Separated totally convex spaces

In this paper we define for every totally convex space a suitable topology, the radial topology. We prove that a morphism in the category TC^sep of separated totally convex spaces is an epimorphism if and only if its image is dense in the radial topology, and that TC^sep is the full subcategory of TC generated by its Hausdorff objects. These results remain valid for finitely totally convex spaces when the radial topology is replaced by the distance-radial topology.Dedicated to Karl Stein     

Semiparametric estimation based on parametric modeling of the cause-specific hazard ratios in competing risks

This paper is intended as an investigation of estimating cause-specific cumulative hazard and cumulative incidence functions in a competing risks model. The proportional model in which ratios of the cause-specific hazards to the overall hazard are assumed to be constant (independent of time) is a well-known semiparametric model. We are here concerned with relaxation of the proportionality assumption. The set C of all causes are decomposed into two disjoint subsets of causes as C=C₁∪C₂. The relative risk of cause A in the sub-causes C₁ can be represented as a function defined by ratio of the cause-specific hazard of cause A to the sum of cause-specific hazards in the sub-causes C₁. We call this function the risk pattern function of cause A in C₁, and consider a semiparametric model in which risk pattern functions in C₁ are not constant (independent of time) but those functional forms, except for finite-dimensional parameters, are known. Based on this model, semiparametric estimators are obtained, and estimated variances of them are derived by delta methods. We investigate asymptotic properties of the semiparametric estimators and compare them with the nonparametric estimators. The semiparametric procedure is illustrated with the radiation-exposed mice data set, which represents lifetimes and causes of death of mice exposed to radiation in two different environments.     

A direct construction of very smooth local Navier-Stokes solutions

We will consider Galerkin approximations to the solution of the Navier-Stokes initial boundary-value problem in three dimensions. Uniform convergence (locally in time) will be proved with respect to the same norm (being stronger than theH ²-norm) in which the solution's initial value is bounded. The result is the best possible if we will avoid a nonlinear, nonlocal compatibility condition for the initial value.Dedicated to Professor Robert Finn on the occasion of his 70th birthday     

Chaos hypothesis for a system interacting through shared resources

Summary We study the chaos hypothesis for a wide class of pure-jump multitype interacting systems. The interaction may be strong, there is no symmetry assumption, and the system is not necessarily Markovian. We use interaction graphs and coupling and study in a precise way how a chain reaction is constituted by a series of direct interactions. We obtain the chaos hypothesis in variation norm with speed of convergence and deduce from it convergence of general empirical measures. We couple the interaction graph to a Boltzmann tree and show that the variation norm between the processes constructed on each goes to zero. This proves propagation of chaos in total variation with speed of convergence when the Boltzmann trees converge. Under light symmetry assumptions, we characterize the limit law by a nonlinear martingale problem.We dedicate this paper to Professor Claude Kipnis, who brought these network problems to our attention.URA CNRS 756URA CNRS 224This article was processed by the author using the Springer-Verlag TEX QPMZGHB macro package 1991.     

Spectral properties of threshold functions

We examine the spectra of boolean functions obtained as the sign of a real polynomial of degreed. A tight lower bound on various norms of the lowerd levels of the function's Fourier transform is established. The result is applied to derive best possible lower bounds on the influences of variables on linear threshold functions. Some conjectures are posed concerning upper and lower bounds on influences of variables in higher order threshold functions.Supported by an Eshkol fellowship, administered by the National Council for Research and Development—Israel Ministry of Science and Development.     

离子交换法分离固相合成胸腺素α1

胸腺素α1是一种重要的免疫增强剂,广泛应用于病毒性慢性肝炎以及恶性肿瘤的临床辅助治疗.本文采用离子交换法对固相合成的胸腺素α1进行了分离纯化研究,考察了pH值、进样量、洗脱方法以及树脂种类对纯化效果的影响,建立了一套基于SourceTM 15Q阴离子交换树脂的纯化方案.利用上述方法纯化Tα1纯度可达95.53%,收率60.4%,经ESI-MS分析,产品分子量与Tα1吻合.该技术可满足规模化、低成本纯化固相合成胸腺素α1的需要.     

An Ω(n 5/4) lower bound on the randomized complexity of graph properties

A decision tree algorithm determines whether an input graph withn nodes has a property by examining the entries of the graph's adjacency matrix and branching according to the information already gained. All graph properties which are monotone (not destroyed by the addition of edges) and nontrivial (holds for somes but not all graphs) have been shown to require (n ²) queries in the worst case.In this paper, we investigate the power of randomness in recognizing these properties by considering randomized decision tree algorithms in which coins may be flipped to determine the next entry to be examined. The complexity of a randomized algorithm is the expected number of entries that are examined in the worst case. The randomized complexity of a property is the minimum complexity of any randomized decision tree algorithm which computes the property. We improve Yao's lower bound on the randomized complexity of any nontrivial monotone graph property from (n log^1/12 n) to (n ^5/4).     

Balancing extensions via Brunn-Minkowski

We give a simple proof, based on the Brunn-Minkowski Theorem, of Theorem. Inany finite poset P not a total order there are elementsx, y such that

Exponential decay near resonance,without analyticity

We consider a quantum mechanical model which displays the behaviour associated with having a resonance or metastable state. The Hamiltonian depends on a parameter . When =0, there is an eigenstate ₀; when 0, ₀ dissolves into the continuous spectrum, showing approximate exponential decay. We prove this result without using dilatation analyticity. The model describes a two-state atom coupled to the quantized radiation field. The state space of the field is truncated, so that only the vacuum and one-photon states are included.This work was partially supported by NSF Grant DMS-8922941