The uv-Decomposition on a Class of D.C. Functions and Optimality Conditions

In this paper,the UV-theory and P-differential calculus are employed to study second-order ex-pansion of a class of D.C.functions and minimization problems.Under certain conditions,some properties ofthe U-Lagrangian,the second-order expansion of this class of functions along some trajectories are formulated.Some first and second order optimality conditions for the class of D.C.optimization problems are given.     

BRD96N光调制吸收增强现象的实验研究

通过光谱响应特性实验和记录／读出图像实验，研究了基因变异型细菌视紫红质（BR_D96N）分子膜对单色光的光调制特性.发现BR_D96N分子膜在550nm—600nm范围内对调制光有吸收增强的现象，且对此范围内不同波长的单色光其调制程度有差异.利用曲线拟和方法发现550nm—600nm吸收增强的变化过程分为快过程和慢过程，其对应的时间常数分别为30s和5min.利用强度调制器的吸收强度与图像灰度之间的关系，分析了560nm—600nm范围内出现图像反转的实验现象. 关键词： 细菌视紫红质D96N分子膜 光谱响应 吸收增强现象 图像反转现象     

Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping

We study von Karman evolution equations with non-linear dissipation and with partially clamped and partially free boundary conditions. Two distinctive mechanisms of dissipation are considered: (i) internal dissipation generated by non-linear operator, and (ii) boundary dissipation generated by shear forces friction acting on a free part of the boundary. The main emphasis is given to the effects of boundary dissipation. Under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension. We also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which, in turn, depends on the behaviour at the origin of the functions describing the dissipation.     

Stability radii of positive linear Volterra-Stieltjes equations

We study stability radii of linear Volterra-Stieltjes equations under multi-perturbations and affine perturbations. A lower and upper bound for the complex stability radius with respect to multi-perturbations are given. Furthermore, in some special cases concerning the structure matrices, the complex stability radius can precisely be computed via the associated transfer functions. Then, the class of positive linear Volterra-Stieltjes equations is studied in detail. It is shown that for this class, complex, real and positive stability radius under multi-perturbations or multi-affine perturbations coincide and can be computed by simple formulae expressed in terms of the system matrices. As direct consequences of the obtained results, we get some results on robust stability of positive linear integro-differential equations and of positive linear functional differential equations. To the best of our knowledge, most of the results of this paper are new.     

Qualitative properties of stationary measures for three-dimensional Navier-Stokes equations

The paper is devoted to studying the distribution of stationary solutions for 3D Navier-Stokes equations perturbed by a random force. Under a non-degeneracy assumption, we show that the support of such a distribution coincides with the entire phase space, and its finite-dimensional projections are minorised by a measure possessing an almost surely positive smooth density with respect to the Lebesgue measure. Similar assertions are true for weak solutions of the Cauchy problem with a regular initial function. The results of this paper were announced in the short note [A. Shirikyan, Controllability of three-dimensional Navier-Stokes equations and applications, in: Sémin. Équ. Dériv. Partielles, 2005-2006, École Polytech., Palaiseau, 2006].     

Resolvability properties via independent families

The authors give a consistent affirmative response to a question of Juhász, Soukup and Szentmiklóssy: If GCH fails, there are (many) extraresolvable, not maximally resolvable Tychonoff spaces. They show also in ZFC that for ω<λ?κ, no maximal λ-independent family of λ-partitions of κ is ω-resolvable. In topological language, that theorem translates to this: A dense, ω-resolvable subset of a space of the form (DI(λ)) is λ-resolvable.     

Low-lying states of 6He studied via the 6Li(t,3He)6He reaction

We present the recent experimental results on the ⁶He structure studied by the ⁶Li(t, ³He)⁶He reaction at 336 MeV. Above the conspicuous peaks for ground and first excited states for ⁶He, we have observed a broad structures at E _x∼ 5 MeV, and E _x∼ 15 MeV. The angular distribution of this structure exhibits the dominance of a ΔL = 1 transition, indicating the existence of intruder dipole states at low excitation energies in ⁶He. A slight admixture of positive-parity states in this structure has been indicated as well. Received: 1 May 2001 / Accepted: 4 December 2001     

Über die abstandsverträglichen Abbildungen auf dem Kreis und auf der reellen Geraden

Zusammenfassung. Eine Abbildung zwischen metrischen R?umen hei?t abstandsvertr?glich, wenn der Abstand der Bilder zweier Punkte nur vom Abstand der Punkte selbst abh?ngt. Wir zeigen, dass eine Abbildung genau dann abstandsvertr?glich ist, wenn der Cauchyschen Funktionalgleichung genügt, also ein Endomorphismus der Gruppe ist. Ein entsprechendes Resultat gilt auch für die abstandsvertr?glichen Abbildungen des Kreises (mit der Multiplikation komplexer Zahlen als Gruppenverknüpfung). Damit kann man sowohl alle messbaren abstandsvertr?glichen Abbildungen von bzw. in sich angeben, als auch einen Nachweis für die Existenz nichtmessbarer abstandsvertr?glicher Abbildungen auf und erbringen. Eingegangen am 20. Juni 2001 / Angenommen am 13. September 2001     

Threshold electrical switching in As45Te55-xInx and As50Te50-xInx glasses

The electrical switching behaviour of As₄₅Te_55-xIn_x (5≤x≤15) and As₅₀Te_50-xIn_x (2.5≤x≤11.5) has been studied over a wide range of compositions. These glasses are found to exhibit threshold switching. The composition dependence of switching voltage (V_t) has been found to exhibit a change in slope and a local minimum at compositions x=10 and 12.5 for As₄₅Te_55-xIn_x and x=7.5 and 10.8 for As₅₀Te_50-xIn_x, respectively. The slope change in V_t verses x and the local minimum have been identified using two network topological effects, namely the rigidity percolation threshold and the chemical threshold. Received: 23 August 2001 / Accepted: 27 August 2001 / Published online: 11 February 2002