A Random Riemann–Liouville Integral Operator by Jorge Sanchez-Ortiz, Omar U. Lopez-Cresencio, Martin P. Arciga-Alejandre, Francisco J. Ariza-Hernandez

“…To illustrate the behavior of this operator, we present two examples involving different random variables acting on specific functions. The sample trajectories and estimated probability density functions of the resulting random integrals are then explored via Monte Carlo simulation.…”
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<i>φ</i>−Hilfer Fractional Cauchy Problems with Almost Sectorial and Lie Bracket Operators in Banach Algebras by Faten H. Damag, Amin Saif, Adem Kiliçman

“…Some examples are introduced as applications for our results in commutative real Banach algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">R</mi></semantics></math></inline-formula> and commutative Banach algebra of the collection of continuous functions in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">R</mi></semantics></math></inline-formula>.…”
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An Improved Multi-Chaotic Public Key Algorithm Based on Chebyshev Polynomials by Chunfu Zhang, Jing Bai, Yanchun Liang, Adriano Tavares, Lidong Wang, Tiago Gomes, Sandro Pinto

“…The proposed algorithm (CMPKC-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></semantics></math></inline-formula>) introduces the selective coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></semantics></math></inline-formula> based on the properties of Chebyshev polynomials, allowing the special functions that need to be negotiated in the original system to be freely and randomly chosen as Chebyshev polynomials, and can also be expanded to m levels. …”
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GSA-KAN: A Hybrid Model for Short-Term Traffic Forecasting by Zhizhe Lin, Dawei Wang, Chuxin Cao, Hai Xie, Teng Zhou, Chunjie Cao

“…The Kolmogorov–Arnold Network (KAN) has shown parameter efficiency with lower memory and computational overhead via spline-parametrized functions to handle high-dimensional temporal data. …”
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Comparing a Gauge-Invariant Formulation and a “Conventional Complete Gauge-Fixing Approach” for <i>l</i>=0,1-Mode Perturbations on the Schwarzschild Background Spacetime by Kouji Nakamura

“…This article provides a comparison of the gauge-invariant formulation for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>l</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn></mrow></semantics></math></inline-formula>-mode perturbations on the Schwarzschild background spacetime, proposed by the same author in 2021, and a “conventional complete gauge-fixing approach” where the spherical harmonic functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Y</mi><mrow><mi>l</mi><mi>m</mi></mrow></msub></semantics></math></inline-formula> as the scalar harmonics are used from the starting point. …”
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Complete Stability Analysis for Delayed Economic Systems by Jun-Xiu Chen, Gao-Xia Fan, Xu Li

“…First, we will review three types of delayed economic systems and will see that the characteristic functions are all in the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>λ</mi><mo>,</mo><mi>τ</mi><mo>)</mo></mrow></semantics></math></inline-formula>. …”
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Finite Difference/Fractional Pertrov–Galerkin Spectral Method for Linear Time-Space Fractional Reaction–Diffusion Equation by Mahmoud A. Zaky

“…For spatial discretization, spectral methods using smooth basis functions are commonly employed. However, spatial–fractional derivatives pose challenges, as they often lack guaranteed spatial smoothness, requiring non-smooth basis functions. …”
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Quantum <i>κ</i>-Entropy: A Quantum Computational Approach by Demosthenes Ellinas, Giorgio Kaniadakis

“…Also, an operational method named “the two-temperatures protocol” is introduced that provides a way to obtain the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>κ</mi></semantics></math></inline-formula>-entropy in terms of the partition functions of two auxiliary Gibbs states with temperatures <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>κ</mi></semantics></math></inline-formula>-shifted above, the hot-system, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>κ</mi></semantics></math></inline-formula>-shifted below, the cold-system, with respect to the original system temperature. …”
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On Diophantine Equations 2^<i>x</i> ± (2^<i>k</i><i>p</i>)^<i>y</i> = <i>z</i>² and −2^<i>x</i> + (2^<i>k</i>3)<sup><i>... by Yuan Li, Torre Lloyd, Angel Clinton

“…In this paper, we solve three Diophantine equations: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>2</mn><mi>x</mi></msup><mo>±</mo><msup><mrow><mo>(</mo><msup><mn>2</mn><mi>k</mi></msup><mi>p</mi><mo>)</mo></mrow><mi>y</mi></msup><mo>=</mo><msup><mi>z</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><msup><mn>2</mn><mi>x</mi></msup><mo>+</mo><msup><mrow><mo>(</mo><msup><mn>2</mn><mi>k</mi></msup><mn>3</mn><mo>)</mo></mrow><mi>y</mi></msup><mo>=</mo><msup><mi>z</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>≥</mo><mn>0</mn></mrow></semantics></math></inline-formula> and prime <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>≡</mo><mo>±</mo><mn>3</mn></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mspace width="4.44443pt"></mspace><mo>(</mo><mo form="prefix">mod</mo><mspace width="0.277778em"></mspace><mn>8</mn><mo>)</mo></mrow></semantics></math></inline-formula>. …”
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Learning Parameter Dependence for Fourier-Based Option Pricing with Tensor Trains by Rihito Sakurai, Haruto Takahashi, Koichi Miyamoto

“…In this study, we focus on another usage of the tensor train, which is to compress functions, including their parameter dependence. Here, we propose a pricing method, where, by a tensor train learning algorithm, we build tensor trains that approximate functions appearing in FT-based option pricing with their parameter dependence and efficiently calculate the option price for the varying input parameters. …”
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Towards Sustainable Energy Solutions: Evaluating the Impact of Floating PV Systems in Reducing Water Evaporation and Enhancing Energy Production in Northern Cyprus by Youssef Kassem, Hüseyin Gökçekuş, Rifat Gökçekuş

