Justification of the Kirchhoff hypotheses and error estimation for two-dimensional models of anisotropic and inhomogeneous plates, including laminated plates

Asymptotic analysis of the problem describing deformation ofa thin cylindrical plate with clamped lateral side is performed.The problem is considered under the most general statement withthe plate being laminated and consisting of an arbitrary numberof nonhomogeneous and anisotropic (21 elastic moduli) layers.Explicit integral representations of the differential operatorswhich form the two-dimensional model of the plate are derived.In the case when the elastic moduli of each of the layers areconstant, these integral representations turn into algebraicones. The asymptotic procedure is justified with the help ofa weighted inequality of Korn's type. The error estimates obtainedgive a rigorous mathematical proof of both of Kirchhoff's hypotheses(kinematic and static) and shed light on the well-known intrinsicinconsistency of two of the hypotheses.     

Ultra-incompressible Ternary Diborides Re_（0.5）Ir_（0.5）B_2,Re_（0.5）Tc_（0.5）B_2,Os_（0.5）W_（0.5）B_2 and Os_（0.5）Ru_（0.5）B_2：Density Functional Calculation

In this paper, density functional computations have been applied to the structural, elastic and electronic properties of ternary transition metal diborides Re0.5Ir0.5B2, Re0.5Tc0.5B2, Os0.5W0.5B2 and Os0.5Ru0.5B2 in hexagonal (P63/mmc) and orthorhombic (Pmmn) structures with both local density approximation and generalized gradient approximation. LDA gives smaller lattice parameters and larger elastic moduli than GGA. Both results show that the hexagonal ones are more stable than orthorhombic ones except Os0.5Ru0.5B2. Moreover, the hexagonal structure has superior elastic property than orthorhombic one. Generally speaking, the calculated elastic moduli of Re0.5Ir0.5B2 and Os0.5Ru0.5B2 are smaller than those values of Re0.5Tc0.5B2 and Os0.5W0.5B2 within the same structure because of the filling of antibonding states. The relativistic effects result in weaker bonds of Tc-B (Ru-B) than those of Re-B (Os-B). All the diborides are ultra-incompressible. Re0.5Tc0.5B2 has the largest shear modulus and it is a promising superhard diboride like Os0.5W0.5B2. The elastic properties are in high correlation with the bond strength. The shear moduli are more sensitive than the bulk moduli to the bond strength.     

Particle speciation during PEG–Fe<Subscript>3</Subscript>O<Subscript>4</Subscript> hybrid nanoparticle self-assembly on Si(Ti)O<Subscript>2</Subscript>

The kinetics of assembly of polyethylene glycol (PEG)-coated superparamagnetic Fe₃O₄ nanoparticles in aqueous suspension on planar Si(Ti)O₂ surfaces have been determined using high-resolution optical waveguide lightmode spectroscopy (OWLS). Analysis of the results revealed that the initially uniform population was spontaneously transformed into two types of particles with significantly different adsorption behaviour.     

Development of XUV lasers at the RAL Central Laser Facility

Recent progress in the development of XUV lasers by research teams using high-power and ultrashort-pulse Nd: glass and KrF laser facilities at the Rutherford Appleton Laboratory is reviewed. Injector-amplifier operation and prepulse enhanced output of the Ge XXIII collisional laser driven by a kilojoule glass laser, enhanced gain in CVI recombination with picosecond CPA drive pulses from a glass laser, and optical field ionization and XUV harmonic generation with a KrF CPA laser are described.     

催化光度法测定痕量钒——钒(Ⅴ)-溴甲酚紫-过氧化氢体系

催化光度法测定钒已有报道[1～3],在0.45 mol·L-1磷酸介质及加热条件下,过氧化氢氧化溴甲酚紫褪色反应非常缓慢,而痕量钒对此反应具有较高的催化活性,且在一定浓度范围内,钒量与褪色反应程度呈线性关系,据此可建立测定痕量钒的方法.方法的检出限为1.9×10-6g·L-1,测定范围为0.003～1.8 mg·L-1.方法操作简便,重现性好,用于钢样中痕量钒的测定,结果满意.     

Preparation of novel 2‐(benzo[b]furan‐2‐yl)‐1H‐imidazolines for photoaffinity labelling and affinity isolation of imidazoline binding

The preparations of 5‐aminoefaroxan 8 and 5‐azidoefaroxan 9 , which retain the capacity to stimulate insulin secretion via the putative I₃ imidazoline receptor and are useful biological tools for affinity chromatography studies and photoaffinity labelling studies of imidazoline binding proteins, are described     

Preliminary studies of radiation coupling between remote soft X-ray laser amplifiers

Coupling of a soft X-ray laser beam with a relaying concave mirror in a sequentially pumped amplifier geometry using the Ne-like Ge system has been studied experimentally. Preliminary observations indicate an increase in the spatial coherence of the amplified relayed beam. In addition, near-field imaging of one of the amplifier plasmas shows a double-lobed intensity pattern of the emergent beam indicating refractive guiding of the amplified beam with components both normal and tangential to the target surface.     

Vibrational energy transfer from chemically activated 1,4-cyclohexadiene

The thermal isomerization of cis, anti, cis-tricyclo[3.1.0.0^2,4] hexane was used to produce highly vibrationally excited 1,4-cyclohexadiene. The competition between unimolecular decomposition of the energized diene (to benzene and hydrogen) and collisional stabilization was studied using the parent compound, SF₆, CO₂, N₂, and He as quenching gases. Quenching efficiencies decreased in the order given above. By applying RRKM theory to the isomerization and decomposition reactions, it was possible to calculate the step size in a stepladder model of the deactivation of cyclohexadiene. The step sizes 〈ΔE〉 deduced (at 528 K and in units of kJ/mol) were: parent compound and SF₆, 7; CO₂, 5; N₂, 4; He, 2. The study confirmed the utility of this unimolecular chemical activation system for energy transfer studies.     

A DFT study of isomeric conjugated,cross-conjugated and semi-conjugated six-membered heterocyclic mesomeric betaines

The structures and electronic properties of seven isomeric six-membered heterocyclic mesomeric betaines (HMBs) and four fully-covalent isomers have been calculated using B3LYP/6-311++G(p,d) methodology. The aromaticity indexes Bird I₆, HOMA, NICS(1) and aromatic stabilisation energy (ASE) have been calculated and compared. In agreement with an earlier study employing connectivity-matrix analysis, the previously unrecognised and little known semi-conjugated HMBs (Class 3) have calculated properties that are quite distinct from the isomeric conjugated HMBs (Class 1) and cross-conjugated HMBs (Class 2). In particular semi-conjugated systems have a higher degree of both classical and magnetic aromaticity than the isomers. In agreement with the calculated vertical ionisation potentials and electron affinities, the six-membered semi-conjugated species have high energy HOMOs and low energy LUMOs and these observations are consistent with the limited experimental data available. The results support the view that semi-conjugated rings should be recognised as a discrete class of dipolar heterocycle.