On the Discretization of Distributed-Parameter Systems with Quadratic and Cubic Nonlinearities

Approximate methods for analyzing the vibrations of an Euler--Bernoulli beam resting on a nonlinear elastic foundation are discussed. The cases of primary resonance ( _n ) and subharmonic resonance of order one-half ( 2 _n ), where is the excitation frequency and _n is the natural frequency of the nth mode of the beam, are investigated. Approximate solutions based on discretization via the Galerkin method are contrasted with direct application of the method of multiple scales to the governing partial-differential equation and boundary conditions. The amplitude and phase modulation equations show that single-mode discretization leads to erroneous qualitative as well as quantitative predictions. Regions of softening (hardening) behavior of the system, the spatial dependence of the response drift, and frequency-response curves are numerically evaluated and compared using both approaches.     

Asymptotic behavior toward nonlinear waves for radially symmetric solutions of the multi-dimensional Burgers equation

The present paper is concerned with the asymptotic behaviors of radially symmetric solutions for the multi-dimensional Burgers equation on the exterior domain in ${\mathbb{R}}^n,n\ge 3$, where the boundary and far field conditions are prescribed. We show that in some case where the corresponding 1-D Riemann problem for the non-viscous part admits a shock wave, the solution tends toward a linear superposition of stationary and rarefaction waves as time goes to infinity, and also show the decay rate estimates. Furthermore, we improve the results on the asymptotic stability of the stationary waves which are treated in the previous papers [2], [3]. Finally, for the case of $n=3$, we give the complete classification of the asymptotic behaviors, which includes even a linear superposition of stationary and viscous shock waves.     

Uniqueness of isometric immersions with the same mean curvature

Motivated by the quasi-local mass problem in general relativity, we study the rigidity of isometric immersions with the same mean curvature into a warped product space. As a corollary of our main result, two star-shaped hypersurfaces in a spatial Schwarzschild or AdS-Schwarzschild manifold with nonzero mass differ only by a rotation if they are isometric and have the same mean curvature. We also prove similar results if the mean curvature condition is replaced by an ${\sigma }_2$-curvature condition.     

Regularity results of the thin obstacle problem for the p(x)-Laplacian

We study thin obstacle problems involving the energy functional with $p(x)$-growth. We prove higher integrability and Hölder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable exponent $p(x)$ is Hölder continuous.     

Synthesis and antiproliferative evaluation of oxime,methyloxime, and amide‐containing quinazolinones

Certain oxime, methyloxime, and amide‐containing quinazolinone derivatives were synthesized and evaluated in vitro for their antiproliferative activities against a panel of human cancer cell lines including nasopharyngeal carcinoma (NPC‐TW01), lung carcinoma (NCI‐H226), and leukemia (Jurkat). Quinazolinone 2 was inactive against all three cell lines tested, while quinazolinone 4 was weakly active against both Jurkat and H226 cancer cells with IC₅₀ values of 6.55 and 12.27 μM, respectively, indicating that the oxime derivative 4 is more favorable than its ketone precursor 2 . Our results have also indicated that quinazolinone 8g and its biphenyl counterpart 8f exhibited more potent antiproliferative activities than the positive control methotrexate against all three cancer cell lines tested. Among these quinazolinone derivatives, 8g was the most active against NPC‐TW01 with an IC₅₀ value of 4.78 μM. Further study on NPC‐TW01 cell cycle distribution indicated that the compound 8g induced cell arrest at the G1/G0 phase in a time‐ and concentration‐dependent manner. Moreover, a characteristic hypo‐diploid DNA content peak (sub‐G1) was found to increase from 1 to 4% in NPC‐TW01 cells treated with 8g for 72 hr. These results indicate that 8g can induce cells arrest in the G1/G0 phase and cause cell death. Further structural optimization of 8g and detailed study of its antiproliferative mechanism are going on.     

On universal entire functions with zero-free derivatives

We prove in this note a generalization of a theorem due to G. Herzog on zero-free universal entire functions. Specifically, it is shown that, if a nonnegative integer q and a nonconstant entire function φ of subexponential type are given, then there is a residual set in the class of entire functions with zero-free derivatives of orders q and q + 1, such that every member of that set is universal with respect to φ (D), where D is the differentiation operator. This work is supported in part by DGICYT grant PB93-0926.     

Minimal and optimal linear discrete time-invariant dissipative scattering systems

For an operator-valued function in the Schur class a new geometric proof, using state space considerations only, of the construction of a minimal and optimal realization is given. A minimal and optimal realization also appears as a restricted shift realization where the state space is the completion of the range of the associated Hankel operator in the de Branges-Rovnyak norm associated with . It is also shown that minimal and optimal, and minimal and star-optimal realizations of a rational matrix function in the Schur class are intimately connected to the extremal positive solutions of the associated Kalman-Yakubobich-Popov operator inequality.The first author thanks the International Association for the promotion of co-operation with scientists from the New Independent States of the former Soviet Union for its support (under project INTAS 93-249), and the Vrije Universiteit, Amsterdam, for its hospitality     

肝内门—腔静脉分流术的应用解剖

目的：为临床进行肝内门—腔静脉分流术提供解剖学基础。方法：在31例成人肝标本上观测肝静脉的汇合类型、开口纵径、横径,肝静脉与门静脉交叉处的长度、横径、两静脉间距离。结果：三条肝静脉注入下腔静脉分三种类型,肝右静脉与门静脉右干及右后上支交叉、肝中、左静脉与门静脉左干交叉。结论：肝内门—腔静脉分流术的首选部位是在肝右静脉与门静脉右干及右肩上支之间;其次是在肝中静脉与门静脉左干之间;肝左静脉不宜行肝内门—腔静脉分流术。     

全科模式培养卓越农村小学教师尝试与思考——以萍乡学院为例

全科模式培养农村小学教师是以萍乡学院为例,从生源质量的保证、课程设置的全科、教师基本素质的培养、农村小学教师队伍的稳定四个方面总结了萍乡学院全科模式培养卓越农村小学教师的尝试。依据实际尝试情况,文章对五年一贯制定向培养农村小学教师提出了建立公费就读制度、强化招生公平透明制度、建立培养过程的督促检查评定制度、实行培养结果的评价再挑选制度四条积极可行建议。     

高校基层党组织建立群众路线教育实践活动长效机制的探索

机制建设对于高校基层党组织推进党的群众路线教育实践活动常态化具有重要意义。建立健全学习教育机制、交流沟通机制、服务师生机制、考核评价机制和监督制约机制是高校基层党组织巩固群众路线教育实践活动成果的重要环节。