2,421 results
Search Results
2. Physics driven behavioural clustering of free-falling paper shapes.
- Author
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Howison, Toby, Hughes, Josie, Giardina, Fabio, and Iida, Fumiya
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PHYSICS , *SET functions , *MACHINE learning , *PHENOMENOLOGICAL theory (Physics) , *CONTINUUM mechanics - Abstract
Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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3. The contribution of cause-effect link to representing the core of scientific paper—The role of Semantic Link Network.
- Author
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Cao, Mengyun, Sun, Xiaoping, and Zhuge, Hai
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COMPLEXITY (Philosophy) , *CAUSATION (Philosophy) , *SEMANTICS , *RESEARCH , *PHILOSOPHY - Abstract
The Semantic Link Network is a general semantic model for modeling the structure and the evolution of complex systems. Various semantic links play different roles in rendering the semantics of complex system. One of the basic semantic links represents cause-effect relation, which plays an important role in representation and understanding. This paper verifies the role of the Semantic Link Network in representing the core of text by investigating the contribution of cause-effect link to representing the core of scientific papers. Research carries out with the following steps: (1) Two propositions on the contribution of cause-effect link in rendering the core of paper are proposed and verified through a statistical survey, which shows that the sentences on cause-effect links cover about 65% of key words within each paper on average. (2) An algorithm based on syntactic patterns is designed for automatically extracting cause-effect link from scientific papers, which recalls about 70% of manually annotated cause-effect links on average, indicating that the result adapts to the scale of data sets. (3) The effects of cause-effect link on four schemes of incorporating cause-effect link into the existing instances of the Semantic Link Network for enhancing the summarization of scientific papers are investigated. The experiments show that the quality of the summaries is significantly improved, which verifies the role of semantic links. The significance of this research lies in two aspects: (1) it verifies that the Semantic Link Network connects the important concepts to render the core of text; and, (2) it provides an evidence for realizing content services such as summarization, recommendation and question answering based on the Semantic Link Network, and it can inspire relevant research on content computing. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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4. Quantifying the impact of scholarly papers based on higher-order weighted citations.
- Author
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Bai, Xiaomei, Zhang, Fuli, Hou, Jie, Lee, Ivan, Kong, Xiangjie, Tolba, Amr, and Xia, Feng
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CITATION analysis , *SCHOLARLY publishing , *BIBLIOMETRICS , *SIMULATION methods & models , *ALGORITHMS - Abstract
Quantifying the impact of a scholarly paper is of great significance, yet the effect of geographical distance of cited papers has not been explored. In this paper, we examine 30,596 papers published in Physical Review C, and identify the relationship between citations and geographical distances between author affiliations. Subsequently, a relative citation weight is applied to assess the impact of a scholarly paper. A higher-order weighted quantum PageRank algorithm is also developed to address the behavior of multiple step citation flow. Capturing the citation dynamics with higher-order dependencies reveals the actual impact of papers, including necessary self-citations that are sometimes excluded in prior studies. Quantum PageRank is utilized in this paper to help differentiating nodes whose PageRank values are identical. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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5. A collaborative approach for research paper recommender system.
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Haruna, Khalid, Akmar Ismail, Maizatul, Damiasih, Damiasih, Sutopo, Joko, and Herawan, Tutut
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CITATION analysis , *SCIENCE & state , *SOCIAL network analysis , *SOCIAL networks , *COMPUTER networks - Abstract
Research paper recommenders emerged over the last decade to ease finding publications relating to researchers’ area of interest. The challenge was not just to provide researchers with very rich publications at any time, any place and in any form but to also offer the right publication to the right researcher in the right way. Several approaches exist in handling paper recommender systems. However, these approaches assumed the availability of the whole contents of the recommending papers to be freely accessible, which is not always true due to factors such as copyright restrictions. This paper presents a collaborative approach for research paper recommender system. By leveraging the advantages of collaborative filtering approach, we utilize the publicly available contextual metadata to infer the hidden associations that exist between research papers in order to personalize recommendations. The novelty of our proposed approach is that it provides personalized recommendations regardless of the research field and regardless of the user’s expertise. Using a publicly available dataset, our proposed approach has recorded a significant improvement over other baseline methods in measuring both the overall performance and the ability to return relevant and useful publications at the top of the recommendation list. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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6. Social and content aware One-Class recommendation of papers in scientific social networks.
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Wang, Gang, He, XiRan, and Ishuga, Carolyne Isigi
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INFORMATION technology , *SOCIAL networks , *SPARSE graphs , *HYBRID computers (Computer architecture) , *HYBRID power systems - Abstract
With the rapid development of information technology, scientific social networks (SSNs) have become the fastest and most convenient way for researchers to communicate with each other. Many published papers are shared via SSNs every day, resulting in the problem of information overload. How to appropriately recommend personalized and highly valuable papers for researchers is becoming more urgent. However, when recommending papers in SSNs, only a small amount of positive instances are available, leaving a vast amount of unlabelled data, in which negative instances and potential unseen positive instances are mixed together, which naturally belongs to One-Class Collaborative Filtering (OCCF) problem. Therefore, considering the extreme data imbalance and data sparsity of this OCCF problem, a hybrid approach of Social and Content aware One-class Recommendation of Papers in SSNs, termed SCORP, is proposed in this study. Unlike previous approaches recommended to address the OCCF problem, social information, which has been proved playing a significant role in performing recommendations in many domains, is applied in both the profiling of content-based filtering and the collaborative filtering to achieve superior recommendations. To verify the effectiveness of the proposed SCORP approach, a real-life dataset from CiteULike was employed. The experimental results demonstrate that the proposed approach is superior to all of the compared approaches, thus providing a more effective method for recommending papers in SSNs. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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7. Linear programming problems with cube constraints.
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Lestari, Himmawati Puji, Caturiyati, and Harini, Lusi
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LINEAR programming , *MATHEMATICAL optimization , *CONVEX domains , *APPLIED mathematics , *CONSTRAINT programming , *CUBES , *CONVEX geometry - Abstract
Linear programming is one of the basic concepts to further study in applied mathematics and optimization. If the constraints of the linear programming problem form a convex region, then the problem must have an optimal solution. Cube is convex and, in terms of geometry, cube is very special. Cube has some special properties that all edges are congruent and also the all sides are congruent. Other special properties of the cube are related to orthogonality and parallelism. This paper discus linear programming problems with cube constraints. This research is study literature research to describe linear programming problems with cube constraints on geometrical angle. Considering the peculiarities of a cube, this linear programming problem must have an optimal solution. The results show the following points: 1) A cube is a convex polyhedron; 2) The steps for solving linear programming with cube constraints are analogous to the steps for solving linear programming in two dimensions using the graphical method, finding all the vertices of the cube and calculating the value of the objective function at all of the vertices, and then determining the vertex point that produces the optimal value; 3) The problem can have a unique solution (vertex) or have infinitely many solutions (the points along the edges or on the side planes of the cube). [ABSTRACT FROM AUTHOR]
- Published
- 2024
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8. PSRMTE: Paper submission recommendation using mixtures of transformer.
