Group-theoretical representation of holohedral forms of crystals by conjugated simple forms. Intergrowth of crystals

The schemes for division of holohedral simple forms of crystals into conjugated simple forms are derived by decomposition of the symmetry group of the primitive sublattice into double cosets. The number of equivalently oriented simple forms in the intergrowth of crystals, whose primitive space sublattices are parallel to one another, is equal to the number of holohedral permutational conjugated simple forms, which has the value 992 for all the 32 symmetry classes.     

Microwave Spectrum and Dipole Moment of 1,3‐dioxolane in the Hindered‐Pseudorotation States v = 0, 1, 2, and 3

The microwave spectrum of 1,3dioxolane (C₃H₆O₂) in the ground and first three excited states of hindered pseudorotation was studied. The transitions corresponding to the _b, _c, and _a components of the dipole moment were identified. The spectrum was analyzed using numerical diagonalization of the effective rotational Hamiltonian for four interacting states of hindered pseudorotation. The rotational constants, centrifugal distortion constants, the constants of interaction between general rotation and hindered pseudorotation, and the distances between the quasidegenerate vibrational levels ₀₁ = 64840.5, ₁₂ = 122231.7 and ₂₃ = 119732.7 MHz are determined. From the Stark effect of microwave transitions, the dipole moment components (in Debye units) in the hinderedpseudorotation states v = 0, 1, 2, and 3 are determined: 0|_b|0 = 1|_b|1 = 1.22, 2|_b|2 = 1.20, 3|_b|3 = 1.21, 0|_c|1 = 0.77, 2|_c3 = 0.66, and 1|_a|2 = 0.19.     

Structure and spectra of 1,3-dioxanes. microwave spectrum,structural parameters and <Emphasis Type="Italic">ab initio</Emphasis> calculations of 1,3-dioxane

Microwave spectra of the 1,3-dioxane molecule (C₄H₈O₂) with the main isotopic composition and four its isotopomers (¹³C(2)¹²C₃H₈ ¹⁶O₂, ¹³C(4)¹²C₃H₈ ¹⁶O₂, ¹³C(5)¹²C₃H₈ ¹⁶O₂, ¹⁸O(1)¹²C₄H₈ ¹⁶O) are investigated in a frequency range of 28–44 GHz. Rotational transitions of b-and c-types with 2 ≤ J ≤ 5 are identified. Rotational constants, quartic constants of centrifugal distortion, isotope-substituted r _s-and effective r ₀-structures of the molecule ring are determined. Experimental data are compared to the results of quantum chemical calculations of different levels.     

Microwave spectrum, rotational parameters, and DFT geometry calculations for trans- and cis-isomers of 2,5-dimethyl-1,3-dioxane

The microwave spectrum of 2,5-dimethyl-1,3-dioxane is studied. The spectrum is identified to have the a and c type rotational transitions of the trans- and cis-isomers of the molecule. The experimental frequencies of the transitions are used to calculate the rotational constants and the quartic centrifugal distortion constants of the isomers. The dipole moments are determined. Quantum chemical calculations are performed by the B3PW91/aug-cc-pVDZ density functional method. The calculated results are compared with the experimental data. The equilibrium geometries of 1,3-dioxane and 2-methyl-, 5-methyl-, and 2,5-dimethyl-1,3-dioxanes are compared. It is found that the alkyl substitution leads to a change in the ring geometry     

Microwave spectrum, centrifugal distortion, dipole moment and conformation of 2-methyl-1,3-dioxane

Microwave spectrum of 2-methyl-1,3-dioxane has been investigated in the frequency range 8–40 GHz. Rotational a-type and c-type transitions with J≤40 have been identified. Rotational constants A = 4658.122(2) MHz, B = 2503.221(1) MHz, C = 1783.950(1) MHz and centrifugal distortion constants for the ground vibrational state have been found. Dipole moment components μ_a = 1.43 ± 0.01 D, μ_c = 1.15±0.01 D and overall dipole moment μ = 1.84±0.02 D have been determined. The data obtained are in accord with the chair conformation of the molecule having equatorial arrangement of the methyl group. Original Russian Text Copyright ? 2006 by A. Kh. Mamleev, R. V. Galeev, L. N. Gunderova, M. G. Faizullin, and A. A. Shapkin __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 47, No.2, pp. 373–375, March–April, 2006.     

