UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE NONLINEARITIES＊

This article deals with a nonlocal heat system subject to null Dirichlet boundary conditions,where the coupling nonlocal sources consist of mixed type asymmetric nonlinearities.We at first give the cri...     

密度函数垂直表示及在非均匀随机数生成中的应用

本文给出密度函数垂直表示法,以及利用该方法产生给定概率密度函数的随机向量的一般算法。     

Weak attractors for the dissipative fractional Heisenberg equation

In this short paper, we consider the long time behaviors of the fractional Heisenberg equation and the existence of a global weak attractor is proved for the shift dynamics in the path space. The key ingredient is some new type of commutator structure introduced in this paper, which seems indispensable in proving the compactness of the dynamics. The technique introduced in this paper may also be useful to other fractional order partial differential equations.     

关于微分方程解的一致非常稳定性与一致距离有界性

讨论了一般非自治方程解的一致非常稳定性与一致距离有界性.     

Generating Uniformly Distributed Random 2‐Designs with Block Size 3

Jacobson and Matthews introduced the most hopeful method known for efficiently generating uniformly distributed random Latin squares. Cameron conjectures that the same Markov chain will also generate all of the other generalized 2‐designs with block size 3 uniformly at random. For a generalization of Latin squares, we give an affirmative result for any admissible parameter values. We also give the first insight and analysis into a generalization of the 1‐factorization of the complete graph by giving an affirmative result for some admissible parameter values. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 368–380, 2012     

Controllability cost of conservative systems: resolvent condition and transmutation

This article concerns the exact controllability of unitary groups on Hilbert spaces with unbounded control operator. It provides a necessary and sufficient condition not involving time which blends a resolvent estimate and an observability inequality. By the transmutation of controls in some time L for the corresponding second-order conservative system, it is proved that the cost of controls in time T for the unitary group grows at most like exp(αL²/T) as T tends to 0. In the application to the cost of fast controls for the Schrödinger equation, L is the length of the longest ray of geometric optics which does not intersect the control region. This article also provides observability resolvent estimates implying fast smoothing effect controllability at low cost, and underscores that the controllability cost of a system is not changed by taking its tensor product with a conservative system.     

Exponential square integrability for non-tangential limits of certain smooth functions

Under the assumption of the boundedness of certain operator (resembling Lusin's area function) of a smooth function u that satisfies certain interior regularity property, we prove the exponential square integrability of the boundary values of u.     

数量特征敏感性问题调查的两个随机化回答模型

研究数量特征敏感性问题的抽样调查,设计了基于离散均匀分布和均匀分布的两个随机化回答模型     

新组合型的三角插值多项式

将被插函数进行组合平均,构造一个新组合型的三角插值多项式Cn(f;t,x),使得它在全轴上一致收敛到每个以2π为周期的连续函数,且对Cj2π连续函数类的逼近阶达到最佳,这里0jt,t为任给的奇自然数.     

Error estimates in S P for cubature formulas exact for haar polynomials in the two-dimensional case

On the spaces S _p , an upper estimate is found for the norm of the error functional δ _N (f) of cubature formulas possessing the Haar d-property in the two-dimensional case. An asymptotic relation is proved for $ \left\| {\delta _N (f)} \right\|_{S_p^* } On the spaces S _p , an upper estimate is found for the norm of the error functional δ _N (f) of cubature formulas possessing the Haar d-property in the two-dimensional case. An asymptotic relation is proved for with the number of nodes N ∼ 2 ^d , where d → ∞. For N ∼ 2 ^d with d → ∞, it is shown that the norm of δ _N for the formulas under study has the best convergence rate, which is equal to N ^−1/p . Original Russian Text ? K.A. Kirillov, M.V. Noskov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 1, pp. 3–13.