Some blow-up problems for a semilinear parabolic equation with a potential

The blow-up rate estimate for the solution to a semilinear parabolic equation ut=Δu+V(x)|u|^p−1u in Ω×(0,T) with 0-Dirichlet boundary condition is obtained. As an application, it is shown that the asymptotic behavior of blow-up time and blow-up set of the problem with nonnegative initial data u(x,0)=Mφ(x) as M goes to infinity, which have been found in [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006], is improved under some reasonable and weaker conditions compared with [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006].     

分子反应动态学中的势能面和非线性

势能面在分子反应动态学中起着无以替代的作用，对它的研究始终是化学物理学界的一个热点问题，而一性科学技术的发展和应用，又为分子反应动态学展示了许多丰富多彩的内容。同时，这两个领域又有许多交叉点。本文综述了这两个领域的最新进展。     

High resolution imaging of contact potential difference using a novel ultrahigh vacuum non-contact atomic force microscope technique

An ultrahigh vacuum scanning Kelvin probe force microscope (UHV SKPM) based on the gradient of electrostatic force was developed using the technique of a UHV non-contact atomic force microscope (NC-AFM) capable of atomic level imaging, and used for simultaneous observation of contact potential difference (CPD) and NC-AFM images. The CPD images with a potential resolution of less than 10 meV were observed in the UHV SKPM, demonstrating an atomic level resolution. The change of potential corresponding to the charges on the insulated surface of polypropylene have been observed in UHV SKPM. We also demonstrated a reliable method to obtain the CPD from the bias voltage dependence curves of the frequency shift in all of the scanning area. The results are consistent with comparing the barrier height images in that the work functions of adatoms are greater than the work function of corner holes.     

Exact solution of external tangential contact problem for a transversely isotropic elastic half-space

Summary  The following mixed boundary-value problem for a transversely isotropic elastic half-space is considered. Arbitrary tangential displacements are prescribed at the exterior of a circle, while the interior of the circle is free of tangential stress, and the normal stress vanishes all over the boundary. The governing integral equation is solved exactly, in closed form, and in terms of elementary functions. The method of continuation of solutions previously published by the author has been used here. Several examples are considered. No similar results has been reported before, even in the case of an isotropic body. Received 8 May 2000; accepted for publication 20 July 2000     

控制电位滴定法的误差分析

研究了影响控制电位滴定法测定结果准确度的因素,得到的结论是:第一,电位的控制误差及滴定剂体积的测定误差是影响控制电位滴定法测定结果准确度的主要因素.计算模型中的比例系数越大,滴定曲线的变化率越大,这种影响越小.第二,多组分体系的测定误差,与组分在计算模型中比例系数的相对大小有关.比例系数越大,测定误差越小.第三,不同浓度(或不同浓度比)待测溶液滴定曲线的差异越大,对控制电位滴定法的测定越有利.     

Potential,value, and coalition formation

In this paper, a simple probabilistic model of coalition formation provides a unified interpretation for several extensions of the Shapley value. Weighted Shapley values, semivalues, weak (weighted or not) semivalues, and the Shapley value itself appear as variations of this model. Moreover, some notions that have been introduced in the search of alternatives to Shapley’s seminal characterization, as ‘balanced contributions’ and the ‘potential’ are reinterpreted from this point of view. Natural relationships of these conditions with some mentioned families of ‘values’ are shown. These reinterpretations strongly suggest that these conditions are more naturally interpreted in terms of coalition formation than in terms of the classical notion of ‘value.’      

Evolutive and nonlinear vibrations of rotor on aerodynamic bearings

The use of air as a lubricant in aerodynamic bearings is advantageous, particularly in the food industry. Aerodynamic bearings with tilting pads have complicated stiffness and damping properties and need a very detailed theoretical and experimental research. Response curves of rigid rotor supported on aerodynamic bearings are presented for a linear but evolutive mathematical model. Due to non-monotone properties of stiffness and damping matrices at variable revolutions, a new resonance appears. The mathematical model of rotor vibrations in the whole area of bearing clearance is also developed in the consideration of strongly nonlinear properties of aerodynamic bearing.     

剪切模量是幂函数的成层土的地震随机反应

基于改进的一维剪切梁模型，对剪切模量是其深度的某一幂函数的成层非均质土层，得到其稳态动力响应的封闭型解析表达式。首次证明了这种土层振型函数的正交性，然后利用随机振动理论，并基于基岩输入地震加速度的功率谱密度函数：白噪声谱和过滤白噪声谱。研究了该土层对地震的随机动力响应问题。计算结果表明，1)在基岩输入地震加速度的功率谱为白噪声谱的情况下，土层的最大期望反应均有别于过滤白噪声谱时的相应值；2)平稳输入与输出过高地估计了土层的随机响应。     

Ab initio study of mechanism of forming germanic bis-heterocyclic compound between germylene carbene (H2GeC:) and acetone

The mechanism of the cycloaddition reaction of forming germanic bis-heterocyclic compound between singlet germylene carbene and acetone has been investigated with MP2/6-31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by CCSD (T)//MP2/6-31G* method. From the potential energy profile, it can be predicted that the dominant reaction pathway of the cycloadditional reaction of forming germanic bis-heterocyclic compound consists of three steps: (1) the two reactants firstly form an intermediate INT4 through a barrier-free exothermic reaction of 181.4 kJ/mol; (2) INT4 further reacts with acetone (R2) to form an intermediate (INT5), which is also a barrier-free exothermic reaction of 148.9 kJ/mol; (3) INT5 then isomerizes to a germanic bis-heterocyclic product P5 via a transition state TS5 with an energy barrier of 53.3 kJ/mol.