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Nguyen, Dac Huu, Huynh, Son Thanh, Dinh, Cuong Viet, Huynh, Phong Tan, and Nguyen, Binh Thanh
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COMPUTATIONAL mathematics , *RECOMMENDER systems , *MACHINE learning , *COMPUTER science , *ELECTRONIC journals , *APPLIED mathematics - Abstract
Nowadays, there has been a rapidly increasing number of scientific submissions in multiple research domains. A large number of journals have various acceptance rates, impact factors, and rankings in different publishers. It becomes time-consuming for many researchers to select the most suitable journal to submit their work with the highest acceptance rate. A paper submission recommendation system is more critical for the research community and publishers as it gives scientists another support to complete their submission conveniently. This paper investigates the submission recommendation system for two main research topics: computer science and applied mathematics. Unlike the previous works (Wang et al., 2018; Son et al., 2020) that extract TF–IDF and statistical features as well as utilize numerous machine learning algorithms (logistics regression and multiple perceptrons) for building the recommendation engine, we present an efficient paper submission recommendation algorithm by using different bidirectional transformer encoders and the Mixture of Transformer Encoders technique. We compare the performance between our methodology and other approaches by one dataset from Wang et al. (2018) with 14012 papers in computer science and another dataset collected by us with 223,782 articles in 178 Springer applied mathematics journals in terms of top K accuracy (K = 1 , 3 , 5 , 10). The experimental results show that our proposed method extensively outperforms other state-of-the-art techniques with a significant margin in all top K accuracy for both two datasets. We publish all datasets collected and our implementation codes for further references. 1 1 https://github.com/BinhMisfit/PSRMTE. • Bidirectional transformer encoders can improve the performance of the paper submission recommendation system. • The Mixture of Transformer Encoders framework shows the efficiency in the paper submission recommendation problem. • Proposed techniques can surpass other recent techniques on two datasets related. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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9. Genealogical Trees of Scientific Papers.
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Waumans, Michaël Charles and Bersini, Hugues
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GENEALOGY , *SCIENCE databases , *CITATION analysis , *EVOLUTIONARY algorithms , *SOCIAL networks - Abstract
Many results have been obtained when studying scientific papers citations databases in a network perspective. Articles can be ranked according to their current in-degree and their future popularity or citation counts can even be predicted. The dynamical properties of such networks and the observation of the time evolution of their nodes started more recently. This work adopts an evolutionary perspective and proposes an original algorithm for the construction of genealogical trees of scientific papers on the basis of their citation count evolution in time. The fitness of a paper now amounts to its in-degree growing trend and a “dying” paper will suddenly see this trend declining in time. It will give birth and be taken over by some of its most prevalent citing “offspring”. Practically, this might be used to trace the successive published milestones of a research field. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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10. The general Bernstein function: Application to χ-fractional differential equations.
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Sadek, Lakhlifa and Bataineh, Ahmad Sami
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DIFFERENTIAL equations , *NONLINEAR differential equations , *APPLIED mathematics , *BERNSTEIN polynomials , *COLLOCATION methods , *CALCULUS of variations , *INTEGRAL equations - Abstract
In this paper, we present the general Bernstein functions for the first time. The properties of generalized Bernstein basis functions are given and demonstrated. The classical Bernstein polynomial bases are merely a subset of the general Bernstein functions. Based on the new Bernstein base functions and the collocation method, we present a numerical method for solving linear and nonlinear χ-fractional differential equations (χ-FDEs) with variable coefficients. The fractional derivative used in this work is the χ-Caputo fractional derivative sense (χ-CFD). Combining the Bernstein functions basis and the collocation methods yields the approximation solution of nonlinear differential equations. These base functions can be used to solve many problems in applied mathematics, including calculus of variations, differential equations, optimal control, and integral equations. Furthermore, the convergence of the method is rigorously justified and supported by numerical experiments. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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11. Investigation of (2+1)-dimensional extended Calogero–Bogoyavlenskii–Schiff equation by generalized Kudryashov method and two variable (G′G,1G)-expansion method.
- Author
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Arshed, Saima, Akram, Ghazala, Sadaf, Maasoomah, Latif, Rimsha, and Ahmad, Hijaz
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APPLIED mathematics , *ORDINARY differential equations , *NONLINEAR differential equations , *PLASMA physics , *SINE-Gordon equation , *FLUID dynamics , *NONLINEAR optics - Abstract
This paper investigates a recently introduced (2 + 1) -dimensional extended Calogero–Bogoyavlenskii–Schiff equation. The considered model is widely used in fluid dynamics, nonlinear optics and plasma physics. The study of the governing equation has provided insights into the dynamical behaviors of wave systems, which is an important area of research in applied mathematics and theoretical physics. Firstly, the description of the generalized Kudryashov and the two variable ( G ′ G , 1 G) -expansion methods is presented. The governing model is converted into a nonlinear ordinary differential equation by utilizing the traveling wave hypothesis. A family of exact traveling wave solutions such as solitons and solitary waves are extracted using the two proposed methods for the governing model. The graphical demonstrations are presented to examine the physical behavior of the constructed solutions. Kink solitary wave, singular kink, W-shape soliton, dark-bright soliton and periodic wave solutions are successfully retrieved. The proposed techniques are utilized to examine the governing model for the first time in this work to the best of our knowledge. The acquired results will help in guiding future investigations of the wave phenomena represented by the considered equation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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12. Investigating wave solutions and impact of nonlinearity: Comprehensive study of the KP-BBM model with bifurcation analysis.
- Author
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Rayhanul Islam, S. M. and Khan, Kamruzzaman
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NONLINEAR evolution equations , *HAMILTON'S principle function , *HOPF bifurcations , *APPLIED mathematics , *DYNAMICAL systems , *EXPONENTIAL functions - Abstract
In this paper, we investigate the (2+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona Mahony equation using two effective methods: the unified scheme and the advanced auxiliary equation scheme, aiming to derive precise wave solutions. These solutions are expressed as combinations of trigonometric, rational, hyperbolic, and exponential functions. Visual representations, including three-dimensional (3D) and two-dimensional (2D) combined charts, are provided for some of these solutions. The influence of the nonlinear parameter p on the wave type is thoroughly examined through diverse figures, illustrating the profound impact of nonlinearity. Additionally, we briefly investigate the Hamiltonian function and the stability of the model using a planar dynamical system approach. This involves examining trajectories, isoclines, and nullclines to illustrate stable solution paths for the wave variables. Numerical results demonstrate that these methods are reliable, straightforward, and potent tools for analyzing various nonlinear evolution equations found in physics, applied mathematics, and engineering. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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13. Programmatic Strategies to Engage and Support Undergraduate Women in Applied Mathematics and Computer Science.
