The Experts below are selected from a list of 112614 Experts worldwide ranked by ideXlab platform
Lin Xin - One of the best experts on this subject based on the ideXlab platform.
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Some identities related to Riemann zeta-function
Journal of Inequalities and Applications, 2016Co-Authors: Lin XinAbstract:It is well known that the Riemann zeta-function $\zeta(s)$ plays a very important role in the study of analytic number theory. In this paper, we use the Elementary Method and some new inequalities to study the computational problem of one kind of reciprocal sums related to the Riemann zeta-function at the integer point $s\geq2$ , and for the special values $s=2, 3$ , we give two exact identities for the integer part of the reciprocal sums of the Riemann zeta-function. For general integer $s\geq4$ , we also propose an interesting open problem.
Piotr Puchala - One of the best experts on this subject based on the ideXlab platform.
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an Elementary Method of calculating an explicit form of young measures in some special cases
Optimization, 2014Co-Authors: Piotr PuchalaAbstract:We present an Elementary Method of explicit calculation of Young measures for a certain class of functions. This class contains, in particular, functions of a highly oscillatory nature which appear in optimization problems and homogenization theory. In engineering such situation occurs, for instance, in nonlinear elasticity (solid–solid phase transition in certain elastic crystals). Young measures associated with oscillating minimizing sequences gather information about their oscillatory nature and therefore about underlying microstructure. The Method presented in this article makes no use of functional analytic tools. There is no need to use a generalized version of the Riemann–Lebesgue lemma and to calculate weak* limits of functions. The main tool is the change of variable theorem. The Method applies both to sequences of periodic and nonperiodic functions.
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an Elementary Method of calculating an explicit form of young measures in some special cases
arXiv: Functional Analysis, 2011Co-Authors: Piotr PuchalaAbstract:We present an Elementary Method of explicit calculation of Young measures for certain class of functions. This class contains in particular functions of a highly oscillatory nature which appear in optimization problems and homogenization theory. In engineering such situation occurs for instance in nonlinear elasticity (solid-solid phase transition in certain elastic crystals). Young measures associated with oscillating minimizing sequences gather information about their oscillatory nature and therefore about underlying microstructure. The Method presented in the paper makes no use of functional analytic tools. There is no need to use generalized version of the Riemann {Lebesgue lemma and to calculate weak* limits of functions. The main tool is the change of variable theorem. The Method applies both to sequences of periodic and nonperiodic functions.
Wei Zu Chen - One of the best experts on this subject based on the ideXlab platform.
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a stochastic dynamics simulation study associated with hydration force and friction memory effect
Journal of Physical Chemistry B, 2000Co-Authors: Benzhuo Lu, Cun Xin Wang, Wei Zu ChenAbstract:A new simulation approach for combining hydration force with generalized Langevin dynamics is developed in this paper. The exponential model is taken for the friction kernel. The hydration force determined by the boundary Elementary Method is taken into account as the mean force terms of the solvent, including the Coulombic interactions with the induced surface charge and the surface pressure of solvent. All simulations were performed on cyclic undecapeptide cyclosporin A (CPA). The simulation results obtained using the new Method were analyzed and compared with those obtained using other Methods, such as molecular dynamics simulations, generalized Langevin dynamics simulations, and conventional stochastic dynamics simulations. We found that the results obtained with the new Method presented in this study show obvious improvements over the other simulation techniques and that the hydration force and friction relaxation together contribute to this improvement.
Reeb David - One of the best experts on this subject based on the ideXlab platform.
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A refinement of Reznick's Positivstellensatz with applications to quantum information theory
HAL CCSD, 2020Co-Authors: Müller-hermes Alexander, Nechita Ion, Reeb DavidAbstract:25 pages, many figuresIn his solution of Hilbert's 17th problem Artin showed that any positive definite polynomial in several variables can be written as the quotient of two sums of squares. Later Reznick showed that the denominator in Artin's result can always be chosen as an $N$-th power of a linear form and gave explicit bounds on $N$. By using concepts from quantum information theory (such as partial traces, optimal cloning maps, and an identity due to Chiribella) we give simpler proofs and minor improvements of both real and complex versions of this result. Moreover, we discuss constructions of Hilbert identities using Gaussian integrals and we review an Elementary Method to construct complex spherical designs. Finally, we apply our results to give improved bounds for exponential de Finetti theorems in the real and in the complex setting
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A refinement of Reznick's Positivstellensatz with applications to quantum information theory
2019Co-Authors: Müller-hermes Alexander, Nechita Ion, Reeb DavidAbstract:In his solution of Hilbert's 17th problem Artin showed that any positive definite polynomial in several variables can be written as the quotient of two sums of squares. Later Reznick showed that the denominator in Artin's result can always be chosen as an $N$-th power of a linear form and gave explicit bounds on $N$. By using concepts from quantum information theory (such as partial traces, optimal cloning maps, and an identity due to Chiribella) we give simpler proofs and minor improvements of both real and complex versions of this result. Moreover, we discuss constructions of Hilbert identities using Gaussian integrals and we review an Elementary Method to construct complex spherical designs. Finally, we apply our results to give improved bounds for exponential de Finetti theorems in the real and in the complex setting.Comment: 25 pages, many figure
Masato Wakayama - One of the best experts on this subject based on the ideXlab platform.
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A variation of Euler's approach to values of the Riemann zeta function
arXiv: Quantum Algebra, 2002Co-Authors: Masanobu Kaneko, Nobushige Kurokawa, Masato WakayamaAbstract:An Elementary Method of computing the values at negative integers of the Riemann zeta function is presented. The principal ingredient is a new q-analogue of the Riemann zeta function. We show that for any argument other than 1 the classical limit of this q-analogue exists and equals the value of the Riemann zeta.
