Two-weight Inequalities for Commutators of Potential Operators on Spaces of Homogeneous Type

We derive the two-weight inequalities for the commutators of potential integral operators in the context of spaces of homogeneous type. The conditions required of the weights involve the Orlicz bumps. As a consequence, we obtain the norm estimates for these commutators for arbitrary weights. Supported by the National Natural Science Foundation of China (Nos. 10771049, 60773174) and the Natural Science Foundation of Hebei Province (08M001).     

Newton Trajectories in the Curvilinear Metric of Internal Coordinates

The reaction path is an important concept of theoretical chemistry. We discuss the definition with the help of the following of the reduced gradient (RGF) [see Quapp et al., Theoret. Chem. Acc. 100 (1998) 285], also named the Newton trajectory. All the important features of the potential energy surface are definable independently of the coordinate system. We demonstrate it for the Newton trajectory. We design a numerical scheme for the RGF method including the intrinsic curvilinear metric of internal coordinates. For the path following we extend the previous method to the use of a generalized singular value decomposition (SVD). An example of the HCN isomerization pathway is discussed.     

Structure and dynamics of cationic van-der-Waals clusters

Ar_nHCl⁺ van-der-Waals clusters for n = 1–13 are investigated with the “minimal diatomics-in-molecules (DIM) model” using ab-initio input data obtained from multi-reference configuration-interaction calculations plus subsequent projection onto valence-bond wavefunctions. The results for the complexes with n = 1–3 are checked against ab-initio calculations at the coupled-cluster (CCSD) level with the same one-electron atomic basis set as for the input data generation (aug-cc-pVTZ from Dunning). In addition to the electronic ground state, the first excited state for the triatomic complex (n = 1) is also studied. The results from the DIM model are shown to be in fair agreement with those from advanced conventional ab-initio calculations, although there are differences in detail. The comparison justifies the extension of the DIM approach to n > 3. Systematic analysis of the local minima of the multi-dimensional potential-energy surfaces (PESs), carried out with the combined method described in part I (Monte-Carlo sampling plus subsequent steepest-descent optimization), reveals simple building-up regularities for the most stable structures (i.e. those corresponding to the global PES minimum) at each n: apart from always having a nearly linear (Ar–H–Cl)⁺ fragment as core, the aggregates show little or no symmetry. Secondary local minima are also determined and their structures interpreted. The PESs for the low-lying excited states reveal a much more complicated topography compared to the Ar_nH⁺ clusters allowing a variety of photo-processes. The energy level sequence of the first five excited electronic states and the stability of the clusters in these states is studied as a function of the cluster size n.     

A quantum chemical approach towards the electronically excited states of helium clusters

We have investigated the electronic energies of the ground and excited states of an octahedral helium cluster by quantum chemical ab initio calculations. The excited levels were calculated for the central atom for a set of different inter atomic separations. Our approach yields potential energy curves which are suited to describe a density dependence of the spectral features as previously observed in photo excitation experiments. The potential energy curves of the 2s and 2p states show a hump at ? caused by the strong perturbation of neighbouring atoms. The existence of this hump explains the experimentally observed blue shift and its dependence on the cluster size or density, respectively. The potential curves of the higher levels show almost constant energies. Perturbations of these levels are small, because the overlap between the Rydberg orbital and the orbitals of the surrounding atoms is small. This is the case for both small R values where the Rydberg orbital is well outside the cluster as well as for large R where the density drastically decreases. These findings coincide with the un-shifted features of small clusters observed in experiments.     

Vortex ring modelling of toroidal bubbles

During the collapse of a bubble near a surface, a high-speed liquid jet often forms and subsequently impacts upon the opposite bubble surface. The jet impact transforms the originally singly-connected bubble to a toroidal bubble, and generates circulation in the flow around it. A toroidal bubble simulation is presented by introducing a vortex ring seeded inside the bubble torus to account for the circulation. The velocity potential is then decomposed into the potential of the vortex ring and a remnant potential. Because the remnant potential is continuous and satisfies the Laplace equation, it can be modelled by the boundary-integral method, and this circumvents an explicit domain cut and associated numerical treatment. The method is applied to study the collapse of gas bubbles in the vicinity of a rigid wall. Good agreement is found with the results of Best (J. Fluid Mech. 251 79–107, 1993), obtained by a domain cut method. Examination of the pressure impulse on the wall during jet impact indicates that the high-speed liquid jet has a significant potential for causing damage to a surface. There appears to be an optimal initial distance where the liquid jet is most damaging.     

