Extended generalized octagons and the groupHe

Let be an extended generalized octagon such that the points of a triple {u, v, w} not on a block are pairwise adjacent if and only if the distance betweenv andw in the local generalized octagon _u equals 3 and there is a thick line through any point of _u . Then is one of the two examples related to the groups 2·L ₃(4).2² andHe. It is also shown that does not admit further extensions.     

Skew-symmetric association schemes with two classes and strongly regular graphs of type L 2n−1(4n−1)

A construction of a pair of strongly regular graphs ⁿ and ⁿ of type L _2n–1(4n–1) from a pair of skew-symmetric association schemes W, W of order 4n–1 is presented. Examples of graphs with the same parameters as ⁿ and ⁿ, i.e., of type L _2n–1(4n–1), were known only if 4n–1=p ³, where p is a prime. The first new graph appearing in the series has parameters (v, k, )=(225, 98, 45). A 4-vertex condition for relations of a skew-symmetric association scheme (very similar to one for the strongly regular graphs) is introduced and is proved to hold in any case. This has allowed us to check the 4-vertex condition for ⁿ and ⁿ, thus to prove that ⁿ and ⁿ are not rank three graphs if n>2.     

Recovery of sludge from alumina production

The carbonation of the sludge slurry was studied. The main characteristics of the initial and carbonated red mud were compared. The carbonation of sludge ensures reduction of the toxicity of a sludge field and enables extraction of some rare metals (scandium, zirconium, titanium), aluminum, and sodium. The possibility of using the treated sludge as an additive in the manufacture of cement and concrete products was determined.     

Near-threshold boson pair production in the model of smeared-mass unstable particles

Near-threshold production of boson pairs is considered within the framework of the model of unstable particles with smeared mass. We describe the principal aspects of the model and consider the strategy of calculations including the radiative corrections. The results of calculations are in good agreement with LEP II data and Monte-Carlo simulations. Suggested approach significantly simplifies calculations with respect to the standard perturbative one.     

Ultrasonic studies of structural transformations and phase transitions in liquid crystal emulsions

The propagation velocity and absorption coefficient of ultrasound in the range of 0.6–150 MHz in a series of liquid crystal emulsions prepared on the basis of thermotropic liquid crystals and isotropic liquids were studied. The dispersity parameters of emulsions were controlled by polarization microscopy and dynamic light scattering. Features of the temperature dependences of the acoustic parameters of emulsions due to the structural transformations and nematic-isotropic liquid transition in disperse and dispersion phases of liquid crystal emulsions were established.     

On polygonal measures with vanishing harmonic moments

A polygonal measure is the sum of finitely many real constant density measures supported on triangles in ?. Given a finite set S ? ?, we study the existence of polygonal measures spanned by triangles with vertices in S, all of whose harmonic moments vanish. We show that for generic S, the dimension of the linear space of such measures is \(\left( {_2^{|S| - 3} } \right)\) . We also investigate the situation in which the density for such measure takes on only values 0 or ±1. This corresponds to pairs of polygons of unit density having the same logarithmic potential at ∞. We show that such (signed) measures do not exist for |S| ≤ 5, but that for each n ≥ 6 one can construct an S, with |S| = n, giving rise to such a measure.     

Scalar Higgs boson production in fusion of two off-shell gluons

The amplitude for scalar Higgs boson production in the fusion of two off-shell gluons is calculated including finite (not infinite) masses of quarks in the triangle loop. In comparison to the effective Lagrangian approach, we have found a new term in the amplitude. The matrix element found can be used in the k_⊥-factorization approach to the Higgs boson production. The results are compared with the calculations for on-shell gluons. Small deviations from the cos²φ-dependence are predicted. The off-shell effects found are practically negligible. PACS 12.38.Bx; 14.80.Bn; 12.38.Qk; 13.85.Qk     

Ultrasound Absorption Anisotropy in the Vicinity of Smectic A-Nematic Transition

The results of a low frequency ultrasonic study of 4-n-butyloxybenzylidene-4'-n-butylaniline (BBBA) in the vicinity of the smectic A-nematic transition are presented. The frequency and temperature dependence of the parameters describing the anisotropic ultrasound absorption are determined experimentally and compared with the predictions of fluctuation and relaxation theories of the smectic A-nematic transition. It is shown that no single theory could explain all of the experimental data.