The logarithmic norm. History and modern theory

In his 1958 thesis Stability and Error Bounds, Germund Dahlquist introduced the logarithmic norm in order to derive error bounds in initial value problems, using differential inequalities that distinguished between forward and reverse time integration. Originally defined for matrices, the logarithmic norm can be extended to bounded linear operators, but the extensions to nonlinear maps and unbounded operators have required a functional analytic redefinition of the concept.This compact survey is intended as an elementary, but broad and largely self-contained, introduction to the versatile and powerful modern theory. Its wealth of applications range from the stability theory of IVPs and BVPs, to the solvability of algebraic, nonlinear, operator, and functional equations. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65L05     

ENSTAR detector forη- mesic studies

We have initiated a search for a new type of nuclear matter, theη-mesic nucleus, using beams from the multi-GeV hadron facility, COSY at Juelich, Germany. A large acceptance scintillator detector, ENSTAR has been designed and built at BARC, Mumbai and fully assembled and tested at COSY. A test run for calibration and evaluation has been completed. In this contribution we present the design and technical details of the ENSTAR detector and how it will be used to detect protons and pions (the decay products ofη-mesic bound state). The detector is made of plastic scintillators arranged in three concentric cylindrical layers. The readout of the detectors is by means of optical fibres. The layers are used to generate ΔE –E spectra for particle identification and total energy information of stopped particles. The granularity of the detector allows for position (θ and ?ø determination making the event reconstruction kinematically complete     

Coloring mixed hypertrees

A mixed hypergraph is a triple (V,C,D) where V is its vertex set and C and D are families of subsets of V, called C-edges and D-edges, respectively. For a proper coloring, we require that each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of a mixed hypergraph is the set of all k's for which there exists a proper coloring using exactly k colors. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of the tree.We prove that feasible sets of mixed hypertrees are gap-free, i.e., intervals of integers, and we show that this is not true for precolored mixed hypertrees. The problem to decide whether a mixed hypertree can be colored by k colors is NP-complete in general; we investigate complexity of various restrictions of this problem and we characterize their complexity in most of the cases.     

关于非线性Schrodinger方程混合问题解的破裂和质量集中

本文讨论了一类非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程混合问题解的破裂现象，ｂｌｏｗ－ｕｐ时刻的估计和质量集中定理，并推广和改进了［ｌ～３］中的结果．     

氢氧化铝镁正电溶胶制备及性能研究

氢氧化铝镁正电溶胶制备及性能研究侯万国，张春光，孙德军，梁晓丽，王果庭（山东大学胶体与界面化学研究所，济南，２５０１００）关键词混合金属氢氧化物，溶胶，超细颗粒混合金属氢氧化物的合成、组成及结构等已得到广泛研究［１，２］．我们也曾用插入法合成了混合金...     

Calorimetric approach to tetronic/water interactions

Tetronic^®comprises X-shaped copolymers formed by four poly(propylene oxide) (PPO) andpoly(ethylene oxide) (PEO) block chains bonded to an ethylene diamine centralgroup. Micellization behaviour of three representative Tetronics (T304, T904and T1307) was characterized to gain an insight into the interactions betweenthe copolymer unimers and the state of water in their solutions. The enthalpyof demicellization, recorded at 37°C in an isoperibol microcalorimeter,indicated that the process was in all cases exothermic and the enthalpy rankedin the order T1307≥T904>>T304. Micellization is entropy-driven owing tohydrophobic interactions between the PPO chains.DSC analysisshowed that the crystallization and melting peaks of the free water remainingin T304 and T904 solutions were progressively shifted toward lower temperaturesas the surfactant proportion increased, owing to a colligative effect. Boundwater corresponded to 3 water molecules per EO repeating unit. In the caseof T1307, which has longer PEO chains, a splitting of the melting peak wasobserved, one peak appearing around 0°C due to free water and anotherat –15°C due to interfacial water. As T1307 proportion raised, theenthalpy of the former decreased, whilst the enthalpy of the latter increased.In 40% T1307 solutions, interfacial water overcame the proportion of freewater; there being 1 interfacial and 3 bound water molecules per EO repeatingunit. Gaussian deconvolution of FTIR spectra also enabled to characterizethe evolution of free water as a function of Tetronic proportion. The dependenceof micellization and water interaction behaviour on Tetronics structure shouldbe taken into account to use these copolymers as drug solubilizers and micellarcarriers.     

