268 results
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2. Generation of Polynomial Automorphisms Appropriate for the Generalization of Fuzzy Connectives.
- Author
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Makariadis, Eleftherios, Makariadis, Stefanos, Konguetsof, Avrilia, and Papadopoulos, Basil
- Subjects
GENERALIZATION ,POLYNOMIALS ,ARTIFICIAL intelligence ,MATHEMATICAL models ,NUMERICAL analysis - Abstract
Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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3. A Symmetric Fourth Party Logistics Routing Problem with Multiple Distributors in Uncertain Random Environments.
- Author
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Gao, Xinyu, Gao, Xin, and Liu, Yang
- Subjects
STOCHASTIC programming ,MATHEMATICAL programming ,MATHEMATICAL models ,ECONOMIC globalization ,DISTRIBUTION (Probability theory) ,WAREHOUSES ,LOGISTICS - Abstract
Economic globalization and the rapid development of the Internet make logistics systems more and more diversified, people and enterprises have greatly increased their requirements for logistics systems, and fourth party logistics has received more and more attention from people and related enterprises. In order to further study the routing problem under uncertain stochastic environments, this paper considers the fourth party logistics routing problem from a single manufacturer to multiple distributors with uncertain times and random supplies under the complete information symmetry scenario and symmetric transportation volume decision space. Then, an uncertain stochastic programming model is established with the minimum total cost as its core objective, and the total transportation time, manufacturer's supply, and distributor's demand as constraints. In order to solve the optimal path of the above problems, this paper transforms the uncertain stochastic programming model into a classical mathematical programming model based on the distribution functions of uncertain time and random supply. Finally, two numerical examples are given to verify the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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4. New Trends on the Mathematical Models and Solitons Arising in Real-World Problems.
- Author
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Baskonus, Haci Mehmet
- Subjects
MATHEMATICAL models ,MATHEMATICAL symmetry ,SOLITONS ,CONIFER wilt ,INVERSE problems ,FRACTIONAL differential equations ,GLOBAL analysis (Mathematics) - Abstract
This document discusses recent trends in mathematical models and solitons used to analyze real-world problems. The focus is on the application of fractional calculus in modeling phenomena such as anomalous diffusion, non-Markovian processes, and random walk. The document provides summaries of 15 papers accepted for publication in a special issue, covering topics such as digestive system modeling, COVID-19 pandemic modeling, control systems for motors, symmetry in pine wilt disease, soliton solutions for various equations, and epidemic modeling. The papers employ various mathematical techniques and provide insights into different aspects of real-world problems. [Extracted from the article]
- Published
- 2024
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5. Convergence of a Family of Methods with Symmetric, Antisymmetric Parameters and Weight Functions.
- Author
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Behl, Ramandeep and Argyros, Ioannis K.
- Subjects
NONLINEAR equations ,MATHEMATICAL models ,EQUATIONS - Abstract
Many problems in scientific research are reduced to a nonlinear equation by mathematical means of modeling. The solutions of such equations are found mostly iteratively. Then, the convergence order is routinely shown using Taylor formulas, which in turn make sufficient assumptions about derivatives which are not present in the iterative method at hand. This technique restricts the usage of the method which may converge even if these assumptions, which are not also necessary, hold. The utilization of these methods can be extended under less restrictive conditions. This new paper contributes in this direction, since the convergence is established by assumptions restricted exclusively on the functions present on the method. Although the technique is demonstrated on a two-step Traub-type method with usually symmetric parameters and weight functions, due to its generality it can be extended to other methods defined on the real line or more abstract spaces. Numerical experimentation complement and further validate the theory. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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6. Generating Chaos in Dynamical Systems: Applications, Symmetry Results, and Stimulating Examples.
- Author
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Kyurkchiev, Nikolay, Zaevski, Tsvetelin, Iliev, Anton, Kyurkchiev, Vesselin, and Rahnev, Asen
- Subjects
DYNAMICAL systems ,STOCHASTIC models ,MATHEMATICAL models ,BEHAVIORAL research ,MODEL theory - Abstract
In this paper, we present a new class of extended oscillators in light of chaos theory. It is based on dynamical complex systems built on the concept of self-describing with a stopping criterion process. We offer an effective studying approach with a specific focus on learning, provoking students' thinking through the triad of enigmatics–creativity–acmeology. Dynamic processes are the basis of mathematical modeling; thus, we can reach the goal of the above-mentioned triad by the proposed differential systems. The results we derive strongly confirm the presence of symmetry in the outcomes of the proposed models. We suggest a stochastic approach to structuring the proposed dynamical systems by modeling the coefficients that drive them by some discrete probability distribution that exhibits symmetry or asymmetry. We propose specific tools for researching the behavior of these systems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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7. Editorial Summary: Mathematical Models and Methods in Various Sciences.
- Author
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Ferreira, Dário
- Subjects
PROPORTIONAL hazards models ,QUALITY control charts ,MATHEMATICAL models ,WIENER processes ,PROPORTIONAL representation ,GARCH model - Abstract
The Special Issue of Symmetry titled "Mathematical Models and Methods in Various Sciences" brings together innovative papers on the theory, methodology, and applications of symmetric/asymmetric mathematical models and methods in various areas of science. The published papers cover a wide range of topics, including estimation methods for mismeasured covariates, empirical models for data analysis, computational approaches for heat transport, investment and pricing strategies, memory-type control charts for monitoring operations, estimation of volatility function in GARCH models, novel weighted distributions, degradation modeling, queueing systems, bivariate proportional hazard models, proportional representation in elections, bounded rational decision-making models, and reliability estimation using a Wiener process. The papers demonstrate the adaptability and capabilities of mathematical modeling in resolving complex issues across diverse scientific fields. [Extracted from the article]
- Published
- 2023
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8. Comparing the Numerical Solution of Fractional Glucose–Insulin Systems Using Generalized Euler Method in Sense of Caputo, Caputo–Fabrizio and Atangana–Baleanu.
- Author
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Alhazmi, Muflih
- Subjects
EULER method ,BLOOD sugar ,SYSTEM dynamics ,PANCREATIC beta cells ,MATHEMATICAL models - Abstract
The purpose of this paper is to present a fractional nonlinear mathematical model with beta-cell kinetics and glucose–insulin feedback in order to describe changes in plasma glucose levels and insulin levels over time that may be associated with changes in beta-cell kinetics. We discuss the solution to the problem with respect to its existence, uniqueness, non-negativity, and boundedness. Using three different fractional derivative operators, the proposed model is examined. To approximate fractional-order systems, we use an efficient numerical Euler method in Caputo, Caputo–Fabrizio, and Atangana–Baleanu sense. Several asymptomatic behaviors are observed in the proposed models based on these three operators. These behaviors do not appear in integer-order derivative models. These behaviors are essential for understanding fractional-order systems dynamics. Our results provide insight into fractional-order systems dynamics. These operators analyze local and global stability and Hyers–Ulam stability. Furthermore, the numerical solutions for the proposed model are simulated using the three methods. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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9. Symmetry and Analysis of Fluid Queueing Systems Driven by Non-Truncated Erlangian Service Queues.
