The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Shimin Zhang - One of the best experts on this subject based on the ideXlab platform.
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Two rapidly Convergent Series for calculating the interaction energies between two dissimilar double layers for Na2SO4 or CaCl2 types asymmetric electrolytes at y0 > 0 > yd ≥ −y0
Colloid Journal, 2020Co-Authors: Shimin Zhang, Jianghong JiangAbstract:Two rapidly Convergent Series for calculating the interaction energies between two dissimilar double layers for Na2SO4 or CaCl2 types asymmetric electrolytes at y0 > 0 > yd ≥ −y0 were derived, the number of the Series terms required to obtain the interaction energies with six significant digits is not more than 4 when the dimensionless surface potential of two dissimilar double layers changes from −20 to + 20. The absolute values of the interaction energies V between two dissimilar double layers for Na2SO4, CaCl2 and NaCl types electrolytes obey the following relations: when −yd = y0, V′Na2SO4 = V′CaCl2; when −yd > y0, V′Na2SO4 > V′CaCl2; when −yd < y0, V′Na2SO4 < V′CaCl2; V′Na2SO4 or V′CaCl2 is always less than V′NaCl. Several approximate expressions were given for interaction energy at y0 and −yd ≪ 1.
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a rapidly Convergent Series for calculation of the interaction between two similar plane double layers for na2so4 type asymmetric electrolytes at positive surface potential
Journal of Colloid and Interface Science, 2006Co-Authors: Shimin ZhangAbstract:Abstract A rapidly Convergent Series for calculation of the interaction energies between two similar plane double layers for Na2SO4 type asymmetric electrolytes at positive surface potential was obtained by introducing a parameter λ into an elliptical integral. When the dimensionless surface potential is less or equal to 20, the number of the Series terms required to obtain the interaction energies with six significant digits is not more than 2. The accurate numeral results were given and they can be used to check up the validity of approximate expressions obtained. The present results are also fit for CaCl2 type asymmetric electrolytes at negative surface potential.
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RAPIDLY Convergent Series FOR THE COMPUTATION OF THE INTERACTION BETWEEN DISSIMILAR PLANE PARALLEL DOUBLE-LAYER (y0 > 0 > yd ≥ -y0)
Surface Review and Letters, 2005Co-Authors: Shimin ZhangAbstract:Several rapidly-Convergent Series for the computation of the interaction energy between dissimilar plane parallel double layers (y0 > 0 > yd ≥ -y0) are derived by expanding the interaction energy in the power Series of ω0[ω0
Jacek Marchwicki - One of the best experts on this subject based on the ideXlab platform.
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levy steinitz theorem and achievement sets of conditionally Convergent Series on the real plane
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Szymon Glab, Jacek MarchwickiAbstract:Abstract Levy–Steinitz theorem characterizes the sum range of conditionally Convergent Series, that is a set of all its Convergent rearrangements; in finitely dimensional spaces – it is an affine subspace. An achievement of a Series is a set of all its subsums. We study the properties of achievement sets of Series whose sum range is the whole plane. It turns out that it varies on the number of Levy vectors of a Series.
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Levy–Steinitz theorem and achievement sets of conditionally Convergent Series on the real plane
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Szymon Gła̧b, Jacek MarchwickiAbstract:Abstract Levy–Steinitz theorem characterizes the sum range of conditionally Convergent Series, that is a set of all its Convergent rearrangements; in finitely dimensional spaces – it is an affine subspace. An achievement of a Series is a set of all its subsums. We study the properties of achievement sets of Series whose sum range is the whole plane. It turns out that it varies on the number of Levy vectors of a Series.
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Subsums of conditionally Convergent Series in finite dimensional spaces
arXiv: Functional Analysis, 2018Co-Authors: Jacek Marchwicki, Vaclav VlasakAbstract:An achievement set of a Series is a set of all its subsums. We study the properties of achievement sets of conditionally Convergent Series in finite dimensional spaces. The purpose of the paper is to answer some of the open problems formulated in \cite{GM}. We obtain general results for Series with harmonic-like coordinates, that is $A((-1)^{n+1}n^{-\alpha_1},\dots,(-1)^{n+1}n^{-\alpha_d})=\mathbb{R}^d$ for pairwise distinct numbers $\alpha_1,\dots,\alpha_d\in(0,1]$. For $d=2$, $\alpha_1=1, \alpha_2=\frac{1}{2}$ it was stated as an open problem in \cite{GM}, that is $A(\frac{(-1)^n}{n},\frac{(-1)^n}{\sqrt{n}})=\mathbb{R}^2$.
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levy steinitz theorem and achievement sets of conditionally Convergent Series on the real plane
arXiv: Functional Analysis, 2017Co-Authors: Szymon Glab, Jacek MarchwickiAbstract:Levy-Steinitz theorem characterize sum range of conditionally Convergent Series, that is a set of all its Convergent rearrangements; in finitely dimensional spaces -- it is an affine subspace. An achievement of a Series is a set of all its subsums. We study the properties of achievement sets of Series whose sum range is the whole plane. It turns out that it varies on the number of Levy vectors of a Series.
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achievement sets of conditionally Convergent Series
arXiv: Functional Analysis, 2016Co-Authors: Artur Bartoszewicz, Szymon Glab, Jacek MarchwickiAbstract:Considering the sets of subsums of Series (or achievement sets) we show that for conditionally Convergent Series the multidimensional case is much more complicated than that of the real line. Although we are far from the full topological classification of such sets, we present many surprising examples and catch the ideas standing behind them in general theorems.
Szymon Glab - One of the best experts on this subject based on the ideXlab platform.
