On the finite-time singularities of the 3D incompressible Euler equations

We prove the finite-time vorticity blowup, in the pointwise sense, for solutions of the 3D incompressible Euler equations assuming some conditions on the initial data and its corresponding solutions near initial time. These conditions are represented by the relation between the deformation tensor and the Hessian of pressure, both coupled with the vorticity directions associated with the initial data and solutions near initial time. We also study the possibility of the enstrophy blowup for the 3D Euler and the 3D Navier-Stokes equations, and prove the finite-time enstrophy blowup for initial data satisfying suitable conditions. Finally, we obtain a new blowup criterion that controls the blowup by a quantity containing the Hessian of the pressure. © 2006 Wiley Periodicals, Inc.     

黑龙江漠河地区冰雪情自动监测系统的设计与应用

基于空气、冰、雪与水物理特性的差异,设计了适应高寒地区内陆河道冰雪情定点自动检测的传感器和数据采集系统设备.该系统被安装在黑龙江省漠河县北极村水位站黑龙江河道断面,进行了3个半月的冰雪情定点连续监测,获取了系统的黑龙江河道内部冰水情以与积雪深度现场数据.采集数据完整地反映了黑龙江河道冬季冰层和雪层生消变化过程,为分析高寒地区冬季冰雪情变化规律以及春季凌汛预警提供了科学的预测数据,并探索出了一种适合野外恶劣环境下工程应用的冰雪情检测方法和系统设备.     

On the consistency of the MLE for Ornstein–Uhlenbeck and other selfdecomposable processes

In this paper we give easy to verify conditions for the strong consistency of the maximum likelihood estimator (MLE) in the case when data is sampled from a parametric family of selfdecomposable distributions. The difficulty arises from the fact that standard conditions for the consistency of the MLE are based on the pdf, which, for most selfdecomposable distributions, is not available in a closed form. Instead, our conditions are based on properties of the Lévy triplet (i.e. the Lévy measure, the Gaussian part, and the shift) of the distribution. Further, we extend out results to certain selfdecomposable stochastic processes, and, in particular, we give conditions in the case when the data is sampled from a Lévy or an Ornstein–Uhlenbeck process.     

From the discrete kinetic theory of vehicular traffic flow to computing the velocity distribution at equilibrium

This paper deals with the identification of the parameters of a model of vehicular traffic flow using experimental data obtained on the highway Padova–Venezia. Subsequently, simulations of the model are developed corresponding to steady uniform flow conditions. These simulations allow us to describe the velocity distribution in the above conditions corresponding to the parameters obtained by identification on the basis of experimental data.     

On the Positive Definiteness of the Information Matrix Under the Binary and Poisson Mixed Models

Binary and Poisson generalized linear mixed models are used to analyse over/under-dispersed proportion and count data, respectively. As the positive definiteness of the information matrix is a required property for valid inference about the fixed regression vector and the variance components of the random effects, this paper derives the relevant necessary and sufficient conditions under both these models. It is found that the conditions for the positive definiteness are not identical for these two nonlinear mixed models and that a mere analogy with the usual linear mixed model does not dictate these conditions.     

On the Reconstruction of the Sturm-Liouville Problems with Spectral Parameter in the Discontinuity Conditions

In this paper, we are concerned with the problem of recovering the Sturm–Liouville problem under the circumstance of the discontinuity conditions involved spectral parameter at finite interior points of a finite interval. We provide procedures for constructing their potentials and boundary conditions either from the Weyl function, or from spectral data, or from two spectra in terms of the method of spectral mappings.     

A two-regime traffic flow model and the consistency of its parameters

An attempt is made to demonstrate the traffic behaviour and phenomena under normal morning peak period conditions, and to examine the suitability of a two-regime traffic flow model for these conditions. This paper has three main parts. First, the consistency of flow and concentration patterns of a 9-mile freeway section is examined and provides a basis for distinguishing between the free-flow and the congested-flow regimes. This distinction clearly indicates the data points obtained from traffic flow situations, which, in time-sequence, approach maximum flow conditions, congested conditions, and through a recovery process backwards to free-flow conditions.

In the second part, a car-following model for the two-regime approach is introduced. By using the analysis of driver performance as a sensitivity measurement, model parameters are defined and evaluated. An overall comparison between the proposed and known generalized car-following models emphasizes the advantages of the proposed model, particularly its simplicity and clarity at both the micro- and macroscopic levels, for the two-regime phenomenon.

In the third part, the steady-state formulation, derived from the proposed car-following model, is evaluated by using the time-sequence data points. The consistency of the two-regime model parameters is apparently well preserved regarding data sets of 3-year period (1972–1975) with respect to three independent variables: years, workdays and locations.     

Maximum likelihood inference for the Cox regression model with applications to missing covariates

In this paper, we carry out an in-depth theoretical investigation for existence of maximum likelihood estimates for the Cox model [D.R. Cox, Regression models and life tables (with discussion), Journal of the Royal Statistical Society, Series B 34 (1972) 187–220; D.R. Cox, Partial likelihood, Biometrika 62 (1975) 269–276] both in the full data setting as well as in the presence of missing covariate data. The main motivation for this work arises from missing data problems, where models can easily become difficult to estimate with certain missing data configurations or large missing data fractions. We establish necessary and sufficient conditions for existence of the maximum partial likelihood estimate (MPLE) for completely observed data (i.e., no missing data) settings as well as sufficient conditions for existence of the maximum likelihood estimate (MLE) for survival data with missing covariates via a profile likelihood method. Several theorems are given to establish these conditions. A real dataset from a cancer clinical trial is presented to further illustrate the proposed methodology.     

