On(e)-reducible 3-manifolds Which Admit Complete Surface Systems

In the present paper, we consider a class of compact orientable 3-manifolds with one boundary component, and suppose that the manifolds are ?-reducible and admit complete surface systems. One of our main results says that for a compact orientable, irreducible and ?-reducible 3-manifold M with one boundary component F of genus n > 0 which admits a complete surface system S′, if D is a collection of pairwise disjoint compression disks for ?M , then there exists a complete surface system S for M , which is equivalent to S′, such that D is disjoint from S . We also obtain some properties of such 3-manifolds which can be embedded in S3.     

A multiobjective immune algorithm based on a multiple-affinity model

This paper presents a new multiobjective immune algorithm based on a multiple-affinity model inspired by immune system (MAM-MOIA). The multiple-affinity model builds the relationship model among main entities and concepts in multiobjective problems (MOPs) and multiobjective evolutionary algorithms (MOEAs), including feasible solution, variable space, objective space, Pareto-optimal set, ranking and crowding distance. In the model, immune operators including clonal proliferation, hypermutation and immune suppression are designed to proliferate superior antibodies and suppress the inferiors. MAM-MOIA is compared with NSGA-II, SPEA2 and NNIA in solving the ZDT and DTLZ standard test problems. The experimental study based on three performance metrics including coverage of two sets, convergence and spacing proves that MAM-MOIA is effective for solving MOPs.     

Heavy alkali metal-arsenic alloy-based graphite intercalation compounds: Investigation of their synthesis and of their physical properties

Heavy alkali metal-arsenic alloys intercalate easily into graphite, leading to the formation of a new family of ternary graphite intercalation compounds (GICs). Pure phases formulated as MAsxC4s (M = K, Rb or Cs; s = stage; x ≤ 1) have been synthesized at the laboratory. This article aims to expose all physical measurements performed on these intercalation compounds to get an idea about their electronic properties.Electrical conductivity measurements have been performed both parallel and perpendicular to the basal planes, between 4.2 and 295 K. Room temperature resistivity values lie between 16 and 35 μΩ cm and the anisotropic resistivity takes a value of an order of magnitude of 10⁴. Dynamic magnetic susceptibility measurements, carried out at low temperature on some phases, showed that they do not exhibit superconducting transition up to 1.3 K. Raman spectroscopy investigation, which is a useful tool to study the electronic and the chemical stability of GICs, highlighted a significant up-shift of the G-band of the carbon intra-layer vibration frequency, compared to the pure graphite vibration mode. Undoubtedly, this is related to the electronic charge transfer established between graphite layers and intercalated species.     

Special Features of the Correlation between the Uranium–Oxygen Interatomic Distances and the Frequencies of the Valence Vibrations of the UO2 2+ Group in Complex Compounds of Uranyl

We considered the factors due to which the dependences between the uranium–oxygen distances R ₀ and the frequencies of valence vibrations _as for complex compounds of uranyl are described by two independent expressions generally represented by equations of the type R ₀ = a + b_as ^–2/3 (b > 0) with the coefficients a and b differing in the regions R ₀ < 0.178 nm and R ₀ > 0.178 nm. It is shown that the reason is that there is a mutual effect of the ligands in the uranyl complex responsible for different partial contributions of the uranium orbitals and of the atoms of the first coordination sphere to the chemical bonding.     

Entanglement of Resonantly Coupled Field Modes in Cavities with Vibrating Boundaries

We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropy coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered — a three-dimensional cavity possessing eigenfrequencies ₃ = 3₁, whose wall oscillates at the frequency _w = 2₁, and a one-dimensional (Fabry–Perot) cavity with an equidistant spectrum _n = n₁ where the distance between perfect mirrors oscillates at the frequencies ₁ and 2₁. The behavior of entanglement measures in these cases turns out to be completely different, although all three coefficients demonstrate qualitatively similar time dependences in each case (except some specific situations where the covariance entanglement coefficient based on traces of covariance submatrices seems to be essentially more sensitive to entanglement than other measures, which are based on determinants of covariance submatrices). Different initial states of the field, namely, vacuum, squeezed vacuum, thermal, Fock, and even/odd coherent states, are considered.     

一阶时滞微分方程解的零点分布

Abstract. The paper gives two estimates of the distance between adjacent zeros of solutions     

The Limit Distribution of the Largest Interpoint Distance from a Symmetric Kotz Sample

Generalizing recent work of P. C. Matthews and A. L. Rukhin (Ann. Appl. Probab.3(1993), 454–466), we obtain the limit law of the largest interpoint Euclidean distance for a spherically symmetric multivariate sample of the Kotz distribution. While going through the proof, some errors in the reasoning given by Matthews and Rukhin are pointed out and corrected.     

Affine-Invariant Distances, Envelopes and Symmetry Sets

Affine invariant symmetry sets of planar curves are introduced and studied in this paper. Two different approaches are investigated. The first one is based on affine invariant distances, and defines the symmetry set as the closure of the locus of points on (at least) two affine normals and affine-equidistant from the corresponding points on the curve. The second approach is based on affine bitangent conics. In this case the symmetry set is defined as the closure of the locus of centers of conics with (at least) 3-point contact with the curve at two or more distinct points on the curve. This is equivalent to conic and curve having, at those points, the same affine tangent, or the same Euclidean tangent and curvature. Although the two analogous definitions for the classical Euclidean symmetry set are equivalent, this is not the case for the affine group. We present a number of properties of both affine symmetry sets, showing their similarities with and differences from the Euclidean case. We conclude the paper with a discussion of possible extensions to higher dimensions and other transformation groups, as well as to invariant Voronoi diagrams.     

Counterexamples in measuring the distance between binary trees

Examples are given to show that the closest partition distance measure need not agree with the nearest neighbor interchange distance for unordered labeled binary trees. Proposed algorithms for computing the closest partition distance are shown to be of exponential complexity and hence may not be useful in approximating the nearest neighbor interchange distance.