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levy steinitz theorem and achievement sets of conditionally Convergent Series on the real plane
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Szymon Glab, Jacek MarchwickiAbstract:Abstract Levy–Steinitz theorem characterizes the sum range of conditionally Convergent Series, that is a set of all its Convergent rearrangements; in finitely dimensional spaces – it is an affine subspace. An achievement of a Series is a set of all its subsums. We study the properties of achievement sets of Series whose sum range is the whole plane. It turns out that it varies on the number of Levy vectors of a Series.
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levy steinitz theorem and achievement sets of conditionally Convergent Series on the real plane
arXiv: Functional Analysis, 2017Co-Authors: Szymon Glab, Jacek MarchwickiAbstract:Levy-Steinitz theorem characterize sum range of conditionally Convergent Series, that is a set of all its Convergent rearrangements; in finitely dimensional spaces -- it is an affine subspace. An achievement of a Series is a set of all its subsums. We study the properties of achievement sets of Series whose sum range is the whole plane. It turns out that it varies on the number of Levy vectors of a Series.
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achievement sets of conditionally Convergent Series
arXiv: Functional Analysis, 2016Co-Authors: Artur Bartoszewicz, Szymon Glab, Jacek MarchwickiAbstract:Considering the sets of subsums of Series (or achievement sets) we show that for conditionally Convergent Series the multidimensional case is much more complicated than that of the real line. Although we are far from the full topological classification of such sets, we present many surprising examples and catch the ideas standing behind them in general theorems.
Zhang Shimin - One of the best experts on this subject based on the ideXlab platform.
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A rapidly Convergent Series for calculation of the interaction between two similar plane double-layers for z+/z- = -2 asymmetric electrolytes at positive surface potential.
Journal of colloid and interface science, 2006Co-Authors: Zhang ShiminAbstract:A rapidly Convergent Series for calculation of the interaction energies between two similar plane double-layers for z+/z- = -2 asymmetric electrolytes at positive surface potential are obtained by introducing a parameter lambda in elliptical integral. When dimensionless surface potential is less or equal to 20, the number of the Series terms required to obtain the interaction energies with six significant digits are not more than 4. The accurate numeral results are given and they can be used to check up the validity of approximate expressions people obtain. The present results are also fit for z+/z- = -1/2 asymmetric electrolytes at negative surface potential.
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Rapidly Convergent Series for the Computation of the Interaction Energy between Dissimilar Plane Parallel Double Layers
Colloid Journal, 2005Co-Authors: Zhang ShiminAbstract:Several rapidly Convergent Series for the computation of the interaction energy between dissimilar plane double layers (y0 > yd > 0) are derived by expanding the interaction energy in the power Series of ω 0 < tanh(y0/64), the Series terms required to obtain the interaction energy with six significant digits do not exceed 1 except C = 2 when the dimensionless surface potential y0 ≤ 20. The results of Devereux and de Bruyn are discovered to be incorrect when y0 and yd are larger, and ξ d is very large or close to −2.00000.
Hirofumi Tsumura - One of the best experts on this subject based on the ideXlab platform.
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A certain class of rapidly Convergent Series representations for ζ(2n+1)
Journal of Computational and Applied Mathematics, 2020Co-Authors: H. M. Srivastava, Hirofumi TsumuraAbstract:AbstractFor a natural number n, the authors propose and develop three new Series representations for the Riemann Zeta function ζ(2n+1). The infinite Series occurring in each of these three representations for ζ(2n+1) converges remarkably faster than that in Wilton's result. Furthermore, one of the three Series representations for ζ(2n+1) involves the most rapidly Convergent Series among all the hitherto known members of the family of Series representations considered here. Relevant connections of the results presented in this paper with many other known Series representations for ζ(2n+1) are also briefly indicated
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Inductive construction of rapidly Convergent Series representations for ?(2>n> + 1)
International Journal of Computer Mathematics, 2003Co-Authors: Hari M. Srivastava, Hirofumi TsumuraAbstract:For a natural number n, the authors propose and develop a method of inductive construction of several (presumably new) rapidly Convergent Series representations for the values of the Riemann Zeta function ζ(2n + 1). Under a certain assumption, the various Series representations for ζ(2n + 1), which are derived here by using this method, converge remarkably rapidly with their general terms having the order estimate: O(k −2n−m · 2−2k ) (k → ∞), where m is an arbitrary natural number. Numerical and symbolic computational aspects of some of the results presented here are also considered.
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a certain class of rapidly Convergent Series representations for z 2n 1
Journal of Computational and Applied Mathematics, 2000Co-Authors: H. M. Srivastava, Hirofumi TsumuraAbstract:Abstract For a natural number n, the authors propose and develop three new Series representations for the Riemann Zeta function ζ(2n+1). The infinite Series occurring in each of these three representations for ζ(2n+1) converges remarkably faster than that in Wilton's result. Furthermore, one of the three Series representations for ζ(2n+1) involves the most rapidly Convergent Series among all the hitherto known members of the family of Series representations considered here. Relevant connections of the results presented in this paper with many other known Series representations for ζ(2n+1) are also briefly indicated.
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A certain class of rapidly Convergent Series representations for z(2n+1)
Journal of Computational and Applied Mathematics, 2000Co-Authors: Hari M. Srivastava, Hirofumi TsumuraAbstract:Abstract For a natural number n, the authors propose and develop three new Series representations for the Riemann Zeta function ζ(2n+1). The infinite Series occurring in each of these three representations for ζ(2n+1) converges remarkably faster than that in Wilton's result. Furthermore, one of the three Series representations for ζ(2n+1) involves the most rapidly Convergent Series among all the hitherto known members of the family of Series representations considered here. Relevant connections of the results presented in this paper with many other known Series representations for ζ(2n+1) are also briefly indicated.