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Han, Sandie, Kennedy, Nadia Stoyanova, Samaroo, Diana, and Duttagupta, Urmi
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SCHOLARSHIPS , *COMPUTER science , *APPLIED mathematics , *UNDERGRADUATES , *SELF-efficacy , *COMMUNITY involvement - Abstract
This paper describes the implementation of a STEM scholarship program which utilized a holistic approach to providing a multi-dimensional student support system. The program has been successful in encouraging and supporting women in Applied Mathematics and Computer Science by offering a diverse suite of extracurricular opportunities, actively engaging them in organized events, research projects, and participation in STEM communities, and helping them achieve higher GPAs and shorter times to graduation. The supported women also benefitted from close mentoring relationships with the faculty mentors. The program emphasized the development of empowering settings for women's engagement and achievement, which act to sustain and expand interest in mathematics and computing, and thereby help them to see themselves as future professionals in the field. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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14. The effect of pore-scale contaminant distribution on the reactive decontamination of porous media.
- Author
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Luckins, Ellen K., Breward, Christopher J. W., Griffiths, Ian M., and Please, Colin P.
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CHEMICAL kinetics , *HAZARDOUS substances , *POROUS materials , *LIQUID-liquid interfaces , *SURFACE area , *APPLIED mathematics - Abstract
A porous material that has been contaminated with a hazardous chemical agent is typically decontaminated by applying a cleanser solution to the surface and allowing the cleanser to react into the porous material, neutralising the agent. The agent and cleanser are often immiscible fluids and so, if the porous material is initially saturated with agent, a reaction front develops with the decontamination reaction occurring at this interface between the fluids. We investigate the effect of different initial agent configurations within the pore space on the decontamination process. Specifically, we compare the decontamination of a material initially saturated by the agent with the situation when, initially, the agent only coats the walls of the pores (referred to as the 'agent-on-walls' case). In previous work (Luckins et al., European Journal of Applied Mathematics, 31(5):782–805, 2020), we derived homogenised models for both of these decontamination scenarios, and in this paper we explore the solutions of these two models. We find that, for an identical initial volume of agent, the decontamination time is generally much faster for the agent-on-walls case compared with the initially saturated case, since the surface area on which the reaction can occur is greater. However for sufficiently deep spills of contaminant, or sufficiently slow reaction rates, decontamination in the agent-on-walls scenario can be slower. We also show that, in the limit of a dilute cleanser with a deep initial agent spill, the agent-on-walls model exhibits behaviour akin to a Stefan problem of the same form as that arising in the initially saturated model. The decontamination time is shown to decrease with both the applied cleanser concentration and the rate of the chemical reaction. However, increasing the cleanser concentration is also shown to result in lower decontamination efficiency, with an increase in the amount of cleanser chemical that is wasted. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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15. Roadmap of the Multiplier Method for Partial Differential Equations.
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Alvarez-Valdez, Juan Arturo and Fernandez-Anaya, Guillermo
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PARTIAL differential equations , *ABSTRACT algebra , *MATHEMATICAL physics , *GROUP theory , *NOETHER'S theorem - Abstract
This review paper gives an overview of the method of multipliers for partial differential equations (PDEs). This method has made possible a lot of solutions to PDEs that are of interest in many areas such as applied mathematics, mathematical physics, engineering, etc. Looking at the history of the method and synthesizing the newest developments, we hope to give it the attention that it deserves to help develop the vast amount of work still needed to understand it and make the best use of it. It is also an interesting and a relevant method in itself that could possibly give interesting results in areas of mathematics such as modern algebra, group theory, topology, etc. The paper will be structured in such a manner that the last review known for this method will be presented to understand the theoretical framework of the method and then later work done will be presented. The information of four recent papers further developing the method will be synthesized and presented in such a manner that anyone interested in learning this method will have the most relevant information available and have all details cited for checking. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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16. Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics.
- Author
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Kim, Jongeun, Leyffer, Sven, and Balaprakash, Prasanna
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NONLINEAR operators , *DATA libraries , *SCIENTIFIC computing , *APPLIED mathematics , *SQUARE root , *HEURISTIC - Abstract
In this paper, we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. Cozad and Sahinidis propose a nonconvex mixed-integer nonlinear program (MINLP), in which binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators, such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program–based method and a neural network–based method from the literature. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the Applied Mathematics activity within the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research [Grant DE-AC02-06CH11357]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0050) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0050). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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17. Optimal Cooperation-Trap Strategies for the Iterated Rock-Paper-Scissors Game.
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Bi, Zedong and Zhou, Hai-Jun
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COOPERATION , *NASH equilibrium , *GAME theory , *MATHEMATICAL models , *MAXIMUM strategies - Abstract
In an iterated non-cooperative game, if all the players act to maximize their individual accumulated payoff, the system as a whole usually converges to a Nash equilibrium that poorly benefits any player. Here we show that such an undesirable destiny is avoidable in an iterated Rock-Paper-Scissors (RPS) game involving two rational players, X and Y. Player X has the option of proactively adopting a cooperation-trap strategy, which enforces complete cooperation from the rational player Y and leads to a highly beneficial and maximally fair situation to both players. That maximal degree of cooperation is achievable in such a competitive system with cyclic dominance of actions may stimulate further theoretical and empirical studies on how to resolve conflicts and enhance cooperation in human societies. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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18. Solution of Integral Equations of Fredholm Kind Involving Incomplete ℵ-Function, Generalized Extended Mittag-Leffler Function and S-Function.
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Kumar, Devendra and Dassani, Rishi
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FREDHOLM equations , *SCHUR functions , *INTEGRAL transforms , *MELLIN transform , *APPLIED mathematics , *INTEGRAL equations - Abstract
The main objective of this paper is to solve Fredholm integral equations (IEs) that involve Sfunction, generalized extended Mittag-Leffler function (GEMLF), and incomplete ℵ-function as the kernel. These types of integral equations appear frequently in applied mathematics, particularly in mathematical physics, engineering, and finance. To solve these integral equations, we employ two powerful mathematical tools, namely fractional calculus (FC) and integral transforms. Specifically, we use the Weyl operator and Mellin transform to solve the integral equation associated with S-functions, GEMLF, and incomplete ℵ-functions. These techniques allow us to express the solution in a closed form, which is essential for practical applications. Moreover, we present several special cases of the solutions obtained, which provide additional insights into the behavior of the solutions. These results are significant for the study of integral equations, as they can be used to derive several known results. Furthermore, the techniques used in this study can be applied to other integral equations that involve different types of functions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
