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Results in Applied Mathematics最新文献

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New upper and lower bounds for the upper incomplete gamma function
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100552
Steven G. From , Suthakaran Ratnasingam
{"title":"New upper and lower bounds for the upper incomplete gamma function","authors":"Steven G. From ,&nbsp;Suthakaran Ratnasingam","doi":"10.1016/j.rinam.2025.100552","DOIUrl":"10.1016/j.rinam.2025.100552","url":null,"abstract":"<div><div>Some new upper and lower bounds for the upper incomplete gamma function <span><math><mrow><mi>Γ</mi><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> are presented. Some of the bounds are given for all real <span><math><mrow><mi>x</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> and some are for only certain combinations of <span><math><mi>a</mi></math></span> and <span><math><mi>x</mi></math></span>. A number of different methods are used to obtain these new bounds. In particular, rational function and perturbations of rational function bounds are presented. Some numerical comparisons are made with previously proposed bounds.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100552"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some fixed point results concerning various contractions in extended b- metric space endowed with a graph
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100524
Neeraj Kumar , Seema Mehra , Dania Santina , Nabil Mlaiki
{"title":"Some fixed point results concerning various contractions in extended b- metric space endowed with a graph","authors":"Neeraj Kumar ,&nbsp;Seema Mehra ,&nbsp;Dania Santina ,&nbsp;Nabil Mlaiki","doi":"10.1016/j.rinam.2024.100524","DOIUrl":"10.1016/j.rinam.2024.100524","url":null,"abstract":"<div><div>Contraction type mappings are crucial for understanding fixed point theory under specific conditions. We propose generalized (Boyd–Wong) type A <strong>F</strong> and (S - N) rational type contractions in an enlarged b-metric space which are represented by a graphically. Also, we gave a contrast of generalized (Boyd–Wong) type A <strong>F</strong> — contraction in 2D and 3D. We use appropriate illustrations to demonstrate the validity and primacy of our outcomes. Additionally, we use our derived conclusions to solve the Fredholm integral problem.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100524"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonnegative weak solution to the degenerate viscous Cahn–Hilliard equation
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100527
Toai Luong
{"title":"Nonnegative weak solution to the degenerate viscous Cahn–Hilliard equation","authors":"Toai Luong","doi":"10.1016/j.rinam.2024.100527","DOIUrl":"10.1016/j.rinam.2024.100527","url":null,"abstract":"<div><div>The Cahn–Hilliard equation is a widely used model for describing phase separation processes in a binary mixture. In this paper, we investigate the viscous Cahn–Hilliard equation with a degenerate, phase-dependent mobility. We define the concept of a weak solution and establish the existence of such a solution by taking limits of solutions to the viscous Cahn–Hilliard equation with positive mobility. Additionally, assuming that the initial data is positive, we demonstrate that the weak solution remains nonnegative and is not identically zero. Finally, we prove that the weak solution satisfies an energy dissipation inequality.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100527"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143150062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new scaled BFGS method for convex constraints monotone systems: Applications in motion control
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100531
Abdullah Shah , Maaz ur Rehman , Jamilu Sabi’u , Muhammad Sohaib , Khaled M. Furati
{"title":"A new scaled BFGS method for convex constraints monotone systems: Applications in motion control","authors":"Abdullah Shah ,&nbsp;Maaz ur Rehman ,&nbsp;Jamilu Sabi’u ,&nbsp;Muhammad Sohaib ,&nbsp;Khaled M. Furati","doi":"10.1016/j.rinam.2024.100531","DOIUrl":"10.1016/j.rinam.2024.100531","url":null,"abstract":"<div><div>This paper introduces a new version of the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm, characterized as a scaled memoryless, projection-based, and derivative-free method for finding approximate solutions of monotone nonlinear equations with convex constraints. The optimal value of the scaling parameter is achieved by minimizing the BFGS update matrix. The theoretical analysis is performed to demonstrate the global convergence of the approach. Numerical analysis and comparisons with prior results indicate that the proposed approach has superior performance for CPU time, iteration count, and function evaluations. The new algorithm is used to solve the motion control issue of a two-jointed coplanar robot manipulator.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100531"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Phase-field model with concentrating-potential terms on the boundary
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100523
Ángela Jiménez-Casas
{"title":"Phase-field model with concentrating-potential terms on the boundary","authors":"Ángela Jiménez-Casas","doi":"10.1016/j.rinam.2024.100523","DOIUrl":"10.1016/j.rinam.2024.100523","url":null,"abstract":"<div><div>In this paper we analyze a generalization of the semilinear phase field model from G. Caginalp (1986, 1991) and A. Jiménez-Casas-A. Rodriguez-Bernal (1996, 2005), where we consider a singular term concentrated in a neighborhood of <span><math><mi>Γ</mi></math></span>, the boundary of domain. The neighborhood shrinks to <span><math><mi>Γ</mi></math></span> as a parameter <span><math><mi>ϵ</mi></math></span> approaches zero.</div><div>We prove that this family of solutions, of the new semilinear phase field model, converges in suitable spaces when this parameter tends to zero, to the solutions of a semilinear phase field problem where the concentrating potential are transformed into an extra flux condition on <span><math><mi>Γ</mi></math></span>.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100523"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143149998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Decay properties of spatial molecular orbitals
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100540
Richard A. Zalik
