Electrofocusing of inorganic ions

The mechanism of formation of apH gradient along a paper strip is discussed, and an equation has been derived making possible the calculation of thepH along the carrier. An equation is given relating thepH and the place of ion focusing to the stability constant. The distances between the focused zones have been estimated for the system Fe−Sr−Y, and the results are compared with the experimental data.     

1-Acyl-3-arylazoindoles in the synthesis of indolo[1,2-c]quinazolines

Treatment of 1-aeyl-3-arylazoindoles with zinc in acetic acid in the presence of acetic anhydride and sodium acetate leads to 12-acetamidoindolo [1,2-c]quinazolines. 12-Aminoindolo[1,2-c]quinazolines are obtained when the reaction is carried out in the absence of acetic anhydride and sodium acetate.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 377–379, March, 1977.     

Synthesis of derivatives of 2-amino-3-ethoxycarbonylthiophene

A number of alkylidene esters are synthesized from the corresponding ketones and cyanoacetic ester, and treatment of the esters with sulfur in the presence of a catalytic amount of diethylamine gives 2-amino-3-ethoxycarbonylthiophene derivatives.     

Structure of a nonparaxial gaussian beam near the focus: III. Stability,eigenmodes, and vortices

Exact analytical structurally stable solutions of the Maxwell equations for singular mode beams propagating in free space or a uniform isotropic medium are obtained. Approximate boundary conditions are chosen in the form of the requirement that in the paraxial approximation the fields of nonparaxial mode beams in the waist plane are transformed into the fields of eigenmodes and vortices of weakly guiding optical fibers with the axial symmetry of refractive index. It is shown that optical vortices, in spite of a rather complex structure of field distribution, do not experience substantial changes in the beam form and reproduce, in general features, the field of paraxial vortices. Linear perturbations of the characteristic parameters of mode beams do not change the structure of their electromagnetic field. Nonparaxial singular beams have one more important property, in addition to the fact that the structure of these beams in the paraxial approximation is similar to the structure of the fields of eigenmodes in a fiber. The propagation constants of eigenmodes of a fiber exactly coincide (in the first approximation of perturbation theory) with the projection of the wave vector of a mode beam on the optical axis (an analog of the propagation constant). The possibility of the paraxial transition for nonparaxial mode beams with arbitrary values of azimuthal and radial indices is shown. The properties of nonparaxial modes are illustrated by numerous examples. The solutions obtained and the results of their analysis can be used for exact matching optical fibers and laser beams in various applications.     

Materials processing with a tightly focused femtosecond laser vortex pulse

In this Letter we present the first (to our knowledge) demonstration of material modification using tightly focused single femtosecond laser vortex pulses. Double-charge femtosecond vortices were synthesized with a polarization-singularity beam converter based on light propagation in a uniaxial anisotropic medium and then focused using moderate- and high-NA optics (viz., NA=0.45 and 0.9) to ablate fused silica and soda-lime glass. By controlling the pulse energy, we consistently machine micrometer-size ring-shaped structures with <100nm uniform groove thickness.     

Natural shaping of the cylindrically polarized beams

We have experimentally and theoretically shown that the circularly polarized beam bearing a singly charged optical vortex propagating through a uniaxial crystal can be split after focusing into the radially and azimuthally polarized beams in the vicinity of the focal area provided that the polarization handedness and the vortex topological charge have opposite signs.     

Kinetics of nanowire formation during vacuum condensation of metals on a crystal surface

The kinetics of nanowire formation on the steps of a crystalline dielectric substrate during vacuum condensation of metals from vapor has been investigated. The time of nanowire formation has been calculated at different temperatures and condensation rates.     

An addition theorem for the manifolds with the Laplacian having discrete spectrum

The question of the preservation of discreteness of the spectrum of the Laplacian acting in a space of differential forms under the cutting and gluing of manifolds reduces to the same problem for compact solvability of the operator of exterior derivation. Along these lines, we give some conditions on a cut Y dividing a Riemannian manifold X into two parts X ₊ and X _? under which the spectrum of the Laplacian on X is discrete if and only if so are the spectra of the Laplacians on X ₊ and X _?.