一个非严格双曲型方程组粘性逼近解的收敛性

本文讨论非严格双曲型方程组的粘性逼近解的收敛性，当ｆ满足一定条件，初值为有界可测函数时，利用补偿紧致的理论及对前进熵波的分析，在没有对粘性解导数一致界估计的情况下，证明了粘性逼近解存在一个子序列在强拓扑意义下收敛．     

Absorption of millimeter to submillimeter waves by atmospheric water molecules

Using the values of the rotational molecular parameters (including cencrifugal distortion terms) of the H₂ ¹⁶O molecule, which can explain 12 observed transitions below 800 GHz, all rotational energy levels with normalized Boltzmann factors larger than 5×10^–8 at 300°K are calculated. Probabilities of all possible electric dipole transitions among these states, 2277 lines, are calculated using the eigenfunctions thus obtained, and the permanent electric dipole moment of 1.8546 Debye. Assuming the single and full Lorentzian line forms, we calculated the absorption coefficient for millimeter to submillimeter region. Our result, using the single term Lorentzian line form, agrees quite well with experiment for 1 Torr of water vapor in 760 Torr air at 300°K.     

Saturating constructions for normed spaces II

We prove several results of the following type: given finite-dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) and (2) every subspace of X, whose dimension is not “too small”, contains a further well-complemented subspace nearly isometric to V. This sheds new light on the structure of large subspaces or quotients of normed spaces (resp., large sections or linear images of convex bodies) and provides definitive solutions to several problems stated in the 1980s by Milman.     

Focussing and defocussing of ballistic phonons in diamond and Nb3Sn

The ballistic propagation of phonons in diamond and Nb₃Sn at 40 and at 4.2 K is examined. The nature of variation of the phonon magnification factor has been analysed both in the wave vector as well as group velocity spaces. Using the Polar Schmidt-net with Pole at (π/2,π/2), the mappings of phonon focussing and defocussing are made. It is shown that the mapping for theFTA mode for Nb₃Sn exhibits islands acting as impenetrable barriers for phonon propagation.     

Influence of structural defects on the magnetization process in high-magnetic fields in the Fe61Co10Y8Nb1B20 alloy in the form of ribbons and plates

Amorphous samples of the Fe₆₁Co₁₀Y₈Nb₁B₂₀ alloy in the form of a ribbon with thickness of approximately 30 μm and in the form of a plate with thickness of 0.5 mm have been investigated. Plates were obtained by a suction-casting method, and ribbons by a single roller melt-spinning method. Microstructural studies, using X-ray spectroscopy, confirmed that samples in the as-quenched state were fully amorphous. Measurements carried out using a vibrating sample magnetometer allowed values of coercivity and saturation magnetization to be obtained; it also facilitated the estimation of size and nature of structural defects in the investigated samples. All of the investigated samples of this alloy in the as-quenched state have high values of saturation magnetization of greater than 1.25 T.     

Stabilization of unbounded bilinear control systems in Hilbert space

We consider bilinear control systems of the form y^′(t)=Ay(t)+u(t)By(t) where A generates a strongly continuous semigroup of contraction (etA)_t?0 on an infinite-dimensional Hilbert space Y whose scalar product is denoted by 〈.,.〉. We suppose that this system is unbounded in the sense that the linear operator B is unbounded from the state Y into itself. Tacking into account eventual control saturation, we study the problem of stabilization by (possibly nonquadratic) feedback of the form u(t)=−f(〈By(t),y(t)〉). Applications to the heat equation is considered.     

基于Fuzzy-Grey关联分析的信息资源聚焦的数学模型

本文运用饱和信息维的增减技术对信息获取子空间进行结构上的剖分,用饱和信息维列作为因子列来构造灰色关联空间,将灰色理论中的关联分析用于模糊综合评判模型,用灰色关联系数来替代隶属度,用关联序来描述信息之间的相关联程度,得到信息资源聚焦的一种新的数学模型。     

A Markov Chain Monte Carlo Convergence Diagnostic Using Subsampling

Abstract

A new diagnostic procedure for assessing convergence of a Markov chain Monte Carlo (MCMC) simulation is proposed. The method is based on the use of subsampling for the construction of confidence regions from asymptotically stationary time series as developed in Politis, Romano, and Wolf. The MCMC subsampling diagnostic is capable of gauging at what point the chain has “forgotten” its starting points, as well as to indicate how many points are needed to estimate the parameters of interest according to the desired accuracy. Simulation examples are also presented showing that the diagnostic performs favorably in interesting cases.     

A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from UK regions

This paper, by using conditional directional distance functions as introduced by Simar and Vanhems [J. Econometrics 166 (2012) 342–354] modifies the model by Färe and Grosskopf [Eur. J. Operat. Res. 157 (2004) 242–245] and examines the link between regional environmental efficiency and economic growth. The proposed model using conditional directional distance functions incorporates the effect of regional economic growth on regions’ environmental efficiency levels. The results from UK regional data reveal a negative relationship between regions’ GDP per capita and environmental inefficiency up to a certain GDP per capita level. After that level it appears that the relationship becomes positive. As an overall result the regional environmental inefficiency-GDP per capita relationship appears to have a ‘U’ shape form.