19. Polyharmonic splines interpolation on scattered data in 2D and 3D with applications.
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Rubasinghe, Kalani, Yao, Guangming, Niu, Jing, and Tsogtgerel, Gantumur
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RADIAL basis functions , *SPLINE theory , *INTERPOLATION , *SPLINES , *INTERPOLATION algorithms , *APPLIED mathematics , *SCIENTIFIC computing , *PARALLEL programming - Abstract
Data interpolation is a fundamental problem in many applied mathematics and scientific computing fields. This paper introduces a modified implicit local radial basis function interpolation method for scattered data using polyharmonic splines (PS) with a low degree of polynomial basis. This is an improvement to the original method proposed in 2015 by Yao et al.. In the original approach, only radial basis functions (RBFs) with shape parameters, such as multiquadrics (MQ), inverse multiquadrics (IMQ), Gaussian, and Matern RBF are used. The authors claimed that the conditionally positive definite RBFs such as polyharmonic splines r 2 n ln r and r 2 n + 1 "failed to produce acceptable results". In this paper, we verified that when polyharmonic splines together with a polynomial basis is used on the interpolation scheme, high-order accuracy and excellent conditioning of the global sparse systems are gained without selecting a shape parameter. The scheme predicts functions' values at a set of discrete evaluation points, through a global sparse linear system. Compared to standard implementation, computational efficiency is achieved by using parallel computing. Applications of the proposed algorithms to 2D and 3D benchmark functions on uniformly distributed random points, the Halton quasi-points on regular or Stanford bunny shape domains, and an image interpolation problem confirmed the effectiveness of the method. We also compared the algorithms with other methods available in the literature to show the superiority of using PS augmented with a polynomial basis. High accuracy can be easily achieved by increasing the order of polyharmonic splines or the number of points in local domains, when small order of polynomials are used in the basis. MATLAB code for the 3D bunny example is shared on MATLAB Central File Exchange (Yao, 2023). [ABSTRACT FROM AUTHOR]
- Published
- 2023
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20. A higher degenerated invasive‐invaded species interaction.
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Díaz Palencia, José Luis
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FIXED point theory , *PARABOLIC operators , *APPLIED mathematics , *POPULATION dynamics , *SPECIES - Abstract
Invasive‐invaded species problems are of relevance in mathematics applied to population dynamics. In this paper, the mentioned dynamics is introduced based on a fourth‐order parabolic operator, together with coupled non‐linear reaction terms. The fourth‐order operator allows us to model a heterogeneous diffusion, as introduced by the Landau–Ginzburg free energy approach. The reaction terms are given by a coupled non‐linear effect in the invasive species, to account for the action of the invaded species and limited resources, and by a non‐Lipschitz term in the invaded species, to account for possible sprouts, once the invasion occurs. The analysis starts by the proof of existence and uniqueness of solutions, making use of the semi‐group theory and a fixed point argument. Asymptotic solutions to the invasive species are explored with an exponential scaling. Afterward, the problem is analyzed with traveling wave profiles, for which a region of positive solutions is explored. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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21. On the metric-based resolving parameter of the line graph of certain structures.
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Koam, Ali N.A., Ahmad, Ali, Azeem, Muhammad, and Qahiti, Raed
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METRIC geometry , *GRAPH theory , *APPLIED mathematics , *MOLECULAR graphs , *MOLECULES , *LINEAR programming - Abstract
Let G be a graph and R = {r1, r2, ..., rk} be an ordered subset of vertices of G, if every two vertices of G have different representation r (v|R) = (d (v, r1) , d (v, r2) , ..., d (v, rk)) with respect to R, then R is said to be a metric-based resolving parameter or resolving set of G and its minimum cardinality is called the metric dimension of graph G. Metric dimension is considered as an important applied concept of graph theory especially in the localization of a network and also in the chemical graph theoretical study of molecular compounds. Therefore, it is hot topic to study for different families of graphs as well. Convex polytopes play an important role both in various branches of mathematics and in applied areas, most notably in linear programming. In this paper, we determine the metric-based resolving parameter of line graph of a convex polytope Sn, and conclude that it has constant metric dimension but vary with the parity of n. This article presents a measurement of the line graph of a convex polytope, denoted as ( S n). The subsequent section provides the metric dimension of the resulting graph. There are two scenarios pertaining to the metric dimension of a selected graph with respect to the metric dimension. The metric dimension of even cycle-based convex polytopes is three, whereas for other values, the metric dimension is four. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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22. Applied Mathematics in the Numerical Modelling of the Electromagnetic Field in Reference to Drying Dielectrics in the RF Field.
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Spoiala, Viorica, Silaghi, Helga, and Spoiala, Dragos
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ELECTROMAGNETIC fields , *COMPUTATIONAL electromagnetics , *APPLIED mathematics , *DIELECTRICS , *RADIO frequency - Abstract
The processing of dielectric materials in the radio frequency field continues to be a concern in engineering. This procedure involves a rigorous analysis of the electromagnetic field based on specific numerical methods. This paper presents an original method for analysing the process of drying wooden boards in a radio frequency (RF) installation. The electromagnetic field and thermal field are calculated using the finite element method (FEM). The load capacity of the installation is also calculated, since the material being heated in the radio frequency heating installations is placed in a capacitor-type applicator. A specific method is created in order to solve the problem related to mass, a quantity which tends to change during the drying of the dielectric. In addition, special consideration is given to issues regarding the coupling of the electromagnetic field and the thermal field, along with aspects pertaining to mass. These are implemented numerically using a program written in the Fortran language, which takes the distribution of finite elements from the Flux2D program, the dielectric thermal module, intended only for the study of RF heating. The results obtained after running the program are satisfactory and they represent a support for future studies, especially if the movement of the dielectric is taken into account. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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23. Analysis of Higher-Order Bézier Curves for Approximation of the Static Magnetic Properties of NO Electrical Steels.
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Rahmanović, Ermin and Petrun, Martin
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ELECTRICAL steel , *MAGNETIC properties , *ANALYTIC functions , *CURVES , *ELECTRIC machines , *MAGNETIZATION - Abstract
Adequate mathematical description of magnetization curves is indispensable in engineering. The accuracy of the description has a significant impact on the design of electric machines and devices. The aim of this paper was to analyze the capability of Bézier curves systematically, to describe the nonlinear static magnetic properties of non-oriented electrical steels, and to compare this approach versus the established mathematical descriptions. First, analytic functions versus measurements were analyzed. The Bézier curves were then compared systematically with the most adequate analytic functions. Next, the most suitable orders of Bézier curves were determined for the approximation of nonlinear magnetic properties, where the influence of the range of the input measurement dataset on the approximation process was analyzed. Last, the extrapolation capabilities of the Bézier curves and analytic functions were evaluated. The general conclusion is that Bézier curves have adequate flexibility and significant potential for the approximation and extrapolation of nonlinear properties of non-oriented electrical steels. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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24. Novel Multistep Implicit Iterative Methods for Solving Common Solution Problems with Asymptotically Demicontractive Operators and Applications.
