On the dimension of Goppa codes

A lower bound for the dimension of geometric BCH codes (i.e. subfield subcodes of Goppa codes) has been given by M. Wirtz [7]. We prove that this bound is actually exact for small enough divisorG.     

量子码[[n,k,d]]_p(p>3,n+k=8)存在性的图论构造方法

量子纠错编码技术在量子信息理论中一直以来有着重要的地位.在量子纠错编码方案中,Schingemann和Werner两人提出了通过构造具有某些性质的图(矩阵)来构造非二元量子码的方法,他们利用这种图论方法构造出了很多好的量子码,并给出了量子码[[5,1,3]]p(p为大于2的素数)存在性的一个新证明.本文利用此法,通过构造Fp上满足特殊性质的8阶对称矩阵,证明对任意大于3的素数p,码长n与维数k之和等于8的所有MDS码(达到量子Singleton界)都存在.     

Factoring ofx n−1 and orthogonalization over finite fields of characteristic 2

We present a new deterministic algorithm which gives a complete factorization ofx ⁿ – 1 over finite fields of characteristic 2. To do so we adapt a well-known procedure of orthogonalization in order to compute primitive idempotents over extensions instead of over GF(2).     

A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators

This paper presents the development of a semi-analytical axisymmetric shell finite element model with piezoelectric layers using the 3D linear elasticity theory. The piezoelectric effect of the material could be used as sensors and/or actuators in way to control shell deformation. In the present 3D axisymmetric model, the equations of motion are expressed by expanding the displacement field using Fourier series in the circumferential direction. Thus, the 3D elasticity equations of motion are reduced to 2D equations involving circumferential harmonics. In the finite element formulation the dependent variables, electric potential and loading are expanded in truncated Fourier series. Special emphasis is given to the coupling between symmetric and anti-symmetric terms for laminated materials with piezoelectric rings. Numerical results obtained with the present model are found to be in good agreement with other finite element solutions.     

图的2-距离控制数为[p/3]的必要条件

N.Sridharan等证明了阶数为p的2-距离控制数γ2(G)≤[p/3],并给出了p=3k(k=1,2,…)时,γ2(G)=p/3的充要条件.在这些结果的基础上,给出当p为任意正整数时,2γ(G)=[p/3]的一个必要条件:设G是阶数为p≥10的连通图,若2γ(G)=[p/3]且G A0,则G至少有一个悬挂点,这里A0是给定的图集.     

Crystallization, microstructure development and dielectric behaviour of glass ceramics in the system [SrO · TiO2]-[2SiO2 · B2O3]-La2O3

Various glasses in the system (65 – x)[SrO · TiO₂]-(35)[2SiO₂ · B₂2O₃]-(x)La₂O₃, where x = 1,5,10 (wt%) were prepared by melting in alumina crucible (1375–1575 K). Heat treatment schedules were selected from DTA plots of respective glasses. X-ray diffraction studies of glass ceramic samples containing different concentrations of La₂O₃ revealed the formation of Sr₂B₂O₅, Sr₃Ti₂O₇ and TiO₂ (rutile) phases. The addition of La₂O₃ results in the development of well formed, elongated crystallites of different phases. Results of the dielectric behaviour demonstrate higher values of dielectric constant for some of the glass ceramic samples. This can be ascribed to the relaxation polarization at the crystal-glass interface due to conductivity differences between crystalline and glassy phases.     

[Mn(H2P2O7)3]3-引发淀粉与丙烯腈和AMPS接枝共聚

首次以[Mn(H2P2O7)3]3-为引发剂,研究了淀粉与丙烯腈和2-丙烯酰胺-2-甲基丙磺酸(AMPS)接枝共聚反应,并用红外光谱和元素分析法证明了接枝共聚物的存在,并考察了皂化后接枝产物的吸水性随反应条件的变化.结果显示,最适宜的反应条件为单体中AMPS的摩尔百分含量为5%;单体/淀粉的摩尔比为1.5;[Mn(H2P2O7)3]3-浓度2.0×10-3 mol/L;反应温度30 ℃.     

Crystal Structure of K[UO2(NO3)3] and Some Features of Compounds M[UO2(NO3)3] (M = K,Rb, and Cs)

Greenish-yellow transparent crystals of K[UO₂(NO₃)₃] were prepared from aqueous solutions as by-product in synthesis of potassium chromatouranylates. The crystal structure was solved by the direct methods and refined to R ₁ = 0.037 (wR ₂ = 0.070) for 1452 reflections with |F _hkl| 4|F _hkl|. Mono- clinic system, space group C2/c, a = 13.4877(10), b = 9.5843(7), c = 7.9564(6) Å, = 116.124(2)°, V = 923.45(12) ų. The structure of K[UO₂(NO₃)₃] contains isolated complex ions [UO₂(NO₃)₃]^- whose uranyl groups are aligned parallel to the [-101] plane. The K⁺ cations, coordinated by twelve oxygen atoms, are located between the complex anions. Comparison of the structure with known data on M[UO₂(NO₃)₃] compounds (M = K, Rb, Cs) suggests the possibility of phase transitions due to relatively small displacements of [UO₂(NO₃)₃]^- anions and K⁺ cations, retaining the general structural motif.     

