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## Assessing local prior influence in Bayesian analysis

### Applied Mathematics (1995-06-01) 10: 123-132 , June 01, 1995

A general method for assessing local influence of minor perturbations of prior in Bayesian analysis is developed in this paper. Using some elementary ideas from differential geometry, we provide a unified approach for handling a variety of problems of local prior influence. As applications, we discuss the local influence of small perturbations of normal-gamma prior density in linear model and investigate local prior influence from the predictive view.

## Bayesian analysis of data with only one failure

### Applied Mathematics (1996-12-01) 11: 435-444 , December 01, 1996

The bearings of a certain type have their lives following a Weibull distribution. In a life test with 20 sets of bearings, only one set failed within the specified time, and none of the remainder failed even after the time of test has been extended. With a set of testing data like that in Table 1, it is required to estimate the reliability at the mission time. In this paper, we first use hierarchical Bayesian method to determine the prior distribution and the Bayesian estimates of various probabilities of failures, p_{i}’s, then use the method of least squares to estimate the parameters of the Weibull distribution and the reliability. Actual computation shows that the estimates so obtained are rather robust. And the results have been adopted for practical use.

## Dichromatic sum equations for outerplanar maps

### Applied Mathematics (1993-03-01) 8: 64-68 , March 01, 1993

This paper provides a functional equation satisfied by the dichromatic sum function of rooted outer-planar maps. By the equation, the dichromatic sum function can be found explicitly.

## On the rates of convergence for probability type operators sequence

### Applied Mathematics (1996-06-01) 11: 199-208 , June 01, 1996

In this paper, the rates of convergence for some probability type operators sequence are obtained. The quantitative Poisson type limit theorem is established as an application.

## On the non-compactness of the core of nonatomic convexσ-continuous measure games

### Applied Mathematics (1995-12-01) 10: 467-470 , December 01, 1995

This paper concerns with the core of nonatomic games of form f(*μ*), where*μ* is a nonatomic nonnegative measure and f is a continuous convex function on the domain of*μ*. The main result of this paper is that the core of the game is not compact under the norm topology unless the game itself is a measure. This shows the largeness of the core in a sense other than that defined by Sharky for finite cases.

## Maximum trees of finite sequences

### Applied Mathematics (1995-06-01) 10: 223-228 , June 01, 1995

Let*n*,*s*_{1},*s*_{2},...,*s*_{n} be non-negative integers and*M*(*s*_{1},*s*_{2},...,*s*_{n})=*a*_{1},*a*_{2},...,*a*_{n})|*a*_{i}is an integer and 0≤*a*_{i}≤*s*_{i} for each*i*∼. In this paper, the cardinality of maximum trees of finite sequences in*M*(*s*_{1},*s*_{2},...,*s*_{n}) is obtained, which generalizes some of Frankl’s results on families of finite sets with prescribed cardinalities for pairwise intersections.

## Global existence for a semilinear differential system

### Applied Mathematics (1995-12-01) 10: 387-398 , December 01, 1995

In this paper, a semilinear elliptic-parabolic PDE system which arises in a two dimensional groundwater flow problem is studied. Existence and uniqueness results are established via the*L*^{p}*−**L*^{q} a priori estimates and the inverse function theorem.

## Asymptotic behavior for a class of elliptic equivalued surface boundary value problem with discontinuous interface conditions

### Applied Mathematics (1995-09-01) 10: 237-250 , September 01, 1995

Spontaneous potential well-logging is one of the important techniques in petroleum exploitation. A spontaneous potential satisfies and elliptic equivalued surface boundary value problem with discontinuous interface conditions. In practice, the measuring electrode is so small that we can simplify the corresponding equalued surface to a point. In this paper, we give a positive answer to this approximation process: when the equivalued surface shrinks to a point, the solution of the original equivalued surface boundary value problem converges to the solution of the corresponding limit boundary value problem.

## Finite element simulations for compressible miscible displacement with molecular dispersion in porous media

### Applied Mathematics (1996-03-01) 11: 17-32 , March 01, 1996

We consider a nonlinear parabolic system describing compressible miscible displacement in a porous medium [5]. Continuous time and discrete time Galerkin methods are introduced to approximate the solution and optimal*H*^{1} error estimates are obtained. One contribution of this paper is a demonstration of how molecular dispersion can be handled.

## Stable doubleLR algorithm and its error analysis

### Applied Mathematics (1994-03-01) 9: 35-43 , March 01, 1994

In this paper, the normative matrices and their double*LR* transformation with origin shifts are defined, and the essential relationship between the double*LR* transformation of a normative matrix and the*QR* transformation of the related symmetric tridiagonal matrix is proved. We obtain a stable double*LR* algorithm for double*LR* transformation of normative matrices and give the error analysis of our algorithm. The operation number of the stable double*LR* algorithm for normative matrices is only four sevenths of the rational*QR* algorithm for real symmetric tridiagonal matrices.