On an extension of distance hereditary graphs

Given a simple and finite connected graph G, the distance d_G(u,v) is the length of the shortest induced {u,v}-path linking the vertices u and v in G. Bandelt and Mulder [H.J. Bandelt, H.M. Mulder, Distance hereditary graphs, J. Combin. Theory Ser. B 41 (1986) 182-208] have characterized the class of distance hereditary graphs where the distance is preserved in each connected induced subgraph. In this paper, we are interested in the class of k-distance hereditary graphs (k∈N) which consists in a parametric extension of the distance heredity notion. We allow the distance in each connected induced subgraph to increase by at most k. We provide a characterization of k-distance hereditary graphs in terms of forbidden configurations for each k≥2.     

铝丝阵Z箍缩非平衡辐射

利用基于细致组态非平衡电离模型和非平衡辐射输运的辐射磁流体力学理论,用数值模拟的方法研究了铝丝阵Z箍缩的内爆过程和辐射特性,获得到了合理的内爆动力学图像和与实验结果基本符合的X光辐射功率和总能量等辐射参数,并研究了铝丝阵Z箍缩过程中产生的辐射能谱结构。结果表明:铝丝阵Z箍缩内爆X光辐射是非平衡的,除了存在可以用普朗克能谱近似描述的低能辐射外,还存在大量的K壳层高能辐射。讨论了各种辐射机制对总辐射的贡献,分别计算了线辐射、复合辐射和轫致辐射在各个光子能量范围内所占的份额,讨论了利用高能段连续辐射能谱诊断电子温度的方法,由能谱反推的电子温度,需要进行修正才能反映辐射吸收的影响。     

Structure of odd–odd La at high spin

The high spin states in the N=79 odd–odd ¹³⁶La nucleus have been investigated by in-beam γ-spectroscopic techniques following the ¹³⁰Te(¹¹B, 5n)¹³⁶La reaction at E=52 MeV using an array, consisting of eight Compton-suppressed clover germanium detectors. Thirty nine new γ rays have been assigned to ¹³⁶La on the basis of γ ray singles and γγ-coincidence data. The level scheme of ¹³⁶La has been extended above the known 115 ms isomer upto an excitation energy of 4.6 MeV and spin 18. Thirty one new levels have been proposed and spin-parity assignments for most of the newly proposed levels have been made on the basis of the deduced asymmetry ratios and polarisation information for the de-exciting transitions. The observed positive parity yrast band has been compared with the theoretical calculation, done within the framework of particle rotor coupling model (PRM) where the two odd quasi-particles are coupled to an axially symmetric core. The level structure has been discussed in the light of the known systematics of the neighbouring N=79 isotonic nuclei.     

An Efficient Implementation of High-Order Coupled-Cluster Techniques Applied to Quantum Magnets

We illustrate how the systematic inclusion of multi-spin correlations of the quantum spin–lattice systems can be efficiently implemented within the framework of the coupled-cluster method by examining the ground-state properties of both the square-lattice and the frustrated triangular-lattice quantum antiferromagnets. The ground-state energy and the sublattice magnetization are calculated for the square-lattice and triangular-lattice Heisenberg antiferromagnets, and our best estimates give values for the sublattice magnetization which are 62% and 51% of the classical results for the square and triangular lattices, respectively. We furthermore make a conjecture as to why previous series expansion calculations have not indicated Néel-like long-range order for the triangular-lattice Heisenberg antiferromagnet. We investigate the critical behavior of the anisotropic systems by obtaining approximate values for the positions of phase transition points.     

Mono-multi bipartite Ramsey numbers, designs, and matrices

Eroh and Oellermann defined BRR(G₁,G₂) as the smallest N such that any edge coloring of the complete bipartite graph K_N,N contains either a monochromatic G₁ or a multicolored G₂. We restate the problem of determining BRR(K_1,λ,K_r,s) in matrix form and prove estimates and exact values for several choices of the parameters. Our general bound uses Füredi's result on fractional matchings of uniform hypergraphs and we show that it is sharp if certain block designs exist. We obtain two sharp results for the case r=s=2: we prove BRR(K_1,λ,K_2,2)=3λ-2 and that the smallest n for which any edge coloring of K_λ,n contains either a monochromatic K_1,λ or a multicolored K_2,2 is λ².     

Empty convex polygons in almost convex sets

A finite set of points, in general position in the plane, is almost convex if every triple determines a triangle with at most one point in its interior. For every ℓ ≥ 3, we determine the maximum size of an almost convex set that does not contain the vertex set of an empty convex ℓ-gon. Partially supported by grants T043631 and NK67867 of the Hungarian NFSR (OTKA).     

Isolating blocks near the collinear relative equilibria of the three-body problem

The collinear relative equilibrium solutions are among the few explicitly known periodic solutions of the Newtonian three-body problem. When the energy and angular momentum constants are varied slightly, these unstable periodic orbits become normally hyperbolic invariant spheres whose stable and unstable manifolds form separatrices in the integral manifolds. The goal of this paper is to construct simple isolating blocks for these invariant spheres analogous to those introduced by Conley in the restricted three-body problem. This allows continuation of the invariant set and the separatrices to energies and angular momenta far from those of the relative equilibrium.