NH4H2PO4/SiO2: a recyclable,efficient heterogeneous catalyst for crossed aldol condensation reaction

Abstract

Crossed aldol condensation of aromatic aldehydes with cyclic ketones in the presence of catalytic amount of NH₄H₂PO₄/SiO₂ (as a safe, green, and cheap heterogeneous catalyst) under solvent-free condition afforded α,?-bis(substituted-benzylidene) cycloalkanones in high yields. This method is general with respect to all types of aromatic aldehydes and is an eco-friendly procedure. And the catalyst is easily prepared, stable, reusable, and efficient under the reaction conditions.     

A note on p-supersolvable groups

The notion of Hankel operators associated with analytic crossed products were introduced and researched in [2]. In this paper, we study the adjoint of Hankel operators and give necessary and sufficient condition that the adjoint of a Hankel operator is again a Hankel operator. This work was supported in part by a Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science.     

优化的合班问题

首次提出了我国高校排课中的合班工作对于排课的影响问题,建立了优化合班问题的数学模型,它是一个非线性的整数规划问题.集中讨论二维合班问题.文章中给出了两个适用于合班模型的其它例子,在此基础上归纳出适用于合班模型的一般数学模式,称之为交叉分类问题.     

微型自由电子激光电子运动特性分析

作者曾首次提出以铁电单晶表面势代替摇摆器磁场的自由电子激光新机制.本文从单电子的洛仑兹方程出发,对电子的单摆方程,共振行为进行了研究,获得了第j个表面势共振态的增益公式.单摆方程和文献[1]中从能量方程得到的一致,本文的研究充实了文献[1]的论据。     

AF-embeddability of crossed products of Cuntz algebras

We investigate crossed products of Cuntz algebras by quasi-free actions of abelian groups. We prove that our algebras are AF-embeddable when actions satisfy a certain condition. We also give a necessary and sufficient condition that our algebras become simple and purely infinite, and consequently our algebras are either purely infinite or AF-embeddable when they are simple.     

Topologically Free Partial Actions and Faithful Representations of Crossed Products

We study the relationship between the topological freeness of partial actions of discrete groups and faithful representations of the corresponding crossed products.     

Spontaneous emission and spectral properties of radiation by relativistic electrons in a gyro‐klystron and optical‐klystron undulator

In this paper spontaneous emission of radiation by relativistic electrons in a gyro‐klystron is studied. The scheme consists of two solenoid sections separated by a dispersive section. In the dispersive section the electrons are made non‐resonant with the radiation. The dispersive section transforms a small change of the velocity into changes of the phases of the electrons. This leads to enhanced radiation due to klystron‐type modulation as compared with a conventional gyrotron‐type device driven by cyclotron maser interaction. It is shown that the klystron‐modulated spectrum depends on the dispersive field strength, finite perpendicular velocity component and length of the solenoids but is independent of the axial magnetic field strength. A simple scheme to design a gyro‐klystron is discussed.     

Undulator beamline optimization with integrated chicanes for X‐ray free‐electron‐laser facilities

An optimization of the undulator layout of X‐ray free‐electron‐laser (FEL) facilities based on placing small chicanes between the undulator modules is presented. The installation of magnetic chicanes offers the following benefits with respect to state‐of‐the‐art FEL facilities: reduction of the required undulator length to achieve FEL saturation, improvement of the longitudinal coherence of the FEL pulses, and the ability to produce shorter FEL pulses with higher power levels. Numerical simulations performed for the soft X‐ray beamline of the SwissFEL facility show that optimizing the advantages of the layout requires shorter undulator modules than the standard ones. This proposal allows a very compact undulator beamline that produces fully coherent FEL pulses and it makes possible new kinds of experiments that require very short and high‐power FEL pulses.     

A note on the crossed product $$ \mathcal{R}(\mathcal{A},\alpha ) $$ associated with PSL2(ℝ)

Given the hyperbolic measure dxdy/y ² on the upper half plane ℍ, the rational actions of PSL₂(ℝ) on ℍ induces a continuous unitary representation α of this group on the Hilbert space L ²(ℍ, dxdy/y ²). Supposing that = {M _f : f ∈ L ^∞ (ℍ, dxdy/y ²)}, we show that the crossed product is of type I. In fact, the crossed product is *-isomorphic to the von Neumann algebra , where is the abelian group von Neumann algebra generated by the left regular representation of K. This work was supported by the Youth Foundation of Sichuan Education Department of China (Grant No. 2003B017)     

Inverse semigroups and combinatorial C*-algebras

We describe a special class of representations of an inverse semigroup S on Hilbert's space which we term tight. These representations are supported on a subset of the spectrum of the idempotent semilattice of S, called the tight spectrum, which is in turn shown to be precisely the closure of the space of ultra-filters, once filters are identified with semicharacters in a natural way. These representations are moreover shown to correspond to representations of the C*-algebra of the groupoid of germs for the action of S on its tight spectrum. We then treat the case of certain inverse semigroups constructed from semigroupoids, generalizing and inspired by inverse semigroups constructed from ordinary and higher rank graphs. The tight representations of this inverse semigroup are in one-to-one correspondence with representations of the semigroupoid, and consequently the semigroupoid algebra is given a groupoid model. The groupoid which arises from this construction is shown to be the same as the boundary path groupoid of Farthing, Muhly and Yeend, at least in the singly aligned, sourceless case. *Partially supported by CNPq.