An experimental analysis of a population based approach for global optimization

In this paper we perform a computational analysis of a population based approach for global optimization, Population Basin Hopping (PBH), which was proven to be very efficient on very challenging global optimization problems by the authors (see ). The experimental analysis aims at understanding more deeply how the approach works and why it is successful on challenging problems.     

Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow

A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded. Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function theorem. Supported by the Swiss National Science Foundation. Fellowship PBEL2–114311.     

How to assess and report the performance of a stochastic algorithm on a benchmark problem: mean or best result on a number of runs?

Some authors claim that reporting the best result obtained by a stochastic algorithm in a number of runs is more meaningful than reporting some central statistic. In this short note, we analyze and refute the main argument brought in favor of this statement.     

Stable determination of an inhomogeneous inclusion by local boundary measurements

We deal with the problem of determining an inclusion within an electrostatic conductor from boundary measurements. Under mild a priori assumptions we establish optimal stability estimates. Measurements are performed on a portion of the boundary of the conductor.     

关于三维各向同性谐振子径向矩阵元计算的讨论

根据广义Laguerre多项式的数学性质，导出了较为简单的三维各向同性谐振子径向矩阵元的普遍公式,并在这基础上计算了一些重要特殊情形的径向矩阵元: 矢径r整数次幂的平均值，电偶极跃迁矩阵元和电四极跃迁矩阵元. 关键词： 三维各向同性谐振子 径向矩阵元 广义Laguerre多项式 偶极跃迁 四极跃迁     

Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization

This paper presents some properties of two restricted classes of multi-degree-of-freedom potential systems subjected to Gaussian white-noise excitations. Specifically, potential systems which exhibit damping terms with energy-dependent polynomial form are referred to. In this context, first systems with coupled stiffness terms and damping terms depending on the total energy are investigated. Then, systems with uncoupled stiffness terms and damping terms depending on the total energy in each degree-of-freedom are considered. For these two classes, it is found that algebraic relations among the stationary statistical moments of the energy functions can be derived by applying standard tools of Itô calculus. Further, it is noted that these relations are very useful within the framework of an equivalent statistical non-linearization technique to build approximate solutions for arbitrary non-linear systems.     

Higher order bad loci

Zero-schemes on smooth complex projective varieties, forcing all elements of ample and free linear systems to be reducible, are studied. Relationships among the minimal length of such zero-schemes, the positivity of the line bundle associated with the linear system, and the dimension of the variety are established. Bad linear spaces are also investigated.     

Looking at Fokker-Planck dynamics with a noisy instrument

We consider the class of experiments which can be characterized by a Fokker-PIanck dynamics corresponding to the overdamped motion of a state point in a suitable stochastic potential. We assume that the general form of the potential is known (or can be guessed with reasonable accuracy), but that its parameters are to be determined experimentally by measurements made with a noisy instrument. This possible method for determining the potential parameters, which exploits the system's own internal stochastic motion in order to explore rapidly its available parameter space, is substantially more efficient than traditional methods involving time averages of single point measurements, and yet does not appear to have been previously considered. The method could be important when, for example, the experiment must be completed in a limited time owing either to the expense of the experimental materials or to the temporary stationarity of the preparation, situations which are commonly encountered in experimental biochemistry and biology.     

Preparation and physical characterization of forms II and III of paracetamol

The polymorphic forms II and III of paracetamol were obtained by melting the marketed form I. Under the melting and cooling conditions used, it was possible to obtain forms I, II and III. The recrystallization conditions and the physical properties of forms II and III were investigated by means of various techniques: thermomicroscopy, DSC analysis, infrared microspectrometry and X-ray powder diffraction at room temperature and as a function of temperature. Form III was found to be very unstable. However, its formation seems to be an important intermediate step in the preparation of form II.     

串联系统可靠性虚拟系统法置信下限的小样本性质

本文讨论了具有r个成败型元件串联系统可靠性的置信下限问题。研究了虚拟系统法置信下限的小样本性质,证明了,在通常情况下虚拟系统法置信下限要大于常见的L-M法置信下限.更一般地,本文证明了在成败型试验中,当成功数与试验数之比保持不变时,试验次数的增加将直接缩小成功率置信区间的长度。