Distance to Ill-Posedness in Linear Optimization via the Fenchel-Legendre Conjugate

We consider the parameter space of all the linear inequality systems, in the n-dimensional Euclidean space and with a fixed index set, endowed with the topology of the uniform convergence of the coefficient vectors. A system is ill-posed with respect to the consistency when arbitrarily small perturbations yield both consistent and inconsistent systems. In this paper, we establish a formula for measuring the distance from the nominal system to the set of ill-posed systems. To this aim, we use the Fenchel-Legendre conjugation theory and prove a refinement of the formula in Ref. 1 for the distance from any point to the boundary of a convex set.This research has been partially supported by grants BFM2002–04114-C02 (01–02) from MEC (Spain) and FEDER (EU) and by grants GV04B-648 and GRUPOS04/79 from Generalitat Valenciana (Spain).     

Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap

Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived analytically. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.     

Sorption-enhanced steam reforming of hydrocarbons with autothermal sorbent regeneration in a moving heat wave of a catalytic combustion reaction

A novel technological concept of sorption-enhanced steam reforming of hydrocarbons is suggested. The peculiarity of the concept is the autothermal regeneration of the carbon dioxide scavenger in the moving super-adiabatic heat wave of an exothermic catalytic combustion reaction performed directly inside the adsorption-catalytic bed. The capability and high efficiency of the proposed technological approach are confirmed by process simulation. The approach proposed is shown to open a way for the creation of an inexpensive, reliable and energy-saving adiabatic packed bed methane processors of unlimited processing capacity.     

Probabilistic derivation of van der Waals' equation

A probabilistic derivation of van der Waals' equation is given where the non-ideal contributions to the entropy coincide with the log-likelihood ratios, at their maxima, of the binomial distribution and the upper or lower bounds on the hypergeometric and Pólya distributions. The hypergeometric distribution accounts for the repulsive interactions of a hard sphere gas while the Pólya distribution accounts for the attractive interactions.1. Work supported in part by contributions from the Ministry of Public Education (M.P.I.) and the National Science Council (C.N.R.).     

Optimizing thermography depth probing with a dynamic thermal point spread function

Derivation of two point spread functions PSFs suitable for infrared thermograms analysis is illustrated, based on two unique approaches, one based on depth decaying limit and one on diffusion limit. Experimental work using PMMA sample with back drilled holes and pulsed thermographic routine is utilized to show the effectiveness of deconvoluting pixel temperature transient history with suggested PSF’s. Synthetic second time derivative thermograms are utilized for comparison and the signal to noise ratio is used as a figure of merit for quantification.     

Enantiopure aryl-[1,2,5,6-tetrahydro-pyridinyl] methanols and their use for heterogeneous hydrogenation of ethyl pyruvate

Both enantiomers of two new chiral modifiers (naphthyl- and anthryl-[1,2,5,6-tetrahydro-pyridinyl] methanols, 4H and 5H) are obtained for the first time from inexpensive d-mannitol in 10 easy steps. Until now erythro-4H is the only synthetic chiral modifier available under both enantiomeric forms, which provide enantioselectivities almost as high as those obtained with natural cinchonidine, for which only one enantiomer is available. It is shown that the anthryl group may be less efficient than the naphthyl (the e.e.% drops from 75% with erythro-4H to 46% with erythro-5H) and that N-methyl substitution (trisubstituted nitrogen as in cinchonidine) leads also to a drop in the e.e.% (from 75% with 4H to 39% with 4Me).     

Molecular weight distribution in free radical polymerization with long-chain branching

A new theory to predict the molecular weight distribution in free radical polymerization that includes chain transfer to polymer is proposed. This theory is based on the branching density distribution of the primary polymer molecules. The branching density distribution provides the information on how each chain is connected to other chains, and therefore, a full molecular weight distribution can be calculated by application of the Monte Carlo simulation. The present theory accounts for the history of the generated branched structure and can be applied to various reaction systems that involve branching and crosslinking regardless of the reactor types used. The present simulation confirmed the validity of the method of moments in a batch polymerization proposed earlier. It was shown clearly why gelation never occurs by chain transfer to polymer without the assistance of other interlinking reaction such as bimolecular termination by combination. © 1993 John Wiley & Sons, Inc.     

排烟增湿脱硫活化反应器内液滴──脱硫剂颗粒碰撞的数值模拟

排烟增湿脱硫活化反应器内液滴──脱硫剂颗粒碰撞的数值模拟唐庆，徐旭常（清华大学热能工程系北京１０００８４）关键词液滴－颗粒碰撞，脱硫，数值模拟要有效的控制ＳＯＺ的污染，降低燃煤电厂排烟中ＳＯＺ的浓度显得尤为重要。在众多的烟气脱硫技术中，排烟增湿活化脱...     

Oldroyd B流体依时性管内流动的变分解析方法

在本文中，研究上随体Ｏｌｄｒｏｙｄ Ｂ流体在水平管内依时性流动，该问题可归结为无量纲速度分量三阶偏微分方程的初边值问题，采用改进的Ｋａｎｔｏｒｏｖｉｃｈ方法，将该方程化为各级近似的二阶常微分方程组的初值问题，通过Ｌａｐｌａｃｅ变换，求得其二阶常微分方程的解析解。在本文中，提出了变分解析的新概念，获得了二级近似变分解析解，其中包括常压力力梯度和周期性压力梯度两种情形，应用计算机符呈处理和Ｌａｐｌａｃ     

Selective catalysts for the production of nitrogen-containing compounds

Herewith are the two processes developed by Nitto, which produce N-containing compounds such as hydrogen cyanide and methylamines. These processes are characterized by unique selective catalysts: an Fe–Sb–O based fluid-bed catalyst for ammoxidation of methanol and a shape-selective zeolite catalyst for ammonolysis of methanol.