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Xu, Hai-Yang and Lan, Heng-You
- Subjects
- *
OPERATOR equations , *NONEXPANSIVE mappings , *APPLIED mathematics - Abstract
It is very meaningful and challenging to efficiently seek common solutions to operator systems (CSOSs), which are widespread in pure and applied mathematics, as well as some closely related optimization problems. The purpose of this paper is to introduce a novel class of multistep implicit iterative algorithms (MSIIAs) for solving general CSOSs. By using Xu's lemma and Maingé's fundamental and important results, we first obtain strong convergence theorems for both one-step and multistep implicit iterative schemes for CSOSs, involving asymptotically demicontractive operators. Finally, for the applications and profits of the main results presented in this paper, we give two numerical examples and present an iterative approximation to solve the general common solution to the variational inequalities and operator equations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
25. To the Problem of Discontinuous Solutions in Applied Mathematics.
- Author
-
Vasiliev, Valery V. and Lurie, Sergey A.
- Subjects
- *
APPLIED mathematics , *MATHEMATICAL physics , *DIFFERENTIAL calculus , *DERIVATIVES (Mathematics) , *EQUATIONS - Abstract
This paper addresses discontinuities in the solutions of mathematical physics that describe actual processes and are not observed in experiments. The appearance of discontinuities is associated in this paper with the classical differential calculus based on the analysis of infinitesimal quantities. Nonlocal functions and nonlocal derivatives, which are not specified, in contrast to the traditional approach to a point, but are the results of averaging over small but finite intervals of the independent variable are introduced. Classical equations of mathematical physics preserve the traditional form but include nonlocal functions. These equations are supplemented with additional equations that link nonlocal and traditional functions. The proposed approach results in continuous solutions of the classical singular problems of mathematical physics. The problems of a string and a circular membrane loaded with concentrated forces are used to demonstrate the procedure. Analytical results are supported with experimental data. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
26. Uniqueness of Two‐Bubble Wave Maps in High Equivariance Classes.
- Author
-
Jendrej, Jacek and Lawrie, Andrew
- Subjects
- *
THRESHOLD energy , *WAVE energy , *WAVE equation , *APPLIED mathematics , *PERIODICAL publishing , *HARMONIC maps - Abstract
This is the second part of a two‐paper series that establishes the uniqueness and regularity of a threshold energy wave map that does not scatter in both time directions. Consider the S2‐valued equivariant energy critical wave maps equation on ℝ1+2, with equivariance class k≥4. It is known that every topologically trivial wave map with energy less than twice that of the unique k‐equivariant harmonic map Q→k scatters in both time directions. We study maps with precisely the threshold energy E=2EQ→k. In the first part of the series [15] we gave a refined construction of a threshold wave map that asymptotically decouples into a superposition of two harmonic maps (bubbles), one of which is concentrating in scale. In this paper, we show that this solution is the unique (up to the natural invariances of the equation) two‐bubble wave map. Combined with our earlier work [14] we obtain an exact description of every threshold wave map. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
27. The Sandpile Group of Polygon Flower with Two Centers.
- Author
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Wei, Lina, Bian, Hong, Yu, Haizheng, and Feng, Yuelong
- Subjects
- *
APPLIED mathematics , *COMPUTATIONAL mathematics , *FLOWERS , *ABELIAN groups , *HEXAGONS - Abstract
Let C k + 1 be a cycle of length k + 1 and C t + 1 be a cycle of length t + 1. A polygon flower with two centers, denoted by F = F (C k + 1 ; P 1 , ... , P k ; C t + 1 ; P k + 1 , ... , P k + t) is obtained by identifying the i th edge of C k + 1 with an edge ei that belongs to an end-polygon of Pi for i = 1 , ... , k , and identifying the j th edge of C t + 1 with an edge ej that belongs to an end-polygon of Pj for j = k + 1 , ... , k + t , where C k + 1 and C t + 1 have a common edge h. In this paper, we determine the order of sandpile group S(F) of F, which can be viewed as generalized of results in paper (Haiyan Chen, Bojan Mohar. The sandpile group of a polygon flower. Discrete Applied Mathematics, 2019). Moreover, the formula and structure for sandpile group of polygon flower can be obtained. Finally, as application of our result, we also present the sandpile group of cata-condensed system with two branched hexagons. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
28. Remarks on a paper by Maharaj and Wulftange
- Author
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Hasegawa, Takehiro
- Subjects
- *
MODULES (Algebra) , *MATHEMATICAL optimization , *CONTINUATION methods , *MATHEMATICAL analysis , *APPLIED mathematics - Abstract
Abstract: In this paper, we determine the modularities of asymptotically optimal towers found by Maharaj and Wulftange in 2005. This is also a continuation of the work of Elkies in 2002. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
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29. Applied and Computational Mathematics for Digital Environments.
- Author
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Demidova, Liliya A.
- Subjects
- *
COMPUTATIONAL mathematics , *DIGITAL technology , *APPLIED mathematics , *ARTIFICIAL intelligence , *CONVOLUTIONAL neural networks , *HUMAN activity recognition , *DIFFERENTIAL evolution - Abstract
Currently, digitalization and digital transformation are actively expanding into various areas of human activity, and researchers are identifying urgent problems and offering new solutions regarding digital environments in industry [[1]], economics [[3]], medicine [[5]], ecology [[7]], education [[9]], etc. Conclusions The purpose of this Special Issue was to attract high-quality new papers in the field of applied and computational mathematics for digital environments, offering original solutions to various problems that are relevant and in demand in various fields of human activity. 10.3390/math10224297 21 Demidova L.A. A Novel Approach to Decision-Making on Diagnosing Oncological Diseases Using Machine Learning Classifiers Based on Datasets Combining Known and/or New Generated Features of a Different Nature. I hope that these selected research papers are recognized as important and meaningful by the international scientific community and can form the basis for further research in the field of applied and computational mathematics for digital environments, solving complex problems in various disciplines and application areas. [Extracted from the article]
- Published
- 2023
- Full Text
- View/download PDF
30. Upper bound estimations of misclassification rate in the heteroscedastic clustering model with sub‐Gaussian noises.
- Author
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Zhang, Zhentao and Wang, Jinru
- Subjects
- *
APPLIED mathematics , *HETEROSCEDASTICITY - Abstract
Clustering is an important tool in statistics, machine learning and applied mathematics. This paper considers the clustering model Y=μlT+Z∈ℝp×n, where the noise matrix Z consists of independent sub‐Gaussian entries Zij and the variance Var(Zij)=σij2 may vary across different coordinates. Our aim is to estimate the error between the label vector l and its defined estimator l^. We provide upper bound estimations for the misclassification rate in the sense of expectation and probability, respectively. Finally, some simulations have been carried out to support our theoretical results and illustrate the advantage of our proposed estimator. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
