Uniform Rectifiability, Carleson measure estimates, and approximation of harmonic functions [PDF]
, 2014 Let $E\subset \mathbb{R}^{n+1}$, $n\ge 2$, be a uniformly rectifiable set of dimension $n$. Then bounded harmonic functions in $\Omega:= \mathbb{R}^{n+1}\setminus E$ satisfy Carleson measure estimates, and are "$\varepsilon$-approximable".
S. Hofmann, J. M. Martell, S. Mayboroda
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On Harmonically (p,h,m)-Preinvex Functions
Journal of Function Spaces, 2017 We define a new generalized class of harmonically preinvex functions named harmonically (p,h,m)-preinvex functions, which includes harmonic (p,h)-preinvex functions, harmonic p-preinvex functions, harmonic h-preinvex functions, and m-convex functions as ...
Shan-He Wu +2 more
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Transformation Method for Solving System of Boolean Algebraic Equations
Mathematics, 2021 In recent years, various methods and directions for solving a system of Boolean algebraic equations have been invented, and now they are being very actively investigated. One of these directions is the method of transforming a system of Boolean algebraic
Dostonjon Barotov +6 more
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Unitary relation between a harmonic oscillator of time-dependent frequency and a simple harmonic oscillator with and without an inverse-square potential [PDF]
, 2000 The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for both cases, this
A.N. Seleznyova +26 more
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Some sharp inequalities involving Seiffert and other means and their concise proofs [PDF]
, 2012 In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic ...
Jiang, Wei-Dong, Qi, Feng
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Perturbing Rational Harmonic Functions by Poles [PDF]
, 2014 We study how adding certain poles to rational harmonic functions of the form $$R(z)-\overline{z}$$R(z)-z¯, with $$R(z)$$R(z) rational and of degree $$d\ge 2$$d≥2, affects the number of zeros of the resulting functions.
O. Sète, R. Luce, J. Liesen
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Some identities on generalized harmonic numbers and generalized harmonic functions
Demonstratio Mathematica, 2023 The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory, and analysis of algorithms.
Kim Dae San, Kim Hyekyung, Kim Taekyun
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Polylinear Transformation Method for Solving Systems of Logical Equations
Mathematics, 2022 In connection with applications, the solution of a system of logical equations plays an important role in computational mathematics and in many other areas.
Dostonjon Numonjonovich Barotov +1 more
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Boundary Integrals and Approximations of Harmonic Functions [PDF]
, 2014 Steklov expansions for a harmonic function on a rectangle are derived and studied with a view to determining an analog of the mean value theorem for harmonic functions.
Giles Auchmuty, Manki Cho
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Best Subordinant for Differential Superordinations of Harmonic Complex-Valued Functions
Mathematics, 2020 The theory of differential subordinations has been extended from the analytic functions to the harmonic complex-valued functions in 2015. In a recent paper published in 2019, the authors have considered the dual problem of the differential subordination ...
Georgia Irina Oros
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