Randomized UMD Banach spaces and decoupling inequalities for stochastic integrals

In this paper we prove the equivalence of decoupling inequalities for stochastic integrals and one-sided randomized versions of the UMD property of a Banach space as introduced by Garling.

     

On the Seneta Sequences

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.     

On Intersection Problem for Perfect Binary Codes

The main result is that to any even integer q in the interval 0 ≤ q ≤ 2^{n+1-2log(n+1)}, there are two perfect codes C₁ and C₂ of length n = 2^m − 1, m ≥ 4, such that |C₁ ∩ C₂| = q.     

Excess isentropic compressibility and speed of sound of the ternary mixture 2-propanol + diethyl ether + n-hexane and the constituent binary mixtures at 298.15 K

Speed of sound and densities of the ternary mixture 2-propanol + diethyl ether + n-hexane and also the binary mixtures 2-propanol + diethyl ether and 2-propanol + n-hexane have been measured at the entire composition range at 298.15 K. The excess isentropic compressibilities and the excess speed of the sound have been calculated from experimental densities and speed of sound. These excess properties of the binary mixtures were fitted to Redlich-Kister equation, while the Cibulka’s equation was used to fit the values related to the values to the ternary system. These excess properties have been used to discuss the presence of significant interactions between the component molecules in the binary mixtures and also the ternary mixtures. Speed of sound of the binary mixtures and the ternary mixture have been compared with calculated values from free length theory (FLT), collision factor theory (CFT), Nomoto’s relation (NR), Van Deal’s ideal mixing relation (IMR) and Junjie’s relation (JR). The results are used to compare the relative merits of these theories and relations in terms of the root mean square deviation relative (RMSD_r).     

Marcinkiewicz–Zygmund inequalities

We study a generalization of the classical Marcinkiewicz–Zygmund inequalities. We relate this problem to the sampling sequences in the Paley–Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz–Zygmund inequalities.     

Exact thermodynamic behavior of a generalized spin-isospin ising system on the Bethe lattice

We study a generalized Ising system consisting of a Bethe lattice on every site of which two spin-1/2 and two isospin-1/2 (or atomic species A) states can be realized, the spin-species interacting with appropriate nearest neighbor couplings. The system is equivalent to that of four states per site and we obtain its exact thermodynamic behavior. The case of a fixed concentration of species is the annealed or liquid magnetic binary alloy. The temperature dependence of the short-range-order (SRO) parameter of such systems is obtained as an application of the theory and discussed in connection with relevant material from the literature. When fixing both the concentration and the nearest neighbor spatial correlation of the species, we obtain Eggarter's formulas for the frozen-in species problem, which therefore are only approximately valid even on the Bethe lattice.     

气固射流床射流深度的研究

在３００×５１×２６００ｍｍ的二维射流床中，采用多路毕托管测试系统，对包括三种双组份混合物在内的五种物料的射流深度进行了考察。结果表明，射流管径、射流气速对射流深度都有影响，本文尤其考察了环隙气量与射流深度的关系，发现在同样的射流气速下，环隙气速增大则射流深度降低，得出了综合各种影响因素的关联式。     

Topological investigations of molar excess volumes of quinoline with alkanols

Excess volumes V ^E of binary liquid mixtures of quinoline with alkanols have been determined from densities at 30°C as a function of composition. The excess volumes are negative over the whole mole fraction range for all the mixtures and decrease with increasing length of alkanol (C₁–C₁₀). The V^E data have been analyzed in terms of an approach which uses graph theoretical connectivity parameters of the third degrees for two components. The analysis gives information regarding associated species in the pure state and in the mixture. It is suggested that, in the mixture state, no change occurs in the association of alkanols.     

Solid-State polymerization of the binary mixture of methacrylate and liquid-crystalline compound by electron beam

Solid-state polymerization of a binary mixture of nonliquid-crystalline monomer and liquidcrystalline compound was carried out using electron beam. The monomers were benzoic acid containing 4-[ω-(meth)acryloyloxyalkyloxy] benzoic acids, in which the alkylene spacer was ethylene, hexamethylene, or undecamethylene. The conversion yield of monomer to polymer to a large extent increased with increasing content of a liquid-crystalline compound with a terminal carboxylic group, such as 4-n-alkyloxybenzoic acid, while the addition of a liquid-crystalline compound without terminal carboxylic group did not affect polymerization of the monomer. Phase diagrams of the mixture of monomer and liquid-crystalline compound were examined using cross-polarizing microscopy and differential scanning calorimetry (DSC). All mixtures of monomer and 4-n-alkyloxybenzoic acid or liquid-crystalline compound without terminal carboxylic group showed liquid-crystallinity in a broad composition range. It was concluded that liquid-crystalline compounds with terminal carboxylic acid may form hydrogen bondings with methacrylate or acrylate monomer having terminal carboxylic acid which enhance polymerizability of the mixture. The stereoregularity of polymers determined by NMR depended on increasing irradiation dose and temperature rather than the content of the added liquid-crystalline 4-n-decanoxybenzoic acid.