31. Well ordering principles for iterated Π11-comprehension.
- Author
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Freund, Anton and Rathjen, Michael
- Subjects
- *
REVERSE mathematics , *COMBINATORICS , *ADMISSIBLE sets , *SET theory , *APPLIED mathematics , *PROOF theory - Abstract
We introduce ordinal collapsing principles that are inspired by proof theory but have a set theoretic flavor. These principles are shown to be equivalent to iterated Π 1 1 -comprehension and the existence of admissible sets, over weak base theories. Our work extends a previous result on the non-iterated case, which had been conjectured in Montalbán's "Open questions in reverse mathematics" (Bull Symb Log 17(3):431–454, 2011). This previous result has already been applied to the reverse mathematics of combinatorial and set theoretic principles. The present paper is a significant contribution to a general approach that connects these fields. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
32. Uniqueness of meromorphic functions with Q-shift difference-differential polynomials sharing finite value.
- Author
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Jayarama, H. R., Chaithraia, C. N., and Naveenkumar, S. H.
- Subjects
- *
MEROMORPHIC functions , *APPLIED mathematics , *POLYNOMIALS , *NEVANLINNA theory , *SHARING - Abstract
The principal objective of the paper, to study the uniqueness problem of Q-shift differencedifferential polynomials of a meromorphic function sharing finite value. A result Chung-Chun Yang and Xinhou. Hua (In Annales-Academiae Scientiarum Fennicae Series A 1 Mathematica 22:395-406,1997) is the starting point of this kind of research. In addition to this, one of our result improve and extend that of Harina R Waghamore and Rajeshwari (International Journal of Pure and Applied Mathematics 107(4):971-981, 2016). Some examples have been exhibited to validate our certain claims in the main result. [ABSTRACT FROM AUTHOR]
- Published
- 2023
33. Sparse Multi-Reference Alignment: Phase Retrieval, Uniform Uncertainty Principles and the Beltway Problem.
- Author
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Ghosh, Subhroshekhar and Rigollet, Philippe
- Subjects
- *
HARMONIC analysis (Mathematics) , *COMBINATORIAL optimization , *APPLIED mathematics , *FOURIER transforms , *POWER spectra , *HEISENBERG uncertainty principle , *HOPFIELD networks , *NOISE , *QUANTUM measurement - Abstract
Motivated by cutting-edge applications like cryo-electron microscopy (cryo-EM), the Multi-Reference Alignment (MRA) model entails the learning of an unknown signal from repeated measurements of its images under the latent action of a group of isometries and additive noise of magnitude σ . Despite significant interest, a clear picture for understanding rates of estimation in this model has emerged only recently, particularly in the high-noise regime σ ≫ 1 that is highly relevant in applications. Recent investigations have revealed a remarkable asymptotic sample complexity of order σ 6 for certain signals whose Fourier transforms have full support, in stark contrast to the traditional σ 2 that arise in regular models. Often prohibitively large in practice, these results have prompted the investigation of variations around the MRA model where better sample complexity may be achieved. In this paper, we show that sparse signals exhibit an intermediate σ 4 sample complexity even in the classical MRA model. Further, we characterize the dependence of the estimation rate on the support size s as O p (1) and O p (s 3.5) in the dilute and moderate regimes of sparsity respectively. Our techniques have implications for the problem of crystallographic phase retrieval, indicating a certain local uniqueness for the recovery of sparse signals from their power spectrum. Our results explore and exploit connections of the MRA estimation problem with two classical topics in applied mathematics: the beltway problem from combinatorial optimization, and uniform uncertainty principles from harmonic analysis. Our techniques include a certain enhanced form of the probabilistic method, which might be of general interest in its own right. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
34. Some new integral inequalities for higher-order strongly exponentially convex functions.
- Author
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Bisht, Jaya, Sharma, Nidhi, Mishra, Shashi Kant, and Hamdi, Abdelouahed
- Subjects
- *
INTEGRAL inequalities , *CONVEX functions , *FRACTIONAL integrals , *APPLIED mathematics , *GENERALIZED integrals , *MATHEMATICS - Abstract
Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
35. Energy classification in a nonstandard fourth‐order parabolic equation with a Navier boundary condition.
- Author
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Liu, Bingchen, Sun, Xizheng, and Wang, Yiming
- Subjects
- *
POTENTIAL well , *EQUATIONS , *APPLIED mathematics , *CLASSIFICATION , *POTENTIAL energy - Abstract
This paper deals with a fourth‐order parabolic equation involving variable exponents, subject to Navier boundary conditions. We firstly give an optimal classification on the initial energy for blow‐up or global solutions, which is characterized by the sign of the Nehari energy and the difference between the initial energy and the depth of the potential well. Then, large time estimates of solutions are obtained. The results of the paper extend and complete the ones in "Applied Mathematics Letters 78(2018)141–146." [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
36. Inverses and Determinants of n × n Block Matrices.
- Author
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Saadetoğlu, Müge and Dinsev, Şakir Mehmet
- Subjects
- *
APPLIED mathematics , *MATRIX multiplications , *DETERMINANTS (Mathematics) - Abstract
Block matrices play an important role in all branches of pure and applied mathematics. In this paper, we study the two fundamental concepts: inverses and determinants of general n × n block matrices. In the first part, the inverses of 2 × 2 block matrices are given, where one of the blocks is a non-singular matrix, a result which can be generalised to a block matrix of any size, by splitting it into four blocks. The second part focuses on the determinants, which is covered in two different methods. In the first approach, we revise a formula for the determinant of a block matrix A, with blocks elements of R; a commutative subring of M n × n (F) . The determinants of tensor products of two matrices are also given in this part. In the second method for computing the determinant, we give the general formula, which would work for any block matrix, regardless of the ring or the field under consideration. The individual formulas for determinants of 2 × 2 and 3 × 3 block matrices are also produced here. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
37. Numerical Analysis of Nonlinear Coupled Schrödinger–KdV System with Fractional Derivative.
- Author
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Alzahrani, Abdulrahman B. M.