- Author
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El-Paoumy, Mahdy Shebl and Radwan, Taha
- Subjects
GENERATING functions ,MANUFACTURING processes ,ECOLOGICAL models ,MATHEMATICAL functions ,MATHEMATICAL models - Abstract
This paper investigates the behavior of a fluid queue driven by a non-truncated Erlangian service queue, focusing on the symmetrical properties within the system. This study determines the formulations of the steady-state distribution of both the buffer content and stationary state probabilities of a background queueing system. The efficient generating function technique is employed, utilizing a new generalization of the modified Bessel function of the second kind. Performance metrics such as mean buffer content and throughput are calculated, and server utilization is examined. The results contribute to the understanding of fluid queueing systems and offer insights into their performance in various applications, including telecommunications, manufacturing systems, healthcare operations, and ecological models, where symmetry plays a critical role in optimizing performance. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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10. The Thermoelastic Dynamic Response of a Rod Due to a Moving Heat Source under the Fractional-Order Thermoelasticity Theory.
- Author
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Liu, Fengjun, Shi, Pengjie, and Guo, Ying
- Subjects
THERMOELASTICITY ,STRESS concentration ,DISPLACEMENT (Psychology) ,MATHEMATICAL models - Abstract
In this paper, the thermoelastic behavior of a rod made of an isotropic material under the action of a moving heat source was investigated using a new theory of thermoelasticity related to fractional-order time with two relaxation times. A mathematical model of the one-dimensional thermoelasticity problem was established based on the new thermoelasticity theory. We considered the symmetry of the material, and the fractional-order thermoelasticity control equation was given. Subsequently, the control equations were solved and analyzed using the Laplace transform and its inverse transform. This study examined the effects of fractional-order parameters, time, two thermal relaxation times, and the speed of movement of the heat source on the displacement, temperature, and stress distribution patterns in the rod. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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11. Research on Genetic Algorithm Optimization with Fusion Tabu Search Strategy and Its Application in Solving Three-Dimensional Packing Problems.
- Author
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Kang, Zhenjia, Guan, Yong, Wang, Jiake, and Chen, Pengzhan
- Subjects
TABU search algorithm ,GENETIC algorithms ,HEURISTIC algorithms ,COMBINATORIAL optimization ,NP-hard problems ,MATHEMATICAL models ,COMPUTATIONAL complexity - Abstract
Symmetry is an important principle and characteristic that is prevalent in nature and artificial environments. In the three-dimensional packing problem, leveraging the inherent symmetry of goods and the symmetry of the packing space can enhance packing efficiency and utilization.The three-dimensional packing problem is an NP-hard combinatorial optimization problem in the field of modern logistics, with high computational complexity. This paper proposes an improved genetic algorithm by incorporating a fusion tabu search strategy to address this problem. The algorithm employs a three-dimensional loading mathematical model and utilizes a wall-building method under residual space constraints for stacking goods. Furthermore, adaptation of fitness variation strategy, chromosome adjustment, and tabu search algorithm are introduced to balance the algorithm's global and local search capabilities, as well as to enhance population diversity and convergence speed. Through testing on benchmark cases such as Bischoff and Ratcliff, the improved algorithm demonstrates an average increase of over 3% in packing space utilization compared to traditional genetic algorithms and other heuristic algorithms, validating its feasibility and effectiveness. The proposed improved genetic algorithm provides new insights for solving three-dimensional packing problems and optimizing logistics loading schedules, offering promising prospects for various applications. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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12. MxPL: A Programming Language for Matrix-Related Operations.
- Author
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Aydoğdu, Mehmet Cemil, Aydoğdu, Özge, and Pehlivan, Hüseyin
- Subjects
PROGRAMMING languages ,MATRICES (Mathematics) ,MODERN languages ,MATHEMATICAL models ,PARSING (Computer grammar) - Abstract
It is important to establish solid mathematical knowledge throughout the education period. Matrices are important mathematical objects commonly used in many diverse disciplines, including mathematics, engineering, and science. Most problems encountered in such disciplines are represented by mathematical models with various types of matrices, and solved through some applications of matrix algebra. Although simple or advanced operations of matrices can be performed by using modern programming languages, it usually results in a large fragment of code with a low level of readability due to a complicated sequence of control statements. On the other hand, special-purpose languages handle these operations via library functions, presenting poor integration with other programming environments, and less programming flexibility and practice. This paper addresses the design and development of a programming language, called MxPL, which supports matrix-related mathematics with the provision of some basic structures and functions. Firstly, a grammar that is compatible with the usual notations of matrices is constructed and the parser is produced. Then, the code verifier and interpreter for MxPL programs are implemented. Some code examples are presented to illustrate the performance of several sophisticated matrix operations. The comparative analysis of MxPL is conducted with modern programming languages based on language features. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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13. Optimal Penetration Guidance Law for High-Speed Vehicles against an Interceptor with Modified Proportional Navigation Guidance.
- Author
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Feng, Lei, Lu, Wang, Wang, Fenglin, Zhang, Fan, and Sun, Qiangui
- Subjects
PROPORTIONAL navigation ,ANALYTICAL solutions ,VEHICLES ,THREE-dimensional modeling ,MATHEMATICAL models - Abstract
Aiming at the penetration problem of high-speed vehicles against a modified proportional guidance interceptor, a three-dimensional mathematical model of attack–defense confrontation between the high-speed vehicle and the interceptor is established in this paper. The modified proportional navigation guidance law of the interceptor is included in the model, and control constraints, pitch angle velocity constraints, and dynamic delay are introduced. Then, the performance index of the optimal penetration of high-speed vehicles is established. Under the condition of considering the 180-degree BTT control, the analytical solutions of the optimal speed roll angle and the optimal overload of high-speed vehicles are obtained according to symmetric Hamilton principle. The simulation results show that the overload switching times of high-speed vehicles to achieve optimal penetration are N − 1, where N is the modified proportional guidance coefficient of the interceptor. When the maximum speed roll angle velocity is [60, 90] degrees per second, the penetration effect of high-speed vehicles is good. Finally, the optimal penetration guidance law proposed in this paper can achieve a miss distance of more than 5 m when the overload capacity ratio is 0.33. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
14. Modeling and Simulation of Physical Systems Formed by Bond Graphs and Multibond Graphs.
- Author
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Gonzalez-Avalos, Gilberto, Gallegos, Noe Barrera, Ayala-Jaimes, Gerardo, Garcia, Aaron Padilla, Ferreyra García, Luis Flaviano, and Rodríguez, Aldo Jesus Parente
- Subjects
BOND graphs ,ELECTRIC power ,SYNCHRONOUS generators ,SIMULATION methods & models ,POWER resources ,MATHEMATICAL models - Abstract
Current physical systems are built in more that one coordinate: for example, electrical power systems, aeronautical systems and robotic systems can be modeled in multibond graphs (M B G) . However, in these systems, some elements use only one axis or dimension—for example, actuators and controllers—which can be modeled in bond graphs (B G) . Therefore, in this paper, modeling of systems in multibond graphs and bond graphs ( M B G - B G ) is presented. Likewise, the junction structure of systems represented by ( M B G - B G ) is introduced. From this structure, mathematical modeling in the state space is presented. Likewise, modeling of systems on a platform ( M B G - B G ) can be seen as symmetric to the mathematical model that represents these systems. Finally, a synchronous generator modeled by ( M B G - B G ) as a case study is developed, and simulation results using 20-Sim software are shown. Furthermore, an electrical power system connected to the power supply of a DC motor as another case study is explained. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
