Applied Mathematics and Computation最新文献

{"title":"Octonionic wavelet transform and uncertainly principle","authors":"Guangbin Ren,&nbsp;Xin Zhao","doi":"10.1016/j.amc.2025.129449","DOIUrl":"10.1016/j.amc.2025.129449","url":null,"abstract":"<div><div>This article centers around the octonion wavelet transform, exploring its transformation function <span><math><msup><mrow><mi>ψ</mi></mrow><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>S</mi></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math></span> derived from the admissible octonionic mother wavelet <em>ψ</em>, incorporating translation, rotation, and dilation components. We establish the inverse transform and the Plancherel formula, unveiling the inner product relationship of transformed functions. The Uncertainty Principle for the octonion wavelet transform reveals inherent bounds in wavelet analysis within the octonionic framework. However, it is essential to note that these discoveries are specific to the alternative properties of octonions and cannot be extended to general Cayley-Dickson algebras, where the sedenion wavelet transform lacks the isometry property observed in the octonionic setting.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129449"},"PeriodicalIF":3.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Univariate interpolation for a class of L-splines with adjoint natural end conditions","authors":"Aurelian Bejancu,&nbsp;Mohamed Dekhil","doi":"10.1016/j.amc.2025.129417","DOIUrl":"10.1016/j.amc.2025.129417","url":null,"abstract":"<div><div>For <span><math><mn>0</mn><mo>≤</mo><mi>α</mi><mo>≤</mo><mi>β</mi></math></span>, let <span><math><mi>L</mi><mo>=</mo><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>, the Euler operator of the quadratic functional<span><span><span><math><munder><mo>∫</mo><mrow><mi>R</mi></mrow></munder><mrow><mo>{</mo><mo>|</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>(</mo><msup><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>|</mo><mi>D</mi><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>|</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>}</mo></mrow><mi>d</mi><mi>t</mi><mo>,</mo></math></span></span></span> where <em>D</em> is the first derivative operator. Given arbitrary values to be interpolated at a finite knot-set, we prove the existence of a unique <em>L</em>-spline interpolant from the natural space of functions <em>f</em>, for which the functional is finite. The natural <em>L</em>-spline interpolant satisfies adjoint differential conditions outside and at the end points of the interval spanned by the knot-set, and it is in fact the unique minimizer of the functional, subject to the interpolation conditions. This extends the approach by Bejancu (2011) for <span><math><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>=</mo><mi>β</mi></math></span>, corresponding to Sobolev spline (or Matérn kernel) interpolation. For <span><math><mn>0</mn><mo>=</mo><mi>α</mi><mo>&lt;</mo><mi>β</mi></math></span>, which is the special case of tension splines, our natural <em>L</em>-spline interpolant with adjoint end conditions can be identified as an “<span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>l</mi><mo>,</mo><mi>s</mi></mrow></msup></math></span>-spline interpolant in <span><math><mi>R</mi></math></span>” (for <span><math><mi>m</mi><mo>=</mo><mi>l</mi><mo>=</mo><mn>1</mn></math></span>, <span><math><mi>s</mi><mo>=</mo><mn>0</mn></math></span>), previously studied by Le Méhauté and Bouhamidi (1992) via reproducing kernel theory. Our <em>L</em>-spline error analysis, confirmed by numerical tests, is improving on previous convergence results for such tension splines.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129417"},"PeriodicalIF":3.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of solutions for Volterra singular integral equations in the class of differentiable functions","authors":"Wenwen Zhang,&nbsp;Pingrun Li","doi":"10.1016/j.amc.2025.129448","DOIUrl":"10.1016/j.amc.2025.129448","url":null,"abstract":"<div><div>In this paper, our purpose is to obtain the general solutions of several kinds of Volterra singular integral equations (VSIEs) in the class of differentiable functions. By constructing some operators and using the properties of integral transforms and conformal mappings, we transform VSIEs in the class of differentiable functions into the Riemann-Hilbert problems with discontinuity on a circle. By means of the principle of analytic continuation and Sokhotski-Plemelj formula, we obtain solutions of Riemann-Hilbert problems in the case of non-normal type, and further discuss the asymptotic properties of the solutions at the nodes.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129448"},"PeriodicalIF":3.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convergence analysis of a Nyström-type method for a class of nonlinear integral equations with highly oscillatory kernels","authors":"Qusay Abdulraheem Kassid,&nbsp;Saeed Sohrabi,&nbsp;Hamid Ranjbar","doi":"10.1016/j.amc.2025.129450","DOIUrl":"10.1016/j.amc.2025.129450","url":null,"abstract":"<div><div>In this paper, we present a Nyström-type method for the numerical solution of a class of nonlinear highly oscillatory Volterra integral equations with a trigonometric kernel. The implementation of this method leads to a nonlinear system that involves oscillatory integrals, which is then addressed using a two-point generalized quadrature rule to construct a fully discretized scheme. The error analysis of the method, in terms of both frequency and step length, is also presented. It is demonstrated that the proposed method outperforms the one recently introduced in the literature. To validate the method, several numerical examples are provided, confirming its efficiency and accuracy.