Approximation by Fourier sums of classes of functions with several bounded derivatives

An ordered estimate is obtained for the approximation by Fourier sums, in the metric ofd=(d ₁ , ...,d _n ), 1<dj<,j=1, ...,_n of classes of periodic functions of several variables with zero means with respect to all their arguments, having m mixed derivatives of order a¹..., a^m., aⁱ rⁿ. which are bounded in the metrics ofp ⁱ =p ₁ ⁱ , ..., p _n ⁱ , i

j ⁱ <,i=i, ...,n, j=1, ...,n by the constants ₁, ., _m, respectively.Translated from Matematicheskie Zametki, Vol. 23, No. 2, pp. 197–212, February, 1978.     

A Lowpass Filter Based on a 2D Microstrip Electromagnetic Crystal

Doklady Physics - A new construction of a lowpass filter was developed based on a two-dimensional microstrip electromagnetic crystal, which had a steeper slope of the frequency response as compared...     

Anomalous electron thermal conductivity across the destroyed magnetic surfaces

New “Semicollisional” regime of the anomalous electron transport pertaining to the weakly collisional plasma is described in the paper. The transition from the collisionless to semicollisional case is determined by the ratio of the phase stochastization length of the parallel electron motion to the mean free path. It was shown also that the anomalous thermal conductivity can be described by the known “selfsimilar” expression $\text{χ}{}_{\mathrm{?}}\text{= χ}{}_{6e}\text{Ь}{}^2{}_0$ only for very strong collisions or high level of magnetic field turbulence.     

EPR of Gd3+ in single crystal colquiriite and analysis of the spin Hamiltonian tensorsB 4 andB 6

In single crystal colquiriite LiCaAlF₆ doped with Gd³⁺ ions two EPR spectra of the Gd³⁺ ions with the Laue site-symmetry groups C_i and C_3i were observed. The spectrum angular dependence for trigonal Gd³⁺ centre was investigated in detail and corresponding spin Hamiltonian parameters were fitted. From analysis of the spin Hamiltonian tensorsB ₄ andB ₆ it was established that Gd³⁺ with the Laue group C_3i substitutes at Ca²⁺ site with the excess charge compensation by an ion located along the threefold axis from this site. The transformation formulas for a sixth-rank irreducible Hermitian tensor under coordinate rotation are tabulated in an explicit form. By using the EPR data for Gd³⁺ substituted in a variety of host crystals, the fourth-rank and sixth-rank tensors of Gd³⁺ spin Hamiltonians were tabulated and correlated with structures of the coordination polyhedra at substitution sites. The results suppose a predominance of quadratic crystal field contributions into the spin Hamiltonian tensorB ₄ of Gd³⁺.     

The reverse shift of the EPR line of paramagnetic centers coupled to species with a fast paramagnetic relaxation

The EPR spectrum of the spin 1/2 paramagnetic centers with a relatively slow relaxation is considered in the case when they are coupled via the Heisenberg exchange interaction to partners which have short times of the longitudinal and transverse paramagnetic relaxation. Under these conditions only the EPR line of paramagnetic centers with a relatively slow relaxation is detectable in experiment. The shape of this line is analyzed by solving numerically kinetic equations for the spin density matrix for simple model systems. Depending on a ratio between the exchange integral and the paramagnetic relaxation rates of partner spins, the EPR line shifts in opposite directions. For moderate relaxation rates, as the relaxation rates decrease, the EPR line shifts toward the gravity center of the total EPR spectrum. In the case of extremely fast relaxation, as the relaxation rates decrease, the reverse shift of the EPR line is expected, the line shifts away from the gravity center of the total EPR spectrum. This type of the non-monotonous line shift was experimentally observed for the monocrystal of [CuNd₂(C₄O₄)₄(H₂O)₁₆] · 2H₂O when relaxation rates were changed by temperature variation.