15. On the Enhanced New Qualitative Results of Nonlinear Integro-Differential Equations.
- Author
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Tunç, Cemil, Tunç, Osman, and Yao, Jen-Chih
- Subjects
NONLINEAR equations ,INTEGRO-differential equations ,MATHEMATICAL models - Abstract
In this article, a class of scalar nonlinear integro-differential equations of first order with fading memory is investigated. For the considered fading memory problem, we discuss the effects of the memory over all the values of the parameter in the kernel of the equations. Using the Lyapunov–Krasovski functional method, we give various sufficient conditions of stability, asymptotic stability, uniform stability of zero solution, convergence and boundedness, and square integrability of nonzero solutions in relation to the considered scalar nonlinear integro-differential equations for various cases. As the novel contributions of this article, the new scalar nonlinear integro-differential equation with the fading memory is firstly investigated in the literature, and seven theorems, which have novel sufficient qualitative conditions, are provided on the qualitative behaviors of solutions called boundedness, convergence, stability, integrability, asymptotic stability and uniform stability of solutions. The novel outcomes and originality of this article are that the considered integro-differential equations are new mathematical models, they include former mathematical models in relation to the mathematical models of this paper as well as the given main seven qualitative results are also new. The outcomes of this paper enhance some present results and provide new contributions to the relevant literature. The results of the article have complementary properties for the symmetry of integro-differential equations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
16. A Highly Accurate Mathematical Model for Analyzing Modular Multilevel Converters in Transformer-Less Applications.
- Author
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Liu, Jinshuo, Xu, Wenhua, and Xu, Tao
- Subjects
MATHEMATICAL models ,CASCADE converters ,ROTATIONAL motion ,MATHEMATICAL analysis - Abstract
Transformer-less connection schemes can provide a feasible solution for lowering the economic cost, occupied space, and device weight of modular multilevel converter (MMC) systems. However, due to the reduction in the converter transformer, the current flow loop is changed; as a result, the existing MMC model is not suitable. In this paper, the ac- and dc-side equivalent circuit models of the MMC system using a transformer-less connection scheme are established in both a–b–c stationary and d–q rotating coordinate systems. Then, a highly accurate mathematical analysis model is proposed, in which the interactions among the electrical quantities can be fully seen. The mathematical model is established in the time domain, and hence the amplitude and phase angle of every harmonic component in each quantity can be directly obtained. The proposed model is verified under various typical situations by comparing the calculated values with the actual waveforms. The comparison results prove that the calculation error is small enough to be negligible. The mathematical model in this paper can provide a powerful tool in terms of the performance analysis and the main circuit parameter design for MMCs in transformer-less applications. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
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17. Symmetry of Sampling Problem Based on Epistemic Uncertainty and Ellsberg Urn.
- Author
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Lio, Waichon and Kang, Rui
- Subjects
EPISTEMIC uncertainty ,URNS ,PROBABILITY theory ,SYMMETRY ,MATHEMATICAL symmetry ,MATHEMATICAL models - Abstract
A general sampling problem can be described by an Ellsberg urn, which is a mathematical model that assumes that balls are randomly drawn from an urn with an uncertain numbers of colored balls. This means that the Ellsberg urn is essentially an intricate model with simultaneous randomness and epistemic uncertainty, and this is the core problem discussed in this paper. Since practical sampling is usually processed in an intricate environment, the solution for an equivalent mathematical problem is necessary. Suppose an Ellsberg urn contains three unknown numbers of colored balls (i.e., a two-degrees-of-freedom Ellsberg urn), and three balls are randomly drawn from the urn. Compared to the published papers, this paper first constructs a chance space with two-dimensional uncertainty space and three-dimensional probability space to rigorously calculate the color distributions for those drawn balls by uncertainty theory, probability theory, and chance theory. Moreover, it is interesting to find that all cases of the drawn balls are symmetric in such a specific situation of a sample problem with epistemic uncertainty. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
18. Conjugation Conditions for Systems of Differential Equations of Different Orders on a Star Graph.
- Author
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Kanguzhin, Baltabek and Auzerkhan, Gauhar
- Subjects
DIFFERENTIAL equations ,BOUNDARY value problems ,MATHEMATICAL models - Abstract
In this paper, a one-dimensional mathematical model for investigating the vibrations of structures consisting of elastic and weakly curved rods is proposed. The three-dimensional structure is replaced by a limit graph, on each arc of which a system of three differential equations is written out. The differential equations describe the longitudinal and transverse vibrations of an elastic rod, taking into account the influence of longitudinal and transverse vibrations on each other. Describing conjugation conditions at joints of four or more rods is an important problem. This article assumes new conjugation conditions that guarantee the all-around decidability and symmetry of the resulting boundary value problems for systems of differential equations on a star graph. In addition, the paper proposes a physical interpretation of the conjugation conditions found. Thus, the work presents one more area of knowledge where symmetry phenomena occur. The symmetry here is manifested in the preservation of conjugation conditions when passing to the conjugate operator. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
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19. Exploring Roughness in Left Almost Semigroups and Its Connections to Fuzzy Lie Algebras.
- Author
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Assiry, Abdullah and Baklouti, Amir
- Subjects
ROUGH sets ,LATTICE theory ,MACHINE learning ,MATHEMATICAL optimization ,PARAMETER estimation ,MATHEMATICAL models ,LIE algebras - Abstract
This paper explores the concept of Generalized Roughness in LA-Semigroups and its applications in various mathematical disciplines. We highlight the fundamental properties and structures of Generalized Roughness, examining its relationships with Fuzzy Lie Algebras, Order Theory, Lattice Structures, Algebraic Structures, and Categorical Perspectives. Moreover, we investigate the potential of mathematical modeling, optimization techniques, data analysis, and machine learning in the context of Generalized Roughness. Our findings reveal important results in Generalized Roughness, such as the preservation of roughness under the fuzzy equivalence relation and the composition of roughness sets. We demonstrate the significance of Generalized Roughness in the context of order theory and lattice structures, presenting key propositions and a theorem that elucidate its properties and relationships. Furthermore, we explore the applications of Generalized Roughness in mathematical modeling and optimization, highlighting the optimization of roughness measures, parameter estimation, and decision-making processes related to LA-Semigroup operations. We showcase how mathematical techniques can enhance understanding and utilization of LA-Semigroups in practical scenarios. Lastly, we delve into the role of data analysis and machine learning in uncovering patterns, relationships, and predictive models in Generalized Roughness. By leveraging these techniques, we provide examples and insights into how data analysis and machine learning can contribute to enhancing our understanding of LA-Semigroup behavior and supporting decision-making processes. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
20. Stability Analysis of a Mathematical Model for Adolescent Idiopathic Scoliosis from the Perspective of Physical and Health Integration.
- Author
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Zhang, Yuhua and Li, Haiyin
- Subjects
ADOLESCENT idiopathic scoliosis ,MATHEMATICAL analysis ,MATHEMATICAL models ,HOPF bifurcations - Abstract
In this paper, we take physical and health integration as the entry point. Firstly, based on the transformation mechanism of adolescent idiopathic scoliosis we construct a time delay differential model. Moreover, using the theory of characteristic equation we discuss the stability of a positive equilibrium under the delays of τ = 0 and τ ≠ 0 . Furthermore, through numerical simulation, it has been verified the delay, τ , exceeds a critical value, the positive equilibrium loses its stability and Hopf bifurcation occurs. Lastly, we determine that sports have a positive effect on adolescent idiopathic scoliosis, directly reducing the number of people with adolescent idiopathic scoliosis. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
21. A Novel Fractional-Order Memristive Chaotic Circuit with Coexisting Double-Layout Four-Scroll Attractors and Its Application in Visually Meaningful Image Encryption.