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129450"},"PeriodicalIF":3.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interaction topology optimization by adjustment of edge weights to improve the consensus convergence and prolong the sampling period for a multi-agent system","authors":"Tongyou Xu ,&nbsp;Ying-Ying Tan ,&nbsp;Shanshan Gao ,&nbsp;Xuejuan Zhan","doi":"10.1016/j.amc.2025.129428","DOIUrl":"10.1016/j.amc.2025.129428","url":null,"abstract":"&lt;div&gt;&lt;div&gt;The second smallest eigenvalue and the largest eigenvalue of the Laplacian matrix of a simple undirected connected graph &lt;em&gt;G&lt;/em&gt; are called the algebraic connectivity &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and the Laplacian spectral radius &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, respectively. For a first-order periodically sampled consensus protocol multi-agent system (MAS), whose interaction topology can be modeled as a graph &lt;em&gt;G&lt;/em&gt;, a larger &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; results in a faster consensus convergence rate, while a smaller &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; contributes to a longer sampling period of the system. Adjusting the weights of the edges is an efficient approach to optimize the interaction topology of a MAS, which improves the consensus convergence rate and prolongs the sampling period. If &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; increases, then the weight of one edge &lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; increases, i.e., the increment &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, and the entries of its eigenvector with respect to &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; are not equal. If &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; decreases, then the weight of one edge &lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; decreases, i.e., the increment &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, and the entries of its eigenvector with respect to &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; are not equal. Moreover, when considering adjusting the weights of edges, some necessary conditions for increasing &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and decreasing &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; are also given respectively, both of which a","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129428"},"PeriodicalIF":3.5,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weak degeneracy of the square of K4-minor free graphs","authors":"Jing Ye ,&nbsp;Jiani Zou ,&nbsp;Miaomiao Han","doi":"10.1016/j.amc.2025.129439","DOIUrl":"10.1016/j.amc.2025.129439","url":null,"abstract":"<div><div>A graph <em>G</em> is called weakly <em>f</em>-degenerate with respect to a function <em>f</em> from <span><math><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> to the non-negative integers, if every vertex of <em>G</em> can be successively removed through a series of valid Delete and DeleteSave operations. The weak degeneracy <span><math><mi>w</mi><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is defined as the smallest integer <em>d</em> for which <em>G</em> is weakly <em>d</em>-degenerate, where <em>d</em> is a constant function. It was demonstrated that one plus the weak degeneracy can act as an upper bound for list-chromatic number and DP-chromatic number. Let <span><math><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>=</mo><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>+</mo><mn>2</mn></math></span> if <span><math><mn>2</mn><mo>≤</mo><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mn>3</mn></math></span>, and <span><math><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>=</mo><mo>⌊</mo><mfrac><mrow><mn>3</mn><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌋</mo></math></span> if <span><math><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mn>4</mn></math></span>. In this paper, we prove that for every <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-minor free graph <em>G</em>, <span><math><mi>w</mi><mi>d</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>≤</mo><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>, which implies that <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> is <span><math><mo>(</mo><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-choosable and <span><math><mo>(</mo><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-DP-colorable. This work generalizes the result obtained by Lih et al. in [Discrete Mathematics, 269 (2003), 303-309] and Hetherington et al. in [Discrete Mathematics, 308 (2008), 4037-4043].</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129439"},"PeriodicalIF":3.5,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling and experimental circuit implementation of fractional single-transistor chaotic oscillators","authors":"Longxiang Fu ,&nbsp;Wanting Zhu ,&nbsp;Bo Yu ,&nbsp;Yaoyao Zhang ,&nbsp;Pedro Antonio Valdes-Sosa ,&nbsp;Chunbiao Li ,&nbsp;Leonardo Ricci ,&nbsp;Mattia Frasca ,&nbsp;Ludovico Minati","doi":"10.1016/j.amc.2025.129438","DOIUrl":"10.1016/j.amc.2025.129438","url":null,"abstract":"<div><div>This study presents the first experimental realization of a single-transistor fractional chaotic oscillator, obtained by extending a minimalistic integer-order circuit by systematically transforming its reactive components, namely two inductors and a capacitor, into fractional elements. Starting from the Grünwald-Letnikov definition and using a string structure finite-order approximation for implementation, the dynamics are studied over a range of fractional orders. Results from equation models, circuit simulations, and experimental measurements are juxtaposed, yielding broadly consistent results. The introduction of fractional elements is found to have profound effects on the chaotic dynamics, influencing oscillation amplitude, spectral flatness, and bifurcation characteristics. In particular, inspection of the resulting Poincaré sections reveals a gradual distortion of the interplay between the relaxation and resonance aspects of the circuit dynamics with decreasing fractional order. While less generative than other manipulations, such as inserting fractal resonators, the ability to introduce fractional components into elementary nonlinear oscillator circuits provides a new, highly versatile, and compact physical tool. Potential applications include modeling electronically real-world phenomena endowed with considerable memory and nonlocality, such as neural activity and viscoelasticity.