Microwave-induced and conventional heterocyclic synthesis: An antimicrobial entites of newer quinazolinyl-Δ2-pyrazolines

Heterocyclic compounds containing pyrazolines were reported to possess significant biological activity. Synthesis of 2-(ω-chloroacetonyl)-3-p-fluorophenyl-6-bromoquinazoline-4(3H)-ones (2), 2-(ω-hydrazinoacetonyl)-3-p-fluorophenyl-6-bromoquinazoline-4(3H)-ones (3) and 1′-[3H-3-p-fluorophenyl-4-oxo-6-bromoquinazoline-2-acetonyl]-3′-[1-o-chlorophenyl-3-methyl-5-azomethine-2-pyrazolidene]-5′-(substituted phenyl)-Δ²-pyrazolines (4a–j) have been described. Some of the new compounds were tested against bacteria (Gram –ve and Gram +ve) and fungi.     

Gibbs-non-Gibbs dynamical transitions for mean-field interacting Brownian motions

We consider a system of real-valued spins interacting with each other through a mean-field Hamiltonian that depends on the empirical magnetisation of the spins. The system is subjected to a stochastic dynamics where the spins perform independent Brownian motions. Using large deviation theory we show that there exists an explicitly computable crossover time $t_c\in [0,\infty ]$ from Gibbs to non-Gibbs. We give examples of immediate loss of Gibbsianness ($t_c=0$), short-time conservation and large-time loss of Gibbsianness ($t_c\in (0,\infty )$), and preservation of Gibbsianness ($t_c=\infty$). Depending on the potential, the system can be Gibbs or non-Gibbs at the crossover time $t=t_c$.     

Electric field perturbation due to impurities in GaAs through single electron transistor

The present work shows the presence of inevitable impurities in the semi-insulating GaAs domains when one is developing a single electron transistor (SET) and alters the quantization mechanism of single electron tunneling through the island. It is also indicated that these impurities decrease the amount of energy required to change the number of electrons on the island, which leads to a drastic reduction of SET quality. A theoretical model has been presented for elucidating the I–V characteristics of GaAs nano-crystals. It is found that this proposed model fits well the experimental data.     

乙烯基自由基(C2H·3)与羟基自由基(OH·)反应势能面的理论研究

在QCISD（T）/6-311G（2df,p)//B3LYP/6-311G（d,p)水平上对自由基反应C2H3^. OH^.进行了计算，结果表明，经过缔合、多步H转移、CH3转移和离解等复杂过程，最终要得到8种产物（P1-P8），茯中产物P2（H2CCO H2）和P6（CH3CO^. H^.）是主要产物。本文得到的CH2CHOH（1或1‘），CH3CHO（2）和CH3COH（3）之间的过渡态TS1/2，TS1‘/3和TS2/3的能量顺序与Wesdemiotis等的实验推测相反，而与Smith等的计算结果一致。     

A novel method for measuring zeta potentials of solid–liquid interfaces

A novel method for measuring the zeta potential of PDMS–electrolyte solution interface is presented in this paper. When an electrolyte solution passes the electrode coated with PDMS film, an electrical current will be induced due to the electrostatic potential difference between the PDMS–air interface and the PDMS–electrolyte solution interface. Based on this principle, the relationship between the measured electrical signal and the zeta potential of PDMS–electrolyte solution interface is experimentally investigated. The results show that the magnitude of the measured signal is linearly proportional to this potential difference. An empirical correlation between the zeta potential and the measured voltage signal was obtained. Good agreement was found when comparing the zeta potential calculated by this empirical equation with that reported in the published journal papers. The zeta potential measurement method presented in this paper is simple and accurate and can be used for measuring zeta potentials of other dielectric–electrolyte interfaces.