Multiple local solutions to nonlinear control processes

We use the topological tool of Nielsen fixed-point theory to study the controllability of perturbed linear control processes whose control space can be reduced to a finite-dimensional one. These methods produce a lower bound on the number of controls that achieve a given target. We concentrate particularly on the case where the perturbation has sublinear growth, and we exhibit examples of multiple controls of various types that are detected by the Nielsen theory method.This research was partly supported by the Research Grant Teoria del Controllo dei Sistemi Dinamici, Ministero della Pubblica Istruzione, Roma, Italy.     

A fixed-point equation for the high-temperature phase of discrete lattice spin systems

A fixed-point equation on an infinite-dimensional space is proposed as an alternative to the usual definition of the infinite-volume limit in discrete lattice spin systems in the high-temperature phase. It is argued heuristically that the free energy and correlation functions one obtains by solving this equation agree with the usual definitions of these quantities. A theorem is then proved that says that if a certain finite-volume condition is satisfied, then this fixed-point equation has a solution and the resulting free energy is analytic in the parameters in the Hamiltonian. For particular values of the temperature this finite-volume condition may be checked with the help of a computer. The two-dimensional Ising model is considered as a test case, and it is shown that the finite-volume condition is satisfied for0.77 _critical.     

On Super-KMS functionals and entire cyclic cohomology

We formulate the super-KMS condition suggested by Connes and Kastler, in the context of entire cyclic cohomology of quantum algebras. We show that the Chern character of Jaffe, Lesniewski, and Osterwalder — associated by Kastler to a super-KMS functional — satisfies the entire growth condition. Hence, a super-KMS functional defines a cocycle for the entire cyclic cohomology of quantum algebras.Supported in part by the National Science Foundation.     

有穷长半模偏序集上的一个定理

本文是对参考文献[1]第二章定理14证明的补充和改进。该定理乃指: 定理14.在任何上(或下)半模的有穷长的偏序集内,Jordan-Dedekind链条件成立。 文献[1]中,考虑上半模情形,谈到已知一个连接链:γ∶a=x_0相似文献   

晶性3，4－聚异戊二烯的结构研究

采用ＷＡＸＤ、ＳＡＸＳ和Ｘ－射线平板照相法研究了不同聚合条件和拉伸倍数下的晶性３，４－聚异戊二烯的结构．结果发现，降低催化体系反应速度有利于产物结晶；不同的含氮类给电子试剂对聚合物的结晶结构影响较大．取向样品随着拉伸倍数的增加结晶度和长周期增大，微晶尺寸变小．ＳＡＸＳ的散射强度计算表明，该聚合物属多分散非均一粒子体系，微孔半径在３．５－１６．４ｎｍ间．     

Oscillation condition for a series piezoelectric sensor. Application to the determination of urease activity in plant seeds

The oscillating conditions for a series piezoelectric quartz crystal (SPQC) are proposed and verified experimentally. The influence of the cell constant and oscillator phase on the oscillational ability of the SPQC was investigated. It is shown that the SPQC possesses excellent oscillational ability in low or high conductivity solutions, but in solution of intermediate conductivity, the oscillational ability decreases with increasing oscillator phase or decreasing cell constant, sometimes resulting in a cease-to-oscillate zone. The SPQC was applied to determine the urease activity in plant seeds with a detection limit of 0.004 U ml⁻¹, based on the change in conductivity.     

边界元法在计算地下水稳定水位和流量中的应用

边界元法是一种新的数值计算方法。该法易于处理无限区域的地下水流问题,并且计算流量也较其他方法准确。本文介绍在二维稳定流的情况下如何计算地下水的水头和流量。承压含水层中的稳定流动,水头H满足拉普拉斯方程。利用格林第二公式,可以得到边界积分方程,即边界元的基本公式。可以用数值方法计算这一边界积分。为此,在边界上选取有限个点,称为节点,两节点间的线段称为单元。本文中选用线性单元和线性插值。引进局部坐标系,可以得到表示H和( H/ n)关系的方程。我们可以选一个节点作为固定的基点,其他节点为动点,对于每一选择都可得到一个方程。依次把每一节点作为基点,可得到N个方程,构成一个线性代数方程组。根据边界条件,每一节点中的H或( H/ n)有一个是已知的,解方程组可求出另一个。解出边界上的全部H和( H/ n)以后,可算出内部的水头和流量。对于非均质问题可划分为几个区域来处理。分界线上要满足相容性方程。对于( H/ n)的不连续点,可用“节点多值法”处理。     

Gap exponents for percolation processes with triangle condition

A study is made of the gap exponents for percolation processes with the triangle condition in the subcritical region. It is show that the gaps are given by _t =2 fort=2, 3,. Scaling theory predicts thatP _p (¦C ₀¦S(p))–(p _c –p) andE _p (1/¦C ₀¦; ¦C ₀¦S(p))–(p _c –p)³, whereS(p) is the typical cluster size. It is found that (p _c –p)P _p (|C ₀S(p) ^1–)(p _c –p)^1–2 and (p _c –p)³E _p (1/|C ₀|;|C ₀|S(p) ^1–))(p _c –p)^3–4.     

Ce(IV) ion initiated graft polymerization of glycidylmethacrylate onto a demineralized bone matrix: effect of reaction parameters

Studies on chemical modification of demineralized bone matrix (DBM) have opened new arenas in the field of clinical orthopedics owing to its potential osteoinductivity with desired chemical functionality. To widen its usage to biomolecular delivery, graft polymerization of glycidylmethacrylate onto DBM was carried out by a free-radical initiating process using ceric ammonium nitrate as an initiator. The evidence of the grafting reaction was examined by chemical analysis using Fourier transform IR spectroscopy. The grafting condition was standardized by regulating the reaction parameters such as the concentrations of the backbone, the monomer and the initiator, the polymerization temperature and time. The optimum polymerization temperature and time to have the maximum grafting yield were 40 °C and 3 h, respectively. The percentage of grafting and the percentage of grafting efficiency were determined as a function of the reaction parameters, and both were found to increasing initially and thereafter decrease in most of the cases. The grafting results are discussed in a detailed fashion and a reaction mechanism is proposed.     

不同交联度的杜仲胶的红外光谱研究

研究了不同交联度的杜仲胶在室温及加热后红外光谱的变化规律．发现在室温下测定的样品红外光谱在低波数内对应链段变形振动的几个特征峰、加热后会消失或弥散，而交联度的改变对其影响不大，即使材料中结晶完全消失而变成高弹态．因此，推测这些特微峰的存在，应该和杜仲胶弹性网络中交联点间链段存在着明显的构象规整性有关．