- Author
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Wu, Yuebo, Wang, Duansong, Zhang, Tan, Zhang, Jinzhong, and Zhou, Jian
- Subjects
IMAGE encryption ,LYAPUNOV exponents ,BIFURCATION diagrams ,WAVELET transforms ,STATISTICS ,MATHEMATICAL models - Abstract
This paper proposes a fractional-order chaotic system using a tri-stable locally active memristor. The characteristics of the memristor, dynamic mechanism of oscillation, and behaviors of the proposed system were analyzed, and then a visually meaningful image encryption scheme was designed based on the chaotic system, DNA encoding, and integer wavelet transform (IWT). Firstly, the mathematical model of the memristor was designed, which was nonvolatile, locally active, and tri-stable. Secondly, the stability, dynamic mechanism of oscillation, bifurcation behaviors, and complexity of the fractional-order memristive chaotic system were investigated and the conditions of stability were obtained. Thirdly, the largest Lyapunov exponent, bifurcation diagram, and complexity of the novel system were calculated and the coexisting bifurcation, coexisting attractors, spectral entropy, and so on are shown. Finally, a visually meaningful image encryption scheme based on the proposed system was designed, and its security was assessed by statistical analysis and different attacks. Numerical simulation demonstrated the effectiveness of the theoretical analysis and high security of the proposed image encryption scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
22. A Decision-Making Approach to Optimize COVID-19 Treatment Strategy under a Conjunctive Complex Fuzzy Environment.
- Author
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Faraz, Muhammad Iftikhar, Alhamzi, Ghaliah, Imtiaz, Aneeza, Masmali, Ibtisam, Shuaib, Umer, Razaq, Abdul, and Razzaque, Asima
- Subjects
COVID-19 treatment ,TECHNOLOGICAL innovations ,COVID-19 pandemic ,DECISION making ,MATHEMATICAL models - Abstract
Symmetry is a key part of the study of basic forces and particles, as well as the creation of mathematical models that help scientists in various scientific disciplines understand complex events. Scientists can figure out what a system is made of and how it works by looking at its symmetry. They can then use this information to make predictions and create new materials and technologies. Humanity has conquered many once-fatal diseases due to medical research and technological advancements. Although this progress is encouraging, there are still a great many areas that require continual human efforts. An effort is made in this article to choose the best treatment strategy to completely manage the pandemic of COVID-19 under conjunctive complex fuzzy knowledge. In this paper, the concept of conjunctive complex fuzzy relations is presented and numerous set theoretical aspects of this phenomenon are established. The investigation of this ideology is further expanded to describe different sorts of essential structural conjunctive complex fuzzy relations. Matrix and graphical representations of the formation of these newly specified relations are also provided. Moreover, this concept has been successfully employed to provide a therapy strategy for a rapid recovery from COVID-19. Furthermore, a comparative analysis is conducted to demonstrate the validity and applicability of the suggested approaches compared to existing methods. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
23. Numerical Approximation of a Time-Fractional Modified Equal-Width Wave Model by Using the B-Spline Weighted Residual Method.
- Author
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AL-saedi, Akeel A. and Rashidinia, Jalil
- Subjects
FRACTIONAL calculus ,MATHEMATICAL models ,FINITE element method - Abstract
Fractional calculus (FC) is an important mathematical tool in modeling many dynamical processes. Therefore, some analytical and numerical methods have been proposed, namely, those based on symmetry and spline schemes. This paper proposed a numerical approach for finding the solution to the time-fractional modified equal-width wave (TFMEW) equation. The fractional derivative is described in the Caputo sense. Indeed, the B-spline Galerkin scheme combined with functions with different weights was employed to discretize TFMEW. The L 2 and L ∞ error norm values and the three invariants I 1 , I 2 , and I 3 of the numerical example were calculated and tabulated. A comparison of these errors and invariants was provided to confirm the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
24. Numerical Simulation for a Hybrid Variable-Order Multi-Vaccination COVID-19 Mathematical Model.
- Author
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Sweilam, Nasser, Al-Mekhlafi, Seham M., Salama, Reem G., and Assiri, Tagreed A.
- Subjects
MATHEMATICAL models ,HYBRID computer simulation ,COMPUTER simulation ,COVID-19 ,RUNGE-Kutta formulas - Abstract
In this paper, a hybrid variable-order mathematical model for multi-vaccination COVID-19 is analyzed. The hybrid variable-order derivative is defined as a linear combination of the variable-order integral of Riemann–Liouville and the variable-order Caputo derivative. A symmetry parameter σ is presented in order to be consistent with the physical model problem. The existence, uniqueness, boundedness and positivity of the proposed model are given. Moreover, the stability of the proposed model is discussed. The theta finite difference method with the discretization of the hybrid variable-order operator is developed for solving numerically the model problem. This method can be explicit or fully implicit with a large stability region depending on values of the factor Θ. The convergence and stability analysis of the proposed method are proved. Moreover, the fourth order generalized Runge–Kutta method is also used to study the proposed model. Comparative studies and numerical examples are presented. We found that the proposed model is also more general than the model in the previous study; the results obtained by the proposed method are more stable than previous research in this area. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
25. Parameter Estimation in the Mathematical Model of Bacterial Colony Patterns in Symmetry Domain.
- Author
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Brociek, Rafał, Wajda, Agata, Capizzi, Giacomo, and Słota, Damian
- Subjects
BACTERIAL colonies ,MATHEMATICAL models ,PARAMETER estimation ,INVERSE problems ,PARTIAL differential equations ,ANT algorithms - Abstract
The paper presents a solution to the problem related to the reconstruction of parameters in the mathematical model of bacterial colony patterns in a domain with symmetry. The inverse problem consists of determining the value of the diffusion coefficient of active bacteria. The model describing the distribution of active bacteria in a given region, as well as the concentration of the substrate over time is considered. Such a model consists of a system of partial differential equations with appropriate initial-boundary conditions. The finite element method was used to solve the direct problem. However, the Fibonacci search method was used to minimize the functional description of the error of the approximate solution. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
26. Developing a Fast-Processing Novel Algorithm for Contact Analysis of Standard Spur Gears.
- Author
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Cazan, Stelian, Bhaumik, Shubrajit, Paleu, Viorel, and Crețu, Spiridon
- Subjects
SPUR gearing ,BOUSSINESQ equations ,ALGORITHMS ,MATHEMATICAL models - Abstract
Numerical methods have gained momentum among specific engineering problems that must be solved in such a manner that accuracy and speed are the two most important aspects to consider regarding the output. This paper presents a fast, semi-analytical method (SAM) and original mathematical algorithms to determine the pressure distribution and von Mises stress for spur gears' meshing teeth. The SAM begins with the Hartnett approach, based on Boussinesq's equation for the half-space theory of linear elasticity, which implicitly means an infinite width of the gear flank. To simulate more realistic quarter-space conditions, corrections based on virtual mirror pressure are introduced in the computational algorithm. Mathematical surfaces modeling is an important aspect for spur gears as an intermediate stage to determine the pressure distribution and von Mises stress. Shaft misalignment changes the contact problem from symmetric, in which the half- or quarter-space model can be used, to asymmetric. In the latter case, the model must determine the entire contact area. The obtained output is validated by comparisons between our original FEA results and results from the literature using SAMs and FEA. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
