相邻平方数之间至少存在两个质数的证明

利用点列光照投影原理找到的质数分布规律,证明了相邻平方数之间至少存在两个质数的杰波夫猜想.     

Influence of (phospho)lipases on properties of mica supported phospholipid layers

The effect of enzymes: lipase from Candida cylindracea (L_Cc), phospholipase A₂ from hog pancreas (PLA₂) and phospholipase C from Bacillus cereus (PLC) to modulate wetting properties of solid supported phospholipid bilayers was studied via advancing and receding contact angle measurements of water, formamide and diiodomethane, and calculation of the surface free energy and its components from van Oss et al. (LWAB) and contact angle hysteresis (CAH) approaches. Simultaneously, topography of the studied layers was determined by Atomic Force Microscopy (AFM). The investigated lipid bilayers were transferred on mica plates from subphase of pure water by means of Langmuir-Blodgett and Langmuir-Schaefer techniques. The investigated phospolipid layers were: saturated DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine), unsaturated DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine), and their mixture DPPC/DOPC. The obtained results revealed that the lipid membrane degradation by the enzymes caused increase in its surface free energy due to the amphiphilic hydrolysis products, which may accumulate in the lipid bilayer. In result activity of the enzymes may increase and then break down the bilayer structure takes place. It is likely that after dissolution of the hydrolysis reaction products in the bulk phase, patches of bare mica surface are accessible, which contribute to the apparent surface free energy changes. Comparison of AFM images and the free energy changes of the layers gives better insight into changes of their properties. The observed gradual increase in the layer surface free energy allows controlling of the hydrolysis process to obtain the surfaces of defined properties.     

Elementary equivalence for the lattices of subalgebras and automorphism groups of free algebras

We find an elementary equivalence criterion for the lattices of subalgebras of free algebras in regular varieties. The question is addressed of elementary equivalence for the automorphism groups of algebras of this type.     

最高阶元素个数为40的非可解群的分类

设$\varphi$为群${\rm Aut}(N)$的同态,记$H_\varphi\times N$为群$N$借助于群$H$的半直积.设$G$为有限不可解群,本文证明: 若$G$中最高阶元素个数为40, 则$G$同构于下列群之一:(1)~$Z_{4\varphi}\times A_5$,\,${\rm ker}\varphi=Z_2$; (2)~$D_{8\varphi}\times A_5,\,{\rm ker}\varphi=Z_2\times Z_2$; (3)~$G/N=S_5$, $N=Z(G)=Z_2$; (4)~$G/N=S_5$, $N=Z_2\times Z_2,\,N\cap Z(G)=Z_2$.     

带有Radon-Nikodym导数的算子值自由Fisher信息量

本文研究了带有Radon-Nikodym导数的算子值自由Fisher信息量.利用模框架理论,得到了一个半圆元和一个子代数之间的合并自由关系,推广了D.Voiculescu等人的工作.     

3150新闻纸机干燥部提速适应性改造

国产3150新闻纸机干燥部车速从550米／分提高到700米／分存在主要问题：一是纸页横幅水份不均匀波动值大于40％；二是转动负荷增大超载跳停。改造的主要内容是转动件校平衡、提高联动齿轮箱的组装精度、增强烘缸内冷凝水及时排出的功能。     

一类四元环上常循环码是自由码的充要条件

本文研究了环F2 uF2上的奇长度的循环码和(1 u)-循环码.运用代数方法,得到了F2 uF2上的循环码和(1 u)-循环码成为自由码的几个充要条件.推广了Bonnecaze(1999)和Aydin(2002)的关于自由码的结果.     

漂浮载体弹性机械臂动力学控制

导出了漂浮载体弹性机械臂系统约束方程和动力学方程，利用逐次近似法讨论了机械臂结构弹性和负载位姿的影响，提出消除弹性影响的控制方法，并通过算例加以说明。     

C_(60)晶体生长初探

:C60单晶的制备是一个动力学过程,与许许多多的因素有关,很小的微扰就可能直接影响到单晶的成核与长大的形状.本文试图用单晶生长理论,对单晶制备中出现的“各种角度的孪晶”,“较大的枝蔓晶”和“台阶生长的空心晶体”等进行分析,以便能找出生长单晶的最佳工艺条件和理论依据.