“…These distribution functions are compared with common distribution functions to assess their suitability. …”
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Complex Techniques of Dialogicity in Author’s Speech of V. M. Shukshin’s Stories-Essays by G. V. Kukueva

“…The object of the research is the author’s speech; the subject of the research is the complex methods of dialogicity functioning in the speech part of the narrator of short stories-essays. …”
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Existence and Uniqueness Analysis for (<i>k</i>, <i>ψ</i>)-Hilfer and (<i>k</i>, <i>ψ</i>)-Caputo Sequential Fractional Differential Equations and Inclusions with Non-Separated Bou... by Furkan Erkan, Nuket Aykut Hamal, Sotiris K. Ntouyas, Jessada Tariboon

“…This paper investigates the existence and uniqueness of solutions to a class of sequential fractional differential equations and inclusions involving the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>k</mi><mo>,</mo><mi>ψ</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>-Hilfer and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>k</mi><mo>,</mo><mi>ψ</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>-Caputo derivatives under non-separated boundary conditions. …”
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Multiple Solutions of Fractional Kazdan–Warner Equation for Negative Case on Finite Graphs by Liang Shan, Yang Liu

“…Our main focus lies in analyzing the nonlinear equation defined on a finite graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>w</mi><mo>)</mo></mrow></semantics></math></inline-formula>: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mo>(</mo><mo>−</mo><mo>Δ</mo><mo>)</mo></mrow><mi>s</mi></msup><mi>u</mi><mo>=</mo><mrow><mo>(</mo><mi>K</mi><mo>+</mo><mi>λ</mi><mo>)</mo></mrow><msup><mi>e</mi><mrow><mn>2</mn><mi>u</mi></mrow></msup><mo>−</mo><mi>κ</mi><mspace width="1.em"></mspace><mi>in</mi><mspace width="4pt"></mspace><mi>V</mi><mo>,</mo></mrow></semantics></math></inline-formula> where the fraction <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> and real parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> are given, and the graph functions <i>K</i> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>κ</mi></semantics></math></inline-formula> satisfy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>max</mi><mrow><mi>x</mi><mo>∈</mo><mi>V</mi></mrow></msub><mi>K</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>≢</mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>∫</mo><mi>V</mi></msub><mi>κ</mi><mi>d</mi><mi>μ</mi><mo><</mo><mn>0</mn></mrow></semantics></math></inline-formula>. …”
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A Fractional PDE-Based Model for Nerve Impulse Transport Solved Using a Conforming Virtual Element Method: Application to Prosthetic Implants by Zaffar Mehdi Dar, Chandru Muthusamy, Higinio Ramos

“…The main objective of this study is to present a fundamental mathematical model for nerve impulse transport, based on the underlying physical phenomena, with a straightforward application in describing the functionality of prosthetic devices. The governing equation of the resultant model is a two-dimensional nonlinear partial differential equation with a time-fractional derivative of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>. novel and effective numerical approach for solving this fractional-order problem is constructed based on the virtual element method. …”
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Implementation of Autonomous Navigation for Solar-Panel-Cleaning Vehicle Based on YOLOv4-Tiny by Wen-Chang Cheng, Xu-Dong Chen

“…By tuning the PID controller parameters, the system achieved an optimal performance, with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi>P</mi></mrow></msub></mrow></semantics></math></inline-formula> = 11, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></semantics></math></inline-formula> = 0.01, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></semantics></math></inline-formula> = 30, maintaining the average value of the error <i>e</i>(<i>t</i>) at −0.0412 and the standard deviation at 0.1826 and improving the inference speed. …”
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Existence and Uniqueness of Fixed-Point Results in Non-Solid <i>C</i>^⋆-Algebra-Valued Bipolar <i>b</i>-Metric Spaces by Annel Thembinkosi Bokodisa, Maggie Aphane

“…We define and analyze <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>F</mi><mi mathvariant="script">H</mi></msub><mo>−</mo><msub><mi>G</mi><mi mathvariant="script">H</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula>-contractions, utilizing positive monotone functions to extend classical contraction principles. …”
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Optimal Regional Control of a Time-Fractional Spatiotemporal SIR Model with Vaccination and Treatment Strategies by Marouane Karim, Issam Khaloufi, Soukaina Ben Rhila, Mahmoud A. Zaky, Maged Z. Youssef, Mostafa Rachik

“…In this study, we analyze a time-fractional spatiotemporal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>I</mi><mi>R</mi><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula> model in a specific area <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo></semantics></math></inline-formula>. …”
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The Bottleneck in the Scalar Dissipation Rate Spectra: Dependence on the Schmidt Number by Paolo Orlandi

“…To comprehend the flow structures responsible for the bottleneck, visualizations of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>θ</mi><msup><mo>∇</mo><mn>2</mn></msup><mi>θ</mi></mrow></semantics></math></inline-formula> and probability density functions at various <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>c</mi></mrow></semantics></math></inline-formula> values are presented and compared with those of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>u</mi><mi>i</mi></msub><msup><mo>∇</mo><mn>2</mn></msup><msub><mi>u</mi><mi>i</mi></msub></mrow></semantics></math></inline-formula>. …”
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Gauge-Invariant Perturbation Theory on the Schwarzschild Background Spacetime Part I: Formulation and Odd-Mode Perturbations by Kouji Nakamura

“…Due to this situation, we propose a strategy of a gauge-invariant treatment of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>l</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn></mrow></semantics></math></inline-formula> mode perturbations through the decomposition of the metric perturbations by singular harmonic functions at once and the regularization of these singularities through the imposition of the boundary conditions to the Einstein equations. …”
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