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129438"},"PeriodicalIF":3.5,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symmetrised fractional variation with L1 fidelity for signal denoising via Grünwald-Letnikov scheme","authors":"Alessandro Lanza ,&nbsp;Antonio Leaci ,&nbsp;Serena Morigi ,&nbsp;Franco Tomarelli","doi":"10.1016/j.amc.2025.129429","DOIUrl":"10.1016/j.amc.2025.129429","url":null,"abstract":"<div><div>We define, study and implement the model SFV-<span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>: a variational approach to signal analysis exploiting the Riemann-Liouville (RL) fractional calculus. This model incorporates an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> fidelity term alongside fractional derivatives of the right and left RL operators to act as regularizers. This approach aims to achieve an orientation-independent protocol. The model is studied in the continuous setting and discretized in one dimension by means of a second-order consistent scheme based on approximating the RL fractional derivatives by a truncated Grünwald-Letnikov (GL) scheme. The discrete optimization problem is solved using an iterative approach based on the alternating direction method of multipliers, with guaranteed convergence.</div><div>A multi-parameter whiteness criterion is introduced which provides automatic and simultaneous selection of the two free parameters in the model, namely the fractional order of differentiation and the regularization parameter. Numerical experiments on one-dimensional signals are presented which show how the proposed model holds the potential to achieve good quality results for denoising signals corrupted by additive Laplace noise.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129429"},"PeriodicalIF":3.5,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discrete Sturm-Liouville operators having the hydrogen atom potential","authors":"Seyfollah Mosazadeh ,&nbsp;Hikmet Koyunbakan","doi":"10.1016/j.amc.2025.129427","DOIUrl":"10.1016/j.amc.2025.129427","url":null,"abstract":"<div><div>In the present paper, we investigate Sturm-Liouville difference operators having <span><math><mfrac><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mi>r</mi><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math></span> type singularity. We study the properties of the eigenvalues of discrete boundary value problem and present the eigenfunction expansion. Finally, we show that the potential can be uniquely determined by the eigenvalues and weight numbers, and some numerical results are given to illustrate the main findings.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129427"},"PeriodicalIF":3.5,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exploring transient neurophysiological states through local and time-varying measures of information dynamics","authors":"Yuri Antonacci ,&nbsp;Chiara Barà ,&nbsp;Giulio de Felice ,&nbsp;Antonino Sferlazza ,&nbsp;Riccardo Pernice ,&nbsp;Luca Faes","doi":"10.1016/j.amc.2025.129437","DOIUrl":"10.1016/j.amc.2025.129437","url":null,"abstract":"<div><h3>Background</h3><div>Studying the temporal evolution of complex systems requires tools able to quantify the strength of predictable dynamics within their output signals. Among information theoretic measures, information storage (IS) reflects the regularity of system dynamics by measuring the information shared between the present and the past system states.</div></div><div><h3>Methods</h3><div>While the conventional IS computation provides an overall measure of predictable information, transient behaviors of predictability occurring during system transitions can be assessed by time resolved measures such as the local information storage (L-IS) and the time-varying information storage (TV-IS).</div></div><div><h3>Results</h3><div>TV-IS tracks sudden changes of the information stored in the system, which is reflected in its average value computed over specific time intervals; on the other hand, the surprise originated by the emergence of a change in the predictability is reflected in the variance of the L-IS computed within specific time intervals. In neurophysiological applications, the distinct phenomena of respiratory activity in sleep apnea and brain activity during somatosensory stimulation both reveal a significant decrease of IS evoked by state transitions, highlighting how such transitions can inject new information in physiological systems, affecting significantly their internal dynamics.</div></div><div><h3>Conclusions</h3><div>TV-IS and L-IS provide different and complementary information about the behavior of the systems under investigation, thereby offering valuable tools for the study of complex physiological systems where both stationary and non-stationary conditions may be present.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129437"},"PeriodicalIF":3.5,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}