{"title":"Decay properties of spatial molecular orbitals","authors":"Richard A. Zalik","doi":"10.1016/j.rinam.2025.100540","DOIUrl":"10.1016/j.rinam.2025.100540","url":null,"abstract":"<div><div>Using properties of the Fourier transform we prove that if a Hartree–Fock molecular spatial orbital is in <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>, then it decays to zero as its argument diverges to infinity. The proof is rigorous, elementary and short. Our result implies that occupied orbitals with positive eigenvalues will decay to zero provided they are in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100540"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143150011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analytical strength-duration curve for the spiking response of the LIF neuron to an alpha-function-shaped excitatory current pulse
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100548
Alexander Paraskevov
{"title":"Analytical strength-duration curve for the spiking response of the LIF neuron to an alpha-function-shaped excitatory current pulse","authors":"Alexander Paraskevov","doi":"10.1016/j.rinam.2025.100548","DOIUrl":"10.1016/j.rinam.2025.100548","url":null,"abstract":"<div><div>Whether or not the neuron emits a spike in response to stimulation by an excitatory current pulse is determined by a strength-duration curve (SDC) for the pulse parameters. The SDC is a dependence of the minimal pulse amplitude required to elicit the spiking response on either the pulse duration or its decay time. Excitatory neurons affect the others through pulses of excitatory postsynaptic current. A simple yet plausible approximation for the time course of such a pulse is the alpha function, with linear rise at the start and exponential decay at the end. However, an exact analytical SDC for this case is hitherto not known, even for the leaky integrate-and-fire (LIF) neuron, the simplest spiking neuron model used in practice. We have obtained general SDC equations for the LIF neuron. Using the Lambert W function — a widely-implemented special function, we have found the exact analytical SDC for the spiking response of the LIF neuron stimulated by an excitatory current pulse in the form of the alpha function. To compare results in a unified way, we have also derived the analytical SDCs for (i) rectangular pulse, (ii) ascending ramp pulse, and (iii) instantly rising and exponentially decaying pulse. In the limit of no leakage, we show that the SDC is reduced to the classical hyperbola for all considered cases.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100548"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scales
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100553
Kazuki Ishibashi
{"title":"Riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scales","authors":"Kazuki Ishibashi","doi":"10.1016/j.rinam.2025.100553","DOIUrl":"10.1016/j.rinam.2025.100553","url":null,"abstract":"<div><div>In this study, we investigate the use of damped linear dynamic equations with the conformable derivative on time scales to provide sufficient conditions to guarantee nonoscillation for nontrivial solutions of both ordinary differential and discrete equations. The nonoscillation theorem is proven using the Riccati technique, and we provide four examples to explain nonoscillation. The four examples include the damped Euler-type dynamic equation on a time scale, the <span><math><mi>q</mi></math></span>-difference equation, and the forward difference and ordinary differential equations with periodic coefficients. In particular, the ordinary differential equation with periodic coefficients is inspired by Whittaker–Hill’s equation, which has applications in the theory of internal rotation in the hydrogen peroxide molecule.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100553"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Enhancing artificial neural network learning efficiency through Singular value decomposition for solving partial differential equations
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100522
Alfi Bella Kurniati , Maharani A. Bakar , Nur Fadhilah Ibrahim , Hanani Farhah Harun
{"title":"Enhancing artificial neural network learning efficiency through Singular value decomposition for solving partial differential equations","authors":"Alfi Bella Kurniati ,&nbsp;Maharani A. Bakar ,&nbsp;Nur Fadhilah Ibrahim ,&nbsp;Hanani Farhah Harun","doi":"10.1016/j.rinam.2024.100522","DOIUrl":"10.1016/j.rinam.2024.100522","url":null,"abstract":"<div><div>Partial differential equations (PDEs) hold significant potential for modelling natural phenomena. It is essential to look at a practical way to solve the PDEs. Recently, Artificial Neural Networks (ANN) have emerged as promising tool for approximating PDE solutions. This approach stands out for its adaptability in hybridizing with various optimization techniques, rendering it a potent tool. One drawback of ANN, however, lies in its tendency for slow convergence. In response, we introduce the matrix decomposition method into the ANN learning process, rooted in Singular Value Decomposition (SVD). Decomposed matrix operates by establishing connections between the weights in the first and second hidden layers of the ANN, allowing the generation of singular matrix values. The process of determining the number of retained singular value components in the decomposition method involves three reduction techniques derived from SVD: Thin SVD, Compact SVD, and Truncated SVD. Six problems of second-order PDE on one- and two-dimensionality were solved using these methods, which were combined into a unique ANN learning framework. The results showed that our proposed method exhibits better performance compared to the conventional ANN or those without the decomposition method.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100522"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Norm decay rates of the Fourier oscillatory integral operators for a class of homogeneous-type polynomial hybrid phases 一类同质型多项式混合相的傅立叶振荡积分算子的规范衰减率
IF 1.4
Results in Applied Mathematics Pub Date : 2024-11-01 DOI: 10.1016/j.rinam.2024.100513
Tuan Anh Pham , Nhat Huy Vu , Minh Tuan Nguyen
{"title":"Norm decay rates of the Fourier oscillatory integral operators for a class of homogeneous-type polynomial hybrid phases","authors":"Tuan Anh Pham ,&nbsp;Nhat Huy Vu ,&nbsp;Minh Tuan Nguyen","doi":"10.1016/j.rinam.2024.100513","DOIUrl":"10.1016/j.rinam.2024.100513","url":null,"abstract":"<div><div>This paper presents a new approach to the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> norm decay rates of the Fourier oscillatory integral operators for some classes of degenerate phases. In particular, the sharp norm decay rates of the Fourier oscillatory integral operators for homogeneous-type polynomial phases, and those for a class of nonsmooth polynomial hybrid phase functions are obtained.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100513"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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