Number of minimum vertex cuts in transitive graphs

Let G be a k-regular vertex transitive graph with connectivity κ(G)=k and let m_k(G) be the number of vertex cuts with k vertices. Define m(n,k)=min{m_k(G): GT_n,k}, where T_n,k denotes the set of all k-regular vertex transitive graphs on n vertices with κ(G)=k. In this paper, we determine the exact values of m(n,k).     

Data analysis for numerical and categorical individual time-series

Principal components analysis and correspondence analysis may be generalized to handle time-dependent data. For real-valued data the basic tool is the Karhunen-Loeve decomposition. For categorical processes harmonic analysis is presented in terms of reciprocal averaging. Details are given for approximated and interpolated solutions.     

Efficient algorithms for decomposing graphs under degree constraints

Stiebitz [Decomposing graphs under degree constraints, J. Graph Theory 23 (1996) 321-324] proved that if every vertex v in a graph G has degree d(v)?a(v)+b(v)+1 (where a and b are arbitrarily given nonnegative integer-valued functions) then G has a nontrivial vertex partition (A,B) such that d_A(v)?a(v) for every v∈A and d_B(v)?b(v) for every v∈B. Kaneko [On decomposition of triangle-free graphs under degree constraints, J. Graph Theory 27 (1998) 7-9] and Diwan [Decomposing graphs with girth at least five under degree constraints, J. Graph Theory 33 (2000) 237-239] strengthened this result, proving that it suffices to assume d(v)?a+b (a,b?1) or just d(v)?a+b-1 (a,b?2) if G contains no cycles shorter than 4 or 5, respectively.The original proofs contain nonconstructive steps. In this paper we give polynomial-time algorithms that find such partitions. Constructive generalizations for k-partitions are also presented.     

Properties of vertex cover obstructions

We study properties of the sets of minimal forbidden minors for the families of graphs having a vertex cover of size at most k. We denote this set by O(k-VERTEX COVER) and call it the set of obstructions. Our main result is to give a tight vertex bound of O(k-VERTEX COVER), and then confirm a conjecture made by Liu Xiong that there is a unique connected obstruction with maximum number of vertices for k-VERTEX COVER and this graph is C_2k+1. We also find two iterative methods to generate graphs in O((k+1)-VERTEX COVER) from any graph in O(k-VERTEX COVER).     

IRREDUCIBLE REPRESENTATIONS FOR THE AFFINE-VIRASORO LIE ALGEBRA OF TYPE B_l

An explicit construction of irreducible representations for the affine-Virasoro Liealgebra of type B_l, through the use of vertex operators and certain oscillator represen-tations of the Virasoro algebra, is given.     

Aryl oxalate chemiluminescence detection for high-performance liquid chromatography

Aryl oxalate chemiluminescence detection for high-performance liquid chromatography offers ultrahigh sensitivity for interactive fluorophores. With optimal analytes, attomole limits of detection can be obtained with conventional instrumentation     

市场研究(Ⅰ):揭示竞争优势

ＳＡＳ系统提供了用于市场数据分析的许多方法，包括直观图示法和关联分析。这篇文章讨论直观图示法及其在ＳＡＳ系统中的实现。     

Distribution of the inter and intra inertia in conditional MCA

Conditional Multiple Correspondence Analysis (MCA), where a control variable plays the role of a partition model, allows us to decompose global inertia into between inertia and within inertia. The problem is to assess when the conditioning variable gives different results with respect to the unconditional analysis. In this paper, we study the asymptotic distribution function of these inertias, which can allow us to determine whether conditioning is significant. Some simulations were performed to corroborate the established results.     

Electric field gradients in EuScFe garnets

The electric quadrupole interactions at the octahedral, tetrahedral, and dodecahedral sites in the Eu_3?ySc_2+yFe₃O₁₂ (0 ≤ y ≤ 0.5) garnet system were studied with ⁵⁷Fe and ¹⁵¹Eu Mössbauer spectroscopy. The electric field gradient tensor at the three sites was calculated using a monopole-point-dipole model. It is shown that the dipole contribution to the electric field gradient tensor is not negligible even for very small values of the oxygen dipole polarizability. The importance of the overlap and second-order 4f contributions is discussed.     

Optisch aktive übergangsmetall-komplexe: LXXXIII. Konfigurationsstabile tetraedrische NiNi′CC′-cluster

The reaction of Ni(C₅H₅)₂ and Ni(C₅H₄COOCH₃)₂ with the acetylene (?)-(R)-C₆H₅CCCONHCH(CH₃)(C₆H₅)(C₆H₅), “CC′”, yields tetrahedral Ni₂C₂ clusters. Besides the compounds with two identical Ni corners (Ni₂CC′ types) also compounds with two different Ni corners (NiNi′CC′ types) are formed. These consist of two diastereomers which, for a given (R)-configuration in the acid amide substituent, differ only in the cluster chirality. They are separated chromatographically and turn out to be configurationally stable with respect to a change of the cluster chirality.