数控机床故障分析的组合群验方法研究

介绍了两个组合群验数学模型,然后根据这两个数学模型,利用组合群验的理论和方法诊断数控机床故障部件,给出了数控机床故障诊断的新方法.     

An upper bound on the number of Steiner triple systems

Richard Wilson conjectured in 1974 the following asymptotic formula for the number of n ‐vertex Steiner triple systems: \begin{align*} STS(n) = \left( (1+o(1))\frac{n}{e^2} \right)^{\frac{n^2}{6}}\end{align*}. Our main result is that The proof is based on the entropy method. As a prelude to this proof we consider the number F(n) of 1 ‐factorizations of the complete graph on n vertices. Using the Kahn‐Lovász theorem it can be shown that We show how to derive this bound using the entropy method. Both bounds are conjectured to be sharp. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 43, 399–406, 2013     

Hadamard Matrices of Order 32

Two Hadamard matrices are considered equivalent if one is obtained from the other by a sequence of operations involving row or column permutations or negations. We complete the classification of Hadamard matrices of order 32. It turns out that there are exactly 13,710,027 such matrices up to equivalence.     

Predicting high-codimension critical transitions in dynamical systems using active learning

Complex dynamical systems, from those appearing in physiology and ecology to Earth system modelling, often experience critical transitions in their behaviour due to potentially minute changes in their parameters. While the focus of much recent work, predicting such bifurcations is still notoriously difficult. We propose an active learning approach to the classification of parameter space of dynamical systems for which the codimension of bifurcations is high. Using elementary notions regarding the dynamics, in combination with the nearest-neighbour algorithm and Conley index theory to classify the dynamics at a predefined scale, we are able to predict with high accuracy the boundaries between regions in parameter space that produce critical transitions.     

Identities for generalized Fibonacci numbers: a combinatorial approach

This note shows a combinatorial approach to some identities for generalized Fibonacci numbers. While it is a straightforward task to prove these identities with induction, and also by arithmetical manipulations such as rearrangements, the approach used here is quite simple to follow and eventually reduces the proof to a counting problem.     

Depth and Stanley Depth of Multigraded Modules

We study the behavior of depth and Stanley depth along short exact sequences of multigraded modules and under reduction modulo an element.     

Geometrical extensions of Wythoff’s game

In 1905 Bouton gave the complete theory of a two-player combinatorial game: the game of Nim. Two years later, Wythoff defined his game as “a modification” of the game of Nim. In this paper, we give the sets of the losing positions of geometrical extensions of Wythoff’s game, where allowed moves are considered according to a set of vectors (v₁,…,v_n). When n=3, we present algorithms and algebraic characterizations to determine the losing positions of such games. In the last part, we investigate a bounded version of Wythoff’s game, and give a polynomial way to decide whether a game position is losing or not.     

Edge decompositions into two kinds of graphs

Let H be an arbitrary graph and let K_1,2 be the 2-edge star. By a {K_1,2,H}-decomposition of a graph G we mean a partition of the edge set of G into subsets inducing subgraphs isomorphic to K_1,2 or H. Let J be an arbitrary connected graph of odd size. We show that the problem to decide if an instance graph G has a {K_1,2,H}-decomposition is NP-complete if H has a component of an odd size and H≠pK_1,2∪qJ, where pK_1,2∪qJ is the disjoint union of p copies of K_1,2 and q copies of J. Moreover, we prove polynomiality of this problem for H=qJ.     

A combinatorial study of full Heusler alloys by first-principles computational methods

A combinatorial scan of a total of 810 full Heusler alloys is performed on the basis of first-principles (GGA) total-energy calculations using pseudopotentials and plane waves to predict their lattice parameters and magnetic moments. About 60% of the investigated intermetallics turn out as being thermochemically stable with respect to the constituting elements. The presentation of the calculated magnetic moments in a periodic system of full Heusler phases is accomplished and yields periodic trends for the physical properties as a function of their compositions and as a function of the valence-electron concentration within a modified Slater-Pauling scheme. In addition, hot synthetic spots with respect to magnetically interesting stable and also presumably metastable phases are identified to propose new and economically lucrative synthetic targets, and a series of new rhodium-containing phases is analyzed in depth with respect to their electronic structures.