On the complexity of some subgraph problems

We study the complexity of the problem of deciding the existence of a spanning subgraph of a given graph, and of that of finding a maximum (weight) such subgraph. We establish some general relations between these problems, and we use these relations to obtain new NP-completeness results for maximum (weight) spanning subgraph problems from analogous results for existence problems and from results in extremal graph theory. On the positive side, we provide a decomposition method for the maximum (weight) spanning chordal subgraph problem that can be used, e.g., to obtain a linear (or O(nlogn)) time algorithm for such problems in graphs with vertex degree bounded by 3.     

-extension of Lie triple systems

In this paper, we introduce the notion of T^*-extension of a Lie triple system. Then we show that T^*-extension is compatible with nilpotency, solvability, and it preserves in certain sense the decomposition properties. In addition, we investigate the equivalence of T^*-extensions using cohomology. Finally, we show that every finite-dimensional nilpotent metrised Lie triple system over an algebraically closed field is the T^*-extension of an appropriate quotient system.     

On 3-Steiner simplicial orderings

Let G be a connected graph and S a nonempty set of vertices of G. A Steiner tree for S is a connected subgraph of G containing S that has a minimum number of edges. The Steiner interval for S is the collection of all vertices in G that belong to some Steiner tree for S. Let k≥2 be an integer. A set X of vertices of G is k-Steiner convex if it contains the Steiner interval of every set of k vertices in X. A vertex x∈X is an extreme vertex of X if X?{x} is also k-Steiner convex. We call such vertices k-Steiner simplicial vertices. We characterize vertices that are 3-Steiner simplicial and give characterizations of two classes of graphs, namely the class of graphs for which every ordering produced by Lexicographic Breadth First Search is a 3-Steiner simplicial ordering and the class for which every ordering of every induced subgraph produced by Maximum Cardinality Search is a 3-Steiner simplicial ordering.     

The dielectric behaviour of doped near-stoichiometric lithium niobate in the terahertz range

The dielectric properties of near-stoichiometric LiNbO₃:Fe and LiNbO₃:Ce single crystals have been investigated using terahertz time domain spectroscopy in a frequency range of 0.7-1.6 THz at room temperature. When coupled with an applied external optical field, obvious photorefractive effects were observed, resulting in a modulation of the complex dielectric constant for the crystals. The variation in refractive index, |Δn|, had a linear relationship with the applied light intensity, accompanied by a step-like decrease at high intensity. The findings were attributed to the internal space charge field of the photorefraction and the light-induced domain reversal in the crystals.     

Labeling bipartite permutation graphs with a condition at distance two

An L(p,q)-labeling of a graph G is an assignment f from vertices of G to the set of non-negative integers {0,1,…,λ} such that |f(u)−f(v)|≥p if u and v are adjacent, and |f(u)−f(v)|≥q if u and v are at distance 2 apart. The minimum value of λ for which G has L(p,q)-labeling is denoted by λ_p,q(G). The L(p,q)-labeling problem is related to the channel assignment problem for wireless networks.In this paper, we present a polynomial time algorithm for computing L(p,q)-labeling of a bipartite permutation graph G such that the largest label is at most (2p−1)+q(bc(G)−2), where bc(G) is the biclique number of G. Since λ_p,q(G)≥p+q(bc(G)−2) for any bipartite graph G, the upper bound is at most p−1 far from optimal.     

Synthesis, structural and magnetic properties of the nanocomposite Fe63B23Nd7Y3Nb3Cr1 magnets

The Fe₆₃B₂₃Nd₇Y₃Nb₃Cr₁ nanocomposite magnets in the form of sheets have been prepared by copper mold casting technique. The phase evolution, crystal structure, microstructural and magnetic properties have been investigated in the as-cast and annealed states. The as-cast sheets show magnetically soft behaviors which become magnetically hard by thermal annealing. The optimal annealed microstructure was composed of nanosize soft magnetic α-Fe (19-29 nm) and hard magnetic Nd₂Fe₁₄B (45-55 nm) grains. The best hard magnetic properties such as intrinsic coercivity, _jH_c of 1119 kA/m, remanence, B_r of 0.44 T, magnetic induction to saturation magnetization ratio, M_r/M_s=0.61 and maximum energy product, (BH)_max of 55 kJ/m³ was obtained after annealing at 680 °C for 15 min. The annealing treatment above 680 °C results in non-ideal phase grains growth, which degrade the magnetic properties.     

