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New Identities Involving Cauchy Numbers, Harmonic Numbers and Zeta Values
In this article, we present a class of identities linking together Cauchy numbers, the special values of the Riemann zeta function and its...
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Recurrence Relations of Poly-Cauchy Numbers by the r-Stirling Transform
We give some formulas of poly-Cauchy numbers by the r -Stirling transform. In the case of the classical or poly-Bernoulli numbers, the formulas are...
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Random Algebraic Numbers
A family of measures on a given set of real algebraic numbers of arbitrary fixed degree is considered. The paper presents a method for constructing a...
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Several Continued Fraction Expansions of Generalized Cauchy Numbers
We consider two types of continued fraction expansions of the generating functions of Cauchy numbers. One type has been often studied by many...
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Perturbations of non-autonomous second-order abstract Cauchy problems
In this paper we present time-dependent perturbations of second-order non-autonomous abstract Cauchy problems associated to a family of operators...
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Confidence Disc and Square for the Cauchy Distributions
We construct a confidence region of parameters for a sample of size N from the Cauchy distributed random variables. Although the Cauchy distribution...
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Cauchy Formulae and Hardy Spaces in Discrete Octonionic Analysis
In this paper, we continue the development of a fundament of discrete octonionic analysis that is associated to the discrete first order...
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Spectral Asymptotics of the Cauchy Operator and its Product with Bergman’s Projection on a Doubly Connected Domain
We found the exact asymptotics of the singular numbers for the Cauchy transform and its product with Bergman’s projection over the space
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Color image restoration with mixed Gaussian–Cauchy noise and blur
In this paper, we present a novel model for recovering color images that have been affected by mixed Gaussian Cauchy noise and blur. Our approach...
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Local Solvability, Blow-Up, and Hölder Regularity of Solutions to Some Cauchy Problems for Nonlinear Plasma Wave Equations: III. Cauchy Problems
AbstractThree Cauchy problems for Sobolev-type equations with a common linear part from the theory of ion acoustic and drift waves in a plasma are...
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Functional Asymptotics of Solutions of the Nonlinear Cauchy–Riemann–Beltrami System
We prove a series of theorems on the asymptotic behavior of regular homeomorphic solutions of the nonlinear Cauchy–Riemann–Beltrami-type equation....
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A Particular Solution for Higher Order Non-homogeneous Discrete Cauchy-Euler Equations
In this paper, we introduce a nonstandard’s method to find a particular solution for non-homogeneous discrete Cauchy-Euler equations of higher order....
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Cauchy type integrals and a boundary value problem in a complex Clifford analysis
Clifford analysis is an important branch of modern analysis; it has a very important theoretical significance and application value, and its...
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Stochastic Model of the Cauchy–Neumann Problem for Nonlinear Parabolic Equations
Stochastic equations are derived to describe reflected diffusion processes associated with the Cauchy–Neumann problem for nonlinear parabolic...
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Condition Numbers
The concept of a condition number has its origin in numerical analysis. It measures how much the output value of a function we wish to evaluate can...
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Cauchy–Binet Determinantal Identity and Enumeration of Plane Partitions in a High Box
The amplitudes of the leading asymptotics of the XX 0 Heisenberg spin chain depend on the generating function of plane partitions with the additional...
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The Cauchy–Kovalevskaya Theorem
The bulk of this chapter is devoted to the fundamental theorem in analytic PDE theory and one of the most important mathematical discoveries of the...
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Bernoulli numbers with level 2
Stirling numbers with higher level may be considered to have been introduced by Tweedie (Proc Edinb Math Soc 37:2–25, 1918). These numbers have been...