Optimal construction of a selection of a subpopulation

Summary The problem of selecting a subpopulation from a given populationII is to be, on the basis of measurements of members ofII, achieved by choosing those members ofII who satisfy the standards determined by a given selection cirterion and rejecting those who do not. Since the optimum selection depends on the unknown parameter of the probability distribution ofII, it is here considered how to construct a decision function from the space of subsidiary sample having infor-mation on θ to the space of selections. Thus the existence of Bayes and minimax decision functions under the constraint defined by the selection criterion is proved. A necessary and sufficient condition for a decision function satisfying the constraint to be a Bayes decision function is also obtained. The Institute of Statistical Mathematics     

On a class of functions with equal infima over a domain and its boundary

In this paper, we present a class of functions:f:X such that inf _xX f(x)= , whereX is a nonempty, finitely compact and convex set in a vector space andB _x ={xX: y aff(X){x:[x, y]X={x}. Our main tool is a recent minimax theorem by Ricceri (Ref. 1).     

On a parabolic equation in a triangular domain

We prove the optimal regularity, in Sobolev spaces, of the solution of a parabolic equation set in a triangular domain T. The right-hand term of the equation is taken in Lebesgue space L^p(T). The method of operators sums in the non-commutative case is referred to.     

On the h-vector of a cohen-macaulay domain in positive characteristic

Here we study the Hilbert function of a Cohen-Macaulay homogeneous domain over an algebraically closed field of positive characteristic. The main tool (and an essential part of the main geometrical results) is the study of the Hilbert function of a general hyperplane section X?P ^r of an integral curve C?P ^r+1 , which is pathological in some sense. In §1, we study the case when Cis a strange curve, i.e., all tangent lines to Cat its simple points pass through a fixed point υ∈P ^r+1 . In §2, we give more refined results under the assumption that the Trisecant Lemma fails for C, i.e., any line spanned by two points of Ccontains one more point of C.     

On power series rings over valuation domains

Let V be a valuation domain and V[[X]] be the power series ring over V. In this paper, we show that if V[[X]] is a locally finite intersection of valuation domains, then V is an SFT domain and hence a discrete valuation domain. As a consequence, it is shown that the power series ring V[[X]] is a Krull domain if and only if V[[X]] is a generalized Krull domain if and only if V[[X]] is an integral domain of Krull type (or equivalently, a PvMD of finite t-character) if and only if V is a discrete valuation domain with Krull dimension at most one.     

On zeros of polynomials orthogonal over a convex domain

We establish a discrepancy theorem for signed measures, with a given positive part, which are supported on an arbitrary convex curve. As a main application, we obtain a result concerning the distribution of zeros of polynomials orthogonal on a convex domain.     

On pairs of free modules over a Dedekind domain

The study of pairs of modules (over a Dedekind domain) arises from two different perspectives, as a starting step in the analysis of tuples of submodules of a given module, or also as a particular case in the analysis of Abelian structures made by two modules and a morphism between them. We discuss how these two perspectives converge to pairs of modules, and we follow the latter one to obtain an alternative approach to the classification of pairs of torsionfree objects. Then we restrict our attention to pairs of free modules. Our main results are that the theory of pairs of free Abelian groups is co-recursively enumerable, and that a few remarkable extensions of this theory are decidable. Work performed under the auspices of GNSAGA-INDAM     

On a thermoelastic plate equation in an exterior domain

Obtained are the existence of solutions and the local energy decay of a linear thermoelastic plate equation in a 3 dim. exterior domain. The thermoplate equation is formulated as a Sobolev equation in the abstract framework. Our proof of the existence theorem is based on an argument due to Goldstein (Semigroups of Linear Operators and Applications. Oxford University Press: New York, 1985). To obtain the local energy decay, we use the commutation method in order to treat the high‐frequency part and a precise expansion of the resolvent operator obtained by constructing the parametrix in order to treat the low‐frequency. Copyright © 2002 John Wiley & Sons, Ltd.     

