Minimal circumscribed Hermitian ellipsoid of Hartogs domains and an application to an extremal problem

In this paper we construct circumscribed Hermitian ellipsoids of Hartogs domains of least volume and as an application, we obtain the Carath′eodory extremal mappings between the Hartogs domains and the unit ball, and also give an explicit formula for calculating the extremal values.     

Modeling and prediction of children’s growth data via functional principal component analysis

We use the functional principal component analysis (FPCA) to model and predict the weight growth in children. In particular, we examine how the approach can help discern growth patterns of underweight children relative to their normal counterparts, and whether a commonly used transformation to normality plays any constructive roles in a predictive model based on the FPCA. Our work supplements the conditional growth charts developed by Wei and He (2006) by constructing a predictive growth model based on a small number of principal components scores on individual’s past. This work was supported by National Natural Science Foundation of China (Grant No. 10828102), a Changjiang Visiting Professorship, the Training Fund of Northeast Normal University’s Scientific Innovation Project (Grant No. NENU-STC07002) and the National Institutes of Health Grant of USA (Grant No. R01GM080503-01A1).     

Morse functions statistics

We answer a question of Arnold concerning the growth rate of the number of Morse functions on the two-sphere. This work was supported in part by the NSF (Grant No. DMS-0303601).     

A class of rank-two ellipsoid algorithms for convex programming

In this paper, we develop a method for constructing minimum volume ellipsoids containing a wedge-shaped subset of a given ellipsoid. This construction yields a class of ellipsoid algorithms for convex programming that use rank-two update formulae. Research supported by the National Science Foundation, Grant No. MC582-01790.     

A new proof of <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates for the parabolic polyharmonic equations

In this paper we obtain local L ^p estimates for the parabolic polyharmonic equations by a straightforward approach. Yao was supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905), Shanghai Leading Academic Discipline Project (Grant No. J50101) and Key Disciplines of Shanghai Municipality (Grant No. S30104). Zhou was supported by the National Basic Research Program of China (Grant No. 2006CB705700), National Natural Science Foundation of China (Grant No. 60532080), and the Key Project of Chinese Ministry of Education (Grant No. 306017)     

Comparison theorems for the volume of a geodesic ball with a product of space forms as a model

We prove two comparison theorems for the volume of a geodesic ball in a Riemannian manifold taking as a model a geodesic ball in a product of two space forms.Work partially supported by the Fundació Caixa Castelló grant n. MI25043/92.Work partially supported by the DGICYT Grant No. PB91-0324.     

The Paley-Wiener theorem in the non-commutative and non-associative octonions

The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved. This work was supported by the National Basic Research Program of China (Grant No. 1999075105), the National Natural Science Foundation of China (Grant No. 10471002) and Research Foundation for Doctoral Programm (Grant No. 20050574002)     

Index theory on locally homogeneous spaces

We describe how the equivariant K homology class of an invariant elliptic operator on a homogeneous space of a linear semisimple Lie group determines the L ²-index of the associated operator on a finite volume locally homogeneous space. The machinery of equivariant K homology and of KK theory can be used to prove theorems about L ²-indices. We give an application motivated by the problem of calculating multiplicities of subrepresentations of quasi-regular representations.Supported by the National Science Foundation under Grant No. DMS-8903472.Supported by the National Science Foundation under Grant No. DMS-8901436.     

Singularities in Gaussian random fields

This paper studies a class of Gaussian random fields defined on lattices that arise in pattern analysis. Phase transitions are shown to exist at a critical temperature for these Gaussian random fields. These are established by showing discontinuous behavior for certain field random variables as the lattice size increases to infinity. The discontinuities in the statistical behavior of these random variables occur because the growth rates of the eigenvalues of the inverse of the variance-covariance matrix at the critical temperature are different from the growth rates at noncritical temperatures. It is also shown that the limiting specific heat has a phase transition with a power law behavior. The critical temperature occurs at the end point of the available values of temperature. Thus, although the critical behavior is not extreme, caution should be exercised when using such models near critical temperatures.Research supported by AFOSR Grant No. 91-0048 and by USARO Grant No. DAAL03-90-G-0103.     

Sharp Minima for Multiobjective Optimization in Banach Spaces

We study sharp minima for multiobjective optimization problems. In terms of the Mordukhovich coderivative and the normal cone, we present sufficient and or necessary conditions for existence of such sharp minima, some of which are new even in the single objective setting.This research was supported by a Central Research Grant of The Hong Kong Polytechnic University (Grant No. G-T 507). Research of the first author was also supported by the National Natural Science Foundation of PR China (Grant No. 10361008) and the Natural Science Foundation of Yunnan Province, China (Grant No. 2003A002M).     

Three kinds of extraneous factors in Dixon resultants

Dixon resultant is a basic elimination method which has been used widely in the high technology fields of automatic control, robotics, etc. But how to remove extraneous factors in Dixon resultants has been a very difficult problem. In this paper, we discover some extraneous factors by expressing the Dixon resultant in a linear combination of original polynomial system. Furthermore, it has been proved that the factors mentioned above include three parts which come from Dixon derived polynomials, Dixon matrix and the resulting resultant expression by substituting Dixon derived polynomials respectively. This work was supported by the National Key Basic Special Funds of China (Grant No. 2004CB318003), the Knowledge Innovation Project of the Chinese Academy of Sciences (Grant No. KJCX2-YW-S02), the National Natural Science Foundation of China (Grant No. 90718041), Shanghai Leading Academic Discipline Project (Grant No. B412) and the Doctor Startup Foundation of East China Normal University (Grant No. 790013J4)     

Growth mechanism and quantum confinement effect of silicon nanowires

The methods for synthesizing one-dimensional Si nanowires with controlled diameter are introduced. The mechanism for the growth of Si nanowires and the growth model for different morphologies of Si nanowires are described, and the quantum confinement effect of the Si nanowires is presented. Project supported by the National Natural Science Foundation of China (Grant No. 19834080) and Zhou Peiyuan Special Foundation of Mathematics and Physics.     