Effect of high pressure on the dielectric properties of relaxor compositions [Pb(Fe1/2Nb1/2)O3]1-x-y-[Pb(Zn1/3Nb2/3)O3]x- [BaTiO3]y

Abstracts are not published in this journal     

Effect of M and M-Ca Substitution on the Structure and Superconductivity of GdBa2Cu3O7−δ [M = Mo, Hf ]

The structural and superconducting properties of (Gd_1?x?y Ca _y M _x )Ba₂Cu₃O _z with M = Mo, Hf are investigated using X-ray diffraction, electrical resistivity, and oxygen content measurements. The effect of increasing the Mo concentration in (Gd_1?x Mo _x )Ba₂Cu₃O _z changes the structure from orthorhombic to tetragonal accompanied by a large increase in resistivity and a fast decrease in T _c at the rate of 1.9 K per at.% of Mo, unlike that of Hf substitution in (Gd_1?x Hf _x )Ba₂Cu₃O _z , which maintains the orthorhombic structure and decreases T _c very slowly at the rate of 0.6 K per atm.% of Hf with nearly no change in resistivity. The suppression of T _c by M = Mo, Hf can be counterbalanced by hole doping by Ca which increases T _c with increasing Ca content showing maximum compensation for Mo. A comparative study of M = Mo, Hf doped samples in (Gd_1?x?y Ca _y M _x )Ba₂Cu₃O _z indicates that the valence of the dopant M = Mo^4+,6+, Hf⁴⁺ and its ionic radius play an important role in controlling the structural and superconducting properties of the systems.     

Synthesis, structure, and properties of [Be(H2O)4][UO2(CH3COO)3]2

Crystals of previously unknown compound [Be(H₂O)₄][UO₂(CH₃COO)₃]₂ were prepared and studied by X-ray diffraction analysis. The compound crystallizes in the tetragonal system, unit cell parameters (at 100 K): a = 10.3647(3), c = 23.4127(8) Å, V = 2515.16(13) ų, space group I4₁/a, Z = 4, R = 0.0194. The structure consists of mononuclear complexes [Be(H₂O)₄]²⁺ and [UO₂(CH₃COO)₃]^? linked with each other by electrostatic interactions and hydrogen bonds formed by water molecules and O atoms of acetate anions. The compound was also studied by methods of thermal analysis and IR spectroscopy.     

Synthesis, Characterization, and Thermochemical Study on a Ternary Complex [Sm(m-MOBA)3phen]2

A new ternary solid complex of samarium chloride hexahydrate with m-methoxybenzoic acid and 1,10-phenanthroline, [Sm(m-MOBA)₃phen]₂ (m-MOBA: m-methoxybenzoic; phen: 1,10-phenanthroline), was synthesized and characterized by elemental analysis, IR spectra, UV spectra, molar conductance, and thermogravimetric analysis. The dissolution enthalpies of SmCl₃·6H₂O (s), m-HMOBA(s), phen·H₂O (s), and [Sm(m-MOBA)₃phen]₂(s) in the calorimetric solvent (V_DMF:V_CYC:V_HCl = 2:1:2) were determined by an advanced solution-reaction isoperibol calorimeter at 298.15 K, respectively. The standard molar enthalpy of reaction was determined to be D_r H_m^q = (233.97 ±1.15) kJ · mol^-1{\Delta_{\rm r} H_{\rm m}^\theta =(233.97 \pm 1.15)\,{\rm kJ}\,{\cdot}\,{\rm mol}^{-1}}. In accordance with Hess’ law, the standard molar enthalpy of formation of the title complex [Sm(m-MOBA)₃phen]₂(s) was estimated to be −(5054.6 ± 9.5) kJ · mol⁻¹.     

Synthesis and crystal structure of a uranyl bichromate, [CH6N3]2[(UO2)(CrO4)(Cr2O7)](H2O)

Crystals of the first uranyl bichromate, [CH₆N₃]₂[(UO₂)(CrO₄)(Cr₂O₇)](H₂O), were obtained by evaporation from aqueous solutions. The compound crystallizes in the triclinic system, space group $P\bar 1$ , a = 7.1829(17), b = 9.304(3), c = 14.884(4) Å, α = 102.43(2)°, β = 97.98(2)°, γ = 101.07(2)°, V = 936.3(5) ų, Z = 2. The structure was solved by direct methods and refined by the full-matrix least-squares method to R ₁ = 0.064 (wR ₂ = 0.138) for 2225 reflections with |F _hkl | ≥ 4σ(|F _hkl |). The structure is based on infinite [(UO₂)(CrO₄)(Cr₂O₇)]^2? chains where [UO₇]^8? pentagonal bipyramids are linked by tridentate [Cr(1)O₄]^2? groups and [Cr₂O₇]^2? groups; these chains run along x axis and are oriented parallel to $(0\bar 11)$ . Trigonal [CH₆N₃]⁺ cations and water molecules are arranged between the chains.     

