一个充分下降的有效共轭梯度法

对于大规模无约束优化问题,本文提出了一个充分下降的共轭梯度法公式,并建立相应的算法.该算法在不依赖于任何线搜索条件下,每步迭代都能产生一个充分下降方向.若采用标准Wolfe非精确线搜索求步长,则在常规假设条件下可获得算法良好的全局收敛性最后,对算法进行大规模数值试验,并采用Dolan和More的性能图对试验效果进行刻画,结果表明该算法是有效的.     

Prophet Regions for Independent [0, 1]-Valued Random Variables with Random Discounting

Abstract

Let X ₁, X ₂… and B ₁, B ₂… be mutually independent [0, 1]-valued random variables, with EB _j  = β > 0 for all j. Let Y _j  = B ₁ … sB _j?1 X _j for j ≥ 1. A complete comparison is made between the optimal stopping value V(Y ₁,…,Y _n ):=sup{EY _τ:τ is a stopping rule for Y ₁,…,Y _n } and E(max _1≤j≤n Y _j ). It is shown that the set of ordered pairs {(x, y):x = V(Y ₁,…,Y _n ), y = E(max _1≤j≤n Y _j ) for some sequence Y ₁,…,Y _n obtained as described} is precisely the set {(x, y):0 ≤ x ≤ 1, x ≤ y ≤ Ψ _{n, β}(x)}, where Ψ _{n, β}(x) = [(1 ? β)n + 2β]x ? β^?(n?2) x ² if x ≤ β ^n?1, and Ψ _{n, β}(x) = min _j≥1{(1 ? β)jx + β ^j } otherwise. Sharp difference and ratio prophet inequalities are derived from this result, and an analogous comparison for infinite sequences is obtained.     

A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.     

An inverse problem in determining the acid and salt diffusivities simultaneously for polymer solution in a wet spinning process

The wet spinning process depends strongly on the acid and salt diffusivity coefficients in the fiber; however, these two coefficients are normally function of concentration of salt and are difficult to be measured directly. For this reason the technology for the inverse mass transfer problems need be applied to resolve these two concentration-dependent diffusivities simultaneously. An Iterative Regularization Method (IRM) using Conjugate Gradient Method (CGM) is applied in this study to determine simultaneously the unknown diffusivities of acid and salt for polymer solution in a wet spinning process by using measurements of concentration components. The accuracy of this inverse mass transfer problem is examined by using the simulated exact and inexact concentration measurements in the numerical experiments. Results show that the diffusivity of acid can be estimated more accurately than the diffusivity of salt and the estimation of the diffusivities can be obtained in a very short CPU time on a HP d2000 2.66 GHz personal computer.     

Endpoint Estimates for Hardy Operator＇s Conjugate Operator with Power Weight on n-Dimensional Space

In this paper, we establish two integral inequalities for Hardy operator＇s conjugate operator at the endpoint on n-dimensional space. The operator Hn is bounded from Lxα1 （Gn） to Lxβq （Gn） with the bound explicitly worked out and the similar result holds for Hn＊.     

Density-functional computation of 53Cr NMR chemical shifts

53Cr chemical shifts of CrO4(2-), Cr2O7(2-), CrO3X-, CrO2X2(X = F, Cl), and Cr(CO)5L (L = CO, PF3, CHNH2, CMeNMe2) are computed, using geometries optimized with the gradient-corrected BP86 density functional, at the gauge-including atomic orbitals (GIAO)-, BPW91-, and B3LYP levels. For this set of compounds, substituent effects on delta(53Cr) are better described with the pure BPW91 functional than with B3LYP, in contrast to most other transition-metal chemical shifts studied so far. For selected cases, 53Cr NMR line widths can be rationalized in terms of electric field gradients (EFGs) computed with the BPW91 functional, but in general other factors such as molecular correlation times appear to be dominating. 53Cr chemical shifts and EFGs are predicted for CrO3, Cr(C6H6)2, Cr(C6H6)CO3, and, with reduced reliability, for Cr2(mu2-O2CH)4.     

A stable and high-order accurate conjugate heat transfer problem

This paper analyzes well-posedness and stability of a conjugate heat transfer problem in one space dimension. We study a model problem for heat transfer between a fluid and a solid. The energy method is used to derive boundary and interface conditions that make the continuous problem well-posed and the semi-discrete problem stable. The numerical scheme is implemented using 2nd-, 3rd- and 4th-order finite difference operators on Summation-By-Parts (SBP) form. The boundary and interface conditions are implemented weakly. We investigate the spectrum of the spatial discretization to determine which type of coupling that gives attractive convergence properties. The rate of convergence is verified using the method of manufactured solutions.     

Preparation and Characterization of New C2‐ and C1‐Symmetric Nitrogen,Oxygen, Phosphorous,and Sulfur Derivatives and Analogs of TADDOL. Part I

The chloro alcohols 4 – 6 derived from TADDOLs (=α,α,α′,α′‐tetraaryl‐1,3‐dioxolan‐4,5‐dimethanols) are used to prepare corresponding sulfanyl alcohols, ethers, and amines (Scheme 1 and Table 1). The dithiol analog of TADDOL and derivatives thereof, 45 – 49 , were also synthesized. The crystal structures of 16 representatives of this series of compounds are reported (Figs. 1–3 and Scheme 2). The thiols were employed in Cu‐catalyzed enantioselective conjugate additions of Grignard reagents to cyclic enones, with cycloheptenone giving the best results (er up to 94 : 6). The enantioselectivity reverses from Si‐addition with the sulfanyl alcohol to Re‐addition with the alkoxy or dimethylamino thiols (Table 4). Cu^I‐Thiolates, 50 – 53 , could be isolated in up to 84% yield (Scheme 2) and were shown to have tetranuclear structures in the gas phase (by ESI‐MS), in solution (CH₂Cl₂, THF; by vapor‐pressure osmometry and by NMR pulsed‐gradient diffusion measurements; Table 5), and in the solid state (X‐ray crystal structures in Scheme 2). The Cu complex 50 of the sulfanyl alcohol is stable in air and in the presence of weak aqueous acid, and it is a highly active catalyst (0.5 mol‐%) for the 1,4‐additions, leading to the same enantio‐ and regioselectivities observed with the in situ generated catalyst (6.5 mol‐%; Scheme 3). Since the reaction mixtures contain additional metal salts (MgX₂, LiX) it is not possible at this stage, to propose a mechanistic model for the conjugate additions.