Necessary and sufficient existence conditions for a boundary control of vibrations of a string and a spherical layer for small times

We find necessary and sufficient conditions for the existence of a boundary control of vibrations of a string or a spherical layer for critical and subcritical times. We completely analyze the existence of a boundary control of vibrations of a spherical layer by a force on two spheres. We find necessary and sufficient existence conditions for the control. Along with the control problem for vibrations of a spherical layer, we consider a similar control problem for string vibrations.     

Lower Bounds for the Rate of Convergence of Dynamic Reconstruction Algorithms for Distributed-Parameter Systems

We obtain lower bounds for the rate of convergence of reconstruction algorithms for distributed-parameter systems of parabolic type. In the case of a pointwise constraint on control for known reconstruction algorithms, we establish a lower bound on the rate of convergence, which shows that, given certain conditions, for each solution of the system one can choose such a collection of measurements so that the reconstruction error will not be less than a certain value. In the case of unbounded controls, we obtain lower bounds for a possible reconstruction error for each trajectory as well as for a given set of trajectories. For a system of special form, we construct an algorithm for which we obtain upper and lower bounds for accuracy having identical order for a specific choice of matching of the parameters.     

Propagation of a plane wave to a materially uniform but inhomogeneous body

We produce the equations of small deformations superimposed upon large for materially uniform but inhomogeneous bodies and specialize to an isotropic material and to a homogeneous finite elastic deformation. By assuming the small deformation to be a plane wave, a set of equations for the amplitude of the wave is produced which is accompanied by an additional set of conditions. By requiring a non-trivial solution for the amplitude, we obtain the secular equation and from it a set of necessary and sufficient conditions for having a real wave speed. The second set of conditions that have to be satisfied is due to the materials inhomogeneity. Essentially, the present analysis enhances the approach of Hayes and Rivlin for materially uniform but inhomogeneous bodies. The outcome is that for such bodies the restrictions on the constitutive law for having real wave speeds for an isotropic material subjected to a pure homogeneous deformation involves the field of the inhomogeneity as well.     

Multiround Unconditionally Secure Authentication

Authentication codes are used to protect communication against a malicious adversary. In this paper we investigate unconditionally secure multiround authentication schemes. In a multiround scheme a message is authenticated by passing back and forth several codewords between the sender and receiver. We define a multiround authentication model and show how to calculate the probability of a successful attack for this model. We prove the security for a 3-round scheme and give a construction for the 3-round scheme based on Reed-Solomom codes. This construction has a very small key size for even extremely large messages. Furthermore, a secure scheme for an arbitrary number of rounds is given. We give a new upper bound for the keys size of an n-round scheme.     

Circle theorems for steady Stokes flow

Two circle theorems for two-dimensional steady Stokes flow are presented. The first theorem gives an expression for the stream function for a Stokes flow past a circular cylinder in terms of the stream function for a slow and steady irrotational flow in an unbounded incompressible viscous fluid. The second theorem gives a more general expression for the stream function for another Stokes flow past the circular cylinder in terms of the stream function for a slow and steady rotational flow in the same fluid.     

Coupled-expanding maps and one-sided symbolic dynamical systems

This paper studies relationships between coupled-expanding maps and one-sided symbolic dynamical systems. The concept of coupled-expanding map is extended to a more general one: coupled-expansion for a transitive matrix. It is found that the subshift for a transitive matrix is strictly coupled-expanding for the matrix in certain disjoint compact subsets; the topological conjugacy of a continuous map in its compact invariant set of a metric space to a subshift for a transitive matrix has a close relationship with that the map is strictly coupled-expanding for the matrix in some disjoint compact subsets. A certain relationship between strictly coupled-expanding maps for a transitive matrix in disjoint bounded and closed subsets of a complete metric space and their topological conjugacy to the subshift for the matrix is also obtained. Dynamical behaviors of subshifts for irreducible matrices are then studied and several equivalent statements to chaos are obtained; especially, chaos in the sense of Li–Yorke is equivalent to chaos in the sense of Devaney for the subshift, and is also equivalent to that the domain of the subshift is infinite. Based on these results, several new criteria of chaos for maps are finally established via strict coupled-expansions for irreducible transitive matrices in compact subsets of metric spaces and in bounded and closed subsets of complete metric spaces, respectively, where their conditions are weaker than those existing in the literature.     