A Laplace transform technique for the analytical solution of a diffusion- convection equation over a finite domain

A Laplace transform technique has been utilized to obtain two different analytic solutions to a single diffusion-convection equation over a finite domain. One analytic solution is continuous at both ends of the domain of interest, while the other solution is discontinuous at the origin. This difference in the two solutions is explained. An application of the Laplace transform technique to a more complex system of equations, on a finite domain, is noted and an error apparent in a previous paper is corrected.     

On coupling wavelets with fictitious domain approaches

We define and analyse a numerical algorithm for the approximation of parabolic equations on a general 2D domain with Dirichlet boundary conditions. It couples wavelet approximations with fictitious domain surface Lagrange multiplier approaches. This algorithm turns out to be precise, fast and numerically efficient.     

On non-decomposable Hermitian forms over Gaussian domain

Methods are presented for the construction of non-decomposable Hermitian forms over the ring of integers of an imaginary quadratic field.     

On the convergence rate of a parallel nonoverlapping domain decomposition method

In recent years,a nonoverlapping domain decomposition iterative procedure,which is based on using Robin-type boundary conditions as information transmission conditions on the subdomain interfaces,has been developed and analyzed.It is known that the convergence rate of this method is 1-O(h),where h is mesh size.In this paper,the convergence rate is improved to be 1-O(h1/2 H-1/2)sometime by choosing suitable parameter,where H is the subdomain size.Counter examples are constructed to show that our convergence estimates are sharp,which means that the convergence rate cannot be better than 1-O(h1/2H-1/2)in a certain case no matter how parameter is chosen.     

Precise asymptotics for a type of order statistics

This paper obtains some results on the precise asymptotics for the order statistics generated by the random samples of maximum domain of attraction of the Fréchet distribution, which reveal the relations among the boundary function, weight function, convergence rate and limit position in a uniform form.Research supported by National Science Foundation of China (NO. 10271087).     

Groupoid structure of Toeplitz algebra over L-shaped domain

The structure of the groupoidG associated with the ToeplitzC ^*-algebraC ^*(Ω) of the L-shaped domain is discussed. The detailed characterization ofM _∞ by the classification of the closed subgroup of the Euclidean space is presented. Project supported partially by the National Natural Science Foundation of China, Fok Yingtung Educational Foundation and the Foundation of the State Education Commission of China.     

Differential quadrature domain decomposition method for problems on a triangular domain

The differential quadrature method (DQM) has been studied for years and it has been shown by many researchers that the DQM is an attractive numerical method with high efficiency and accuracy. The conventional DQM is mostly effective for one‐dimensional and multidimensional problems with geometrically regular domains. But to deal with problems on a triangular domain, we will meet difficulties. In this article we will study how to solve problems on a triangular domain by using DQM combined with the domain decomposition method (DDM). © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

On a fictitious domain method with distributed Lagrange multiplier for interface problems

In this paper we propose a new variational formulation for an elliptic interface problem and discuss its finite element approximation. Our formulation fits within the framework of fictitious domain methods with distributed Lagrange multipliers. For the underlying mixed scheme we prove stability and convergence. Some preliminary numerical tests confirm the theoretical investigations.     

On approximation in the fictitious domain method for a bidimensional transport equation

In this article a numerical method for solving a two‐dimensional transport equation in the stationary case is presented. Using the techniques of the variational calculus, we find the approximate solution for a homogeneous boundary‐value problem that corresponds to a square domain D₂. Then, using the method of the fictitious domain, we extend our algorithm to a boundary value problem for a set D that has an arbitrary shape. In this approach, the initial computation domain D (called physical domain) is immersed in a square domain D₂. We prove that the solution obtained by this method is a good approximation of the exact solution. The theoretical results are verified with the help of a numerical example. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

On roots of random polynomials

We study the distribution of the complex roots of random polynomials of degree with i.i.d. coefficients. Using techniques related to Rice's treatment of the real roots question, we derive, under appropriate moment and regularity conditions, an exact formula for the average density of this distribution, which yields appropriate limit average densities. Further, using a different technique, we prove limit distribution results for coefficients in the domain of attraction of the stable law.