On a characterization of the normal distribution by means of identically distributed linear forms

Let X₁, X₂,…, be independent, identically distributed random variables. Suppose that the linear forms L₁ = Σ_j=1^∞a_jX_j and L₂ = Σ_j=1^∞b_jX_j exist with probability one and are identically distributed; necessary and sufficient conditions assuring that X₁ is normally distributed are presented. The result is an extension of a theorem of Linnik (Ukrainian Math. J.5 (1953), 207–243, 247–290) concerning the case that the linear forms L₁ and L₂ have a finite number of nonvanishing components. This proof only makes use of elementary properties of characteristic functions and of meromorphic functions.     

On copowers of an ordered skew field

It is shown that the double of an ordered skew fieldE over a subfieldK, which is its own bicentralizer, can again be ordered, and a corresponding result for groups is deduced.     

Analysis of dielectric relaxations of w/o emulsions in the light of theories of interfacial polarization

An attempt is made to apply dielectric theories of interfacial polarization to observations of dielectric relaxations for W/O emulsions. Approximate formulas for disperse systems in a W/O type were derived from the two theories: one proposed by Maxwell and Wagner for dilute disperse systems of spherical particles, and the other developed by Hanai for concentrated disperse systems. Dielectric measurements were carried out on concentrated W/O emulsions prepared from kerosene and distilled water or KCl aqueous solutions by minimal use of emulsifiers. Marked dielectric relaxations were observed with the emulsions, the dielectric parameters having been determined to characterize the relaxation data. Phase parameters such as relative permittivity, electric conductivity and volume fraction of the disperse phase were evaluated from the dielectric parameters by use of the approximate formulas of the respective theories. The phase parameters evaluated and the frequency dependence of complex permittivity of the W/O emulsions deduced from the theory for concentrated disperse systems are in excellent agreement with the observed data in comparison to that for dilute disperse systems. It is concluded that the dielectric relaxations due to the interfacial polarization of disperse systems of spheres are explained satisfactorily by the theory for concentrated disperse systems.     

Thermodynamic Insight into the Origin of a Calix[n]arene-[60]fullerene Interaction and its Application to a Porphyrin-[60]fullerene Energy Transfer System

The calixarene-fullerene interaction,which causes only a slight change in the absorptionspectra, has been substantiated by calorimetricmeasurements: the H° values arecomparable with those obtained from the associationconstants estimated by a spectroscopic method. Furthermore, we determined the association constantbetween homooxacalix[3]arene and [60]fullerenederivatives with a porphyrin moiety by fluorescencespectra.     

水溶性含C_(60)聚电解质的制备及其与重氮树脂自组装膜AFMFFM的初步研究

通过BPO引发的溶液聚合 ,合成了水溶性的星状C6 0 苯乙烯 苯乙烯磺酸钠的三元共聚物 [Star shapedC6 0 poly(St SS) ],运用自组装技术 ,在水溶液中 ,含C6 0 的三元共聚物与重氮树脂 (Diazoresin)通过正负离子间的吸附力在云母基片上交替一层一层有序地组装成固体膜 .自组装膜经紫外光幅照反应 ,通过重氮基的分解 ,层间连接的离子键转变成共价键 ,从而增加薄膜的稳定性和堆砌密度 .用原子力显微镜 摩擦力显微镜(AFM FFM)考察了C6 0 在膜中的承载作用及比较不同链结构、不同链长、不同层数自组装膜的表面形貌和微摩擦性能 .初步的研究结果显示了聚合物薄膜的微摩擦性能与聚合物的化学结构、链长和膜的层数有密切关系     

Peptides-XXXXVI: Studies in the synthesis of an analogue of hen egg white lysozyme

The previously synthesised (1–37), (38–75), (76–93), (94–104), (105–117) and (118–129) fragments of the analogue were combined making extensive use of the DCCI/HONSu method. The final coupling involved the (1–75) and (76–129) sub-fragments. Aggregation of the latter fragment caused problems in purification by routine gel filtration methods employing Enzacryl K2 or Sephadex LH60. The fully protected (1–129) product was partially purified by washing, then deprotectcd and purified by gel filtration and ion exchange chromatography. Satisfactory removal of the acetamidomethyl group used for cysteine protection could not be achieved.     

An extremal problem related to probability

Summary We consider a walk from a stateA ₁ to a stateA _n+1 in which the probability of remaining atA _i isp _i , and the probability of progressing fromA _i toA _i+1 is 1 –p _i . The probabilityW _nk of reachingA _n+1 fromA ₁ in exactlyn + k steps can then be expressed as a polynomial of degreen + k in then variablesp ₁,,p _n . We determine the maximum value ofW _nk and the (unique) choice (p ₁,,p _n ) for which this extremum occurs.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday     

Characterization of SiO2-P2O5-ZrO2 Sol-Gel/NAFION™ Composite Membranes

Composite membranes were prepared by (a) infiltrating NAFION with SiO₂-P₂O₅-ZrO₂ sol, and (b) recasting a film using NAFION solution containing SiO₂-P₂O₅-ZrO₂ sol. The membranes were characterized by Differential Thermal Analysis and ac-impedance spectroscopy as a function of relative humidity. The influences of the heat treatment (80°C–150°C) and cleaning on the electrical properties were investigated. The incorporation of SiO₂-P₂O₅-ZrO₂ gels into NAFION lead to improvements in its thermal stability and proton conductivity.     

球壳烯类的化学修饰

自从Kratschmer和Huffman发表了较为简便的制备和分离碳-60,碳-70的方法以来,对于球壳烯类,特别是碳-60的表征和物化性质已进行了较为翔实的研究。关于球壳烯类的化学修饰,尽管起步较晚,对其兴趣也日益高涨。本文综述了球壳烯类的化学修饰,特别在球壳烯外壳的化学反应方面。     

Radiation sterilization of enzyme hybrids with biodegradable polymers

Ionizing radiations, which have already been utilized for the sterilization of medical supplies as well as gas fumigation, should be the final candidate to decontaminate “hybrid” biomaterials containing bio-active materials including enzymes because irradiation induces neither heat nor substances affecting the quality of the materials and our health. In order to check the feasibility of ⁶⁰Co-gamma rays on these materials, we selected commercial proteases including papain and bromelain hybridized with commercial activated chitosan beads and demonstrated that these enzyme-hybrids suspended in water showed the significant radiation durability of more than twice as much as free enzyme solution at 25-kGy irradiation. Enhanced thermal and storage stability of the enzyme hybrids were not affected by the same dose level of irradiation, either, indicating that commercial irradiation sterilization method is applicable to enzyme hybrids without modification.