On holomorphic extension of functions on singular real hypersurfaces in ℂn by Tejinder S. Neelon

“…When n=2, we prove the following: every C1 function on Σ that satisfies the tangential Cauchy-Riemann equation on boundary of {(z,w)∈ℂ2:|z|k<P(w)}, P∈C1, P≥0 and P≢0, extends holomorphically inside provided the zero set P(w)=0 has a limit point or P(w) vanishes to infinite order. …”
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Dynamic crack propagation between two bonded orthotropic plates by M. S. Matbuly

“…Then, using Fourier transforms and asymptotic analysis, the problem is reduced to a pair of singular integral equations with Cauchy-type singularity. These equations are solved using Gauss-Chebyshev quadrature formulae. …”
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Regularization of Inverse Initial Problem for Conformable Pseudo-Parabolic Equation with Inhomogeneous Term by L. D. Long, Reza Saadati

“…The error between the regularized solution and the exact solution is obtained in Lp under some suitable assumptions on the Cauchy data.…”
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Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications by Jürgen Geiser

“…A numerical analysis is presented of the system of semidiscretised differential equations as abstract Cauchy problems. In the applications, we present benchmark and initial realistic applications to transport problems with scattering terms. …”
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Non-Integer Valued Winding Numbers and a Generalized Residue Theorem by Norbert Hungerbühler, Micha Wasem

“…The computation of this winding number relies on the Cauchy principal value but is also possible in a real version via an integral with bounded integrand. …”
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Optimal Lp–Lq-Type Decay Rates of Solutions to the Three-Dimensional Nonisentropic Compressible Euler Equations with Relaxation by Rong Shen, Yong Wang

“…In this paper, we consider the three-dimensional Cauchy problem of the nonisentropic compressible Euler equations with relaxation. …”
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LOESS WAS FORMED, BUT NOT SEDIMENTED by NICOLAE FLOREA

“…En continuation cette couche est transformée par diagenèse en loess avec ses propriétés spécifiques. …”
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Multi-Strategy Enhanced Slime Mould Algorithm for Optimization Problems by Zaixin Duan, Xuezhong Qian, Wei Song

“…An adaptive search operator leveraging the Cauchy inverse cumulative distribution is employed to dynamically adjust step sizes, improving exploration and efficiency. …”
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The trajectory-coherent approximation and the system of moments for the Hartree type equation by V. V. Belov, A. Yu. Trifonov, A. V. Shapovalov

“…The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter ℏ (ℏ→0), are constructed with a power accuracy of O(ℏ N/2), where N is any natural number. …”
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Tricomi problem and integral equations by N. B. Pleshchinskii

“…An explicit solution of the characteristic singular equation with a Cauchy kernel was obtained without involving the theory of boundary value problems for analytic functions.…”
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Qualitative results and numerical approximations of the $ (k, \psi) $-Caputo proportional fractional differential equations and applications to blood alcohol levels model by Weerawat Sudsutad, Chatthai Thaiprayoon, Aphirak Aphithana, Jutarat Kongson, Weerapan Sae-dan

“…The initial value problem in Cauchy-type under the $ (k, \psi) $-Caputo proportional fractional operators was our focus in this paper. …”
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On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements by Christian Daveau, Diane Manuel Douady, Abdessatar Khelifi

“…In this paper, we prove that the knowledge of the partial Cauchy data for this class of hyperbolic PDE on any open subset Γ of the boundary determines explicitly the coefficient c provided that c is known outside a bounded domain. …”
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Seasonal Variation in Patch Test Results with European Baseline Series by Aïcha Brahem, Haifa Aroui, Asma Gaddour, Asma Chouchene, Asma Aloui, Imen Kacem, Maher Maoua, Houda Kalboussi, Olfa ElMaalel, Souhail Chatti, Faten Dabbabi, Nejib Mrizek

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Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces by Manuel De la Sen, Erdal Karapınar

“…This paper investigates properties of convergence of distances of p-cyclic contractions on the union of the p subsets of an abstract set X defining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. …”
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Degenerate Poly-Lah-Bell Polynomials and Numbers by Taekyun Kim, Hye Kyung Kim

“…Many mathematicians studied “poly” as a generalization of the well-known special polynomials such as Bernoulli polynomials, Euler polynomials, Cauchy polynomials, and Genocchi polynomials. In this paper, we define the degenerate poly-Lah-Bell polynomials arising from the degenerate polyexponential functions which are reduced to degenerate Lah-Bell polynomials when k=1. …”
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On the Topological and Uniform Structure of Diversities by Andrew Poelstra

“…In this note, we consider the analytical properties of diversities, in particular the generalizations of uniform continuity, uniform convergence, Cauchy sequences, and completeness to diversities. …”
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Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application by A. Asif, M. Alansari, N. Hussain, M. Arshad, A. Ali

“…An important approach used in the article is, though a subset closed ball of a complete convex b-metric space is not necessarily complete, the convergence of the Cauchy sequence is confirmed in the subset closed ball. …”
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Riemann problems with non--local point constraints and capacity drop by Boris Andreianov, Carlotta Donadello, Ulrich Razafison, Massimiliano D. Rosini

“…We also give the detailed proof of some results announced in the paper [Andreianov, Donadello, Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop], which is devoted to existence and stability for a more general class of Cauchy problems subject to Lipschitz continuous non--local point constraints.…”
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VVC coded distortion prediction model based on frame-level transform coefficient modeling of generalized Gaussian distribution by Yiyin GU, Hongkui WANG, Haibin YIN

“…In versatile video coding (VVC), a variety of advanced coding tools work together to achieve excellent coding performance.Compared with high efficient video coding (HEVC), the transform coefficient distribution (TCD) of VVC has sharper peaks.In order to solve this phenomenon, the probability density function (PDF) of frame-level TCD was modeled, and a frame-level coding distortion prediction model based on statistical modeling was proposed, which modeled frame-level distortion as a function of TCD distribution parameters and quantization parameters.The experimental results show that compared with the Laplace distribution and Cauchy distribution, the generalized Gaussian distribution has the best performance in TCD probability density fitting.The prediction results based on the generalized Gaussian distribution distortion prediction model are closest to the actual coding distortion.…”
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The Global Dynamics of an Age-Structured Hand-Foot-Mouth Disease Model with Saturation Incidence and Time Delay by Dongxue Yan, Mengqi Zhang, Jiashan Tang

“…Firstly, the model is expressed as an abstract Cauchy problem. The presence of equilibria is then pointed; meanwhile, we define the model’s basic reproduction number R0. …”
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