Electron Energies, Dipole Electric Moments, and Distribution of the Laurdan Molecule over the Conformation States of Methyl Groups

Using the methods of molecular simulation and HyperChem v.5.0 programs (PM3 method), we carried out calculations of the principal spectroscopic characteristics and of the structure of the laurdan molecule in the ground and the first excited electronic states. The thermal static distribution of molecules over various possible orientations of the plane of methyl groups relative to the plane of the naphthalene bicycle was taken into account. The energies and dipole moments of these electronic states have been calculated as functions of the torsion angle of methyl groups. The existence of an additional mechanism of electronic spectrum broadening is shown; it is associated with thermal mismatch of the equilibrium orientations of the rotational fragment of the molecule and with the dependence of the electron transition frequency on the degree of deviation of the angle from the equilibrium value. The dependence of dipole moments on this angle has been found and calculated. This dependence is the strongest for the ground state. The maximum values of dipole moments in the ground and excited states are 4.0 and 7.6 D.     

Molecular dynamics of polycrystalline cellobiose studied by solid-state NMR

Molecular motions of polycrystalline cellobiose have been investigated by measuring proton spin–lattice relaxation times, T₁ and T_1ρ, and the second moment, M₂, in both protonated and D₂O exchanged forms over the temperature range 120–380 K. T₁ relaxation is dominated by the motions of hydroxyl groups between 150 and 380 K, characterised by an activation energy of about 8.74 kJ/mol, whereas T_1ρ relaxation is driven by the motions of the same groups between 120 and 300 K. T_1ρ results suggest that hydroxyl groups have a distribution of dynamics. Motion of methylene groups was detected in the second-moment experiments at about 350 K, characterised by activation energy of about 40 kJ/mol. Consideration of the calculated and observed rigid-lattice second moments suggests that the reported X-ray data are incorrect for the inter-proton distance on C6′. ¹³C CPMAS spectra of both protonated and deuterated cellobiose have also been measured. Spectra of the deuterated material showed the existence of a second crystalline form in addition to the normal form.     

Almost-Sure Results for a Class of Dependent Random Variables

The aim of this note is to establish almost-sure Marcinkiewicz-Zygmund type results for a class of random variables indexed by _d ⁺ —the positive d-dimensional lattice points—and having maximal coefficient of correlation strictly smaller than 1. The class of applications include filters of certain Gaussian sequences and Markov processes.     

用动力学法测杨氏模量实验及其实验装置的研制

介绍了新研制的用动力学法杨氏模量的实验装置,它具有功耗低,灵敏度高的特点;教学中测量悬线不同位置时的共振频率,用作图法拟合出其精确值,以减少由于悬线不在节点引起的系统性误差,测量精密度比传统的静态拉伸法高一个量级以上。     

Studies on Fast Algorithm for the Scattering of a Large Array of Waveguide-Fed Wide-Slot Antennas in Millimeter Wave Region

We present an effective numerical technique to characterize the scattering of wide-slot antennas fed by waveguides with arbitrary terminations in terms of the method of moment (MoM) and the mixed potential integral equation (MPIE). In particular, the precorrected-fast Fourier transform (P-FFT) eliminates the need to generate and store the usual square impedance matrix andthus leads to speed up the matrix-vector multiplication in the resultant system. This property makes the Rao-Wilton-Glisson (RWG) functions to be useful in simulating electrically large-scale problems. In addition, the scattering from the finite ground surfaces is accounted for in the total scattered field by using the method of equivalent edge currents. The numerical results are presented and compared with both the traditional method of moment results obtained using the entire-domain basis functions and the experimental results, to demonstrate the proposed method to be a good candidate for study on the scattering of arbitrary wide-slot large array.     

Calculation of the Slip Velocity of a Rarefied Gas on a Solid Spherical Surface with Allowance for Accommodation Coefficients

The slip velocity of a rarefied gas with inhomogeneous temperature and mass velocity on a solid spherical surface is calculated with the use of a twomoment boundary condition in the linear approximation in terms of the Knudsen number. The dependence of the slip velocity on accommodation coefficients of the two first moments of the distribution function is studied.     

Matrix Christoffel Functions

We introduce and study matrix Christoffel functions for a matrix weight W. We find an explicit expression of the matrix Christoffel functions in terms of any sequence of orthonormal matrix polynomials with respect to W. An extremal property related to the matrix moment problem defined by W is established for the matrix Christoffel functions. We finally find the relative asymptotic behavior of the matrix Christoffel functions associated to matrix weights in the matrix Nevai class.     

Dynamic Behavior of Rigid–Plastic Sector Plates

The paper studies the dynamic behavior of perfect rigid-plastic plates in the form of a sector with hinged or clamped sides under short-term intensive loads. Two dynamic deformation mechanisms are demonstrated. The dynamic equation is derived for each of the mechanisms. The realization conditions for the mechanisms are analyzed. Analytical expressions are derived for the ultimate (high) loads and the maximum residual deflection. Numerical examples are given