Prime ideals in restricted differential operator rings

In this paper restricted differential operator rings are studied. A restricted differential operator ring is an extension of ak-algebraR by the restricted enveloping algebra of a restricted Lie algebra g which acts onR. This is an example of a smash productR #H whereH=u (g). We actually deal with a more general twisted construction denoted byR * g where the restricted Lie algebra g is not necessarily embedded isomorphically inR * g. Assume that g is finite dimensional abelian. The principal result obtained is Incomparability, which states that prime idealsP ₁ ⊆P ₂ ⊂R * g have different intersections withR. We also study minimal prime ideals ofR * g whenR is g-prime, showing that the minimal primes are precisely those having trivial intersection withR, that these primes are finite in number, and their intersection is a nilpotent ideal. Prime and primitive ranks are considered as an application of the foregoing results.     

Eye tissue structure and refraction alterations upon nondestructive laser action

A new approach to alterations in eye refraction upon nondestructive laser action on the sclera and cornea is studied. It is demonstrated in in vivo experiments on rabbit eyes that sequential laser irradiation of the sclera and cornea yields a significant alteration in the eye refraction. The collagen structure of the sclera and cornea is studied after the nondestructive laser action with noninvasive polarization-sensitive optical coherence tomography. It is demonstrated that collagen fibers that provide for the cornea tension and applanation partially survive in the zone of the local denaturation of sclera. An irradiation mode that corresponds to an increase in the cornea’s plasticity and does not cause visible structural changes is chosen. The simplest theoretical model for alterations in the eye refraction upon the nonablative laser action on sclera is analyzed. The alteration in the cornea curvature upon stretching resulting from the local sclera coagulation and the corresponding decrease in its volume is calculated. The model makes it possible to approximately estimate the laser irradiation modes that provide the desired alterations in eye refraction.     

Spatial coherence and coherent interactions of broadband dispersed laser beams

Analytical expressions are obtained that describe the changes in the degree of coherence and in the thickness of the coherence layers occurring upon propagation of a dispersed broadband laser beam. It is found that the greater the tilting of the coherence layers with respect to the phase fronts, the more rapidly the spatial coherence is violated with increasing distance. A comparison with the case of an undispersed beam is performed. It is shown that, as the beam propagates, the decrease in the degree of coherence is accompanied by the appearance of spatial fluctuations of this parameter. The degree of mutual coherence of intersecting dispersed beams with parallel correlated coherence layers, which determines the efficiency of their coherent interaction, is investigated. The existence of spatial fluctuations of the degree of mutual coherence is established.     

Finite-Band Potentials with Trigonal Curves

We construct Dubrovin equations and trace formulas for finite-band operators with trigonal curves and present some examples.     

Structural evolution in amorphous silicon and germanium thin films.

The structural evolution in amorphous silicon and germanium thin films has been investigated by high-resolution transmission electron microscopy (HRTEM) in conjunction with autocorrelation function (ACF) analysis. The results established that the structure of as-deposited semiconductor films is of a high density of nanocrystallites embedded in the amorphous matrix. In addition, from ACF analysis, the structure of a-Ge is more ordered than that of a-Si. The density of embedded nanocrystallites in amorphous films was found to diminish with annealing temperature first, then to increase. The conclusions also corroborate well with the results of diminished medium-range order in annealed amorphous films determined previously by a variable coherence microscopy method.     

Can Millimeter Waves Generate Electroporation?

Analysis of the field distributions in a single biological cell under electromagnetic wave is given. With Debye approximation, the dielectric relaxation of each part of the cell, including the extracellular and cellular media, the cell membrane and the nuclear membrane, was taken into account. Making use of some typical parameters for a cell, the voltage across nuclear and cytoplasma membranes under electromagnetic waves are calculated up to millimeter wave frequency range. The calculated result indicates that it is unlikely to generate electroporation by present available millimeter wave sources.     

Diode-pumped 671 nm laser frequency doubled by CPM LBO

A design of diode-pumped high-efficiency Nd:YVO₄/LBO red laser is reported. Using critical phase-matching (CPM) LBO, 671 nm red laser was obtained from 1342 nm light by intracavity frequency doubling. With an incident pump laser of 800 mW, using type-I and type-II CPM LBO, 97 and 52 mWTEM₀₀ mode red laser outputs were obtained, with optical-to-optical conversion efficiencies of up to 12.1% and 6.5%, respectively.