Faddeev-Jackiw canonical path integral quantization for a general scenario, its proper vertices and generating functionals

We generalize the Faddeev-Jackiw canonical path integral quantization for the scenario of a Jacobian with J=1 to that for the general scenario of non-unit Jacobian, give the representation of the quantum transition amplitude with symplectic variables and obtain the generating functionals of the Green function and connected Green function. We deduce the unified expression of the symplectic field variable functions in terms of the Green function or the connected Green function with external sources. Furthermore, we generally get generating functionals of the general proper vertices of any n-points cases under the conditions of considering and not considering Grassmann variables, respectively; they are regular and are the simplest forms relative to the usual field theory.

Entanglement conditions for mixed SU(2) and SU(1,1) systems

We derive a class of inequalities for detecting entanglement in the mixed SU(2) and SU(1, 1) systems based on the Schrodinger-Robertson indeterminacy relations in conjugation with the partial transposition. These inequalities are in general stronger than those based on the usual Heisenberg uncertainty relations for detecting entanglement. Furthermore, based on the complete reduction from SU(2) and SU(1,1) systems to bosonic systems, we derive some entanglement conditions for two-mode systems. We also use the partial reduction to obtain some inequalities in the mixed SU(2) (or SU(1, 1)) and bosonic systems.

Unified expressions of all integral variational principles

In terms of the quantitative causal principle, this paper obtains a general variational principle, gives unified expressions of the general, Hamilton, Voss, Holder, Maupertuis-Lagrange variational principles of integral style, the invariant quantities of the general, Voss, Holder, Maupertuis-Lagrange variational principles are given, finally the Noether conservation charges of the general, Voss, Holder, Maupertuis-Lagrange variational principles axe deduced, and the intrinsic relations among the invariant quantities and the Noether conservation charges of all the integral variational principles axe achieved.

Differential and Integral Cross Sections for Electron Impact Excitation of Lithium

The differential and integral cross sections for electron impact excitation of lithium from the ground state 1s(2)2s to excited states 1s(2)2p, 1s(2)3l (l = s,p,d) and 1s(2)4l (l = s,p,d,f) at incident energies ranging from 5 eV to 25 eV are calculated by using a full relativistic distorted wave method. The target state wavefunctions are calculated by using the Grasp92 code. The continuum orbitals are computed in the distorted-wave approximation, in which the direct and exchange potentials among all the electrons are included. A part of the cross sections are compared with the available experimental data and with the previous theoretical values. It is found that, for the integral cross sections, the present calculations are in good agreement with the time-independent distorted wave method calculation, for differential cross sections, our results agree with the experimental data very well.

N-arylamides from selenium-catalyzed reactions of nitroaromatics and amides in the presence of carbon monoxide and mixed organic bases

N-Arylamides were exclusively obtained in moderate to good yields from selenium-catalyzed reactions of nitroaromatics with amides in the presence of CO and mixed organic bases Et3N and DBU.

Reduction property and catalytic activity of Ce1-XNiXO2 mixed oxide catalysts for CH4 oxidation

Ce1-XNiXO2 oxides with X varying from 0.05 to 0.5 were prepared by different methods and characterized by XRD and TPR techniques. Ce(0.7)Mi(0.3)O(2) sample prepared by sol-gel method shows the highest reducibility and the highest catalytic activity for methane combustion. Three kinds of Ni phases co-exist in the Ce1-XNiXO2 catalysts prepared by sol-gel method: (i) aggregated NiO on the support CeO2, (ii) highly dispersed NiO with strong interaction with CeO2 and (iii) Ni atoms incorporated into CeO2 lattice. The distribution of different Ni species strongly depends on the preparation methods. The highly dispersed NiO shows the highest activity for methane combustion. The NiO aggregated on the support CeO2 shows lower catalytic activity for methane combustion, while the least catalytic activity is found for the Ni species incorporated into CeO2. Any oxygen vacancy formed in CeO2 lattice due to the incorporating of Ni atoms adsorbs and activates the molecular oxygen to form active oxygen species. So the highest catalytic activity for methane combustion on Ce0.7Ni0.3O2 catalyst is attributed not only to the highly dispersed Ni species but also to the more active oxygen species formed. (C) 2002 Elsevier Science B.V. All rights reserved.

Kinetics of acetic acid esterification with 2-ethoxyethanol over an Al-pillared clay catalyst

The Al-pillared clay catalyst obtained by exposing activated clay powder to sulfuric acid and aluminium salts and calcining in air at 373-673 K, was found to be highly active for the title reaction. The results indicated that pillared layer clay of the mixed oxide has been employed as parent catalysts for their definite structure and special properties which can be modified by the substitution of L and B acid sites cations. Solid acid catalyst of Supported aluminium was found to be highly active and selective at the 373-473 K temperature range for heterogeneous esterification. The activity is mainly attributed to the Lewis (and a considerably small number of Bronsted) acid sites whose number and strength increased due to pillaring. The water produced in the esterification can be induced by Al3+, which makes the catalyst surface to form strong B acid. Their acidities are obtained by pH measurement. If only B acid sites are > 70%, and pH < 1 in the 2-ethoxyethanol, there exists an activity of esterification. The used catalyst gave identical results with that of the fresh one. X-ray diffraction spectra show that the composition and active phase of the used catalysts are the same as the fresh ones. The kinetic study of the reaction was carried out by an integral method of analysis. The kinetic equation of surface esterification is y = 2.36x - 0.98.