Electric-field and stress effects on depoling and overpoling phenomena in [001]-poled transverse mode Pb(Zn1/3Nb2/3)O3-(6-7)%PbTiO3 single crystal of [110] length cut

Solid-solution Pb(Zn(1/3)Nb(2/3))O(3)-PbTiO(3) (PZN-PT) single crystals, touted as next-generation piezoelectric materials, have been studied extensively in the past decade. This work addresses the advantages and limitations of transducers made of transverse mode PZN-(6-7)%PT single crystals of [110](L) X [001](T)(P) cut. This cut exhibits superior electromechanical properties, with k(31) ≈ 0.85 and d(31) ≈-1450 pC/N, and an extremely high d(31)/S(E)(11) value of >35 C/m(2). It also has relatively high overpoling, i.e., rhombohedralto- tetragonal phase transformation, field of ≈2 kV/mm. This overpoling field further decreases with increase in axial compressive stress. Despite these good attributes, this crystal cut has a low depoling field of ≤ 0.3 kV/mm, a result of low coercive fields of [001]-poled relaxor-based single crystals, which decreases further with increasing axial compressive stress, limiting its bipolar drive capability. The axial compressive stress required to cause overpoling via rhombohedral-to-tetragonal phase transformation of relevant domain variants in the crystal is found to be >90 MPa. In contrast, this crystal cut depolarizes at comparatively low axial tensile stress of ≈15 MPa, the magnitude of which is not significantly affected by the moderate forward field applied.     

The Influence of Halide on the Silver-Catalysed Oxidation of N,N-Dimethyl-p-phenylenediamine by [CoIII(NH3)5Cl]2+

The mechanism of the silver colloid catalysed oxidation of N,N-dimethyl-p-phenylenediamine by Co^III(NH₃)₅Cl₂₊ was studied in the presence of halides in aqueous solution at a pH of about 5. The silver colloids were prepared by reduction of silver nitrate with ascorbic acid or with sodium boranate in the absence of a special stabilizing agent. The course of the reaction could easily be followed in a double wavelength photometer because of the strong absorbance of p- semiquinonediimine, the first oxidation product of p-phenylenediamine. Both the reaction rate and the irreversible course of the reaction depend on the kind and the concentration of halide present in the solution. Apart from the electrocatalytic redox reaction, the oxidative formation of silver halide by cobalt (III) and the reduction of this silver halide by p-phenylenediamine occur simultaneously. Therefore, the mechanism of at least three important photographic processes can be studied at the same time in this redox system.     

Ferroelectric phase transition in Ba5RTi3Nb7O30 [R=Nd, Eu, Gd] ceramics

Polycrystalline samples of Ba₅RTi₃Nb₇O₃₀ [R=Nd, Eu, Gd], were prepared using high-temperature solid-state reaction technique. Preliminary X-ray structural analysis of the compounds shows the formation of single phase compounds (orthorhombic crystal system) at room temperature. Detailed studies of dielectric properties (ɛ, tanδ,σ) as a function of frequency (400 Hz to 10 kHz) and temperature (30° to 380°C) show that these compounds exhibit diffuse ferroelectric phase transition.     

A semi-analytical finite element model for the analysis of laminated 3D axisymmetric shells: Bending, free vibration and buckling

A general semi-analytical finite element model is developed for bending, free vibration and buckling analysis of shells of revolution made of laminated orthotropic elastic material. The 3D elasticity theory is used and the equations of motion are obtained by expanding the displacement field and load in the Fourier series in terms of the circumferential coordinate, θ. The coefficients of the expansion are functions of (r, z), and they are approximated using the finite element method. This leads to a semi-analytical finite element in the (r, z) plane. The element is validated by comparing the present results with the analytical and numerical solutions available in the literature.     

The effect of anisotropy on post-buckling behavior of laminated plates using semi-energy finite strip method

The effects of anisotropy (i.e. the ratio of longitudinal modulus of elasticity to transverse modulus of elasticity of a rectangular plate) on buckling and post-buckling performance of laminated plates under uniform end-shortening have been studied in this paper by implementing a Rayleigh–Ritz approach and a finite strip approach based on the concept of a rigorous post-buckling solution for composite plates and plate structures, namely the semi-energy approach. To validate the results, they are compared with those obtained from finite element method of analysis. The study of results has revealed that the buckling and post-buckling response of the laminates is significantly influenced by the changing of the anisotropy ratio.     

La2Ni7和LaMgNi7储氢合金电子结构的研究

采用密度泛函理论研究了La2Ni7和LaMg-Ni7储氢合金的电子结构,探讨了微观结构和合金宏观性能之间的关联性.结果表明,含Mg元素的LaMgNi7体系形成成键作用的Ni-Mg键,体系稳定性高于纯La2Ni7体系.同时LaMgNi7体系中的Ni-Ni键强度弱于La2Ni7体系中的相应键,降低了H进入体系的能量壁垒,改...