A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP

In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the Lp-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.     

Efficient computation of natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder

In this work, the natural convection in a concentric annulus between a cold outer square cylinder and a heated inner circular cylinder is simulated using the differential quadrature (DQ) method. The vorticity‐stream function formulation is used as the governing equation, and the coordinate transformation technique is introduced in the DQ computation. It is shown in this paper that the outer square boundary can be approximated by a super elliptic function. As a result, the coordinate transformation from the physical domain to the computational domain is set up by an analytical expression, and all the geometrical parameters can be computed exactly. Numerical results for Rayleigh numbers range from 104 to 106 and aspect ratios between 1.67 and 5.0 are presented, which are in a good agreement with available data in the literature. It is found that both the aspect ratio and the Rayleigh number are critical to the patterns of flow and thermal fields. The present study suggests that a critical aspect ratio may exist at high Rayleigh number to distinguish the flow and thermal patterns. Copyright © 2002 John Wiley & Sons, Ltd.     

Spectral line suppression and sideband narrowing via quantum interference

We reveal that for a realistic system, interference effects are obtained such as the suppression of central line and inner sidebands and the narrowing of the outer fluorescence sidebands. For this purpose, we consider a spontaneous decay from an excited state to a metastable state when the excited and metastable states are resonantly coupled to an auxiliary metastable state by a laser field and a microwave field, respectively. The fluorescence spectrum evolves from a five-peaked structure into a doublet of ultrasharp lines as the ratio of the laser field Rabi frequency to the microwave Rabi frequency is decreased. The physical origin is presented in terms of dressed states.     

The study and applications of photochemical-dynamical gravity wave model II

A nonlinear, compressible, non-isothermal gravity wave model that involves photochemistry is used to study the effects of gravity wave on atmospheric chemical species distributions in this paper. The changes in the distributions of oxygen compound and hydrogen compound density induced by gravity wave propagation are simulated. The results indicate that when a gravity wave propagates through a mesopause region, even if it does not break, it can influence the background distributions of chemical species. The effect of gravity wave on chemical species at night is larger than in daytime.     

Soliton interaction under the influence of higher-order effects

In this paper, we present exact N-soliton solution by employing simple, straightforward Darboux transformation based on the Lax pair for Hirota equation, a higher-order nonlinear Schrödinger (HNLS) equation. As examples, one- and two-soliton solutions in explicit forms are given and their properties are also analyzed. A bound solution without interaction will be theoretically predicted if one can adjust frequency shift for each soliton appropriately. Further, we obtain the approximate eigenvalues by employing two-soliton solution and discuss analytically the interaction between neighboring solitons under the influence of the higher-order effects. It is shown that the combined effects of the higher-order effects can restrain the interaction between neighboring solitons to some extent. The results are proved by directly solving HNLS equation numerically.     

The effects of crystal structure on optical absorption/photoluminescence of bis(8-hydroxyquinoline)zinc

In this paper, the transformation processes of two types of bis(8-hydroxyquinoline)zinc: Znq₂ dihydrate and anhydrous (Znq₂)₄ were investigated by X-ray diffraction (XRD), infrared spectra (IR), scanning electron microscope (SEM), differential scanning calorimetry (DSC) and thermogravimetry (TG). The effects of crystal structure on optical properties of bis(8-hydroxyquinoiline)zinc were analyzed. Znq₂ dihydrate can be transformed into anhydrous (Znq₂)₄ during heating under vacuum. Reversal transformation occurs by the interaction between chloroform and (Znq₂)₄. But (Znq₂)₄ was partially transformed into Znq₂ dihydrate by the interaction between ethanol and (Znq₂)₄. The different molecular structure results in different crystal stacking and electronic structure, thereby affect its optical properties.     

Analysis of queueing policies in QoS switches

It is widely accepted that next-generation networks will provide guaranteed services, in contrast to the “best effort” approach today. We study and analyze queueing policies for network switches that support the QoS (Quality of Service) feature. One realization of the QoS feature is that packets are not necessarily all equal, with some having higher priorities than the others. We model this situation by assigning an intrinsic value to each packet. In this paper we are concerned with three different queueing policies: the nonpreemptive model, the FIFO preemptive model, and the bounded delay model. We concentrate on the situation where the incoming traffic overloads the queue, resulting in packet loss. The objective is to maximize the total value of packets transmitted by the queueing policy. The difficulty lies in the unpredictable nature of the future packet arrivals. We analyze the performance of the online queueing policies via competitive analysis, providing upper and lower bounds for the competitive ratios. We develop practical yet sophisticated online algorithms (queueing policies) for the three queueing models. The algorithms in many cases have provably optimal worst-case bounds. For the nonpreemptive model, we devise an optimal online algorithm for the common 2-value model. We provide a tight logarithmic bound for the general nonpreemptive model. For the FIFO preemptive model, we improve the general lower bound to 1.414, while showing a tight bound of 1.434 for the special case of queue size 2. We prove that the bounded delay model with uniform delay 2 is equivalent to a modified FIFO preemptive model with queue size 2. We then give improved upper and lower bounds on the 2-uniform bounded delay model. We also show an improved lower bound of 1.618 for the 2-variable bounded delay model, matching the previously known upper bound.     

Circular perfect graphs

For 1 ≤ d ≤ k, let K_k/d be the graph with vertices 0, 1, …, k ? 1, in which i ～j if d ≤ |i ? j| ≤ k ? d. The circular chromatic number χ_c(G) of a graph G is the minimum of those k/d for which G admits a homomorphism to K_k/d. The circular clique number ω_c(G) of G is the maximum of those k/d for which K_k/d admits a homomorphism to G. A graph G is circular perfect if for every induced subgraph H of G, we have χ_c(H) = ω_c(H). In this paper, we prove that if G is circular perfect then for every vertex x of G, N_G[x] is a perfect graph. Conversely, we prove that if for every vertex x of G, N_G[x] is a perfect graph and G ? N[x] is a bipartite graph with no induced P₅ (the path with five vertices), then G is a circular perfect graph. In a companion paper, we apply the main result of this paper to prove an analog of Haj?os theorem for circular chromatic number for k/d ≥ 3. Namely, we shall design a few graph operations and prove that for any k/d ≥ 3, starting from the graph K_k/d, one can construct all graphs of circular chromatic number at least k/d by repeatedly applying these graph operations. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 186–209, 2005     

物理模型教学与创新能力的培养

现代教学以能力培养为重点.学生获得研究问题、探索问题的能力是十分重要的,物理模型的教学过程对培养学生研究问题、探索问题、发展创造思维、培养辩证唯物主义思想方法都极为有利,因此,必须重视物理模型教学.     

Radiative lifetimes in Ce I and Ce II

New radiative lifetime measurements based on time-resolved laser-induced fluorescence techniques are reported for 18 even-parity levels belonging to the 4f5d^26p and 4f ²5d ² configurations of Ce I and 6 even-parity levels belonging to the 5d^26s, 4f5d6p, and 4f6s6p configurations of Ce II. Free neutral and singly ionized cerium atoms were produced by laser ablation. The Ce I and Ce II levels range in energy from 26 545 to 29 102 cm^-1, and 42 573 to 48 152 cm^-1, respectively. Received 25 September 2002 Published online 4 March 2003