis. The fundamental solution and loading operator matrices in the first time substep are numerically computed employing a known unconditionally stable method (referred to as original method in this paper). By using efficient recursive algorithms to evaluate these matrices in the first time-step, the same numerical results as those using the original method with small time-step are obtained. The proposed method avoids the need of matrix inversion and numerical quadrature formulae, while the particular solution obtained has the same accuracy as that of the homogeneous solution. Through setting a proper value of the time substep, satisfactory accuracy and numerical dissipation can be achieved.
- Published
- 2018
- Full Text
- View/download PDF
47. A Nonhomogeneous Multivariable Grey Prediction NMGM Modeling Mechanism and Its Application
- Author
-
Haixia Wang and Lingdi Zhao
- Subjects
Article Subject ,Mechanism (biology) ,Computer science ,Differential equation ,General Mathematics ,Multivariable calculus ,lcsh:Mathematics ,010102 general mathematics ,General Engineering ,02 engineering and technology ,Extension (predicate logic) ,Function (mathematics) ,lcsh:QA1-939 ,01 natural sciences ,Least squares ,lcsh:TA1-2040 ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) - Abstract
The purpose of this paper is to explore modeling mechanism of a nonhomogeneous multivariable grey prediction NMGM(1, m, kα) model and its application. Although multi-variable grey prediction MGM(1, m) model has been employed in many fields, its prediction results are not always satisfactory. Traditional MGM(1, m) model is constructed on the hypothesis that original data sequences are in accord with homogeneous index trend; however, the nonhomogeneous index data sequences are the most common data existing in all systems, and how to handle multivariable nonhomogeneous index data sequences is an urgent problem. This paper proposes a novel nonhomogeneous multivariable grey prediction model termed NMGM(1, m, kα) to deal with those data sequences that are not in accord with homogeneous index trend. Based on grey prediction theory, by least square method and solutions of differential equations, the modeling mechanism and time response function of the proposed model are expounded. A case study demonstrates that the novel model provides preferable prediction performance compared with traditional MGM(1, m) model. This work is an extension of the multivariable grey prediction model and enriches the study of grey prediction theory.
- Published
- 2018
- Full Text
- View/download PDF
48. A New Approach to Derive Priority Weights from Additive Interval Fuzzy Preference Relations Based on Logarithms
- Author
-
Chengxiang Yin, Wenning Hao, Xingdang Kang, Xiuli Qi, and Hongjun Zhang
- Subjects
0209 industrial biotechnology ,Transitive relation ,Article Subject ,Logarithm ,Linear programming ,General Mathematics ,lcsh:Mathematics ,General Engineering ,Linear model ,02 engineering and technology ,Interval (mathematics) ,lcsh:QA1-939 ,Fuzzy logic ,020901 industrial engineering & automation ,Consistency (statistics) ,lcsh:TA1-2040 ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,lcsh:Engineering (General). Civil engineering (General) ,Preference (economics) ,Mathematics - Abstract
This paper investigates the consistency definition and the weight-deriving method for additive interval fuzzy preference relations (IFPRs) using a particular characterization based on logarithms. In a recently published paper, a new approach with a parameter is developed to obtain priority weights from fuzzy preference relations (FPRs), then a new consistency definition for the additive IFPRs is defined, and finally linear programming models for deriving interval weights from consistent and inconsistent IFPRs are proposed. However, the discussion of the parameter value is not adequate and the weights obtained by the linear models for inconsistent IFPRs are dependent on alternative labels and not robust to permutations of the decision makers’ judgments. In this paper, we first investigate the value of the parameter more thoroughly and give the closed form solution for the parameter. Then, we design a numerical example to illustrate the drawback of the linear models. Finally, we construct a linear model to derive interval weights from IFPRs based on the additive transitivity based consistency definition. To demonstrate the effectiveness of our proposed method, we compare our method to the existing method on three numerical examples. The results show that our method performs better on both consistent and inconsistent IFPRs.
- Published
- 2018
49. Further Results on Diagonally Invariant Exponential Stability of Switching Linear Systems
- Author
-
Mihaela-Hanako Matcovschi and Octavian Pastravanu
- Subjects
0209 industrial biotechnology ,Article Subject ,lcsh:Mathematics ,General Mathematics ,020208 electrical & electronic engineering ,Linear system ,Diagonal ,General Engineering ,Matrix norm ,02 engineering and technology ,Invariant (physics) ,lcsh:QA1-939 ,020901 industrial engineering & automation ,Exponential stability ,lcsh:TA1-2040 ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Analysis method ,Eigenvalues and eigenvectors ,Mathematics - Abstract
The concept of diagonally invariant exponential stability (DIES) was originally introduced for single-model linear systems and subsequently expanded in the study of linear systems with interval-type uncertainties and linear systems with arbitrary switching. The results presented in this article refer to new approaches to DIES characterization for arbitrary switching systems, which exploit mathematical tools completely different from earlier work. The previous papers are based on the properties of matrix norms and measures applied to the constituent matrices defining the switching system, while the present paper uses the eigenvalues and eigenvectors of the column and row representatives built for a set of matrices derived from the constituent matrices of the switching system. The applicability of previous and new results, respectively, is illustrated by case studies (in both continuous- and discrete-time) that lead to relevant comparisons between the two classes of analysis methods.
- Published
- 2018
- Full Text
- View/download PDF
50. Bounding the Dynamics of a Chaotic-Cancer Mathematical Model
- Author
-
Corina Plata, Paul A. Valle, Diana Gamboa, and Luis N. Coria
- Subjects
0301 basic medicine ,Lyapunov stability ,education.field_of_study ,Mathematical model ,Article Subject ,lcsh:Mathematics ,General Mathematics ,Population ,General Engineering ,Chaotic ,Ode ,lcsh:QA1-939 ,03 medical and health sciences ,030104 developmental biology ,0302 clinical medicine ,lcsh:TA1-2040 ,030220 oncology & carcinogenesis ,Ordinary differential equation ,Attractor ,Applied mathematics ,Initial value problem ,lcsh:Engineering (General). Civil engineering (General) ,education ,Mathematics - Abstract
The complexity of cancer has motivated the development of different approaches to understand the dynamics of this large group of diseases. One that may allow us to better comprehend the behavior of cancer cells, in both short- and long-term, is mathematical modelling through ordinary differential equations. Several ODE mathematical models concerning tumor evolution and immune response have been formulated through the years, but only a few may exhibit chaotic attractors and oscillations such as stable limit cycles and periodic orbits; these dynamics are not that common among cancer systems. In this paper, we apply the Localization of Compact Invariant Sets (LCIS) method and Lyapunov stability theory to investigate the global dynamics and the main factors involved in tumor growth and immune response for a chaotic-cancer system presented by Itik and Banks in 2010. The LCIS method allows us to compute what we define as the localizing domain, which is formulated by the intersection of all lower and upper bounds of each cells population in the nonnegative octant, R+,03. Bounds of this domain are given by inequalities in terms of the system parameters. Then, we apply Lyapunov stability theory and LaSalle’s invariance principle to establish existence conditions of a global attractor. The latter implies that given any nonnegative initial condition, all trajectories will go to the largest compact invariant set (a stable equilibrium point, limit cycles, periodic orbits, or a chaotic attractor) located either inside or at the boundaries of the localizing domain. In order to complement our analysis, numerical simulations are performed throughout the paper to illustrate all mathematical results and to better explain their biological implications.
- Published
- 2018
- Full Text
- View/download PDF
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