BATE curve in assessment of clinical utility of predictive biomarkers

In this paper,for time-to-event data,we propose a new statistical framework for casual inference in evaluating clinical utility of predictive biomarkers and in selecting an optimal treatment for a particular patient.This new casual framework is based on a new concept,called Biomarker Adjusted Treatment Effect (BATE) curve.The BATE curve can be used for assessing clinical utility of a predictive biomarker,for designing a subsequent confirmation trial,and for guiding clinical practice.We then propose semi-parametric methods for estimating the BATE curves of biomarkers and establish asymptotic results of the proposed estimators for the BATE curves.We also conduct extensive simulation studies to evaluate finite-sample properties of the proposed estimation methods.Finally,we illustrate the application of the proposed method in a real-world data set.     

树的稳定子集和稳定指标

一个实矩阵的符号稳定性问题在经济学、生态学等诸多领域中都有应用背景．本文利用[1]中给出的不可约矩阵的符号稳定性的有关结论，将一个实矩阵的符号稳定性判定问题转化为一个等价的图论问题，即判定无向树中一个点子集的稳定性问题．本文引入了树的稳定子集的概念并给出了稳定子集的递归判别方法．本文还提出井研究了树的稳定指标，即树中所有稳定子集的最小基数，证明了关于稳定指标的一个min—max型定理，井给出了n阶树的稳定指标的最好上界及达到上界的极树的完全刻划。     

Connection between sets of uniqueness for multiplicative systems of functions and sets of uniqueness for multiplicative transforms

A problem of uniqueness for series over multiplicative systems of functions and for multiplicative transforms is considered. It is shown that each set of uniqueness for a multiplicative transform is specified by a countable collection of sets of uniqueness for series over the corresponding multiplicative system of functions. Each set of uniqueness for a series over a multiplicative system of functions is a portion on [0, 1) of some set of uniqueness for the corresponding multiplicative transform.     

Density results for subspace multiwindow Gabor systems in the rational case

Let S be a periodic set in R and L2(S) be a subspace of L2 (R). This paper investigates the density problem for multiwindow Gabor systems in L2(S) for the case that the product of time-frequency shift parameters is a rational number. We derive the density conditions for a multiwindow Gabor system to be complete (a frame) in L2(S). Under such conditions, we construct a multiwindow tight Gabor frame for L2(S) with window functions being characteristic functions. We also provide a characterization of a multiwindow Gabor frame to be a Riesz basis for L2(S), and obtain the density condition for a multiwindow Gabor Riesz basis for L2(S).     

Nonlinear spectral problem for a singular system of ordinary differential equations with a nonlocal condition

We consider a nonlinear spectral problem for a system of ordinary differential equations defined on an unbounded half-line and supplemented with a nonlocal condition specified by a Stieltjes integral. We suggest a numerically stable method for finding the number of eigenvalues lying in a given bounded domain of the complex plane and for the computation of these eigenvalues and the corresponding eigenfunctions. Our approach uses a simpler (with uncoupled boundary conditions) auxiliary boundary value problem for the same equation.     

On nonlinear time-dependent multivelocity transport equations

The aim of this paper is to show the existence and uniqueness of a solution for a class of nonlinear multivelocity neutron transport equations and to present a method for the determination of the solution. A recursion formula for the construction of a solution by the method of successive approximations and an error estimate for approximate solutions are given. Both global and local solutions are discussed. The conditions imposed on the nonlinear equation are directly applicable to the linear multivelocity transport problem, and a recursion formula for this system is also given. In the process of approximations, only successive integrations are involved. This fact indicates a promising possibility for the calculation of numerical results by using a computer. A brief discussion of this possibility and the applicability of the results on nonlinear problems are included.     

Diffusion in poro‐plastic media

A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial‐boundary‐value problem is a system that consists of the diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto‐visco‐plastic type. The variational form of this problem in Hilbert space is a non‐linear evolution equation for which the existence and uniqueness of a global strong solution is proved by means of monotonicity methods. Various degenerate situations are permitted, such as incompressible fluid, negligible porosity, or a quasi‐static momentum equation. The essential sufficient conditions for the well‐posedness of the system consist of an ellipticity condition on the term for diffusion of fluid and either a viscous or a hardening assumption in the constitutive relation for the porous solid. Copyright © 2004 John Wiley & Sons, Ltd.     

