Note on a Littlewood-Paley inequality

We show that a recent result of Littlewood-Paley type, due to the author, is essentially best-possible.     

加权均值T-统计量推广

本文将[1]提出的一维异方差正态总体均值的加权T-统计量估计推广到多维异方差正态总体均值的估计,并应用于其假设检验。     

Growth, Band Structure and Optical Properties of LiSrBO3 Crystal

The bulk crystal of LiSrBO3 (8.39 g) with a size of 21mm×20mm×15mm was grown by high temperature solution growth method. The relationship between growth habit and crystal structure was discussed. The transmission spectrum shows an UV absorption edge at about 300 nm. The melting temperature of this crystal was determined to be 942 ℃ by DTA-TG measurement. The band structure of the LiSrBO3 crystal was studied by means of the first principle method. An indirect band gap was found to be about 4.0 eV,and a low dielectric constant was estimated to be about 1.9 in terms of theoretical results.     

Synthesis and Crystal Structure of N-Phenylbis（ferrocenecarboxyl）imide

The ferrocenyl compound,N-phenylbis(ferrocenecarboxyl)imide (C28H23NO2Fe2,Mr=517.17),was synthesized and structurally characterized by means of X-ray single-crystal dif-fraction. It crystallizes in monoclinic,space group C2/c with a=21.374(14),b=10.430(7),c= 10.741(7) ,β=114.184(8)°,V=2184(2) 3,Z=4,Dc=1.573 g/cm3,F(000)=1064,μ(MoKα)= 1.355 mm–1,T=291(2) K,the final R=0.0548 and wR=0.1437 for 1524 observed reflections with I > 2σ(I). In this compound,the nitrogen atom links two ferrocenyl groups and one phenyl group forming a novel imido derivative.     

Are Field Derivatives Needed in Linear Constitutive Relations?

General linear constitutive relations need not contain any dependence on field derivatives, and the standard boundary conditions need not be modified. We show that the answer to the question asked as the title of this communication is therefore in the negative.     

GLOBAL BLOWUP AND BLOWUP RATE ESTIMATES OF SOLUTIONS FOR A CLASS OF NONLINEAR NON-LOCAL REACTION-DIFFUSION PROBLEMS

In this paper, the global blowup properties of solutions for a class of non-linear non-local reaction-diffusion problems are investigated by the methods of the priorestimates. Moreover, the blowup rate estimate of the solution is given.     

Convergence rate of spherical harmonic expansions of smooth functions

We extend a well-known result of Bonami and Clerc on the almost everywhere (a.e.) convergence of Cesàro means of spherical harmonic expansions. For smooth functions measured in terms of φ-derivatives on the unit sphere, we obtained the sharp a.e. convergence rate of Cesàro means of their spherical harmonic expansions.     

向径函数上的球面平均及其点态收敛性

设球面平均函数为,则当f∈LP(Rn)是向径函数, n≥3,1≤P≤n/n-1时,几乎处处成立.     

A non-smooth version of the Lojasiewicz-Simon theorem with applications to non-local phase-field systems

We consider a simple system modelling phase transition phenomena with long term interactions. It is shown that any solution converges with growing time to a single stationary state. To this end, a non-smooth version of the celebrated Simon-Lojasiewicz theorem is proved.