On Nash Equilibria for Noncooperative Games Governed by the Burgers Equation

Existence of a Nash equilibrium in a noncooperative game governed by the one-dimensional Burgers equation, proposed in the case of pointwise controls in Ref. 1, is proved under data qualifications that guarantee the diffusion term in the Burgers’ equation to be dominant enough with respect to the uniform convexity of the payoffs. This work was partly supported by Grants 201/03/0934 (GA čR) and MSM 0021620839 (MšMT čR). Inspiring discussions with Angel M. Ramos are acknowledged.     

Patterns in parabolic problems with nonlinear boundary conditions

We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of eigenvalues and eigenfunctions of the Laplace operator in such domains. This information is used to show that the asymptotic dynamics of the heat equation in this domain is equivalent to the asymptotic dynamics of a system of two ordinary differential equations diffusively (weakly) coupled. The main tools employed are the invariant manifold theory and a uniform trace theorem.     

利用富铈混合稀土改善工业纯铝中富铁相形貌的研究

利用金相分析方法研究了富Ce混合稀土变质对含不同Fe量的工业纯铝的组织和其中富铁相形貌的影响。试验结果表明,随着Fe含量的增加,富铁相由弥散细小的颗粒状向短棒状、长针状转变;富Ce混合稀土变质使铝中的富铁相由长针状变为弥散细小的颗粒状。随着稀土含量的增加,-αAl晶粒逐渐细化,富铁相尺寸及数量逐渐减小。添加0.5%稀土时,-αAl晶粒细化效果最佳,而且富铁相呈细小颗粒状均匀分布在-αAl基体的晶界处。本文还对稀土改善富铁相的机制进行了分析。     

Phosphonate electrochemical recognition by molecularly imprinted deposited film

In this paper, thin films of titanium oxide imprinted with O,O-dimethyl-(2,4-dichlorophenoxyacetoxyl)(3′-nitrobenyl) methinephosphonate (Phi-NO₂) were prepared via liquid phase deposition (LPD) method on a glassy carbon electrode. The imprinted molecular in the films was removed by treatment with immersion in CH₂Cl₂. X-ray diffraction (XRD) and electrochemical methods were introduced to show the evidence of the molecular imprinting phenomenon. It was also found that the recognition ability of the sensor depended on the substituents associated with tridimensional structures of the nitro-compounds. Under the optimized condition, the sensor showed better sensitivity, selectivity and reproducibility to the imprinted molecule and the linear relationship between the current and the concentration of analyte in the range of 0.1-50 μM was obtained. LPD proved to be a powerful method for imprinting titanium oxide thin sense films.     

Making equation of state models predictive: Part 2: An improved PCP-SAFT equation of state

We use the PCP-SAFT equation of state, which is of the Van der Waals type and has a sound physical basis, to predict mixture properties, such as vapor–liquid and liquid–liquid equilibria, as well as excess enthalpies. We use molecular properties, such as dipole moment, quadrupole moment, polarizability and dispersion interaction coefficients, that have been determined quantum mechanically in Part I of this publication and adjust the remaining three pure compound parameters to pure compound data. We finally present a new combination rule for the dispersion energy parameter ? that is based on the quantum mechanically determined data. The predictions based on quantum mechanically determined pure compound properties along with the new combination rule show an improved performance compared to the original PCP-SAFT combination rule.     

Solvothermal synthesis of TiO2: anatase nanocrystals and rutile nanofibres from TiCl4 in acetone

This work reports a new synthetic approach for single‐phase TiO₂ nanomaterials by solvothermal treatment of titanium tetrachloride in acetone at 80–110 °C. Small, uniform, and yet size‐tunable (5–10 nm) anatase titania nanocrystallites were obtained using a low concentration of TiCl₄ in acetone (i.e., at molar ratios of TiCl₄/acetone ≤ 1:15) in the temperature range of 80–110 °C, while rutile nanofibers were synthesized using a high concentration of TiCl₄ (e.g., TiCl₄/acetone = 1:10) at 110 °C. Copyright © 2007 John Wiley & Sons, Ltd.     

Stability of the steady state for the Falk model system of shape memory alloys

In this article a stability result for the Falk model system is proven. The Falk model system describes the martensitic phase transitions in shape memory alloys. In our setting, the steady state is a nonlocal elliptic problem. We show the dynamical stability for the linearized stable critical point of the corresponding functional. Copyright © 2007 John Wiley & Sons, Ltd.     

KNSBN晶体猫式互抽动相位共轭光特性

在KNSBN：Ce晶体中，利用二波耦合作用，在单一光束无法获得相位共轭光的条件下，实现了“猫”式互抽运相位共轭光输出，获得较高的共轭光发射率，实验结果表明，晶体的二波耦合作用可以使晶体的自抽运相位共轭光的阈值光强降低。入射光的入射角范围增大，响应时间缩短。     

Nash平衡的存在性与稳定性

本文对Nash平衡的存在性与稳定性作了较为详细的研究和综述.     

Nash Equilibria,Variational Inequalities,and Dynamical Systems

In this paper, we introduce some relationships between Nash equilibria, variational equilibria, and dynamical equilibria for noncooperative games.