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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Derivation of the Vlasov equation from quantum many-body Fermionic systems with singular interaction
奇异相互作用 量子多体 费米子系统 弗拉索夫方程
2023/5/12
We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...
Abelianizations of derivation Lie algebras of free associative algebra and free Lie algebra
moduli space of curves Lie algebra homology graph homology derivation
2011/9/14
Abstract: We determine the abelianizations of the following three kinds of graded Lie algebras in a certain stable range: derivations of the free associative algebra, derivations of the free Lie algeb...
Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
Noncommutative oscillators Hopf algebra twist deformation principles derivation
2011/3/3
Noncommutative oscillators are first-quantized through an abelian Drinfel’d twist deformation of a Hopf algebra and its action on a module. Several impor-tant and subtle issues making possible the qua...
Gauss Sums of the Cubic Character over $GF(2^m)$: an elementary derivation
Gauss sum character binary finite fields
2011/2/25
An elementary approach is shown which derives the value of the Gauss sum of a cubic char-
acter over a finite field F2s without using Davenport-Hasse’s theorem (namely, if s is odd the
Gauss sum is ...
Some remarks about the derivation operator and generalized Stirling numbers
formal power series derivation operator Stirling num-bers
2011/2/22
Studying expressions of the form (f(x)D)p, where D = d dx is the derivation operator, goes back to Scherk’s Ph.D.
On the derivation algebra of the free Lie algebra and trace maps
derivation algebra free Lie algebra trace maps
2011/1/20
In this paper, we mainly study the derivation algebra of the free Lie algebra and the Chen Lie algebra generated by the abelianization H of a free group, and trace maps.
Physical Equivalence of Pure States and Derivation of Qubit in General Probabilistic Theories
Physical Equivalence Pure States Derivation of Qubit General Probabilistic Theories
2011/3/4
In this paper, we investigate a characterization of Quantum Mechanics by two physical principles based on general probabilistic theories.
Finite derivation type property on the Chinese monoid
Chinese Monoid Finite Derivation Type
2010/9/21
Squier introduced the notion finite derivation type which is a combinatorial condition satisfied by certain rewriting systems. The main result in this paper states that the Chinese monoid has finite d...
This document derives the CPHD filter for extended targets. Only the update step is derived here. Target generated measurements, false alarms and prior are all assumed to be independent identically d...
Derivation of an integral of Boros and Moll via convolution of Student t-densities
Quartic integral Student t-density
2010/12/6
We show that the evaluation of an integral considered by Boros and Moll is a special case of a convolution result about Student t-densities obtained by the authors in 2008.
In the 1950s, the Nobel Prize winner John F. Nash has shown that under certain conditions, the best solution to the bargaining problem is when the product of the (increase in) utilities is the largest...
A unifying framework for the derivation and analysis of effective classes of one-step methods for ODEs
Ordinary differential equations Runge-Kutta methods one-step methods Hamiltonian problems
2010/12/8
In this paper, we provide a simple framework to derive and analyse several classes of effective one-step methods. The framework consists in the discretization of a local Fourier expansion of the conti...
A note on the derivation of Frechet and Gateaux
Fr´ echet differentiability Gˆ ateaux differentiability
2010/9/13
The purpose of this note is in addition to establishing Fr´echet derivatives and Gˆateuax, considering the basic different implications between them. Also be considered a counterexample of ...
Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation
twisted derivation super KdV equation quasideterminant solutions
2010/4/7
This paper is concerned with a generalized type of Darboux transformations defined in terms of a twisted derivation $D$ satisfying $D(AB)=D(A)+\sigma(A)B$ where $\sigma$ is a homomorphism. Such twiste...
Derivation of the Laplace-Beltrami operator for the zonal polynomials of positive definite Hermitian matrix argument
Laplace-Beltrami operator linear structures
2010/9/14
Some aspects of the complex linear structure theory, extending the real case due to Magnus (1988), are defined and studied. This theory provides complete proofs of conjectures given in literature arou...