The Experts below are selected from a list of 53568 Experts worldwide ranked by ideXlab platform
Hideki Inoue - One of the best experts on this subject based on the ideXlab platform.
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Explicit Formula for schrodinger wave operators on the half line for potentials up to optimal decay
Journal of Functional Analysis, 2020Co-Authors: Hideki InoueAbstract:Abstract We give an Explicit Formula for the wave operators for perturbations of the Dirichlet Laplacian by a potential on the half-line. The potential is assumed to decay strictly faster than the polynomial of degree minus two. The Formula consists of the main term given by the scattering operator and a function of the generator of the dilation group, and a Hilbert-Schmidt remainder term. Our method is based on the elementary construction of the generalized Fourier transforms in terms of the solutions of the Volterra integral equations. The Hilbert-Schmidt property of the remainder term follows from a decay estimate for the Jost solution, which is established by performing a perturbation expansion of sufficiently high order. As a corollary, a topological interpretation of Levinson's theorem is established via an index theorem approach.
Hidenori Katsurada - One of the best experts on this subject based on the ideXlab platform.
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an Explicit Formula for the extended gross keating datum of a quadratic form
arXiv: Number Theory, 2017Co-Authors: Sungmun Cho, Tamotsu Ikeda, Hidenori Katsurada, Chulhee Lee, Takuya YamauchiAbstract:In this paper, we give a Formula for the extended Gross-Keating datum of a quadratic form defined over a finite extension of $\mathbb{Z}_p$ (for $p>2$) or a finite unramified extension of $\mathbb{Z}_2$. As an application, we describe an Explicit Formula for the Siegel series for $\mathbb{Z}_p$. We also present the details of algorithms implemented in a Mathematica package to compute the extended Gross-Keating datum and the Siegel series.
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an Explicit Formula for the siegel series of a quadratic form over a non archimedian local field
arXiv: Number Theory, 2016Co-Authors: Tamotsu Ikeda, Hidenori KatsuradaAbstract:Let F be a non-archimedian local field of characteristic 0, and O the ring of integres in F. We give an Explicit Formula for the Siegel series of a half-integral matrix over O. This Formula expresses the Siegel series of a half-integral matrix $B$ Explicitly in terms of the Gross-Keating invariant of $B$ and its related invariants.
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an Explicit Formula for siegel series
American Journal of Mathematics, 1999Co-Authors: Hidenori KatsuradaAbstract:Combining induction Formulas for local densities with a functional equation for the Siegel series, we give an Explicit Formula for the Siegel series. By this Formula, we also give an Explicit Formula for the Fourier coefficients of the Siegel Eisenstein series.
E Minguzzi - One of the best experts on this subject based on the ideXlab platform.
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differential aging from acceleration an Explicit Formula
American Journal of Physics, 2005Co-Authors: E MinguzziAbstract:We consider a clock paradox where an observer leaves an inertial frame, is accelerated, and after an arbitrary trip returns. We discuss a simple equation that gives an Explicit relation in 1+1 dimensions between the time elapsed in the inertial frame and the acceleration measured by the accelerating observer during the trip. A non-closed trip with respect to an inertial frame appears closed with respect to another suitable inertial frame. We use this observation to define the differential aging as a function of proper time. The reconstruction problem of special relativity is discussed and it is shown that its solution would allow the construction of an inertial clock.
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Differential aging from acceleration, an Explicit Formula
American journal of physics, 2004Co-Authors: E MinguzziAbstract:We consider a clock 'paradox' framework where an observer leaves an inertial frame, is accelerated and after an arbitrary trip comes back. We discuss a simple equation that gives, in the 1+1 dimensional case, an Explicit relation between the time elapsed on the inertial frame and the acceleration measured by the accelerating observer during the trip. A non-closed trip with respect to an inertial frame appears closed with respect to another suitable inertial frame. Using this observation we define the differential aging as a function of proper time and show that it is non-decreasing. The reconstruction problem of special relativity is also discussed showing that its, at least numerical, solution would allow the construction of an 'inertial clock'.
Baini Guo - One of the best experts on this subject based on the ideXlab platform.
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an Explicit Formula for bernoulli polynomials in terms of boldsymbol r stirling numbers of the second kind
Rocky Mountain Journal of Mathematics, 2016Co-Authors: Baini Guo, Istvan MezőAbstract:In this paper, the authors establish an Explicit Formula for computing Bernoulli polynomials at nonnegative integer points in terms of $r$-Stirling numbers of the second kind.
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a new Explicit Formula for the bernoulli and genocchi numbers in terms of the stirling numbers
Global Journal of Mathematical Analysis, 2015Co-Authors: Baini GuoAbstract:In the paper, the authors concisely review some Explicit Formulas and establish a new Explicit Formula for the Bernoulli and Genocchi numbers in terms of theStirlingnumbers of the second kind.
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an Explicit Formula for bell numbers in terms of stirling numbers and hypergeometric functions
Global Journal of Mathematical Analysis, 2014Co-Authors: Baini GuoAbstract:In the paper, by two methods, the authors find an Explicit Formula for computing Bell numbers in terms of Kummer confluent hypergeometric functions and Stirling numbers of the second kind. Moreover, the authors supply an alternative proof of the well-known ``triangular'' recurrence relation for Stirling numbers of the second kind. In a remark, the authors reveal the combinatorial interpretation of the special values for Kummer confluent hypergeometric functions and the total sum of Lah numbers. Keywords: Explicit Formula; Bell number; conuent hypergeometric function of the first kind; Stirling number of the second kind; combinatorial interpretation; alternative proof; recurrence relation; polylogarithm
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a new Explicit Formula for bernoulli and genocchi numbers in terms of stirling numbers
arXiv: Number Theory, 2014Co-Authors: Baini GuoAbstract:In the paper, the authors review some Explicit Formulas and establish a new Explicit Formula for Bernoulli and Genocchi numbers in terms of Stirling numbers of the second kind.
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an Explicit Formula for bernoulli polynomials in terms of r stirling numbers of the second kind
arXiv: Combinatorics, 2014Co-Authors: Baini Guo, Istvan MezőAbstract:In the paper, the authors establish an Explicit Formula for computing Bernoulli polynomials at non-negative integer points in terms of $r$-Stirling numbers of the second kind.
Berg, Imme Van Den - One of the best experts on this subject based on the ideXlab platform.
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On the Explicit Formula for Gauss-Jordan elimination
2020Co-Authors: Van Tran Nam, Justino Julia, Berg, Imme Van DenAbstract:The elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure have the form of quotients of minors. Instead of the proof using identities of determinants of \cite{Li}, a direct proof by induction is given.Comment:
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The Explicit Formula for Gauss-Jordan elimination and error analysis
2020Co-Authors: Van Tran Nam, Justino Julia, Berg, Imme Van DenAbstract:The Explicit Formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure for the solution of systems of linear equations is applied to error analysis. Stability conditions in terms of relative uncertainty and size of determinants are given such that the Gauss-Jordan procedure leads to a solution respecting the original imprecisions in the right-hand member. The solution is the same as given by Cramer's Rule. Imprecisions are modelled by scalar neutrices, which are convex groups of (nonstandard) real numbers. The resulting calculation rules extend informal error calculus, and permit to keep track of the errors at every stage.Comment: 47 page