- Subjects
- *
NONLINEAR analysis , *NUMERICAL analysis , *POWER series , *APPLIED mathematics , *MATHEMATICAL physics , *CAPUTO fractional derivatives - Abstract
In this paper, we propose two efficient methods for solving the fractional-order Schrödinger–KdV system. The first method is the Laplace residual power series method (LRPSM), which involves expressing the solution as a power series and using residual correction to improve the accuracy of the solution. The second method is a new iterative method (NIM) that simplifies the problem and obtains a recursive formula for the solution. Both methods are applied to the Schrödinger–KdV system with fractional derivatives, which arises in many physical applications. Numerical experiments are performed to compare the accuracy and efficiency of the two methods. The results show that both methods can produce highly accurate solutions for the fractional Schrödinger–KdV system. However, the new iterative method is more efficient in terms of computational time and memory usage. Overall, our study demonstrates the effectiveness of the residual power series method and the new iterative method in solving fractional-order Schrödinger–KdV systems and provides a valuable tool for researchers and practitioners in applied mathematics and physics. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
38. Solitons solutions to the high-order dispersive cubic–quintic Schrödinger equation in optical fibers.
- Author
-
Zabihi, Ali, Shaayesteh, Mayssam Tarighi, Rezazadeh, Hadi, Ansari, Reza, Raza, Nauman, and Bekir, Ahmet
- Subjects
- *
OPTICAL fibers , *NONLINEAR Schrodinger equation , *SOLITONS , *HYPERBOLIC functions , *SEPARATION of variables , *APPLIED mathematics , *SCHRODINGER equation , *ULTRASHORT laser pulses - Abstract
In this paper, solitons solutions of higher-order dispersive cubic–quintic Schrödinger equationincluding third-order as well as fourth-order derivatives with respect to time, that describes the dynamics of ultrashort pulses in optical fibers are investigated in detail. In this respect,a solution procedure in the locality of applied mathematics called the hyperbolic function method is appliedusing multi-linear variable separation approach (MLVSA). As an outcome, a bunch of soliton solutions isderived in conjunction with plotting dark and periodic wave solutions. The credibility of the results is examined by setting each solution back into its governing equation. Through portraits, different forms of wave solutions are depicted. Moreover, the restrictions on the parameters are also given for the existence of the obtained solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
39. Determination of the Motion Parameters of Near-Earth Objects from Position Measurements Performed at the Terskol Observatory.
- Author
-
Levkina, P. A. and Chuvashov, I. N.
- Subjects
- *
NEAR-Earth objects , *OBSERVATORIES , *APPLIED mechanics , *ORBITS (Astronomy) , *APPLIED mathematics - Abstract
The paper presents a method for processing positional observations of near-Earth objects using a numerical model of satellite motion developed at the Research Institute of Applied Mathematics and Mechanics of Tomsk State University (NII PMM TSU). The root-mean-square error of orbit improvement without rejection of observations for such objects does not exceed 0.3″ over a seven-day time interval. The results of the presentation of observations for the next occurrence of the object are obtained, which makes it possible to find the object in a time interval of five months. The orbit has been refined in the joint processing of measurements on several occurrences of the object over a six-month time interval. All results were obtained from observations made on the equipment of the Terskol Observatory Shared Use Center. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
40. Various exact optical soliton solutions for time fractional Schrodinger equation with second-order spatiotemporal and group velocity dispersion coefficients.
- Author
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Murad, Muhammad Amin Sadiq, Hamasalh, Faraidun Kadir, and Ismael, Hajar Farhan
- Subjects
- *
GROUP velocity dispersion , *SOLITONS , *FRACTIONAL differential equations , *NONLINEAR Schrodinger equation , *APPLIED mathematics , *NONLINEAR equations , *HYPERBOLIC functions , *SCHRODINGER equation - Abstract
In this paper, the extended simplest equation technique is considered to construct various exact optical solutions to the time-fractional nonlinear Schrodinger equation with second-order spatiotemporal and group velocity dispersion coefficients. The acquired novel optical soliton solutions are illustrated by the hyperbolic functions, the rational functions, and the trigonometric functions. The singular, dark, bright, mixed bright, dark–bright, and wave soliton solutions of the proposed model are successfully constructed. Further, to clarify the magnitude of the present nonlinear time-fractional Schrodinger model several solutions of the new exact optical solutions are plotted via two-dimensional and three-dimensional graphs using suitable values of physical parameters. The results acquired illustrate that the utilized technique is simple and quite efficient for exploring exact soliton solutions for different differential equations of fractional and integer orders arising in optics and applied mathematics. The novel optical solutions can assist researchers with an interest in plasma physics to unravel the mystery of numerous nonlinear phenomena that arise in various plasma models. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
41. Banach's theorem in higher-order reverse mathematics.
- Author
-
Hirst, Jeffry L. and Mummert, Carl
- Subjects
- *
REVERSE mathematics , *APPLIED mathematics , *NATURAL numbers , *METRIC spaces , *ARITHMETIC - Abstract
In this paper, methods of second-order and higher-order reverse mathematics are applied to versions of a theorem of Banach that extends the Schröder–Bernstein theorem. Some additional results address statements in higher-order arithmetic formalizing the uncountability of the power set of the natural numbers. In general, the formalizations of higher-order principles here have a Skolemized form asserting the existence of functionals that solve problems uniformly. This facilitates proofs of reversals in axiom systems with restricted choice. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
42. Reproducing kernels of Sobolev–Slobodeckij˘ spaces via Green's kernel approach: Theory and applications.
- Author
-
Mohebalizadeh, Hamed, Fasshauer, Gregory E., and Adibi, Hojatollah
- Subjects
- *
APPLIED mathematics , *FUNCTION spaces , *INTERPOLATION spaces , *DIFFERENTIAL operators , *COLLOCATION methods , *LAPLACIAN operator , *GREEN'S functions - Abstract
This paper extends the work of Fasshauer and Ye [Reproducing kernels of Sobolev spaces via a Green kernel approach with differential operators and boundary operators, Adv. Comput. Math. 38(4) (2011) 891921] in two different ways, namely, new kernels and associated native spaces are identified as crucial Hilbert spaces in applied mathematics. These spaces include the following spaces defined in bounded domains Ω ⊂ ℝ d with smooth boundary: homogeneous Sobolev–Slobodeckij̆ spaces, denoted by H 0 s (Ω ¯) , and Sobolev–Slobodeckij̆ spaces, denoted by H s (Ω) , where s > d 2 . Our goal is accomplished by obtaining the Green's solutions of equations involving the fractional Laplacian and fractional differential operators defined through interpolation theory. We provide a proof that the Green's kernels satisfying these problems are symmetric and positive definite reproducing kernels of H 0 s (Ω ¯) and H s (Ω) , respectively. Constructing kernels in these two ways enables the characterization of functions in native spaces based on their regularity. The Galerkin/collocation method, based on these kernels, is employed to solve various fractional problems, offering explicit or simplified calculations and efficient solutions. This method yields improved results with reduced computational costs, making it suitable for complex domains. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
43. Analysis of ill-conditioned cases of a mass moving on a sphere with friction.
- Author
-
McDaniel, Terry W.
