Abstract:
A system of distinct representatives (SDR) of a family $F = (A_1, \cdots, A_n)$ is a sequence $(x_1, \cdots, x_n)$ of $n$ distinct elements with $x_i \in A_i$ for $1 \le i \le n$. Let $N(F)$ denote the number of SDRs of a family $F$; two SDRs are considered distinct if they are different in at least one component. For a nonnegative integer $t$, a family $F=(A_1,\cdots,A_n)$ is called a $(t,n)$-family if the union of any $k\ge 1$ sets in the family contains at least $k+t$ elements. The famous Hall's Theorem says that $N(F)\ge 1$ if and only if $F$ is a $(0,n)$-family. Denote by $M(t,n)$ the minimum number of SDRs in a $(t,n)$-family. The problem of determining $M(t,n)$ and those families containing exactly $M(t,n)$ SDRs was first raised by Chang [European J. Combin.{\bf 10}(1989), 231-234]. He solved the cases when $0\le t\le 2$ and gave a conjecture for $t\ge 3$. In this paper, we solve the conjecture. In fact, we get a more general result for so-called valued $(t,n)$-family.

Abstract:
A "floorplan" is a rectangle subdivided into smaller rectangular sections by horizontal and vertical line segments. Each section in the floorplan is called a "block". Two floorplans are considered equivalent if and only if there is a one-to-one correspondence between the blocks in the two floorplans such that the relative position relationship of the blocks in one floorplan is the same as the relative position relationship of the corresponding blocks in another floorplan. The objects of "Mosaic floorplans" are the same as floorplans, but an alternative definition of equivalence is used. Two mosaic floorplans are considered equivalent if and only if they can be converted to each other by sliding the line segments that divide the blocks. Mosaic floorplans are widely used in VLSI circuit design. An important problem in this area is to find short binary string representations of the set of n-block mosaic floorplans. The best known representation is the "Quarter-State Sequence" which uses 4n bits. This paper introduces a simple binary representation of n-block mosaic floorplan using 3n-3 bits. It has been shown that any binary representation of n-block mosaic floorplans must use at least (3n-o(n)) bits. Therefore, the representation presented in this paper is optimal (up to an additive lower order term). "Baxter permutations" are a set of permutations defined by prohibited subsequences. Baxter permutations have been shown to have one-to-one correspondences to many interesting objects in the so-called "Baxter combinatorial family". In particular, there exists a simple one-to-one correspondence between mosaic floorplans and Baxter permutations. As a result, the methods introduced in this paper also lead to an optimal binary representation of Baxter permutations and all objects in the Baxter combinatorial family.

Abstract:
Photostimulated luminescence (PSL) is observed in BaBrCl: Eu2+ after X-ray irradiation at room temperature. It is suggested by PSL stimulation spectrum and difference absorption spectrum (DAS) that F centers are formed upon X-ray irradiation and both spectra show two bands which are centered at about 550 nm and 675 nm respectively. This enables the use of semiconductor light-emitting diodes (LED) instead of gas lasers for photostimulation. The PSL intensity increases linearly with X-ray irradiation dose increasing, and the conversion efficiency is 29% that for the standard commercial storage phosphor BaFBr:Eu from Fuji imaging plate.

Abstract:
We study distribution functions (DF) of mesoscopic hopping conductance numerically by searching for the shortest path. We have found that the distributions obtained by choosing randomly the chemical potentials (for a fixed impurity configuration), which corresponds to a typical experimental situation, coincide with those obtained when both impurity configuration and chemical potential is chosen randomly, in agreement with the ergodicity hypothesis. The DFs obtained for one-dimensional systems were found to be quite close to the independent predictions of V.I. Mel'nikov, A.A. Abrikosov and P. Lee et al. For D=2, the DFs both for narrow system and thin film look similar (and close to the 1D case).The distribution function for the conductance of the square sample is nearly Gaussian as predicted by both Altshuler et al and Serota et al.

Abstract:
Seymour and, independently, Kelmans conjectured in the 1970s that every 5-connected nonplanar graph contains a subdivision of $K_5$. This conjecture was proved by Ma and Yu for graphs containing $K_4^-$, and an important step in their proof is to deal with a 5-separation in the graph with a planar side. In order to establish the Kelmans-Seymour conjecture for all graphs, we need to consider 5-separations and 6-separations with less restrictive structures. The goal of this paper is to deal with special 5-separations and 6-separations, including those with an apex side. Results will be used in subsequent papers to prove the Kelmans-Seymour conjecture.

Abstract:
去年央视从英国BBC公司引进的CG纪录片“与恐龙同行”(Walking with Dinosaurs)，大家一定还记忆犹新吧。相信第一次看到片中造型逼真、动作细腻的远古地球霸主时，你的惊讶程度一定不亚于看见了UFO。虽然心里明白那些残酷或感人的细节不可能是考古得来的确切结论，但还是忍不住一直问自己：“那时候……真的是这样的吧?……”现在来看看另一部堪与“恐龙”媲美、拥有更多更稀奇古怪的远古兽类的CG纪录片“与兽同行”吧。看看是否会同样让你瞠目结舌。

Abstract:
We report a transient absorption microscopy study of charge carrier dynamics in bulk MoS2 crystals at room temperature. Charge carriers are injected by interband absorption of a 555-nm pulse, and probed by measuring differential reflection of a time-delayed and spatially scanned 660-nm pulse. We find an intervalley transfer time of about 0.35 ps, an energy relaxation time of hot carriers on the order of 50 ps, and a carrier lifetime of 180 ps. By monitoring the spatiotemporal dynamics of carriers, we obtained a diffusion coefficient of thermalized electrons of 4.2 cm2/s, corresponding to a mobility of 170 cm2/Vs. We also observed a time-varying diffusion coefficient of hot carriers.

Abstract:
In this paper, we propose a Fast Iteration Method for solving mixture regression problem, which can be treated as a model-based clustering. Compared to the EM algorithm, the proposed method is faster, more flexible and can solve mixture regression problem with different error distributions (i.e. Laplace and t distribution). Extensive numeric experiments show that our proposed method has better performance on randomly simulations and real data.

Abstract:
Mixture regression is a regression problem with mixed data. Specifically,
in the observations, some data are from one model, while others from other
models. Only after assuming the quantity of the model is given, EM or other
algorithms can be used to solve this problem. We propose an information
criterion for mixture regression model in this paper. Compared to ordinary information
citizen by data simulations, results show our citizen has better performance on
choosing the correct quantity of models.

Abstract:
by using the method
of literature, questionnaire and mathematical statistics and comparative analysis
and ？research method of sichuan university high level
survey of the Track and field team, sichuan university high level Track and
field team and the analysis of existing problems and research, in order to
sichuan university of high level Track and field teams development to provide
the reference.