Extremally distant normed spaces with additional restrictions

We study the relationship between the Banach—Mazur distance and the modified Banach—Mazur distance. We sharpen the Szarek theorem on the construction of invariant norms with specific properties and construct extremally distant normed spaces with norms invariant under groups of automorphisms of small cardinality. We prove that the trivial upper bound for the Banach—Mazur distance obtained in terms of the modified Banach—Mazur distance is order-sharp.     

A Modified Quasi-Newton Method for Structured Optimization with Partial Information on the Hessian

This paper develops a modified quasi-Newton method for structured unconstrained optimization with partial information on the Hessian, based on a better approximation to the Hessian in current search direction. The new approximation is decided by both function values and gradients at the last two iterations unlike the original one which only uses the gradients at the last two iterations. The modified method owns local and superlinear convergence. Numerical experiments show that the proposed method is encouraging comparing with the methods proposed in [4] for structured unconstrained optimization Presented at the 6th International Conference on Optimization: Techniques and Applications, Ballarat, Australia, December 9–11, 2004     

RLW—Burgers方程的精确解

借助未知函数的变换，ＲＬＷ－Ｂｕｒｇｅｒｓ方程和ＫｄＶ－Ｂｕｒｇｅｒｓ方程化为易于求解的齐次形式的方程，从而得到ＲＬＷ－Ｂｕｒｇｅｒｓ方程和ＫｄＶ－Ｂｕｒｇｅｒｓ方程的精确解。     

丝网印刷普鲁士蓝修饰电极催化还原测定过氧化氢

制备了普鲁士蓝修饰的丝网印刷过氧化氢传感器,研究了过氧化氢在该修饰电极上的电催化还原特性,考察了有关修饰膜制备和试验条件对传感器性能的影响。结果表明,pH4.0的0.2mol·L-1KH2PO4 K2HPO4缓冲溶液(PBS)中,修饰电极对过氧化氢显示出快速的电化学响应,较高的稳定性、重现性和催化活性,测定的线性范围为1.0×10-5～1.0×10-3mol·L-1,相关系数为0.999,检出限为6.0×10-6mol·L-1(3σ)。电极制作方法简便,可用于实际样品的测定。     

一种检验定性指标的有效方法

介绍了一种检验定性指标的有效方法,可用于确定产品的合格率和评价检验人员的检验水平。用该方法分析了某厂产品的一项实际指标,合格率为91 4%,还对该厂10名检验员的检验水平作了客观的评价。     

Nuclearity of a nonnegative definite integral kernel on a separable metric space

The aim of this paper is to characterize the nuclearity of an integral operator, defined by a continuous non-negative definite square integrable kernel on a separable metric space, in terms of the integrability of the trace of the kernel function. Nuclearity here plays a role forU-statistics.     

添加剂与铝合金的相互作用研究 Ⅰ.静态反应膜及油润滑下的摩擦学性能

静态下分别于２５℃，９０℃及１８０℃下进行硫化异丁烯（ＳＯ）、亚磷酸二正丁酯（ＤＢＰ）、ＳＯ＋ＤＢＰ的混合物（质量比２０∶１）、二烷基二硫代磷酸锌（ＺＤＤＰ）及十二酸（ＬＡ）５种添加剂均以质量分数为２％的比例添加到液体石蜡（ＬＰ）中与铝合金进行油浸试验．用动－静摩擦系数精密测定仪评价了在铝合金表面上所形成的静态反应膜的摩擦磨损行为，并考察了上述添加剂在ＬＰ中对铝合金－钢摩擦副的润滑作用．结果表明：静态反应膜的摩擦磨损行为与添加剂的化学活性密切相关，其中ＤＢＰ最易与铝合金发生反应，故其反应膜具有最低的摩擦系数和最长的耐磨寿命；ＺＤＤＰ在１８０℃下的静态反应膜具有较低的摩擦系数和较长的耐磨寿命；ＳＯ、ＳＯ与ＤＢＰ的混合物及ＬＡ的静态反应膜则不具有减摩抗磨性能，预示这些添加剂在ＬＰ中不与铝合金发生较强的化学作用．含上述添加剂的ＬＰ润滑下的摩擦磨损试验显示，ＤＢＰ与ＺＤＤＰ具有较好的摩擦学性能．这表明添加剂在铝合金表面静态反应膜的摩擦磨损试验结果与其在常规润滑下的具有较好的相关性．     

Regime diagram of the development of long-wave near-wall disturbances in a hypersonic boundary layer

A regime diagram of the development of slow near-wall disturbances induced by an unsteady self-induced pressure perturbation in a hypersonic boundary layer is constructed for a disturbance wavelength greater than the boundary layer thickness. It is shown that the main factors shaping the perturbed flow are the gas enthalpy near the body surface, the intensity of the viscous-inviscid interaction, and the nature (sub- or supersonic) of the main part of the boundary layer. Nonlinear boundary-value problems are formulated for regimes in which the near-wall boundary layer region plays a decisive role. Numerical and analytical solutions are obtained in the linear approximation. It is shown that intensification of the viscous-inviscid interaction or an increase in the role of the supersonic main region of the boundary layer impart generally supersonic properties to the main part of the boundary layer, i.e. the upstream propagation of the disturbances is damped and the disturbance growth downstream becomes more intense. Damping of the viscous-inviscid interaction and an increase in the role of the subsonic main part of the boundary layer have the opposite effect. Surface cooling increases the effect of the main part of the boundary layer on the formation of pressure disturbances and surface heating leads to an increase in the effect of the near-wall boundary layer region. It is also shown that for the regimes considered disturbances propagate in a direction opposite to that of the free stream from the turbulent flow region located downstream of the local disturbance development region.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 59–71. Original Russian Text Copyright © 2004 by Bogolepov and Neiland.     

A Trigger of Coupled Singularities

By using example of nonlinear dynamics of a pair of coupled gears, the phenomenon of appearance and disappearance of a trigger of coupled singularities and homoclinic orbits in the form of number eight in the phase portrait in the phase plane is investigated. That phenomenon is an accompanying phenomenon of loss of stability of the local unique equilibrium position. For a generalized case under certain conditions, a theorem of the appearance of a trigger of coupled singularities in a nonlinear dynamical conservative system, the first derivative of the system potential energy which is a product of two periodic functions with different periods, and one bifurcation parameter, which is the cause for the appearance of new roots of these two functions, is defined.     

Effect of a Shock Pulse on a Floating Ice Sheet

The vibrations of a viscoelastic plate lying on an elastic liquid base subjected to pulse loading have been studied theoretically and experimentally. The effect of the variable depth of the reservoir, plate thickness, and strain relaxation time on the value of the plate vibration amplitude and the length and curvature of the flexural gravity wave profile are analyzed. Good agreement of theoretical and experimental results is obtained.