Graph-distance convergence and uniform local boundedness of monotone mappings

In this article we study graph-distance convergence of monotone operators. First, we prove a property that has been an open problem up to now: the limit of a sequence of graph-distance convergent maximal monotone operators in a Hilbert space is a maximal monotone operator. Next, we show that a sequence of maximal monotone operators converging in the same sense in a reflexive Banach space is uniformly locally bounded around any point from the interior of the domain of the limit mapping. The result is an extension of a similar one from finite dimensions. As an application we give a simplified condition for the stability (under graph-distance convergence) of the sum of maximal monotone mappings in Hilbert spaces.

     

Convex integral functionals of regular processes

This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be identified with the space of optional random measures with essentially bounded variation. Combined with classical Banach space techniques, our results allow for a systematic treatment of stochastic optimization problems over BV processes and, in particular, yields a maximum principle for a general class of singular stochastic control problems.     

Preparation of 4-Vinyl-2(5H)-Furanoid Structural Unit via Organosilicon and - Selenium Intermediates

Two syntheses of the 2(5H)-furanoid structural unit (especially the 3-methyl derivative 1) have been reported from this laboratory.^1,2 The unit 1 is found in many naturally occurring compounds (especially sesqui terpenes). The 4-substi tuted d erivatives of 1 also occur frequently i n natural products, e.g. furospongolide³ 2.     

Stochastic programs without duality gaps

This paper studies dynamic stochastic optimization problems parameterized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programming equations, whose validity is established under new relaxed conditions that generalize certain no-arbitrage conditions from mathematical finance.     

Shadow price of information in discrete time stochastic optimization

Mathematical Programming - The shadow price of information has played a central role in stochastic optimization ever since its introduction by Rockafellar and Wets in the mid-seventies. This...     

Epi-convergent discretization of the generalized Bolza problem in dynamic optimization

The paper is devoted to well-posed discrete approximations of the so-called generalized Bolza problem of minimizing variational functionals defined via extended-real-valued functions. This problem covers more conventional Bolza-type problems in the calculus of variations and optimal control of differential inclusions as well of parameterized differential equations. Our main goal is find efficient conditions ensuring an appropriate epi-convergence of discrete approximations, which plays a significant role in both the qualitative theory and numerical algorithms of optimization and optimal control. The paper seems to be the first attempt to study epi-convergent discretizations of the generalized Bolza problem; it establishes several rather general results in this direction. Research of B. S. Mordukhovich was partially supported by the USA National Science Foundation under grants DMS-0304989 and DMS-0603846 and by the Australian Research Council under grant DP-0451168. Research of T. Pennanen was supported by the Finnish Academy of Sciences under contract No. 3385.     

Nuclear magnetic resonance chemical shift in an arbitrary electronic spin state

We present a general and systematic electronic structure theory of the nuclear magnetic resonance shielding tensor and the associated chemical shift for paramagnetic atoms, molecules, and nonmetallic solids. The approach is for the first time rigorous for an arbitrary spin state as well as arbitrary spatial symmetry and is formulated without reference to spin susceptibility. The leading-order magnetic-field dependence of shielding is derived. The theory is demonstrated by first principles calculations of organometallic molecules.     

Nuclear magnetic resonance chemical shifts and quadrupole couplings for different hydrogen-bonding cases occurring in liquid water: a computational study

Nuclear magnetic resonance (NMR) parameters are determined theoretically for the oxygen and hydrogen/deuterium nuclei of differently hydrogen-bonded water molecules in liquid water at 300 K. The parameters are the chemical shift, the shielding anisotropy, the asymmetry parameter of shielding, the nuclear quadrupole coupling constant, and the asymmetry parameter of the nuclear quadrupole coupling. We sample instantaneous configurations from a Car-Parrinello molecular dynamics simulation and feed nuclear coordinates into a quantum chemical program for the calculation of NMR parameters using density-functional theory with the three-parameter hybrid exchange-correlation (B3LYP) functional. In the subsequent analysis, molecules are divided into groups according to the number of hydrogen bonds they possess, and the full average NMR tensors are calculated separately for each group. The classification of the hydrogen-bonding cases is performed using a simple distance-based criterion. The analysis reveals in detail how the NMR tensors evolve as the environment changes gradually from gas to liquid upon increasing the number of hydrogen bonds to the molecule of interest. Liquid-state distributions of the instantaneous values of the NMR properties show a wide range of values for each hydrogen-bonding species with significant overlap between the different cases. Our study shows how local changes in the environment, along with classical thermal averaging, affect the NMR parameters in liquid water. For example, a broken or alternatively extra hydrogen bond induces major changes in the NMR tensors, and the effect is more pronounced for hydrogen or deuterium than for oxygen. The data sheds light on the usefulness of NMR experiments in investigating the local coordination of liquid water.     

自由曲面光学虚拟制造与检测系统的探讨

自由曲面光学产品设计、制造与检测的工艺流程，通常采取试凑法逐次逼近。由于加工 检测 再加工，循环往复，既费时，成本又高，产生了瓶颈问题。为了解决此弊端，本文运用虚拟制造技术，提出光学虚拟制造的基本构想，即虚拟制造系统结构模型，给出光学系统虚拟原型的构成和光学系统成像质量虚拟检测系统的构成，讨论光学成像质量的仿真检测以及敏度分析方法。研究结果表明：运用虚拟制造与检测技术，可缩短研发周期，降低成本，优化工艺并提高产品质量。