Prädikatives und funktionales Denken in der Wahrscheinlichkeitsrechnung

In order to emphasize functional thinking in mathematical education, arguments are brought forward for an early and frequent use of tree diagrams in teaching stochastics. Since set and tree diagrams can be regarded as two sides of the same matter, Bayes’ theorem, which is strongly associated with predicative set diagrams, need not be dealt with explicitly any longer. Set diagrams are replaced by tree diagrams that are labelled in detail and by tree inversion as a functional instrument of dealing with conditioned probabilities. This technique is demonstrated by three typical problems in the context of conditioned probability. Finally, two letters by Pascal to Fermat are analysed in order to illustrate that predicative and functional approaches were already pursued in the early stages of probability calculus in the 17^th century.     

Synthesis of some chiral liquid crystals and study of the effect of intramolecular hydrogen bonding on the phase behaviour

The synthesis of three new series of chiral Schiff's bases containing benzilideneaniline and 2-hydroxybenzilideneaniline moieties as mesogenic cores is presented. Differential scanning calorimetry, optical polarizing microscopy and X-ray diffraction measurements were used to study the phase transition temperatures and behaviour. The results reveal that most of these materials show chiral smectic mesomorphism.     

Role of Na(+)-Ca2+ exchange system in the pathogenesis of myocardial ischemia-reperfusion damage

Results from a systematic experiment on isolated perfused rat heart and isolated myocytes of adult rat showed that the mechanism of calcium influx during myocardial ischemia-reperfusion is due to the development of intracellular sodium overload during ischemic period; on reperfusion, the high intracellular Na+ content activated the reverse direction of Na(+)-Ca2+ exchange over myocardial sarcolemma (SL), thus a large quantity of extracellular Ca2+ fluxed over the SL to the intracellular space, forming a condition of intracellular Ca2+ overload, which leads to irreversible damage of the myocardium.     

Ethylene–propylene copolymerization with bis(β‐enaminoketonato) titanium complexes activated with modified methylaluminoxane

Ethylene–propylene copolymerization, using [(Ph)NC(R₂)CHC(R₁)O]₂TiCl₂ (R₁ = CF₃, Ph, or t‐Bu; R₂ = CH₃ or CF₃) titanium complexes activated with modified methylaluminoxane as a cocatalyst, was investigated. High‐molecular‐weight ethylene–propylene copolymers with relatively narrow molecular weight distributions and a broad range of chemical compositions were obtained. Substituents R₁ and R₂ influenced the copolymerization behavior, including the copolymerization activity, methylene sequence distribution, molecular weight, and polydispersity. With small steric hindrance at R₁ and R₂, one complex (R₁ = CF₃; R₂ = CH₃) displayed high catalytic activity and produced copolymers with high propylene incorporation but low molecular weight. The microstructures of the copolymers were analyzed with ¹³C NMR to determine the methylene sequence distribution and number‐average sequence lengths of uninterrupted methylene carbons. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5846–5854, 2006     

Template atom transfer radical polymerization of a diaminopyrimidine‐derivatized monomer in the presence of a uracil‐containing polymer

Uracil‐derivatized monomer 6‐undecyl‐1‐(4‐vinylbenzyl)uracil and diaminopyrimidine‐derivatized monomer 2,6‐dioctanoylamido‐4‐methacryloyloxypyrimidine (DMP) were synthesized and polymerized by atom transfer radical polymerization (ATRP). A well‐defined, highly soluble, uracil‐containing polymer, poly[6‐undecyl‐1‐(4‐vinylbenzyl)uracil] (PUVU), was prepared in dioxane at 90 °C with CuBr/1,1,4,7,10,10‐hexamethyltriethylenetetramine as the catalyst and methyl α‐bromophenylacetate as the initiator. PUVU was further used as a template for the ATRP of DMP. The enhanced apparent rate constant of the DMP polymerization in the presence of PUVU indicated that the ATRP of DMP occurred along the PUVU template. The template polymerization produced a stable and insoluble macromolecular complex, PUVU/poly(2,6‐dioctanoylamido‐4‐methacryloyloxypyrimidine). An X‐ray diffraction study confirmed that the complex had strandlike domains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6607–6615, 2006     

