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.     

Research of Composite Materials BaSm2S4–ZrS2, CaY2S4–ZrS2

Russian Journal of Electrochemistry - Composite materials CaY2S4–ZrS2 and BaSm2S4–ZrS2 synthesized from oxide precursors by ceramic and citrate–nitrate methods, are certified with...     

Bilinear Hardy–Steklov Operators

Mathematical Notes - The weighted inequality in Lebesgue norms with bilinear Hardy–Steklov operators is characterized.     

Non-Toxic Ternary Quantum Dots AgInS2 and AgInS2/ZnS: Synthesis and Optical Properties

Optics and Spectroscopy - Colloidal ternary quantum dots of AgInS2 and AgInS2/ZnS were synthesized in water in the presence of mercapto alkyl carboxylic acid. Selective size separation of AIS and...     

Calibration of the spectral sensitivity of instruments for the near infrared region

We present an analysis of methods for calibration of the spectral sensitivity of instruments in the near IR region of the spectrum (0.90–2.05 μm), using as an example recording of the luminescence spectra of PbS semiconductor quantum dots using a diffraction monochromator and an InGaAs photodiode as the detector. We show that when high-sensitivity detectors are employed for calibration using the emission spectrum of an ideal black body, the problem of attenuation of the radiation flux is still important. Instead of neutral density glass and mesh light filters for attenuation of the radiation, we propose using UFS ultraviolet optical glasses (together with PS purple glasses), the maximum optical density of which is within the region of maximum spectral sensitivity of InGaAs photodiodes. We give examples of spectral calibration, taking into account instrumental characteristics and the effect of absorption by water vapor in the air, and also corrections of the luminescence spectra of quantum dots.     

Synthesis of complex sulfide phases BaSm<Subscript>2</Subscript>S<Subscript>4</Subscript>-Tm<Subscript>2</Subscript>S<Subscript>3</Subscript> and studies of their electrolytic properties

The possibility of synthesizing complex sulfide phases in the BaSm₂S₄-Tm₂S₃ system has been studied. Tm₂S₃ solid solutions were obtained with BaSm₂S₄ (CaFe₂O₄ structural type). The samples were identified by X-ray diffraction analysis and electron microscopy. The range of the solid solutions was determined. The total conductance was studied, and the conductance activation energy was calculated for samples with different dopant contents. The electrolytic properties of basic ternary sulfide and complex sulfide phases in the BaSm₂S₄-x mol % Tm₂S₃ system were investigated. A possible mechanism of defect formation was proposed.     

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.     

On estimation of stability in the problem of reconstructing symmetric types of distributions

New estimates of the stability of characterization of distribution types are obtained both for additive and complete types under the additional assumption that all distributions belong to symmetric types. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part II     

Photosensitive n-Ox/p-CuIn3Se5 heterostructures

We have created photosensitive heterostructures n-Ox/p-CuIn₃Se₅ for the first time. The synthesis process is based on thermal reaction of the ternary compound with atmospheric oxygen. We have studied the voltage-current characteristics and the photoconversion quantum efficiency spectra of the indicated structures. We discuss charge transport mechanisms and photosensitivity of the created structures. We show that n-Ox/p-CuIn₃Se₅ heterostructures can be used in designing solar cells and photoanalyzers for linearly polarized radiation. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 6, pp. 782–785, November–December, 2006.