Phase transition of layer structure of poly(p-benzenedithiol-co-p-diethynylbenzene) by heat or photon mode

Phase transition of the layer structure of poly(p-benzenedithiol-co-p-diethylbenzene) obtained in solid state polymerization was studied by a thermal treatment or UV irradiation under a nitrogen atmosphere. The peak intensities in the X-ray diffraction diagram of polymers gradually decreased with the thermal treatment time above 55°C. Below 50°C the layer structure of polymers hardly changed. The apparent activation energy for the phase transition was about 15 Kcal/mol [63 KJ/mol] at the initial stage and gradually decreased to a few Kcal/mol [ca. 2 KJ/mol]. UV light from a high-pressure mercury lamp also gradually induced the phase transition from the layer structure to an amorphous one. The pristine polymer possesses phase transition points at 75, 95 and 130°C. The exothermic transition at 75°C can be understood as the thermal destruction of the semistable layer structure. The exothermic transition at 95°C may be correspond to the cis → trans thermal isomerization of the C?°C bond in the polymer main chain. The diffuse reflectance spectrum of the pristine polymer differed from that of the amorphous polymer obtained by the thermal treatment of the pristine polymer. SEM photographs of the pristine polymer showed a particular surface structure, i.e. entangled fibrous material. TEM photographs of the pristine polymer exhibited a bright valley-and-hill structure, whereas that of the amorphous polymer obtained by thermal treatment exhibited a plain surface.     

Singular integral operators on 53-0153-0153-01-spaces

Summary It is shown that certain singular integral operators with variable kernels leave invariant theL ^v, -spaces studied by Campanato, Stampacchia, Peetre and others. Our results extend Peetre's work on convolution operators.     

Association Schemes and Fusion Algebras (An Introduction)

We introduce the concept of fusion algebras at algebraic level, as a purely algebraic concept for the fusion algebras which appear in conformal field theory in mathematical physics. We first discuss the connection between fusion algebras at algebraic level and character algebras, a purely algebraic concept for Bose-Mesner algebras of association schemes. Through this correspondence, we establish the condition when the matrix S of a fusion algebra at algebraic level is unitary or symmetric. We construct integral fusion algebras at algebraic level, from association schemes, in particular from group association schemes, whose matrix S is unitary and symmetric. Finally, we consider whether the modular invariance property is satisfied or not, namely whether there exists a diagonal matrix T satisfying the condition (ST)³ = S ². We prove that this property does not hold for some integral fusion algebras at algebraic level coming from the group association scheme of certain groups of order 64, and we also prove that the (nonintegral) fusion algebra at algebraic level obtained from the Hamming association scheme H(d, q) has the modular invariance property.     

Strategy-proofness, solidarity, and consistency for multiple assignment problems

We consider a problem of allocating indivisible objects when agents may desire to consume more than one object and no monetary transfers are allowed. We are interested in allocation rules that satisfy desirable properties from an economic and social point of view. In addition to strategy-proofness and Pareto efficiency, we consider consistency and two solidarity properties (replacement-domination and population-monotonicity). In most of the cases, these properties are satisfied only by serially dictatorial rules. Received: November 1999/Final version: December 2001     

Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz–Morrey spaces of the third kind

Positivity - In the present paper, we will characterize the boundedness of the generalized fractional integral operators $$I_{rho }$$ and the generalized fractional maximal operators $$M_{rho }$$...     

丝光沸石复合膜的制备及其影响因素

采用在多孔氧化铝支撑体上预涂纳米丝光沸石晶种,再用水热晶化的方法制备丝光沸石复合膜.系统考察了反应母液陈化、碱度、盐以及反应温度等因素对丝光沸石晶体在预涂晶种支撑体上成膜化过程的影响.研究发现,膜表面晶体间空隙随反应母液陈化时间的增加而略有增大;高碱度的反应母液不利于连续丝光沸石复合膜的形成;反应母液中盐的浓度对丝光沸石晶体沿各个轴方向上的生长速率有不同程度的影响,膜表面晶体间空隙随盐浓度的增加而增大;晶化温度过高,容易形成细棒状晶体,导致晶体间空隙增大.     

Construction of an atomic decomposition for functions with compact support

Chang, Krantz and Stein [D.-C. Chang, S.G. Krantz, E.M. Stein, Hp theory on a smooth domain in Rn and elliptic boundary value problems, J. Funct. Anal. 114 (1993) 286-347] proved that if f∈Hp(Rn) and f vanishes outside , then f has an atomic decomposition whose atoms are contained in Ω. The purpose of this paper is to give another proof for the case n/(n+1)<p?1 and Ω a cube. Our argument provides a simple, direct construction of the desired atomic decomposition, and it works in a class of function spaces more general than the usual Hardy spaces.     

Two-dimensional measurement of laser-induced target movement by face-on interferometry

Initial movement of laser irradiated foil targets has been measured by face-on interferometry with two-dimensional resolution. This interferometric method provides direct and precise information about the initial movement of the rear surface of the target compared with conventional diagnostics. Target movement of 20–500 nm from the original position has been observed.