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Averaging principle for quasi-linear parabolic PDE’s and related diffusion processes
Quasi linear disturbance two dimensional flow parabola and small parameter
2015/9/28
Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding parabolic PDE’s with a small parameter at the second order derivatives are considered in th...
Di€usion approximation for nonparametric autoregression
Nonparametric experiments de® ciency distance likelihood ratio process stochastic di€ erential equation autoregression di€ usion sampling asymptotic su ciency
2015/8/25
A nonparametric statistical model of small di€usion type is compared with its discretization by a stochastic Euler di€erence scheme. It is shown that the discrete and continuous models are a...
2014年8月8日下午，国际著名数学家、阿贝尔奖获得者安德烈·塞迈雷迪（Endre Szemerédi）到访北大北京国际数学研究中心，并在数学中心报告厅作题为“子集合问题（On Subset Sums）”的学术报告。学术报告由数学科学学院院长、国际数学研究中心主任田刚院士主持。
A Critical Exponent of Fujita Type for a Nonlinear Reaction-Di usion System on Riemannian Manifold
critical exponent reaction-di usion system Riemannian manifold.
2018/4/19
In this paper, we study the global existence and nonexistence of positive solutions to the
following nonlinear reaction-di usion system
8>>>>>>>>>>>><
>>>>>>>>>>>>:
ut u = W(x)vp + S(x...
Endre Szemerédi荣获2012年度阿贝尔奖
Endre Szemerédi 荣获 2012年度 阿贝尔奖 数论
2012/3/22
匈牙利数学家Endre Szemerédi由于“在离散数学和理论计算机科学方面的根本性贡献，以及这些贡献对堆垒数论和遍历理论方面产生的深刻而持久的影响”而荣获2012年度阿贝尔奖。他最重要的成果之一是Szemerédi定理，该定理表明，对于任何具有正密度的整数集合，存在任意长的算术级数。Szemerédi是匈牙利科学院阿尔弗雷德·莱利数学研究所终身研究员、新泽西州罗格斯大学计算机科学讲座教授。阿贝...
Sparse Di®erential Resultant
Sparse di erential resultant di erentially essential system degree bound single exponential algorithm
2013/9/9
In this paper, the concept of sparse di®erential resultant for a di®erentially essential system of di®erential polynomials is introduced and its properties are proved.In particular, a d...
A new algorithm for computing the multivariate Faà di Bruno's formula
multivariate composite function Fa`a di Bruno’s formula multivariate cumulant
2011/3/1
A new algorithm for computing the multivariate Fa`a di Bruno’s formula is provided.We use a symbolic approach based on the classical umbral calculus that turns the computation of the multivariate Fa`a...
A new algorithm for computing the multivariate Faà di Bruno's formula
algorithm computing multivariate Faà di Bruno's formula
2011/1/4
A new algorithm for computing the multivariate Fa\`a di Bruno's formula is provided. We use a symbolic approach based on the classical umbral calculus that turns the computation of the multivariate Fa...
The polynomial multidimensional Szemerédi Theorem along shifted primes
Arithmetic progressions higher degree uniformity multiple recurrence
2010/12/1
If ~q1, . . . , ~qm: Z → Zℓ are polynomials with zero constant terms and E ⊂Zℓ has positive upper Banach density, then we show that the set E ∩ (E − ~q1(p − 1)) ∩. . .∩(E...
Ritt-Wu's Characteristic Set Method For Ordinary Di®erence Polynomial Systems With Arbitrary Ordering
dierence polynomial ascending chain characteristic set Ritt-Wu's zero decomposition theorem
2013/9/9
In this paper, a new Ritt-Wu's characteristic set method for ordinary di®erence systems is proposed, which is valid for any admissible ordering. New deˉnition for irreducible chains and new zero ...
A Characteristic Set Method For Ordinary Di®erence Polynomial Systems
di® erence polynomial ascending chain characteristic set coherence irreducibility zero decomposition theorem automated theorem proving
2013/9/9
We prove several basic properties for di®erence ascending chains including a necessary and su±cient condition for an ascending chain to be the characteristic set of its saturation ideal and a nec...
Decomposition of Ordinary Di®erence Polynomials
Functional decomposition dierence polynomial dierence operator dierence degree.
2013/9/9
In this paper, we present an algorithm to decompose ordinary nonlinear dierence polynomials with rational functions as coe±cients. The algorithm provides an eective reduction of the decomposition of d...
Viability Results for Nonautonomous DiÞerential Inclusions
Viability Results Nonautonomous DiÞ erential Inclusions
2009/1/19
We obtain measurable viability results for the diÞerential inclusion y0(t) 2 F(t; y(t)) via the approximation of F through the Aumann integral means. The admissibility of a preorder is also stud...
The di®erence of the variance functions between two estimated responses for a fourth order rotatable design in two dimensions
variance functions estimated responses rotatable design
2009/1/4
In this paper the di®erence of the variance functions between
two estimated responses for a fourth order design at any two points in the
factor space is developed. In particular, the variance fu...
Solution of the system of di®erential equations related to Marangoni convections in one °uid layer
Navier-Stokes equation Chebyshev polynomials Magnetic equations Marangoni Convections Magnetic ¯ eld and Solute Non-dimensionalization
2009/1/4
A linear stability analysis applied to a system consisting of a
horizontal layers which contains conducting °uid, a®ected by uniform ver-
tical magnetic ¯eld and solute, the °uid with unifo...