On analytic solutions to the generalized Cauchy problem with data on three surfaces for a quasilinear system

The generalized Cauchy problem with data on three surfaces is under consideration for a quasilinear analytic system of the third order. Under some simplifying assumption, we find necessary and sufficient conditions for existence of a solution in the form of triple series in the powers of the independent variables. We obtain convenient sufficient conditions under which the data of the generalized Cauchy problem has a unique locally analytic solution. We give counterexamples demonstrating that in the case we study it is impossible to state necessary and sufficient conditions for analytic solvability of the generalized Cauchy problem. We also show that the analytic solution can fail to exist even if the generalized Cauchy problem with data on three surfaces has a formal solution since the series converge only at a sole point, the origin.     

Necessary and sufficient conditions for the solvability of the inverse problem for the matrix Sturm-Liouville operator

The matrix Sturm-Liouville operator on a finite interval with Dirichlet boundary conditions is studied. Properties of its spectral characteristics and the inverse problem of recovering the operator from these characteristics are investigated. Necessary and sufficient conditions on the spectral data of the operator are obtained. Research is conducted in the general case, with no a priori restrictions on the spectrum. A constructive algorithm for solving the inverse problem is provided.     

A note on reduction of the number of parameters in linear statistical models

In certain settings the mean response is modeled by a linear model using a large number of parameters. Sometimes it is desirable to reduce the number of parameters prior to conducting the experiment and prior to the actual statistical analysis. Essentially, it means to formulate a simpler approximate model to the original “ideal” one. The goal is to find conditions (on the model matrix and covariance matrix) under which the reduction does not influence essentially the data fit. Here we try to develop such conditions in regular linear model without and with linear restraints. We emphasize that these conditions are independent of observed data.     

On the high smoothness of the solution of an abstract hyperbolic-parabolic system like systems of thermoelasticity equations

We study the Cauchy problem for a hyperbolic-parabolic system of abstract differential equations in a Hilbert space, which generalizes a number of linear coupled thermoelasticity problems. We establish results on the high smoothness of the solution with respect to time as well as with respect to the spatial variables under appropriate smoothness conditions on the right-hand side and data coordination conditions.     

On the stability of the σ-scheme with transparent boundary conditions for parabolic equations

Initial-boundary value problems for self-adjoint parabolic equations on a semiaxis and a semibounded strip are considered. For finite-difference σ-schemes, an alternative method for stating approximate transparent boundary conditions is suggested and conditions ensuring unconditional stability in the energy norm with respect to the initial data and free terms for a weight σ ≥ 1/2 are presented. The validity of these stability conditions in the case of discrete transparent boundary conditions is proved (by several methods), and the derivation of the latter conditions is revisited. Published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 4, pp. 671–692. This article was translated by the author.     

On the existence of nonnegative solutions to the Dirichlet boundary value problem for the p-Laplace equation in the presence of exterior mass forces

We consider the Dirichlet problem for an inhomogeneous p-Laplace equation with nonlinear source in the presence of exterior mass forces.We obtain new sufficient conditions for the existence of a weak nonnegative bounded solution. The sufficient conditions are written in explicit form through the data of the problem.     

Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model

We study a Penrose-Fife phase transition model coupled with homogeneous Neumann boundary conditions. Improving previous results, we show that the initial value problem for this model admits a unique solution under weak conditions on the initial data. Moreover, we prove asymptotic regularization properties of weak solutions.     

On Robinsonian dissimilarities, the consecutive ones property and latent variable models

A dissimilarity measure on a set of objects is Robinsonian if its matrix can be symmetrically permuted so that its elements do not decrease when moving away from the main diagonal along any row or column. The Robinson property of a dissimilarity reflects an order of the objects. If a dissimilarity is not observed directly, it must be obtained from the data. Given that an ordinal structure is assumed to underlie the data, the dissimilarity function of choice may or may not recover the order correctly. For four dissimilarity measures for binary data it is investigated what ordinal data structure of 0s and 1s is correctly recovered. We derive sufficient conditions for the dissimilarity functions to be Robinsonian. The sufficient conditions differ with the dissimilarity measures. The paper concludes with some limitations of the study.     

A Mixed Problem for the Heat Equation with Advanced Time in Boundary Conditions

We study a one-dimensional mixed problem for the heat equation, with time advance in nonlocal and non-self-adjoint boundary conditions, describing a real physical process. Under minimal conditions on the initial data, we prove its unique solvability and obtain an explicit representation for the solution.     

具有非线性梯度吸收项的快速扩散方程的有限熄灭

本文研究快速扩散方程ut-Δum +｜ u｜p =0的柯西问题 ,其中m ,p∈ ( 0 ,1) .对于 0

相似文献   

The self-similar solutions of the one-dimensional semilinear Tricomi-type equations

In this article we investigate the issue of existence of global in time solutions of semilinear Tricomi-type equations. We give conditions that relate the nonlinearity, the speed of propagation, and the order of singularities of initial data. These conditions guarantee existence of global in time solutions. In particular, we prove existence of solutions invariant under dilation by solving the Cauchy problem with initial data which are homogeneous functions.     

An integral semiclassical method for calculating the spectra for centrally symmetric potentials

We develop a new approach to semiclassical quantization conditions that does not involve asymptotic expansions and is based on exact general properties of wave equations and their spectra. For centrally symmetric potentials, the quantization conditions depend only on a collection of integrals involving powers of the classical momentum. The energy levels calculated using these conditions are in good agreement with numerical data. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 3, pp. 463–480, September, 2000.