An analysis of Chinese Super League partial results

Some of the history of soccer/world football in China is presented. Then consideration turns to the 2008 Chinese Super League. It has 16 teams. The results from the first half of the season, i.e. 15 rounds, are studied. The response of interest for a specific game is whether the home team won, tied or lost, who the home team was, and who the opponent was. The response is ordinal-valued. A generalized linear model is fit and then, given the remaining fixtures, used to predict the final standings of the season. Other explanatories, such as round number, are considered for inclusion in the model. Simulation is employed to estimate probabilities of interest. This work was supported by US National Science Foundation (Grant No. DMS-0707157)     

The Littlewood-Offord problem and invertibility of random matrices

We prove two basic conjectures on the distribution of the smallest singular value of random n×n matrices with independent entries. Under minimal moment assumptions, we show that the smallest singular value is of order n−1/2, which is optimal for Gaussian matrices. Moreover, we give a optimal estimate on the tail probability. This comes as a consequence of a new and essentially sharp estimate in the Littlewood-Offord problem: for i.i.d. random variables Xk and real numbers ak, determine the probability p that the sum k_∑akXk lies near some number v. For arbitrary coefficients ak of the same order of magnitude, we show that they essentially lie in an arithmetic progression of length 1/p.     

漫谈物理学的过去、现在与未来

文章试图对物理学的发展历史作一透视，从而理解其现状，并进而窥测其未来的前景，我们希望这一看法对于当今从事物理学教学与科研的人士有所助益，由于物理世界的层次化，诸层次之间既可能存在耦合，又可能出现脱耦，因而大量粒子所构成的复杂体系中所涌现的各种层展性质就不能简单地还原成个别粒子所服从的规律，我们根据这一观点并结合物理学的未来前景，讨论了当今物理学研究的若干前沿问题，一切迹象预示着物理学将有光明的前景     

A harmonious unifying hybrid preferential model and its universal properties for complex dynamical networks

To describe the real world which is a harmonious unification world with both de- terminism and randomness, we propose a harmonious unifying hybrid preferential model (HUHPM) of a certain class of complex dynamical networks. HUHPM is gov- erned only by the total hybrid ratio d/r according to the practical need. As some typical examples, the concepts and methods of the HUHPM are applied to the un-weighted BA model proposed by Barabási et al., the weighted BBV model pro- posed by Barat et al. and the weighted TDE model proposed by Wang et al. to get the so-called HUHPM-BA network, HUHPM-BBV network and HUHPM-TDE network. These HUHPM networks are investigated both analytically and numerically. It is found that the HUHPM reveals several universal properties, which more approach to the real-world networks for both un-weighted and weighted networks and have potential for applications.     

On the code generated by the incidence matrix of points and hyperplanes in <Emphasis Type="Italic">PG</Emphasis>(<Emphasis Type="Italic">n</Emphasis>,<Emphasis Type="Italic">q</Emphasis>) and its dual

In this paper, we study the p-ary linear code C(PG(n,q)), q = p ^h , p prime, h ≥ 1, generated by the incidence matrix of points and hyperplanes of a Desarguesian projective space PG(n,q), and its dual code. We link the codewords of small weight of this code to blocking sets with respect to lines in PG(n,q) and we exclude all possible codewords arising from small linear blocking sets. We also look at the dual code of C(PG(n,q)) and we prove that finding the minimum weight of the dual code can be reduced to finding the minimum weight of the dual code of points and lines in PG(2,q). We present an improved upper bound on this minimum weight and we show that we can drop the divisibility condition on the weight of the codewords in Sachar’s lower bound (Geom Dedicata 8:407–415, 1979). G. Van de Voorde’s research was supported by the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen).     

Two Hard Spheres in a Spherical Pore: Exact Analytic Results in Two and Three Dimensions

The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a relation valid for any dimension between these partition functions, second virial coefficient for inhomogeneous systems in a spherical pore, and third virial coefficients for polydisperse hard spheres mixtures. Using the established relation we were able to evaluate the cluster integral b ₂(V) related with the second virial coefficient for the Hard Disc system into a circular pore. Finally, we analyse the behaviour of the obtained expressions near the maximum density.     

SMALL INTO ISOMORPHISM FROM (Co) INTO C(Ω) TYPE

If T is an isomorphism of (co) into C(Ω) (where Ω is a sequentially compact and paracompact space, or a compact metric space in particular), which satisfies the con- dition ‖T‖.‖T-1‖<1 e for some ∈∈ (0,1/5), then T/‖T‖ is close to an isometry with an error less than 9∈. The proof of this article is simple without using the dual space or adjoint operator.     

The state constrained bilateral minimal time function

We generalize, to the bilateral case (that is, with variable initial and end points), the main results of Nour and Stern [C. Nour, R.J. Stern, Regularity of the state constrained minimal time function, Nonlinear Anal. 66 (1) (2007) 62–72] and Stern [R.J. Stern, Characterization of the state constrained minimal time function, SIAM J. Control Optim. 43 (2004) 697–707], where the regularity and Hamilton–Jacobi characterization of the state constrained (unilateral) minimal time function were studied.     

E.U. Condon: Science, Religion, and the Politics of World Peace

I set forth and discuss E.U. Condon’s views on science and society, focusing specifically on Condon’s views on science and religion, science and government, and the necessity for world peace. Even disregarding his contributions to theoretical physics, Condon proves an interesting case study for several reasons. He had extensive experience in academia, industry, and government, and was a scientist who easily crossed the insider-outsider divide between scientists in Cold War America. Moreover, Condon was a person of the Progressive Left advocating World Government as necessary for peace and warning of the dangers of the militarization of American society as well as of science itself. Known for being outspoken, he became an inviting target for the forces of anticommunism in Cold War America. In March 1948, the House Un-American Activities Committee charged that Condon was “one of the weakest links in our atomic security.” Michael A. Day is Professor of Physics at Lebanon Valley College. He holds doctorates in both physics and philosophy.     

Direct limit groups do not have small subgroups

We show that countable direct limits of finite-dimensional Lie groups do not have small subgroups. The same conclusion is obtained for suitable direct limits of infinite-dimensional Lie groups.