正态分布的共轭分布及贝叶斯估计

本文介绍含有一个或两个未知参数的正态分布Ｎ（μ，）的共轭分布，以及对正态总体的未知参数进行估计的贝叶斯方法。     

Further Applications of the Additive Min-type Coupling Function

Applying for the additive min-type coupling function $$ varphi (x, w) = mathop {min }limits_{1 le i le n} (x_1 + w_i )quad (x = (x_i ), w = (w_i ) in {shadR}^n ) $$ the techniques from abstract convex analysis, developed in [I. Singer (1997). Abstract Convex Analysis . Wiley-Interscience, New York], we show that the conjugate of type Lau f L ( } ) of f with respect to } has the simple expression $ f^{L(varphi )} (w) = - f( - w), (w in {shadR}^n ) $ if and only if f is increasing and upper semi-continuous. As a consequence, we obtain that for topical (i.e., increasing additively homogeneous) functions f the Fenchel-Moreau conjugate of f with respect to } and the conjugate of type Lau of f with respect to } coincide.     

Applying the Powell's Symmetrical Technique to Conjugate Gradient Methods with the Generalized Conjugacy Condition

This article proposes new conjugate gradient method for unconstrained optimization by applying the Powell symmetrical technique in a defined sense. Using the Wolfe line search conditions, the global convergence property of the method is also obtained based on the spectral analysis of the conjugate gradient iteration matrix and the Zoutendijk condition for steepest descent methods. Preliminary numerical results for a set of 86 unconstrained optimization test problems verify the performance of the algorithm and show that the Generalized Descent Symmetrical Hestenes-Stiefel algorithm is competitive with the Fletcher-Reeves (FR) and Polak-Ribiére-Polyak (PRP⁺) algorithms.     

Duality theorems for certain programs involving minimum or maximum operations

The relation of two mathematical programs—the so-called primal, (P) and dual, (D)—Are studied when (P) is a maximization of the minimum of two functions and (D) is the minimization of the maximum of two functions, and the function-pair of (D) are derived by certain, conjugate-like operators from that of (P). It is demonstrated that the weak duality holds when at least one of the pair is continuous. When further premises are met the strong duality is proved. From these results the usual Fenchel-duality may be deducted as well as few other primal-dual pairs.     

在Armijo型线搜索下共轭梯度法簇的全局收敛性

本文我们讨论了一簇共轭梯度法，它可被看作是FR法和DY法的凸组合．我们提出了两种Armijo型线搜索，并在这两种线搜索下，讨论了共轭梯度法簇的全局收敛性．     

一类分布族的损失函数和风险函数的Bayes推断

本文考虑如下一类分布族:F(t)=[g(t)]θ,-∞A0(1)其中g(t)是关于t单调递增的可微函数,且g(A)=0,g(B)=1.在共轭先验分布下研究了未知参数η=1θ的损失函数和风险函数的B ayes估计及其保守性质,并给出相应的B ayes估计的合理性.     

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＊.     

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.     

On Conjugacy of Maximal Subalgebras of Solvable Lie Algebras

The purpose of this paper is to consider when two maximal subalgebras of a finite-dimensional solvable Lie algebra L are conjugate, and to investigate their intersection.     

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.