- Subjects
- *
CLASSICAL mechanics , *FRICTION , *NUMERICAL integration , *APPLIED mathematics , *MATHEMATICAL analysis - Abstract
Previous work treated the problem of a mass sliding over a rough spherical surface in broad generality, providing both analytic and numerical solutions. This paper examines special cases of 2D motion along a surface meridian when the initial speed is precisely chosen so that the sliding mass nearly stops before speeding up and subsequently leaving the surface. Carrying the solution for these critical cases into the time domain via both an analytical method and numerical integration adds richness that might otherwise be missed. The numerical method raises practical mathematical issues that must be handled carefully to obtain accurate results. Although conceptually simple, this classical mechanics problem is an excellent vehicle for students to gain proficiency with mathematical analysis tools and further their appreciation for how applied mathematics can bring new insight into situations where intuition may fall short. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
44. Flow optimization in network systems with graph theory.
- Author
-
Sitio, Bimo Chantio, Mawengkang, Herman, and Tulus
- Subjects
- *
SYSTEMS theory , *MATHEMATICAL optimization , *APPLIED mathematics , *OPERATIONS research , *COMPUTER science , *GRAPH theory - Abstract
Graph theory can be said as one of the branches of applied mathematics that is currently developing. A problem can be explained in detail by simplifying it with graph theory. This paper concerns with graphs that are used in everyday life as a network system to describe parts of a structure in order to make it simpler and easier to understand. The network flow system is then applied in many disciplines, including applied mathematics, computer science, operations research, management, and engineering. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. Academic english course for Russian students engaged in astrodynamics.
- Author
-
Ovchinnikova, O. M.
- Subjects
- *
ASTRODYNAMICS , *PREREQUISITES (Education) , *APPLIED mathematics , *STUDENTS , *SPACE flight - Abstract
The paper summarizes the experience of teaching the academic English course to Russian students engaged in spaceflight dynamics studies at the Keldysh Institute of Applied Mathematics (KIAM) of RAS. Prerequisites for the course, methodological principles of teaching and some features of the course, as well as its perspectives, are described. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
46. Some New Results for the Kampé de Fériet Function with an Application.
- Author
-
Kim, Insuk, Paris, Richard B., and Rathie, Arjun K.
- Subjects
- *
HYPERGEOMETRIC functions , *HYPERGEOMETRIC series , *APPLIED mathematics , *PARTIAL differential equations , *MATHEMATICAL physics , *SET functions - Abstract
The generalized hypergeometric functions in one and several variables and their natural generalizations appear in many mathematical problems and their applications. The theory of generalized hypergeometric functions in several variables comes from the fact that the solutions of the partial differential equations appearing in a large number of applied problems of mathematical physics have been expressed in terms of such generalized hypergeometric functions. In particular, the Kampé de Fériet function (in two variables) has proved its practical utility in representing solutions to a wide range of problems in pure and applied mathematics, statistics, and mathematical physics. In this context, in a very recent paper, Progri successfully calculated the 2 F 2 generalized hypergeometric function for a particular set of parameters and expressed the result in terms of the difference between two Kampé de Fériet functions. Inspired by his work, in the present paper, we obtain three results for a terminating 3 F 2 series of arguments 1 and 2, together with a transformation formula of a 3 F 2 (z) generalized hypergeometric function in terms of the difference between two Kampé de Fériet functions. One application of this result is also provided. The paper concludes with six reduction formulas for the Kampé de Fériet function. Of note, symmetry occurs naturally in the generalized hypergeometric functions p F q and the Kampé de Fériet function involving two variables, which are the two most important functions discussed in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
47. Analysis Of Crystallographic Patterns Of Iban Pua Kumbu.
- Author
-
Truna, Liyana, Tugang, Noria, Shaipullah, Norhunaini Mohd, and Mahyan, Nur Rasfina
- Subjects
- *
VISUAL perception , *APPLIED mathematics , *MATHEMATICS students , *WEAVERS , *SYMMETRY - Abstract
One of the famous traditional textiles in Sarawak is the Iban Pua Kumbu. This paper presents the crystallographic patterns, geometry concept and symmetry analysis present in the Iban Pua Kumbu patterns. This paper will also look at the colour-symmetrical patterns and motifs used in these textiles. The Ibans' weaving technique subtly incorporates geometric concepts using exquisite and precious designs. The Pua Kumbu of the Iban can be similarly classified according to the patterns displayed in the wallpaper and frieze. The current research findings could assist students to learn mathematics. In this study, samples comprising eight (8) repeated patterns were collected from field visits, museums in the Sarawak, and personal collections of scholars. From the findings, it shows that all Pua Kumbu patterns bear at least one of the seventeen crystallographic groups. Most of the Pua Kumbu motifs are symmetrical and those motifs is mathematically identified as a design. The Pua Kumbu contains decorative patterns whose relevance and imaginative portrayal are demonstrated by the intricacy of the creative process. Pua Kumbu weavers appear to have excellent memory skills, strong visual perception, and an innate aptitude for applying mathematics to their work. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
48. A note on the paper “On Brlek-Reutenauer conjecture”
- Author
-
Bašić, Bojan
- Subjects
- *
ERROR analysis in mathematics , *PROOF theory , *MATHEMATICAL sequences , *MATHEMATICS theorems , *MATHEMATICAL analysis , *APPLIED mathematics - Abstract
Abstract: In this short note we point to an error in the proof of a theorem stated in [L. Balková, E. Pelantová, Š. Starosta, On Brlek-Reutenauer conjecture, Theoret. Comput. Sci. 412 (2011) 5649–5655]. By constructing a counterexample, we show that the assertion of the theorem is actually incorrect. Although this theorem is of a technical character, it was used in an argument leading to a corollary of a general interest to the Brlek-Reutenauer conjecture, and thus as a consequence of this note we have that the proof of the mentioned corollary is also flawed. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
49. IN MEMORY OF L. G. AFANASYEVA: (14.09.1937 - 26.08.2022).
- Subjects
- *
OPERATIONS research , *QUEUING theory , *PROCESS control systems , *APPLIED mathematics , *INVENTORY theory , *PROBABILITY theory , *QUEUEING networks - Abstract
This article is a memorial tribute to Larisa Grigor'evna Afanasyeva, a prominent mathematician and professor at Lomonosov Moscow State University. Afanasyeva specialized in queuing theory, particularly the ergodicity of various queuing systems. She made significant contributions to the field and published over 130 research papers and two books. Afanasyeva's work was recognized internationally, and she was an active scientist until her passing in August 2022. [Extracted from the article]
- Published
- 2023
- Full Text
- View/download PDF
50. INTELLIGENT SUPPORT SYSTEM APPLIED TO SCHOOL MATHEMATICS LESSONS.
- Author
-
BRĂNOAEA, Gabriela Cristina
- Subjects
- *
ARTIFICIAL intelligence , *APPLIED mathematics , *MATHEMATICS , *NEUROSCIENCES - Abstract
This paper presents the relevance of artificial intelligence in the teaching of mathematics by using an Intelligent Support System made in Wolfram Mathematica. This system allows the design of an unlimited number of personalized items necessary for the training of students passionate about mathematics. Neuroscience research in collaboration with artificial intelligence can lead to deeper and faster personalized math learning, increasing the potential of every student. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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