Sarason’s interpolation theorem for analytic crossed products

Saito (Math. Proc. Camb. Phil. Soc., 117, 11–20, 1995) proved Sarason’s interpolation theorem for an analytic crossed product determined by a finite von Neumann algebra. We extend this result without the assumption that the von Neumann algebra is finite.     

Random attractors for stochastic differential equations driven by two-sided Lévy processes

Abstract

In this paper, the asymptotic behavior of solutions for a nonlinear Marcus stochastic differential equation with multiplicative two-sided Lévy noise is studied. We plan to consider this equation as a random dynamical system. Thus, we have to interpret a Lévy noise as a two-sided metric dynamical system. For that, we have to introduce some fundamental properties of such a noise. So far most studies have only discussed two-sided Lévy processes which are defined by combining two-independent Lévy processes. In this paper, we use another definition of two-sided Lévy process by expanding the probability space. Having this metric dynamical system we will show that the Marcus stochastic differential equation with a particular drift coefficient and multiplicative noise generates a random dynamical system which has a random attractor.     

New Braided Crossed Categories and Drinfel'd Quantum Double for Weak Hopf Group Coalgebras

A simple and nice structure theorem for orthogroups was given by Petrich in 1987. In this paper, we consider a generalized orthogroup, that is, a quasi-completely regular semigroup with a band of idempotents in which its set of regular elements, namely, RegS, forms an ideal of S. A method of construction of such semigroups is provided and as a result, the Petrich structure theorem of orthogroups becomes an immediate corollary of our theorem on generalized orthogroups. An example of such generalized orthogroup is also constructed. This example provides some useful information for the construction of various kinds of quasi-completely regular semigroups.     

Synthesis of novel β2,2-amino acid from D-mannose and attempted synthesis of peptides from the amino acid

The study describes the synthesis of new α,α-disubstituted β-amino acid (β^2,2-Caa) and attempts the synthesis of peptides from it. The β^2,2-Caa was prepared from D-(+)-mannose, using crossed aldol and Cannizzaro reactions.     

Crossed Modules and Quantum Groups in Braided Categories

Let A be a Hopf algebra in a braided category . Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group the corresponding braided category of modules is identified with a full subcategory in . The connection with cross products is discussed and a suitable cross product in the class of quantum braided groups is built. Majid–Radford theorem, which gives equivalent conditions for an ordinary Hopf algebra to be such a cross product, is generalized to the braided category. Majid's bosonization theorem is also generalized.     

Development of Methods for the Synthesis of Neopentyl Glycol by Hydrogenation of Hydroxypivaldehyde

Neopentyl glycol (NPG) is a precursor for the manufacture of many valuable products of industrial importance such as polyester, polyurethane and alkyd resins, synthetic lubricants, hydraulic fluids, drugs, etc. The structure of NPG provides the resins with excellent hydrolytic stability, resistance to weather conditions, good flexibility-hardness balance, and outstanding functional properties. The paper presents a literature review on the development of methods for NPG preparation, focusing primarily on the synthesis of NPG by hydrogenation of hydroxypivaldehyde, which is obtained by the crossed aldol condensation of isobutyraldehyde and formaldehyde. Preparation of the substrates, catalysts, technical and apparatus solutions, and NPG purification were discussed.     

Photofragment translational spectroscopy of iodobenzene at 266 nm

The photofragmentation of C_6 H_5I at 266 nm is investigated on the nuiversal crossed molecular beam machine, and the translational spectroseopy as well as the angular distribution of I atom is measured. The results reveal that under the laser intensity of 10~8 W/cm~2 the single-phuton dissociation competes with multi-photon processes. In singlephoton dissociation the anisotropy parameter β is 0.4 and the average translational energy is only 1.04 keal/mol, which indicates that this process is a slow predissociation. In two-photon phutofragmentation the average translational energy is 51.64 kcal/mol, which accounts for about 35% of the available energy. Another photofragmentation channel is even more faster, whose peak in time-of-flight spectra corresponds to four or five photon absorptions. The branching ratio of these three channels is determined to be about 3: 3: 4.     

利用双面腔制备n原子GHZ态

提出了一种利用双面腔制备多原子GHZ态的方法.当腔中囚禁原子处于特定态时,腔可能反射入射的单光子脉冲,也可能透射它.这个特性可以引起囚禁原子和输入腔肠的纠缠.数值模拟显示制备的多原子GHZ态具有很高的保真度和成功率.而且原子自发辐射等内禀噪声只对成功率有影响,而对保真度几乎没有影响.另外,对高Q腔和原子的L-D条件的不要求,提升了试验实现的可行性.     

Weak crossed biproducts and weak projections

In this paper, we present the general theory and universal properties of weak crossed biproducts. We prove that every weak projection of weak bialgebras induces one of these weak crossed structures. Finally, we compute explicitly the weak crossed biproduct associated with a groupoid that admits an exact factorization.