27. Intelligent Separation and Identification of Sub-Information Based on Dynamic Mathematical Model.
- Author
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Zhang, Xiuquan and Shen, Lin
- Subjects
MATHEMATICAL models ,CANTOR sets ,DYNAMIC models - Abstract
P-sets (P stands for Packet), a set pair with dynamic and law characteristics, are made up of an internal and an outer P-set, which is obtained by introducing dynamic characteristics into the Cantor set and improving the Cantor set. The concepts of α F -sub-information, α F ¯ -sub-information, and (α F , α F ¯ ) -sub-information are presented in this paper based on P-sets, and it is then suggested that the relationship between the generation of sub-information and its attribute, the process of attribute reasoning, reasoning structure, and sub-information intelligent separation-acquisition be explored. These findings were used to design a sub-information intelligent separation-identification algorithm. By using these results, the application of intelligent separation and the identification of case information are given. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
28. Mathematical Modeling of Spherical Shell-Type Pattern of Tumor Invasion.
- Author
-
Amereh, Meitham, Struchtrup, Henning, and Nadler, Ben
- Subjects
MATHEMATICAL models ,INTERFACIAL stresses ,HEAT equation ,BREAST tumors ,CELL migration ,CHEMOTAXIS ,CANCER cell migration - Abstract
Cancer cell migration, as the principal element of tumor invasion, involves different cellular mechanisms. Various modes of cell migration including single and collective motions contribute to the invasion patterns. The competition between adhesive cell–cell and cell–matrix forces is a key factor that determines such patterns. In this paper, we study a distinct shell-type mode of tumor invasion observed in brain and breast tumors. In this mode, cells at the outer layer of the tumor collectively move away from the core and form a shell-type shape. Both the core and the shell sustain a sharp interface between cells and the surrounding matrix. To model the preserved interface, we adopted a Cahn–Hilliard-type free energy relation with the contribution of the interfacial stress. This nonconvex form of free energy allows for cells to remain together and preserve the tumor core via adhesive cell–cell forces while separating the core from the surrounding matrix across a continuous sharp interface. In addition, the motion of the shell was modeled using the chemotactic migration of cells in response to the gradient of nutrients. The associated fluxes of cells were implemented in a general form of balance law. A non-Michaelis–Menten kinetics model was adopted for the proliferation rate of cells. The flux of nutrients was also modeled using a simple diffusion equation. The comparison between the model predictions and experimental observations indicates the ability of the model to manifest the salient features of the invasion pattern. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
29. On the Solution of Fractional Biswas–Milovic Model via Analytical Method.
- Author
-
Sunthrayuth, Pongsakorn, Naeem, Muhammad, Shah, Nehad Ali, Shah, Rasool, and Chung, Jae Dong
- Subjects
MATHEMATICAL models ,INTEGRATED software ,INFINITE series (Mathematics) ,COMPUTER simulation ,POLYNOMIALS ,EQUATIONS - Abstract
Through the use of a unique approach, we study the fractional Biswas–Milovic model with Kerr and parabolic law nonlinearities in this paper. The Caputo approach is used to take the fractional derivative. The method employed here is the homotopy perturbation transform method (HPTM), which combines the homotopy perturbation method (HPM) and Yang transform (YT). The HPTM combines the homotopy perturbation method, He's polynomials, and the Yang transform. He's polynomial is a wonderful tool for dealing with nonlinear terms. To confirm the validity of each result, the technique was substituted into the equation. The described techniques can be used to find the solutions to these kinds of equations as infinite series, and when these series are in closed form, they give a precise solution. Graphs are used to show the derived numerical results. The maple software package is used to carry out the numerical simulation work. The results of this research are highly positive and demonstrate how effective the suggested method is for mathematical modeling of natural occurrences. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
30. Extended Graph of Fuzzy Topographic Topological Mapping Model: G 0 4 ( F T T M n 4 ).
- Author
-
Shukor, Noorsufia Abd, Ahmad, Tahir, Idris, Amidora, Awang, Siti Rahmah, Mukaram, Muhammad Zillullah, and Alias, Norma
- Subjects
TOPOGRAPHIC maps ,FUZZY graphs ,INVERSE problems ,TOPOLOGICAL spaces ,MATHEMATICAL models - Abstract
Fuzzy topological topographic mapping ( F T T M ) is a mathematical model that consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. The key to the model is its topological structure that can accommodate electrical or magnetic recorded brain signal. A sequence of FTTM, F T T M n , is an extension of FTTM whereby its form can be arranged in a symmetrical form, i.e., polygon. The special characteristic of F T T M , namely, the homeomorphisms between its components, allows the generation of new F T T M . The generated F T T M s can be represented as pseudo graphs. A pseudo-graph consists of vertices that signify the generated F T T M and edges that connect their incidence components. A graph of pseudo degree zero, G 0 (F T T M n k ) , however, is a special type of graph where each of the F T T M components differs from its adjacent. A researcher posted a conjecture on G 0 3 (F T T M n 3) in 2014, and it was finally proven in 2021 by researchers who used their novel grid-based method. In this paper, the extended G 0 3 (F T T M n 3) , namely, the conjecture on G 0 4 (F T T M n 4) that was posed in 2018, is narrated and proven using simple mathematical induction. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
31. Some New Optical Solitons of the Generalized Radhakrishnan–Kundu–Lakshmanan Equations with Powers of Nonlinearity.
- Author
-
Chen, Cheng, Li, Lu, and Liu, Wei
- Subjects
OPTICAL solitons ,NONLINEAR equations ,NONLINEAR optics ,EQUATIONS ,MATHEMATICAL models - Abstract
In this paper, the new generalized Radhakrishnan–Kundu–Lakshmanan equations with powers of nonlinearity are studied, which is one of the important mathematical models in nonlinear optics. Using the complex envelope traveling wave solution, the new generalized Radhakrishnan–Kundu–Lakshmanan equations are transformed into the nonlinear systems of ordinary differential equations. Under certain constraint conditions, the obtained equations are transformed into a special nonlinear equation. With the help of the solution of this nonlinear equation, some new optical solutions of the new generalized Radhakrishnan–Kundu–Lakshmanan equations with powers of nonlinearity are obtained, which include the solitary wave, singular soliton, periodic soliton, singular-periodic soliton, and exponential-type soliton. By numerical simulation, the corresponding graphs of the optical soliton solution of the new generalized Radhakrishnan–Kundu–Lakshmanan equations are given under the given fixed parameter values, which include the 3D graphics of the module and the 3D graphics of the imaginary part. By analyzing the 2D graphics of the module changing with n, the amplitude of the wave is symmetrical or asymmetrical. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
32. A Novel Discrete-Time Chaos-Function-Based Random-Number Generator: Design and Variability Analysis.
- Author
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Magfirawaty, Magfirawaty, Lestari, Andriani Adi, Nurwa, Agus Reza Aristiadi, MT, Suryadi, and Ramli, Kalamullah
- Subjects
RANDOM numbers ,NONLINEAR functions ,INFORMATION measurement ,CRYPTOSYSTEMS ,MATHEMATICAL models - Abstract
This paper presents a novel discrete-time (DT) chaotic map-based random-number generator (RNG), namely the Siponi map, which is a modification of the Logistic map. The Logistic map is usually applied to cryptosystems, mainly for the purposes of generating random numbers. In addition to being easy to implement, it has a better security level than other nonlinear functions. However, it can only process positive real-number inputs. Our proposed map is a deterministic function that can process positive and negative real values. We explored the map comprehensively and investigated its characteristics and parameters. We calculated the optimum parameter values using empirical and theoretical mathematical models to yield the maximum randomness of a sequence of bits. The limit variation of the maximum parameter value was determined based on a practical information measure. Empirical verification was performed for the Siponi map to generate bit sequences unrelated to the previous bit with high entropy values, and we found the extractor function threshold value to be 0.5, while the parameter control was −2 or 2. Using our proposed map, a simple RNG without post-processing passed DieHard statistical tests and all the tests on the NIST SP 800-22. Finally, we have implemented a Siponi map-based RNG on the FPGA board and demonstrated that the sources used are LUT = 4086, DSP = 62, and register = 2206. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