Reduced order observer design for nonlinear systems

This work is a geometric study of reduced order observer design for nonlinear systems. Our reduced order observer design is applicable for Lyapunov stable nonlinear systems with a linear output equation and is a generalization of Luenberger’s reduced order observer design for linear systems. We establish the error convergence for the reduced order estimator for nonlinear systems using the center manifold theory for flows. We illustrate our reduced order observer construction for nonlinear systems with a physical example, namely a nonlinear pendulum without friction.     

A Simple Method for Computing the Observed Information Matrix When Using the EM Algorithm with Categorical Data

Abstract

A simple matrix formula is given for the observed information matrix when the EM algorithm is applied to categorical data with missing values. The formula requires only the design matrices, a matrix linking the complete and incomplete data, and a few simple derivatives. It can be easily programmed using a computer language with operators for matrix multiplication, element-by-element multiplication and division, matrix concatenation, and creation of diagonal and block diagonal arrays. The formula is applicable whenever the incomplete data can be expressed as a linear function of the complete data, such as when the observed counts represent the sum of latent classes, a supplemental margin, or the number censored. In addition, the formula applies to a wide variety of models for categorical data, including those with linear, logistic, and log-linear components. Examples include a linear model for genetics, a log-linear model for two variables and nonignorable nonresponse, the product of a log-linear model for two variables and a logit model for nonignorable nonresponse, a latent class model for the results of two diagnostic tests, and a product of linear models under double sampling.     

Two-person game forms guaranteeing the stability against commitment and delaying tactics

The notions of the struggle for leadership or for followership, introduced by H. Moulin for two-person games, are considered for game forms. Necessary and sufficient conditions for a game form never to generate a game with the struggle of either kind are derived. Connections between these properties and the existence of a Nash equilibrium for any preference profile as well as the possibility to select a Nash equilibrium in an incentive compatible way are established.I thank V. Gurvich for a fruitful discussion, H. Moulin for his comment on a draft version of the paper and several helpful suggestions, and an anonymous referee, whose recommendations helped me to enhance the quality of presentation. I have benefited from the hospitality of Universidad de Alicante and Instituto Valenciano de Investigaciones Económicas. Some financial assistance from the Cultural Initiative Foundation and Academy of Natural Sciences is also acknowledged.     

Competence-driven project portfolio selection,scheduling and staff assignment

This paper presents a new model for project portfolio selection, paying specific attention to competence development. The model seeks to maximize a weighted average of economic gains from projects and strategic gains from the increment of desirable competencies. As a sub-problem, scheduling and staff assignment for a candidate set of selected projects must also be optimized. We provide a nonlinear mixed-integer program formulation for the overall problem, and then propose heuristic solution techniques composed of (1) a greedy heuristic for the scheduling and staff assignment part, and (2) two (alternative) metaheuristics for the project selection part. The paper outlines experimental results on a real-world application provided by the E-Commerce Competence Center Austria and, for a slightly simplified instance, presents comparisons with the exact solution computed by CPLEX.     

Continuous selection from the sets of best and near-best approximation

The paper studies approximation and structural geometric-topological properties of sets in normed and more general (asymmetric) spaces for which there exists a continuous selection for the best and near-best approximation operators. Sufficient conditions on the metric projection of sets which ensure the existence of a continuous selection for this projection are obtained, and the structural properties of such sets are determined. The existence of a continuous selection for the near-best approximation operator on a finite-dimensional space more general than a normed space is investigated. It is shown that the lower semicontinuity of the metric projection is sufficient for the existence of a continuous selection for the near-best approximation operator in the general case.     

Multiscale inference for a multivariate density with applications to X-ray astronomy

In this paper, we propose methods for inference of the geometric features of a multivariate density. Our approach uses multiscale tests for the monotonicity of the density at arbitrary points in arbitrary directions. In particular, a significance test for a mode at a specific point is constructed. Moreover, we develop multiscale methods for identifying regions of monotonicity and a general procedure for detecting the modes of a multivariate density. It is shown that the latter method localizes the modes with an effectively optimal rate. The theoretical results are illustrated by means of a simulation study and a data example. The new method is applied to and motivated by the determination and verification of the position of high-energy sources from X-ray observations by the Swift satellite which is important for a multiwavelength analysis of objects such as Active Galactic Nuclei.