对于工学硕士的《数理统计》教学的研究

工学硕士的《数理统计》教学 ,要根据工学硕士的培养目标和数理统计课程的特点编写教材、确定讲授内容和授课方式 .力求使学员掌握处理随机数据的思考方法 ,培养解决问题、分析问题和善于应用知识的能力 .改革《数理统计》教学 ,实现和普及多媒体教学是时代发展的趋势 .     

Synthesis,characterization and properties of methylaminocellulose

Homogeneously prepared tosylcelluloses (TC) with degrees of substitution (DS) of DS_Tos 0.1–1.8 were used as intermediates for the synthesis of methylaminocelluloses (MAC) by nucleophilic substitution with methylamine. TC with DS_Tos up to 1.1 were shown to be valuable intermediates for selective synthesis of MAC with DS_MA varying from 0.1 to approximately 1. No nucleophilic substitution was observed at higher DS_Tos. At the chosen reaction conditions (60 °C, 48 h) residual tosyl moieties remained unchanged and little hydrolysis took place. The samples obtained were characterized by means of elemental analysis, FTIR and ¹³C CP/MAS NMR spectroscopy. ¹³C CP/MAS NMR spectroscopy was found to be an efficient tool for quantification of DS_MA. Furthermore, the swelling behaviour in water was investigated and preliminary tests concerning the bilirubin adsorption capacity of MAC were carried out.     

Lyapunov-type inequalities for nonlinear systems

In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of differential equations, special cases of which contain the well-known equations such as Emden-Fowler-type and half-linear equations. The inequalities obtained here can be used as handy tools in the study of qualitative behaviour of solutions of the associated equations.     

Unsteady MHD flow of a non-Newtonian fluid on a porous plate

This paper deals with the study of the MHD flow of non-Newtonian fluid on a porous plate. Two exact solutions for non-torsionally generated unsteady hydromagnetic flow of an electrically conducting second order incompressible fluid bounded by an infinite non-conducting porous plate subjected to a uniform suction or blowing have been analyzed. The governing partial differential equation for the flow has been established. The mathematical analysis is presented for the hydromagnetic boundary layer flow neglecting the induced magnetic field. The effect of presence of the material constants of the second order fluid on the velocity field is discussed.     

Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation

In this paper, we prove the Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation. This is applied to investigate homomorphisms between quasi-Banach algebras. The concept of Hyers-Ulam-Rassias stability originated from Th.M. Rassias' stability theorem that appeared in his paper [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300].     

Hard collisions of spinning protons: Past,present and future

There will be a review of the history of polarized proton beams, and a discussion of the unexpected and still unexplained large transverse spin effects found in several high-energy proton-proton spin experiments at the ZGS, AGS and Fermilab. Next, there will be a discussion of present and possible future experiments on the violent elastic collisions of polarized protons at IHEP-Protvino's 70GeV U-70 accelerator in Russia and the new high-intensity 50GeV J-PARC facility being built at Tokai in Japan.     

系综分布和它的小涨落近似

由“从正则分布出发，在小涨落近似下得出的能量涨落分布公式”求得的能量涨落的二次矩与直接由正则分布求得的二次矩完全相同，但分别由二求得的高次矩并不完全相同。     

炉液倾动重心近似计算的数学分析

为给转炉设计提供依据,需要计算炉液倾动的重心.利用数学方法将实际问题进行简化,通过分析炉液倾动过程中变量间的相互关系,来确定每个倾动角度对应情况下的液面位置.利用数学中三重积分的有关应用,进一步得出转炉在每个倾动角度为α∈(0,π2)时的重心计算方法及相关结论,在理论上为工程计算重心的方法提供参考.     

Hyers–Ulam stability of linear differential operator with constant coefficients

Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anderson transition in dilute systems with pure exponential interactions

Summary Assuming a completely disordered lattice it is shown that all the states are localized when the disorder parameterx=a ₀/0 reachesthe value 0.31, wherea is the mean atomic separation anda ₀ is the Bohr radius.