33. A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus.
- Author
-
Munteanu, Florian
- Subjects
IMMUNE system ,SOCIAL interaction ,MATHEMATICAL models ,DYNAMICAL systems ,SYSTEMS theory - Abstract
In this paper, we will consider three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of these three models based on dynamical systems theory will be performed by studying the local behavior of the equilibrium points and obtaining the local dynamics properties from the linear stability point of view. Additionally, we will compare these models in order to understand which is more appropriate to model the interaction between the human immune system and a virus. Some natural medical interpretations will be obtained, which are available for all three models and can be useful to the medical community. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
34. Recent Advances in Surrogate Modeling Methods for Uncertainty Quantification and Propagation.
- Author
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Wang, Chong, Qiang, Xin, Xu, Menghui, and Wu, Tao
- Subjects
ADAPTIVE sampling (Statistics) ,ENGINEERING systems ,SYSTEMS engineering ,MATHEMATICAL models ,SAMPLING (Process) - Abstract
Surrogate-model-assisted uncertainty treatment practices have been the subject of increasing attention and investigations in recent decades for many symmetrical engineering systems. This paper delivers a review of surrogate modeling methods in both uncertainty quantification and propagation scenarios. To this end, the mathematical models for uncertainty quantification are firstly reviewed, and theories and advances on probabilistic, non-probabilistic and hybrid ones are discussed. Subsequently, numerical methods for uncertainty propagation are broadly reviewed under different computational strategies. Thirdly, several popular single surrogate models and novel hybrid techniques are reviewed, together with some general criteria for accuracy evaluation. In addition, sample generation techniques to improve the accuracy of surrogate models are discussed for both static sampling and its adaptive version. Finally, closing remarks are provided and future prospects are suggested. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
35. Numerical Modeling and Symmetry Analysis of a Pine Wilt Disease Model Using the Mittag–Leffler Kernel.
- Author
-
Padmavathi, V., Magesh, N., Alagesan, K., Khan, M. Ijaz, Elattar, Samia, Alwetaishi, Mamdooh, and Galal, Ahmed M.
- Subjects
CONIFER wilt ,MEDICAL model ,MATHEMATICAL symmetry ,SYMMETRY ,MATHEMATICAL models - Abstract
The existence of man is dependent on nature, and this existence can be disturbed by either man-made devastations or by natural disasters. As a universal phenomenon in nature, symmetry has attracted the attention of scholars. The study of symmetry provides insights into physics, chemistry, biology, and mathematics. One of the most important characteristics in the expressive assessment and development of computational design techniques is symmetry. Yet, mathematical models are an important method of studying real-world systems. The symmetry reflected by such a mathematical model reveals the inherent symmetry of real-world systems. This study focuses on the contagious model of pine wilt disease and symmetry, employing the q-HATM (q-Homotopy Analysis Transform Method) to the leading fractional operator Atangana–Baleanu (AB) to arrive at better understanding. The outgrowths are exhibited in the forms of figures and tables. Finally, the paper helps to analyze the practical theory, assisting the prediction of its manner that corresponds to the guidelines when contemplating the replica. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
36. The Study of the Dynamic Behavior for a Tamping Rammer.
- Author
-
Morariu-Gligor, Radu Mircea
- Subjects
MECHANICAL models ,MATHEMATICAL models - Abstract
The paper presents a mechanical and a mathematical model, developed by the author for the study of the dynamical behavior of a tamping rammer. At first, some aspects related to the compaction of soil for construction works are presented. In this study, the soil was modeled using the Kelvin–Voigt model. To validate the mathematical model, a program written in C language, that allows to analyze the parameters that influence the operation of the tamping rammer, was developed. Three constructive variants of tamping rammers, following the variation of the displacements of the frame and the sole and the variation of the impact force were analyzed. In the final part, the variation of the studied parameters is illustrated by means of graphical representations. The variation of the studied parameters becomes symmetrical, related to an equilibrium position. Using the application, developed by the author, the variation of the sole and frame displacements, and the variation of the impact force can be traced. The numerical results obtained by running the application, (using three sets of input data), demonstrate the accuracy and the correctness of the proposed mathematical model by analogy with the values provided by the manufacturers. Finally, further research in this field is presented. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
37. Constraining Forces Stabilizing Superconductivity in Bismuth.
- Author
-
Krüger, Ekkehard
- Subjects
SUPERCONDUCTIVITY ,BISMUTH ,HEISENBERG model ,COOPER pair ,ELECTRON-electron interactions ,MATHEMATICAL models - Abstract
As shown in former papers, the nonadiabatic Heisenberg model presents a mechanism of Cooper pair formation generated by the strongly correlated atomic-like motion of the electrons in narrow, roughly half-filled "superconducting bands" of special symmetry. The formation of Cooper pairs is not only the result of an attractive electron-electron interaction but is additionally the outcome of quantum mechanical constraining forces. There is theoretical and experimental evidence that only these constraining forces operating in superconducting bands may produce eigenstates in which the electrons form Cooper pairs. Here, we report evidence that also the experimentally found superconducting state in bismuth at ambient as well as at high pressure is stabilized by constraining forces. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
38. EMG Pattern Classification by Split and Merge Deep Belief Network.
- Author
-
Hyeon-min Shim, Hongsub An, Sanghyuk Lee, Eung Hyuk Lee, Hong-ki Min, and Sangmin Lee
- Subjects
ELECTROMYOGRAPHY ,PATTERN recognition systems ,DEEP learning ,ALGORITHMS ,LAW of large numbers ,MATHEMATICAL models - Abstract
In this paper; we introduce an enhanced electromyography (EMG) pattern recognition algorithm based on a split-and-merge deep belief network (SM-DBN). Generally, it is difficult to classify the EMG features because the EMG signal has nonlinear and time-varying characteristics. Therefore, various machine-learning methods have been applied in several previously published studies. A DBN is a fast greedy learning algorithm that can identify a fairly good set of weights rapidly--even in deep networks with a large number of parameters and many hidden layers. To reduce overfitting and to enhance performance, the adopted optimization method was based on genetic algorithms (GA). As a result, the performance of the SM-DBN was 12.06% higher than conventional DBN. Additionally, SM-DBN results in a short convergence time, thereby reducing the training epoch. It is thus efficient in reducing the risk of overfitting. It is verified that the optimization was improved using GA. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
39. Attribute Control Chart Construction Based on Fuzzy Score Number.
- Author
-
Shiwang Hou, Hui Wang, and Shunxiao Feng
- Subjects
FUZZY control systems ,PRODUCT quality ,MATHEMATICAL models ,ADAPTIVE fuzzy control ,MANUFACTURING processes ,QUALITY control charts - Abstract
There is much uncertainty and fuzziness in product quality attributes or quality parameters of a manufacturing process, so the traditional quality control chart can be difficult to apply. This paper proposes a fuzzy control chart. The plotted data was obtained by transforming expert scores into fuzzy numbers. Two types of nonconformity judgment rules--necessity and possibility measurement rules--are proposed. Through graphical analysis, the nonconformity judging method (i.e., assessing directly based on the shape feature of a fuzzy control chart) is proposed. For four different widely used membership functions, control levels were analyzed and compared by observing gaps between the upper and lower control limits. The result of the case study validates the feasibility and reliability of the proposed approach. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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- View/download PDF
40. Correction: Hezam et al. A Systematic Literature Review on Mathematical Models of Humanitarian Logistics. Symmetry 2021, 13 , 11.