混合二烃基二氯化锡与水杨醛缩苯胺类Schiff碱1∶1配合物的合成和表征

由混合二烃基二氯化锡（ＲＲ＇ＳｎＣｌ＿２）与水杨醛缩苯胺类Ｓｃｈｉｆｆ碱（２－ＨＯＣ＿６Ｈ＿４ＣＨ＝ＮＡｒ）反应，合成了１４种新的有机锡配合物。经元素分析、ＩＲ、ＮＭＲ和ＴＧ－ＤＳＣ测定，确定配合物的组成是有机锡与Ｓｃｈｉｆｆ碱的１：１配合物，配体以酚羟基氧原子与锡原子配位，摩尔电导率测定表明配合物均为非电解质。     

葡萄糖和水混合溶液多组分电解质热力学 Ⅱ.HCl-NaCl-d-Glucose-H_2O体系(5—45℃)

本文续前报在恒定溶液总离子强度I=1.00mol·kg~(-1),改变葡萄糖在混合溶液中的质量百分数x=5%、15%和20%的条件下,应用电动势法测定了无液接界电池(A)和电池(B)的电动势: Pt,H_2(1.013×10~5Pa)|HCl(m),d-Glucose(x),H_2O(1-x)|AgCl-Ag (A) Pt,H_2(1.013×10~5Pa)|HCl(m_A),NaCl(m_B),d-Glucose(x),H_2O(1-x)|AgCl-Ag(B) 其中x代表葡萄糖在水中的质量百分数,m_A和m_B分别是HCl和NaCl在混合溶液中的质量摩浓度。利用电池(A)的电动势数据得到了AgCl-Ag电极在d-Glucose-H_2O混合溶液中的标准电极电势Φ_m~0,讨论了HCl的迁移性质,利用电池(B)的电动势数据,确定了HCl在HCl-NaCl-d-Glucse-H_2O体系中的活度系数γ_A,实验结果表明:在恒定总离子强度下,HCl的活度系数服从Harned规则。HCl的迁移自由能与葡萄糖的质量百分数x成线性关系。计算了HCl     

X-ray investigation of the role of the mixed emulsifier in the structure formation in o/w creams

The aim of this research work was to clarify the role of the mixed emulsifier in the structure formation and water binding mode in the case of o/w creams prepared with different surfactants. The swelling behavior of mixed emulsifiers was examined by means of direct investigation methods such as transmission electron microscopy (TEM) and X-ray diffraction. The detailed structure image of the creams was created with the help of the latter. The influence of the structure of the hydrophilic gel phase, and the structural changes during storage were studied with rheological methods. On the basis of the results, it can be stated that the investigated creams had different structures from those mentioned in the literature: surfactant did not create a mixed bilayer with the structure to furnish fatty amphiphile; instead, micelles were formed. These results correlated well with the results of the rheological tests.     

丙酮肟与某些芳烃相互作用的~1H核磁共振研究

Hatton和Richards通过对酰胺分子的~1H NMR谱溶剂效应的研究,提出了DMF与苯生成分子络合物的模型.如果络合物按1:1生成,那么将出现一个“饱和点”,在这点上甲基的芳香溶剂诱导位移(ASIS)的变化趋势或程度将出现一个明显的变化,事实上随着苯的摩尔分数从0到1逐渐增加时,化学位移总是有规则的逐渐移向高场.这就显示了分子络合物观点的局限性.它能被一些研究者所支持和接受,是因为它能够解释两个甲基共振峰先重合而后又分离的现象.