Structural, elastic, and electronic properties of orthorhombic NH3BH3: An ab initio study

At the generalized gradient approximation (GGA), the elastic constants of the orthorhombic phase of NH₃BH₃ were calculated with plane-wave pseudo-potential method. Our calculation showed that the orthorhombic phase NH₃BH₃ is a loose and brittle material, as well as hard to be deformed, also we calculated the elastic anisotropies and the Debye temperatures from the elastic constants. And from the band structure and density of state (DOS), we concluded that NH₃BH₃ is a wide-gap semiconductor and the band gap is almost 6.0 eV. The bonds between N atoms and H atoms show a strong covalent characteristic, B atoms and H atoms form ironic bonds, and so as to the B-N bonds. Electrons from the B atoms are absorbed by the H atoms around the B atoms, and the H atoms display electronegativity.     

Magnetization reversal within Dzyaloshinskii—Moriya interaction under on-site Coulomb interaction in BiCrO3

First-principals calculations show that magnetization reversal is accompanied by the opposite sense of rotation of the neighboring oxygen octahedra along the [1 1 1] direction which is called the antiferrodistortive displacement in BiCrO3. The coupling between magnetization and antiferrodistortive distortion is mainly caused by Dzyaloshinskii- Moriya interaction which is driven by the eg-eg states antiferromagnetic interaction in Cr-3d. A critical value of on-site Coulomb interaction prohibiting the Dzyaloshinskii-Moriya interaction and thus the magnetization reversal is found to be 1.3 eV.     

Improvement of dielectric tunability and loss tangent of (Ba,Sr)TiO3 thin films with K doping

Ba_0.6Sr_0.4TiO₃ thin films doped with K were deposited on Pt/Ti/SiO₂/Si substrates by chemical solution deposition method. The structure, surface morphology, and dielectric and tunable properties of Ba_0.6Sr_0.4TiO₃ thin films have been studied in detail. The K content in Ba_0.6Sr_0.4TiO₃ thin films has a strong influence on the material's properties including surface morphology, dielectric and tunable properties. It is found that the Curie temperature of K-doped Ba_0.6Sr_0.4TiO₃ films shifts to higher values compared with that of undoped Ba_0.6Sr_0.4TiO₃ thin films, which leads to a dielectric enhancement of K-doped Ba_0.6Sr_0.4TiO₃ films at room temperature. At the optimized content of 0.02 mol, the dielectric loss tangent is reduced significantly from 0.057 to 0.020. Meanwhile, the tunability is enhanced obviously from 26% to 48% at the measured frequency of 1 MHz and the maximum value of the figure of merit is 23.8. This suggests that such films have potential applications for tunable devices.     

Tunable Ba0.5Sr0.5TiO3 film bulk acoustic resonators using SiO2/Mo Bragg reflectors

Tunable and switchable Ba 0.5 Sr 0.5 TiO 3 film bulk acoustic resonators（FBARs） based on SiO 2 /Mo Bragg reflectors are explored,which can withstand high temperature for the deposition of Ba x Sr 1 x TiO 3（BST） films at 800 C.The dc bias-dependent resonance may be attributed to the piezoelectricity of the BST film induced by an electrostrictive effect.The series resonant frequency is strongly dc bias-dependent and shifts downwards with dc bias increasing,while the parallel resonant frequency is only weakly dc bias-dependent and slightly shifts upwards at low dc bias（ 45 V） while downwards at higher dc bias.The calculated relative tunability of shifts at series resonance frequency is around 2.3% and the electromechanical coupling coefficient is up to approximately 8.09% at 60-V dc bias,which can be comparable to AlN FBARs.This suggests that a high-quality tunable BST FBAR device can be achieved through the use of molybdenum（Mo） as the high acoustic impedance layer in a Bragg reflector,which not only provides excellent acoustic isolation from the substrate,but also improves the crystallinity of BST films withstanding higher deposition temperature.