- Author
-
Hezam, Ibrahim M., Nayeem, Moddassir k., and Lee, Gyu M.
- Subjects
MATHEMATICAL models ,SYMMETRY ,MERGERS & acquisitions ,LOGISTICS - Abstract
This document is a correction notice for a paper titled "A Systematic Literature Review on Mathematical Models of Humanitarian Logistics." The correction includes the addition of an author and a change in the corresponding author. The authors apologize for any inconvenience caused and state that the scientific conclusions are unaffected. The correction also includes an updated author contribution statement and a correction in the funding part. The research was originally funded and started while Ibrahim and Moddassir were at Pusan National University, and it was also funded in part by the National Research Foundation of Korea and the Deputyship for Research and Innovation in Saudi Arabia. [Extracted from the article]
- Published
- 2024
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- View/download PDF
41. Path Planning of AS/RS Based on Cost Matrix and Improved Greedy Algorithm.
- Author
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Li, Dongdong, Wang, Lei, Geng, Sai, and Jiang, Benchi
- Subjects
GREEDY algorithms ,ALGORITHMS ,PROBLEM solving ,MATHEMATICAL models ,GENETIC algorithms ,MATRICES (Mathematics) - Abstract
Logistics plays an important role in the field of global economy, and the storage and retrieval of tasks in a warehouse which has symmetry is the most important part of logistics. Generally, the shelves of a warehouse have a certain degree of symmetry and similarity in their structure. The storage and retrieval efficiency directly affects the efficiency of logistics. The efficiency of the traditional storage and retrieval mode has become increasingly inconsistent with the needs of the industry. In order to solve this problem, this paper proposes a greedy algorithm based on cost matrix to solve the path planning problem of the automatic storage and retrieval system (AS/RS). Firstly, aiming at the path planning mathematical model of AS/RS, this paper proposes the concept of cost matrix, which transforms the traditional storage and retrieval problem into the element combination problem of cost matrix. Then, a more efficient backtracking algorithm is proposed based on the exhaustive method. After analyzing the performance of the backtracking algorithm, combined with some rules, a greedy algorithm which can further improve efficiency is proposed; the convergence of the improved greedy algorithm is also proven. Finally, through simulation, the time consumption of the greedy algorithm is only 0.59% of the exhaustive method, and compared with the traditional genetic algorithm, the time consumption of the greedy algorithm is about 50% of the genetic algorithm, and it can still maintain its advantage in time consumption, which proves that the greedy algorithm based on cost matrix has a certain feasibility and practicability in solving the path planning of the automatic storage and retrieval system. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
42. Application of Lie Symmetry to a Mathematical Model that Describes a Cancer Sub-Network.
- Author
-
Matadi, Maba Boniface
- Subjects
MATHEMATICAL symmetry ,MATHEMATICAL models ,ORDINARY differential equations ,CELL cycle ,CYCLIN-dependent kinases - Abstract
In this paper, a mathematical model of a cancer sub-network is analysed from the view point of Lie symmetry methods. This model discusses a human cancer cell which is developed due to the dysfunction of some genes at the R-checkpoint during the cell cycle. The primary purpose of this paper is to apply the techniques of Lie symmetry to the model and present some approximated solutions for the three-dimensional system of first-order ordinary differential equations describing a cancer sub-network. The result shows that the phosphatase gene (Cdc25A) regulates the cyclin-dependent kinases inhibitor ( P 27 K i p 1 ). Furthermore, this research discovered that the activity that reverses the inhibitory effects on cell cycle progression at the R-checkpoint initiates a pathway. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
43. Some Aspects of Nonlinearity and Self-Organization In Biosystems on Examples of Localized Excitations in the DNA Molecule and Generalized Fisher--KPP Model.
- Author
-
Shapovalov, A. V. and Obukhov, V. V.
- Subjects
SOLITONS ,DNA models ,NONLINEAR systems ,BIOLOGICAL systems ,MATHEMATICAL models ,QUANTUM mechanics - Abstract
This review deals with ideas and approaches to nonlinear phenomena, based on different branches of physics and related to biological systems, that focus on how small impacts can significantly change the state of the system at large spatial scales. This problem is very extensive, and it cannot be fully resolved in this paper. Instead, some selected physical effects are briefly reviewed. We consider sine-Gordon solitons and nonlinear Schrodinger solitons in some models of DNA as examples of self-organization at the molecular level, as well as examine features of their formation and dynamics under the influence of external influences. In addition, the formation of patterns in the generalized Fisher--KPP model is viewed as a simple example of self-organization in a system with nonlocal interaction at the cellular level. Symmetries of model equations are employed to analyze the considered nonlinear phenomena. In this context the possible relations between phenomena considered and released activity effect, which is assessed differently in the literature, are discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
44. Advanced Statistical Approach for the Mathematical Modeling of Transfer Processes in a Layer Based on Experimental Data at the Boundary.
- Author
-
Chernukha, Olha, Pukach, Petro, Bilushchak, Halyna, Bilushchak, Yurii, and Vovk, Myroslava
- Subjects
NUMERICAL solutions to differential equations ,MATHEMATICAL models ,BOUNDARY layer (Aerodynamics) ,STATISTICAL sampling ,STATISTICAL models - Abstract
In this work, a mathematical model of the transfer process in a layer under the condition of given experimental data on a part of the layer boundary is presented and investigated. Such research is important for the mathematical description of the objects and systems for which, based on physical considerations, it is impossible to correctly impose boundary or initial conditions, even in a sufficiently general form, but there are experimental data on the desired function or its derivative at the boundary of the body or at the initial time. The values of the desired function at the boundary are known at certain moments in time. The boundary condition is constructed by the experimental data and the initial-boundary value problem, with such a boundary condition, is formulated and solved. The influence of the statistical characteristics of the sample of experimental data on the solution to the initial-boundary value problem is analyzed, and a two-sided statistical estimation of the solution is determined. The confidence intervals for the coefficients of the regression equation and the corresponding confidence intervals for the sought function are established. The influence of the statistical characteristics of the sample on the sought function at the lower boundary of the layer is investigated. Numerical analysis of the solution to the initial-boundary value problem is carried out depending on the statistical characteristics of the sample. Various cases of samples by size and variance are considered. Numerical solutions are studied under the conditions of large and small time intervals of the considered process. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
45. Four-Point Bending of Basic Rails: Theory and Experimental Verification.
- Author
-
Dong, Zhikui, Liu, Chunjiang, Ma, Long, Yang, Jiahao, and Jiang, Yunhong
- Subjects
TUBE bending ,PREDICTION models ,MATHEMATICAL models ,BENDING moment - Abstract
Mathematical models of prediction provide theoretical support for basic rail automation. The three-point bending method for basic rails is characterized by its simplicity and flexibility, and, as such, it is widely used in bending processes. However, due to the significant curvature changes that occur after bending, it is not suitable for scenarios requiring large arc bending, and its range of achievable deflections is limited. This study focuses on four-point bending, dividing the bending process into three stages and using a power-law material hardening model to establish different bending moment expressions for each stage. We derived the relationships between curvature, elastic zone ratio, load, and deflection, ultimately creating a load–deflection model. Based on the simple springback law, we developed the final bending prediction model. Finite element simulations were conducted to simulate the bending process under various conditions, using top punch distances ranging from 200 mm to 400 mm and die distances ranging from 600 mm to 1000 mm. These simulations validated the advantages and accuracy of the four-point bending prediction model in large arc bending. Additionally, a four-point bending experimental setup was established under specified conditions. The experimental results were compared with the theoretical model calculations, showing errors within 0.2 mm and thus verifying the accuracy of the four-point bending prediction model. The mathematical model developed in this study provides theoretical support for the automation of basic rail bending. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
46. Research on Mathematical Modeling of Critical Impact Force and Rollover Velocity of Coach Tripped Rollover Based on Numerical Analysis Method.