Ruin probability of the renewal model with risky investment and large claims

The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper. For claim sizes with common distribution of extended regular variation, we study the asymptotic behaviour of the ruin probability. As a corollary, we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims. This work was supported by National Natural Science Foundation of China (Grant Nos. 10571167, 70501028), the Beijing Sustentation Fund for Elitist (Grant No. 20071D1600800421), the National Social Science Foundation of China (Grant No. 05&ZD008) and the Research Grant of Renmin University of China (Grant No. 08XNA001)     

Scalar labelings for homotopy paths

Two scalar labelings are introduced for obtaining approximate solutions to systems of nonlinear equations by simplicial approximation. Under reasonable assumptions the new scalar-labeling algorithms are shown to follow, in a limiting sense, homotopy paths which can also be tracked by piecewise linear vector labeling algorithms. Though the new algorithms eliminate the need to pivot on a system of linear equations, the question of relative computational efficiency is unresolved.The work of this author was supported in part by NSF Grant No. MCS-77-15509 and by ARO Grant No. DAAG-29-78-G-0160.The work of this author was supported in part by ONR Grant No. N00014-75-C-0495 and NSF Grant No. 81058.     

A finite-state,finite-memory minimum principle

A class of finite-state, finite-memory stochastic control problems is considered. A minimum principle is derived. Signaling strategies are defined and related to the necessary conditions of the minimum principle. Min-H algorithms for the problem are described.This research has been conducted in the MIT Electronic Systems Laboratory with support from AFOSR Grant No. 72-2273, NASA/AMES Grant No. NGL-22-009(124), and NSF Grant No. GK-25781.     

A note on a theorem of Yamamuro

Conditions are presented which are necessary for the existence of a regular fixed point of aC ¹ map.Work supported in part by NSF Grant No. MCS 77-15509.Work supported in part by ONR Grant No. N0014-75-C-0495 and NSF Grant No. Eng. 76-81058.     

Gaining efficiency via weighted estimators for multivariate failure time data

Multivariate failure time data arise frequently in survival analysis. A commonly used technique is the working independence estimator for marginal hazard models. Two natural questions are how to improve the efficiency of the working independence estimator and how to identify the situations under which such an estimator has high statistical efficiency. In this paper, three weighted estimators are proposed based on three different optimal criteria in terms of the asymptotic covariance of weighted estimators. Simplified close-form solutions are found, which always outperform the working independence estimator. We also prove that the working independence estimator has high statistical efficiency, when asymptotic covariance of derivatives of partial log-likelihood functions is nearly exchangeable or diagonal. Simulations are conducted to compare the performance of the weighted estimator and working independence estimator. A data set from Busselton population health surveys is analyzed using the proposed estimators. This work was supported by National Natural Science Foundation of China (Grant No. 10628104), Fan was also supported by National Institutes of Health (Grant No. R01-GM072611) and Natural Science Foundation (Grant No. DMS-0714554), Zhou was supported by National Natural Science Funds for Distinguisheel Young Scholar (Grant No. 70825004), National Natural Science Foundation of China (Grant Nos. 10731010, 10628104), the National Basic Research Program (Grant No. 2007CB814902), Creative Research Groups of China (Grant No. 10721101) and Leading Academic Disipline Program, the 10 ^th five year plan of 211 Project for Shanghai University of Finance and Economics (the 3 ^rd phase), Cai was supported by National Institutes of Health (Grant No. R01-HL57444)     

Volume estimate for a cone with a submanifold as vertex

We give some estimates for the volume of a cone with vertex a submanifold P of a Riemannian or Kaehler manifold M. The estimates are functions of bounds of the mean curvature of P and the sectional curvature of M. They are sharp on cones having a basis which is contained in a tubular hypersurface about P in a space form or in a complex space form.Work partially supported by DGICYT Grant No. PB90-0014-C03-01.     

Existence,uniqueness and continuity of solutions of integral equations. An addendum

Summary This note corrects au error in the continuous dependence theorem of an earlier paper on the subject stated in the title. Here it is shows that the topology of one of the spaces of functions can be modified in order to obtain the desired continuity results. This research was support in part by the National Aeronautics Space Administration under Grant No. NGL-40-002-015, and in part by the U. S. Air Force under Grant No. AF-AFOSR-67-0693A. This research was supported in part by the National Science Foundation under Grant No. GP-3904 and GP-7041 and in part by the U.S. Army under Grant No. D1-31-124-ARO-D-265. Entrata in Redazione il 10 aprile 1970.     

Heuristic reliability optimization by tabu search

A new heuristic algorithm, based on the tabu search methodology, is proposed for constrained redundancy optimization in series and in complex systems. It has the advantage of not being blocked as soon as a local optimum is found. Results given by the new method are compared with those of previous heuristics on a series of examples.We are grateful to R. Bulfin for making the code for reliability optimization of series systems he wrote with C.-Y. Liu available to us.Work of the first author was supported by NSERC Grant No. GP0105574, FCAR Grant No. 92EQ1048 and AFOSR Grant No. 90-0008 to Rutgers University.Work of the second author was partly supported by AFOSR Grant No. 90-0008 to Rutgers University while he was a graduate student.