Second-harmonic conversion of partially coherent radiation of neodymium glass laser

The experimental results on the conversion of multimode radiation of a neodymium glass laser with controlled spatial and temporal coherence to the second optical harmonic in nonlinear KDP crystal during the oee interaction implementation are presented. The dependence of the efficiency of the conversion to the second harmonic on the fundamental radiation power density on the crystal in the range I = 0.2 ? 5 GW/cm² is studied at the number of transverse modes in the cavity N = 1000; the radiation divergence φ = 3.5, 4.7, and 5 mrad; the emission spectral width δλ = 5and 42 Å; and the pulse duration of 2.5 ns. The breakdown power density of the KDP crystal is determined, the interference properties of the converted radiation of the second harmonic are studied.     

Chiral phase transition from string theory

The low energy dynamics of a certain D-brane configuration in string theory is described at weak t'Hooft coupling by a nonlocal version of the Nambu-Jona-Lasinio model. We study this system at finite temperature and strong t'Hooft coupling, using the string theory dual. We show that for sufficiently low temperatures chiral symmetry is broken, while for temperatures larger then the critical value, it gets restored. We compute the latent heat and observe that the phase transition is of the first order.     

Double Complexes and Cohomological Hierarchy in a Space of Weakly Invariant Lagrangians of Mechanics

For a given configuration space M and a Lie algebra G acting on M, the space V _0.0 of weakly G-invariant Lagrangians, i.e., Lagrangians whose motion equations left-hand sides are G-invariant, is studied. The problem is reformulated in terms of the double complex of Lie algebra cochains with values in the complex of Lagrangians. Calculating the cohomology of this complex by the method of spectral sequences, we arrive at the hierarchy in the space V _0.0: The double filtration {V _s.}, s = 0, 1, 2, 3, 4, = 0, 1, and the homomorphisms on every space {V _s.} are constructed. These homomorphisms take values in the cohomologies of the algebra G and the configuration space M. Every space {V _s.} is the kernel of the corresponding homomorphism, while the space itself is defined by its physical properties.     

Investigation of the Nucleophilic Rearrangement of 2-(Cyanomethyl)-1,4,6-trimethylpyrimidinium Iodide Into 4,6-Dimethyl-2-methylaminonicotinic Acid Nitrile

2-(Cyanomethyl)-1,4,6-trimethylpyrimidinium iodide is rearranged into 4,6-dimethyl-2-methylaminonicotinic acid nitrile by interaction with alcoholic solutions of sodium ethylate, methylamine, and also glycine and -alanine ethyl esters. This conversion was also observed for the first time for pyrimidinium salts during the process of recording ¹H NMR spectra in CD₃OD solution containing CD₃ONa. After the rearrangement deuterium exchange of the protons of the pyridine ring methyl groups was noted spectrally. It was demonstrated experimentally that for carrying out and completing the recyclization a quantity of nucleophilic reagent must convert the molar equivalent quantity of pyridinium salt.     

Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side

A singular integral equation with a Cauchy kernel and a logarithmic singularity on its righthand side is considered on a finite interval. An algorithm is proposed for the numerical solution of this equation. The contact elasticity problem of a П-shaped rigid punch indented into a half-plane is solved in the case of a uniform hydrostatic pressure occurring under the punch, which leads to a logarithmic singularity at an endpoint of the integration interval. The numerical solution of this problem shows the efficiency of the proposed approach and suggests that the singularity has to be taken into account in solving the equation.     

Stevens rearrangement of heterocyclic ammonium salts containing prop-2-yn-1-yl group

Stevens rearrangement was studied of ammonium salts where piperidinium or morpholinium groups are linked to prop-2-yn-1-yl moiety and labile hydrogen atom functions (methoxycarbonylmethyl, phenacyl, cyanomethyl). In the case of phenacyl analog furan derivatives were formed, in other cases dienamines were the reaction products.     

Synthesis,X-ray structure,and stevens rearrangement of 1,1-di(prop-2-yn-1-yl)-2,5-dihydro-1H-pyrrol-1-ium bromide

1,1-Di(prop-2-yn-1-yl)-2,5-dihydro-1H-Pyrrol-1-ium bromide was obtained with interaction of 3-pyrroline with propargyl bromide and its structure was studied by X-ray analysis. It has been shown that the Stevens rearrangement of obtaining salt leads to the formation of 1-(hexa-4,5-dien-1-yn-3-yl)-2,5-dihydro-1H-pyrrol.