On tangential deformations of homogeneous polynomials

The Jacobian ideal provides the set of infinitesimally trivial deformations for a homogeneous polynomial, or for the corresponding complex projective hypersurface. In this article, we investigate whether the associated linear deformation is indeed trivial, and show that the answer is no in a general situation. We also give a characterization of tangentially smoothable hypersurfaces with isolated singularities. Our results have applications in the local study of variations of projective hypersurfaces, complementing the global versions given by J. Carlson and P. Griffiths, R. Donagi and the author, and in the study of isotrivial linear systems on the projective space, showing that a general divisor does not belong to an isotrivial linear system of positive dimension.     

选取最大载荷为岩石KIC测试中临界载荷的合理性研究

本文对选取最大载荷为岩石 K_(IC)测试中临界载荷的合理性从理论上和实验上进行了研究,结果表明,选取最大载荷为岩石 K_(IC)测试中的临界载荷是合理的,正确的。     

Parametric Identification of a Base-Excited Single Pendulum

A harmonic balance based identification algorithm was applied to the simulated single pendulum with horizontal base-excitation. The purpose of this simulation was to examine the applicability of the algorithm on parametrically excited, whirling chaotic systems. Modifications were adopted to adapt to the whirling systems. The system was supposed to be unknown except only the excitation frequency. Linear interpolation functions and the Fourier series functions were tested to approximate unknown nonlinear functions in the governing differential equation. After extracting unstable periodic orbits, all of the parameters were simultaneously identified. By direct comparison, Poincaré section plots and reconstructed phase portrait techniques, it was shown that the identified system had similar dynamical characteristics to the original simulated pendulum, which implies the effectiveness of the examined algorithm.     

Evolution of Limit Cycles in the Stability Domain of a Double Pendulum under a Variable Follower Force

It is shown that stable and unstable limit cycles are born at a certain value of the follower force. As the absolute value of the force increases, the cycles move with different velocities in opposite directions. The unstable limit cycle moves toward the origin in the four-dimensional phase space. At a certain value of the follower force, this cycle gets at the origin, disturbing its stability as a singular point of the dynamic system. If the absolute value of the follower force decreases, then death of both cycles is possible. In this case, the attraction domain of the origin becomes infinite     

A new method for determining droplet size distribution of an unstable dispersion

The droplet size distribution (DSD) of unstable water/oil dispersions has been studied with a new technique. The technique is based on a fast dilution of the dispersion injected into an analysis vessel where the DSD is analyzed with a video camera and a image analyzing tool. Dispersions generated with no pressure drop in the flow rig were compared to those generated with a pressure drop over a needle valve. The latter dispersion showed a much narrower DSD and a lower average droplet diameter. The results are from preliminary experiments in order to evaluate the method.     

颜色不稳定黄色蓝宝石的谱学特征与颜色成因

颜色不稳定黄色蓝宝石广泛存在市场中,如何有效鉴别颜色不稳定黄色蓝宝石的特征是当前宝石学研究的热点。利用改色实验、紫外-可见光谱（UV-Vis）、三维荧光光谱对颜色不稳定黄色蓝宝石进行深入的谱学特征研究。改色实验表明斯里兰卡黄色蓝宝石中部分存在光致变色的现象,短波紫外光会导致样品着色,而太阳光会导致样品褪色。紫外光照后黄色蓝宝石的颜色由稳定部分和不稳定部分共同组成。颜色不稳定蓝宝石的“着色态”和“褪色态”紫外-可见光谱可见明显的蓝紫区吸收,这可能与蓝宝石中O2--Fe3+的电荷转移有关,导致了蓝宝石稳定的黄色调。蓝宝石的紫外-可见光谱在“着色态”相比“褪色态”可见明显的蓝紫区吸收增强,可能由于紫外光照射增强了O2--Fe3+之间的电荷转移。紫外-可见光谱测试表明样品中具有弱的与Fe有关的吸收峰,这与样品含有较低的Fe含量一致,不足以产生稳定黄色调。三维荧光光谱分析结果表明颜色不稳定黄色蓝宝石的“着色态”和“褪色态”具有一致的激发光波长Ex=325～335 nm、发射光波长Em=560～570 nm的特征荧光中心,在“着色态”时的荧光强度明显高于“褪色态”。含铁黄色蓝宝石具有荧光效应且特征的荧光中心可作为识别这种颜色不稳定黄色蓝宝石的潜在鉴定手段。综合报道了颜色不稳定黄色蓝宝石的谱学特征与可能的颜色成因,为识别颜色不稳定的蓝宝石提供了鉴定依据,同时为后续改色处理的工艺提供了理论基础。     

一类输出耦合混沌复杂动态网络不稳定平衡点的控制

研究节点输出耦合混沌复杂动态网络不稳定平衡点的控制问题,基于输出控制思想,提出网络节点不稳定平衡点的全局控制方法以及牵制控制方法,将混沌复杂动态网络的所有节点镇定到其平衡点.利用李稚普诺夫稳定性理论,得到控制器参数选择条件,以蔡氏混沌电路作为网络节点动态进行仿真研究,证明该方法的有效性.     

带线性坍塌项和竞争势的非线性波动方程柯西问题的稳定集和不稳定集(英文)

本文考虑带线性坍塌项和竞争势的非线性波动方程柯西问题,定义了新的稳定集和不稳定集,证明了如果初值进入不稳定集,则解在有限时间爆破;如果初值进入稳定集,则整体解存在.运用势井讨论,回答了当初值在多么小的时候,该柯西问题的整体解存在.     

基于正交试验的诱导轮前置孔板的参数化研究

为明确前置各种参数的孔板对抑制GSB-80/300型的诱导轮离心泵小流量不稳定特性的影响程度,选择孔板离诱导轮前缘的距离L,孔板的孔径D,孔板的厚度B作为3因素,每个因素各取3水平,制定了L9(3~3)正交数值模拟试验方案。数值模拟试验方案采用雷诺时均N-S控制方程和标准κ-ε湍流模型。通过数值模拟,得到了前置各种参数的孔板下诱导轮离心泵流场的分布情况,得到了较佳的三种参数组合,并揭示了各个因素对流场的影响顺序是:孔板的孔径D,孔板的厚度B,孔板离诱导轮前缘的距离L。在此基础上,对三种较佳参数组合下的孔板进行了全工况点的数值模拟,分别得到了它们的扬程流量特性曲线。通过流场,外特性曲线分析比较,得到了有效抑制GSB-80/300型的诱导轮离心泵小流量不稳定特性的最佳参数组合的孔板。     

Oscillating Decay of an Unstable System

We study the medium-time behavior of the survival probability in the frame of the N-level Friedrichs model. The time evolution of an arbitrary unstable initial state is determined. We show that the survival probability may oscillate significantly during the so-called exponential era. This result explains qualitatively the experimental observations of the NaI decay. The Gamow states for N-level Friedrichs model are constructed. The time evolution in terms of the complex spectral representation including the Gamow states is discussed.