- Author
-
Wu, Xinye, Wang, Zhiwei, and Chen, Shenghui
- Subjects
NUMERICAL analysis ,MATHEMATICAL models ,CRITICAL velocity ,CONSERVATION of energy ,INTELLIGENT control systems ,PROPORTIONAL navigation - Abstract
Although the probability of a rollover accident is lower than that of other forms of collision, rollover is a serious accident that can break the symmetry of the vehicle and cause serious loss of life and property. There are many factors affecting rollovers, such as the environment, the vehicle, and the driving control. A coach comprises a complex dynamic system; as such, the accuracy and rationality of the used mathematical model are decisive in the study of coach rollover warning and control. By analogy with the modeling method of an automobile collision accident, the general process of a coach rollover accident is analyzed in this study in combination with the contact form and freedom of motion characteristic of the coach body and external environment. According to the principle of conservation of energy, the mathematical models of critical rollover impact force in a collision between vehicles and obstacles and in a collision between two vehicles are established, allowing for analysis of the relationships between the critical tripped rollover impact forces required for a 90° rollover and the continuous action time and collision point height. During the collision between the vehicle and the obstacle, the occurrence of a vehicle rollover is related not only to the impact force in the collision process but also to the collision duration time. Even if the impact force is relatively small, the collision lasts long enough that a second collision may occur until the vehicle rolls over. In the process of a two-vehicle collision, the critical rollover impact force is not only related to the vehicle mass but also to the vehicle wheelbase and the height of the collision point. Based on the law of conservation of momentum, the mathematic models of 90-degree rollover and 180-degree rollover are established, and the critical rollover velocities are calculated. The purpose of this study is to provide reference and guidance for the research methods of vehicle rollover stability and anti-rollover control in the intelligent vehicle era. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
47. A Higher Dimensional Description of the Structure of β-Mn.
- Author
-
Lidin, Sven and Fredrickson, Daniel
- Subjects
MATHEMATICAL crystallography ,CRYSTALLOGRAPHY ,MATHEMATICS ,MATHEMATICAL models ,CRYSTAL lattices - Abstract
Copyright of Symmetry (20738994) is the property of MDPI and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2012
- Full Text
- View/download PDF
48. A Full-Period Mathematical Model for a Hybrid-Rotor Bearingless Switched Reluctance Motor.
- Author
-
Liu, Zeyuan, Chen, Mei, Yang, Yan, Liu, Chengzi, and Gao, Hui
- Subjects
RELUCTANCE motors ,MAGNETIC bearings ,SWITCHED reluctance motors ,MATHEMATICAL models ,MAGNETIC structure ,MAGNETISM - Abstract
A bearingless switched reluctance motor (BSRM) has the combined characteristics of a switched reluctance motor (SRM) and a magnetic bearing. The hybrid-rotor BSRM (HBSRM) discussed in the paper has a twelve-pole stator and an eight-pole hybrid rotor, which is composed of a cylindrical rotor and a salient-pole rotor. Although the asymmetry of the hybrid rotor makes the structure and magnetic field of the HBSRM more complex, it can always produce a significant amount of magnetic pulling force to levitate a rotor shaft at all the rotor angular positions of each phase, which is not available in a traditional BSRM. The classical mathematical model for a conventional BSRM is valid only when its rotor rotates from the start of the overlap position to the aligned position, and the radial force and torque derived from this model are discontinuous at the aligned positon, which is harmful to the motor's stable operation. In this paper, a full-period mathematical model on the assumption that the gap permeance is cut apart by straight lines or improved elliptical lines for a 12/8-pole HBSRM is provided. On the basis of this mathematical model, the continuity of the radial force and torque at all the rotor angular positions can be guaranteed, and the fine characteristics of this mathematical model have been verified by simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
49. Mathematical Modeling of Integral Characteristics of Repair Process under Maintenance Contracts.
- Author
-
Kontrec, Nataša, Vujaković, Jelena, Tošić, Marina, Panić, Stefan, and Panić, Biljana
- Subjects
SERVICE contracts ,MATHEMATICAL models ,MATHEMATICAL forms ,PROBABILITY density function ,STOCHASTIC integrals - Abstract
The repair rate is a very important parameter for system maintainability and can be defined as a frequency of successfully performed repair actions on a failed component per unit of time. This paper analyzes the integral characteristics of a stochastic repair rate for corresponding values of availability in a system operating under maintenance contracts. The probability density function (PDF) of the repair rate has been studied extensively and it was concluded that it is not a symmetric function so its mean value does not correspond to its maximum. Based on that, the equation for the envelope line of the PDF maximums of the repair rate has been provided. Namely, instead of repair rate PDF equations, we can use envelope line parameters for certain calculations, which are expressed in a simpler mathematical form. That will reduce time required for calculations and prediction and enhance reactions in failure events. Further, for the analytical and numerical evaluation of a system performance, the annual repair rate PDFs are analyzed, such as particular solutions of corresponding differential equation, while the existence of a singular solution is considered and analyzed under different conditions. Moreover, we derived optimal values of availability for which the PDF maximums have been obtained. Finally, in order to generalize the behavior of the repair process, a partial differential equation, as a function of the repair rate process and availability parameter, has been formed. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
50. Forecasting Based on High-Order Fuzzy-Fluctuation Trends and Particle Swarm Optimization Machine Learning.
- Author
-
Jingyuan Jia, Aiwu Zhao, and Shuang Guan
- Subjects
PARTICLE swarm optimization ,MACHINE learning ,FUZZY algorithms ,MATHEMATICAL models of forecasting ,TIME series analysis ,MATHEMATICAL models - Abstract
Most existing fuzzy forecasting models partition historical training time series into fuzzy time series and build fuzzy-trend logical relationship groups to generate forecasting rules. The determination process of intervals is complex and uncertain. In this paper, we present a novel fuzzy forecasting model based on high-order fuzzy-fluctuation trends and the fuzzy-fluctuation logical relationships of the training time series. Firstly, we compare each piece of data with the data of theprevious day in a historical training time series to generate a new fluctuation trend time series (FTTS). Then, we fuzzify the FTTS into a fuzzy-fluctuation time series (FFTS) according to the up, equal, or down range and orientation of the fluctuations. Since the relationship between historical FFTS and the fluctuation trend of the future is nonlinear, a particle swarm optimization (PSO) algorithm is employed to estimate the proportions for the lagged variables of the fuzzy AR (n) model. Finally, we use the acquired parameters to forecast future fluctuations. In order to compare the performance of the proposed model with that of the other models, we apply the proposed method to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) time series datasets. The experimental results and the comparison results show that the proposed method can be successfully applied in stock market forecasting or similarkinds of time series. We also apply the proposed method to forecast Shanghai Stock Exchange Composite Index (SHSECI) and DAX30 index to verify its effectiveness and universality. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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