Convergence of diagonally stationary sequences in convex optimization

LetX be a real normed linear space,f, f ⁿ, n , be extended real-valued proper closed convex functions onX. A sequence {x _n} inX is called diagonally stationary for {f ⁿ} if for alln there existsx* _n f ⁿ (x _n) such that x* _{n *} 0. Such sequences arise in approximation methods for the problem of minimizingf. Some general convergence results based upon variational convergence theory and appropriate equi-well-posedness are presented.     

On some properties of solutions of second-order linear functional differential equations

The properties of solutions of the equationu″(t) =p ₁(t)u(τ₁(t)) +p ₂(t)u′(τ₂(t)) are investigated wherep _i :a, + ∞[→R (i=1,2) are locally summable functions τ₁ :a, + ∞[→R is a measurable function, and τ₂ :a, + ∞[→R is a nondecreasing locally absolutely continuous function. Moreover, τ _i (t) ≥t (i = 1,2),p ₁(t)≥0,p ₂ ² (t) ≤ (4 - ɛ)τ ₂ ^′ (t)p ₁(t), ɛ =const > 0 and . In particular, it is proved that solutions whose derivatives are square integrable on [α,+∞] form a one-dimensional linear space and for any such solution to vanish at infinity it is necessary and sufficient that .     

Brownian confinement and pinning in a Poissonian potential. II

Summary We continue our study ofd-dimensional Brownian motion in a soft repulsive Poissonian potential over a long time interval [0,t]. We prove here a pinning effect: for typical configuratons, with probability tending to 1 ast tends to , the particle gets trapped close to locations of near minima of certain variational problems. These locations lie at distances growing almost linearly witht from the origin, and the particle gets pinned within distance smaller than any positive power oft of one such location. In dimension 1, we can push further our estimates and show that in a suitable sense, the particle gets trapped with high probability, within time t and within distance (logt)²⁺ from a suitable location at distance of ordert/(logt)³ from the origin.This article was processed by the author using the LATEX style filepljour1m from Springer-Verlag     

On some global well-posedness and asymptotic results for quasilinear parabolic equations

We prove that the quasilinear parabolic initial-boundary value problem (1.1) below is globally well-posed in a class of high order Sobolev solutions, and that these solutions possess compact, regular attractors ast+.     

Relations on the period mapping giving extensions of mixed hodge structures on compact Riemann surfaces

We consider a period map from Teichmüller space to K}_2 {\text{,}}\mathcal{H}^1 {\text{)}}_\mathbb{R} $$ " align="middle" border="0"> , which is a real vector bundle over the Siegel upper half space. This map lifts the Torelli map. We study the action of the mapping class group on this period map. We show that the period map from Teichmüller space modulo the Johnson kernel is generically injective. We derive relations that the quadratic periods must satisfy. These identities are generalizations of the symmetry of the Riemann period matrix. Using these higher bilinear relations, we show that the period map factors through a translation of the subbundle and is completely determined by the purely holomorphic quadratic periods. We apply this result to strengthen some theorems in the literature. One application is that the quadratic periods, along with the abelian periods, determine a generic marked compact Riemann surface up to an element of the kernel of Johnson's homomorphism. Another application is that we compute the cocycle that exhibits the mapping class group modulo the Johnson kernel as an extension of the group SP _g () by the group .     

Three distinct distances in the plane

For n6 all sets of n points in the plane with three distinct distances are determined.Dedicated to Professor Dr. Laszlo Fejes Töth on the occasion of his eightieth birthday     

Second-order subdifferentials of C1,1 functions and optimality conditions

We present second-order subdifferentials of Clarke's type of C ^1,1 functions, defined in Banach spaces with separable duals. One of them is an extension of the generalized Hessian matrix of such functions in ⁿ , considered by J. B. H.-Urruty, J. J. Strodiot and V. H. Nguyen. Various properties of these subdifferentials are proved. Second-order optimality conditions (necessary, sufficient) for constrained minimization problems with C ^1,1 data are obtained.This work was partially supported by the National Foundation for Scientific Investigations in Bulgaria under contract No. MM-406/1994.     

K 16Mn连铸坯热装炉轧制对轧材组织性能影舷

采用高温固溶加热法,在φ300轧机上模拟现场连铸坯热装炉轧制工艺,分别考察了K16Mn钢不同热装温度和开轧温度对轧材组织性能的影响.结果表明,热装轧制和常规冷装轧制屈服、抗拉强度相当,热装轧制成品塑性、韧性均较好.热装轧制工艺对K16Mn钢组织的影响,随着热装温度的提高,轧前奥氏体晶粒变得粗大,并且轧后组织混晶程度提高.这可通过提高开轧温度,首道次采用大压下量促使铸坯发生完全再结晶来消除.从而细化晶粒.改善成品组织性能.     

一个求解P_*(K)-矩阵线性互补问题的宽邻域路径跟踪算法(英)

基于预校正方法,对P*（K）-矩阵线性互补问题给出了一个迭代复杂性为O（k＋1）n2/3L）的宽邻域路径跟踪算法,算法改进了Zhang等的可行宽域路径跟踪算法的迭代复杂性;比迭代复杂性为O的小邻域路径跟踪算法为好．     

The integrable nonlinear degenerate diffusion equationu t=[f(u)u x −1 x and its relatives

The nonlinear diffusion equationu _t=[f(u)g(u _x )] arises in recent models of turbulent transport and of stress dissipation in rock blasting. A Lie point symmetry analysis produces many similarity reductions of exponential and power-law forms, and reveals that for all choices off the equation is always integrable wheng(u _x )=1/u _x . We identify the functionsf(u) which guarantee equivalence to the linear heat equation. For all other choices off, the linear canonical form leads to a self-adjoint differential equation by separation of variablesx andt. We construct a number of explicit solutions with simple boundary conditions, which illustrate behavior in the vicinity of the degenerate region withu _x =. If zero flux and constant concentration are maintained on free boundaries, then steep concentration gradients may evolve from smooth initial conditions. For other boundary conditions, unlike the examples of strong degeneracy, smoothing will occur at initial step discontinuities.