几类数列通项的矩阵求法

本利用矩阵给出了几类数列的通项公式的求法，把数列通项公式的求法转化为矩阵幂的计算，思路简单、计算简便，并能判别其敛散性。     

Linear Ramsey numbers of sparse graphs

The Ramsey number R(G₁,G₂) of two graphs G₁ and G₂ is the least integer p so that either a graph G of order p contains a copy of G₁ or its complement G^c contains a copy of G₂. In 1973, Burr and Erd?s offered a total of $25 for settling the conjecture that there is a constant c = c(d) so that R(G,G)≤ c|V(G)| for all d‐degenerate graphs G, i.e., the Ramsey numbers grow linearly for d‐degenerate graphs. We show in this paper that the Ramsey numbers grow linearly for degenerate graphs versus some sparser graphs, arrangeable graphs, and crowns for example. This implies that the Ramsey numbers grow linearly for degenerate graphs versus graphs with bounded maximum degree, planar graphs, or graphs without containing any topological minor of a fixed clique, etc. © 2005 Wiley Periodicals, Inc. J Graph Theory     

含k-次增生算子的Ishikawa迭代的收敛性问题

主要研究了非线性方程x Tx=f的Ishikawa迭代解．其中T为k-次增生的或增生的，并在一致光滑和任意的实Banach空间分别研究了上述方程的带误差的Ishikawa迭代解，从而推广了已知的一些结果。     

Transverse displacement at total reflection near the grazing angle: a way to discriminate between theories

The transverse shift is observed and precisely measured at total internal reflection on a dielectric interface for a circularly polarized light beam when the incident angle is scanned from the critical angle up to the grazing angle close to 90°. The experimental results show with no doubt that the transverse displacement exists far away from the critical angle and only vanishes at grazing angle. A comparison with theories also allows a discrimination between the most different theoretical models traditionally used to interpret physically this effect.     

Analysis and modeling for time-dependent behavior of polymers exhibited in nanoindentation tests

Through the arrangement of the applied load, experimental nanoindentation results of polymethylmethacrylate (PMMA) and polyurethane (PU) employed to establish a mechanical model. The proposed model consists of irreversible delayed plastic (viscoplastic) deformation, irreversible viscous deformation, and reversible delayed elastic (viscoelastic) deformations. The phase lag exhibited between the responding depth and the oscillating load is found to be linear proportional to frequency in the range of 1-50 Hz. The residual cavity profile of the PMMA scanned by an atomic force microscope gives a validity of accommodation assumption applied in the present model. The effects of overshooting, which occurred in the dwelling process, are also discussed.     

Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

一个素变数丢番图不等式

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ON MATRIX UNITARILY INVARIANT NORM CONDITION NUMBER

1.IntroductionSince1984,severalchinesemathematicianshaveobtailledmanyresultsboutmatrixoperatornormcondition.umbe.[ll'12'18].Twokindsmatrixconditionnllmbers[9]are:(1)IfAECoxsisnonsingular,thellunlberK.(A)~IIAll.llA--'if.iscalledtheor--normconditionnumberof…     

Number albedo measurements from stratified layers of iron,concrete and aluminium

A layer of stratified combination composed of selected radiation shielding materials acquires better shielding property. Albedo is used in such measurements as an integral measure ofγ-ray scattering. The stratified slabs of alternating heterogeneous layers have been found to have a virtual homogeneous property with a definite effective atomic number. The angular distribution of back-scattered photons as well as the total number albedo values for iron, aluminium and concrete in stratified combination for 662 keV and 1250 keV photons are reported.     

Uniform random number generation

In typical stochastic simulations, randomness is produced by generating a sequence of independent uniform variates (usually real-valued between 0 and 1, or integer-valued in some interval) and transforming them in an appropriate way. In this paper, we examine practical ways of generating (deterministic approximations to) such uniform variates on a computer. We compare them in terms of ease of implementation, efficiency, theoretical support, and statistical robustness. We look in particular at several classes of generators, such as linear congruential, multiple recursive, digital multistep, Tausworthe, lagged-Fibonacci, generalized feedback shift register, matrix, linear congruential over fields of formal series, and combined generators, and show how all of them can be analyzed in terms of their lattice structure. We also mention other classes of generators, like non-linear generators, discuss other kinds of theoretical and empirical statistical tests, and give a bibliographic survey of recent papers on the subject.