Effects of the architecture and environment on polymeric molecular assemblies of novel amphiphilic diblock copolynorbornenes with narrow polydispersity via living ring‐opening metathesis polymerization

Diblock copolymers of 5‐(methylphthalimide)bicyclo[2.2.1]hept‐2‐ene (NBMPI) and 1,5‐cyclooctadiene were synthesized by living ring‐opening metathesis polymerization with a well‐defined catalyst {RuCl₂(CHPh)[P(C₆H₁₁)₃]₂}. Unhydrogenated diblock copolymers showed two glass transitions due to poly(NBMPI) and polybutadiene segments, such as two glass‐transition temperatures at ?86.5 and 115.3 °C for poly 1a and ?87.2 and 115.3 °C for poly 1b . However, only one melting temperature could be observed for hydrogenated copolymers, such as 119.8 °C for poly 2a and 121.7 °C for poly 2b . The unhydrogenated diblock copolymer with the longer poly(NBMPI) chain (poly 1a ; temperature at 10% mass loss = 400 °C) exhibited better thermal stability than the one with the shorter poly(NBMPI) chain (poly 1b ; temperature at 10% mass loss = 385 °C). Two kinds of hydrogenated diblock copolymers, poly 2a and poly 2b , exhibited relatively poor solubility but better thermal stability than unhydrogenated diblock copolymers because of the polyethylene segments. Poly[(hydrochloride quaternized 2‐norbornene‐5‐methyleneamine)‐b‐butadiene]‐1 (poly 3a ) was obtained after the hydrolysis and quaternization of poly 1a . Dynamic light scattering measurements indicated that the hydrodynamic diameters of the cationic copolymer (poly 3a ) in water (hydrodynamic diameter = 1580 nm without salt), methanol/water (4/96 v/v; hydrodynamic diameter = 1500 nm without salt), and tetrahydrofuran/water (4/96 v/v; hydrodynamic diameter = 1200 nm without salt) decreased with increasing salt (NaCl) concentration. The effect of temperature on the hydrodynamic diameter of hydrophobically modified poly 3a was also studied. The inflection point of the hydrodynamic diameter of poly 3a was observed at various polymer concentrations around 30 °C. The critical micelle concentration of hydrophobically modified poly 3a was observed at 0.018 g dL^?1. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2901–2911, 2006     

Simultaneous electrochemical determination of uric acid and ascorbic acid on a glassy carbon electrode modified with cobalt(II) tetrakisphenylporphyrin.

A cobalt(II) tetrakisphenylporphyrin (Co(II)TPP) film modified glassy carbon electrode (Co(II)TPP-GCE) was prepared by just coating Co(II)TPP solution on the surface of the electrode. It can be used for the simultaneous determination of ascorbic acid and uric acid. The anodic peaks of AA and UA can be separated well. Owing to the strongly hydrophobic property of porphyrin, the modified electrode has good stability and long life. The linear range for UA and AA were 2.0 x 10(-6)-1.0 x 10(-4) M and 9.0 x 10(-6)-2.0 x 10(-3) M with detection limits of 5.0 x 10(-7) and 5.0 x 10(-6) M, respectively. Furthermore, metalloporphyrins of other kinds were also used to construct modified electrodes. Their performances were inferior compared with that of the Co(II)TPP modified electrode.     

微型硅谐振式力传感器的振动分析

介绍了谐振式力传感器的工作原理，并从理论上和实验上对中科院合肥智能所研制的第一代微型硅谐振梁（３×０．４×０．０４５ｍｍ＾３）式测力传感器进行了全面的振动分析，所得结构为其进一步优化设计提供了科学根据，文中使用的实验分析方法，为其它微小物体的动态和识别提供了一条有效途径。     

Complex homogeneous splines on the torus

We construct functions M_α which are piecewise homogeneous polynomials on the (d+1)-dimensional torus U^d+1. These functions possess complete symmetry with respect to the independent variables. The symmetry and homogeneous relations for these functions are exploited to obtain a recurrence relation and explicit representations. Furthermore, we show that , where ω=e^12x/k, 0≤j_t≤k−1, are linearly independent. By restricting M_α to U^d, we obtain the complex analogue of polynomial box splines on a (d+1)-direction mesh on U^d, which is a multivariate analogue of B-splines on the circle studied by I.J. Schoenberg^[8].