On Inequalities with Measures of Sobolev Type Embedding Theorems on Open Sets of the Real Axis

We consider some Sobolev-type spaces and obtain a necessary and sufficient condition for their embedding in a Lebesgue space.     

Global and uniform convergence of subspace correction methods for some convex optimization problems

This paper gives some global and uniform convergence estimates for a class of subspace correction (based on space decomposition) iterative methods applied to some unconstrained convex optimization problems. Some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems.

     

Properties of large-scale TIDs observed in Central China

This paper investigates the large scale travelling ionospheric disturbances (LSTIDs) using the observation data of an HF Doppler array located in Central China. The data observed in a high solar activity year (year 1989) are analyzed to obtain the main propagation parameters of LSTIDs such as period, horizontal phase velocity and propagating direction. Results are outlined as follows: Most of the LSTIDs propagate southward; others tend to propagate northward, mostly in summer; dispersion of most LSTIDs is matched with that of Lamb pseudomode, while others have the dispersion of long period gravity wave mode. The horizontal phase velocities of these two modes are about 220 and 450 m/s respectively. The analysis shows that LSTIDs are strongly pertinent to solar activity and space magnetic storms; thus the results presented here are significant for the research of ionospheric weather in mid-low latitude region.     

Quantization of Underdamped, Critically Damped, and Overdamped Electric Circuits with a Power Source

We have investigated the quantum mechanical effect of the underdamped, critically damped, and overdamped electric circuits with a power source. The charge of the underdamped circuit oscillates while those of the critically damped and overdamped ones don't. The wave function of the system of overdamped circuit represented parabolic cylinder function while underdamped circuit was represented by well-known Hermite polynomial. The eigenvalues of underdamped circuit is discrete while those of the critically damped and overdamped ones are given as continuously.     

Lower Bounds from State Space Relaxations for Concave Cost Network Flow Problems

In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving transitions that go across several stages, as is the case of network flow problems. Applications for these LBs include: estimation of the quality of heuristic solutions; local search methods that use information of the LB solution structure to find initial solutions to restart the search (Fontes et al., 2003, Networks, 41, 221–228); and branch-and-bound (BB) methods having as a bounding procedure a modified version of the LB algorithm developed here, (see Fontes et al., 2005a). These LBs are iteratively improved by penalizing, in a Lagrangian fashion, customers not exactly satisfied or by performing state space modifications. Both the penalties and the state space are updated by using the subgradient method. Additional constraints are developed to improve further the LBs by reducing the searchable space. The computational results provided show that very good bounds can be obtained for concave cost network flow problems, particularly for fixed-charge problems.     

An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss

A subclass of the scale-parameter exponential family is considered and for the rth power of the scale parameter, which is lower bounded, an admissible minimax estimator under scale-invariant squared-error loss is presented. Also, an admissible minimax estimator of a lower-bounded parameter in the family of transformed chi-square distributions is given. These estimators are the pointwise limits of a sequence of Bayes estimators. Some examples are given.     

一致Banach空间中非扩张映象的弱收敛定理

设犈是一致凸Ｂａｎａｃｈ空间，满足Ｏｐｉａｌ条件或具有Ｆｒｅｃｈｅｔ可微范数，犆是犈的非空闭凸子集，且犜：犆→犆是非扩张映象．又设对任何初始数据狓１ ∈犆，序列｛狓狀｝由下列修改了的Ｉｓｈｉｋａｗａ迭代程序生成：狓狀＋１ ＝狋狀犜狀（狊狀犜狀狓狀＋ （１－狊狀）狓狀）＋ （１－狋狀）狓狀，　狀≥１， （Ｉ）其中，数列｛狋狀｝与｛狊狀｝满足下列条件（ｉ）和（ｉｉ）之一：（ｉ）狋狀∈ ［犪，犫］且狊狀∈ ［０，犫］；（ｉｉ）狋狀∈ ［犪，１］且狊狀∈ ［犪，犫］，这里，常数犪，犫满足０＜犪≤犫＜１．作者证明了，犜有不动点的充要条件是，｛狓狀｝ 弱收敛且｛‖狓狀－犜狓狀‖｝收敛到０．而且，由此即知，若犜有不动点，则｛狓狀｝弱收敛到犜的一个不动点．     

T 1 theorem for Besov spaces on nonhomogeneous spaces

Suppose μ is a Radon measure on ℝ ^d , which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀>0 such that for all x∈supp(μ) and r>0, μ(B(x, r))⪯C₀rⁿ, where 0<n⪯d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa’s results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7].     

Ergodic properties and thermodynamic behavior of elementary reversible cellular automata. I. Basic properties

This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems.