Invertible point transformations,Painlevé test,and the second Painlevé transcendent

The techniques of invertible point transformations and the Painlevé analysis can be used to construct integrable ordinary differential equations. We compare both techniques for the second Painlevé transcendent.     

An algorithm for the asymptotic solution of a singularly perturbed linear time-optimal control problem

An algorithm for the approximate solution (in the asymptotic sense) of a singularly perturbed linear time-optimal control problem is proposed. A computational procedure is outlined, which permits the use of the resulting asymptotic approximation for. the exact solution of the problem with a prescribed value of the small parameter.     

Sound field variations caused by intense internal waves in a shallow sea with a weak thermocline

Results of an experiment on investigating the fluctuations of a sound signal with a frequency of 295 Hz on a stationary 32-km-long acoustic path in a shallow sea are presented. Hydrological conditions on the path were characterized by the presence of a weak thermocline and a frequent occurrence of intense internal wave trains. The space-time characteristics of these internal waves were measured in detail. Experimental evidence of the repetition of the forms of internal solitons in the variations of the amplitude and phase of an acoustic signal was obtained.     

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.     

High pressure X-ray diffraction study of CdAl2Se4 and Raman study of AAl2Se4 (A=Hg, Zn) and CdAl2X4 (X=Se, S)

We report the results of an X-ray diffraction study of CdAl₂Se₄ and of Raman studies of HgAl₂Se₄ and ZnAl₂Se₄ at room temperature, and of CdAl₂S₄ and CdAl₂Se₄ at 80 K at high pressure. The ambient pressure phase of CdAl₂Se₄ is stable up to a pressure of 9.1 GPa above which a phase transition to a disordered rock salt phase is observed. A fit of the volume pressure data to a Birch-Murnaghan type equation of state yields a bulk modulus of 52.1 GPa. The relative volume change at the phase transition at ∼9 GPa is about 10%. The analysis of the Raman data of HgAl₂Se₄ and ZnAl₂Se₄ reveals a general trend observed for different defect chalcopyrite materials. The line widths of the Raman peaks change at intermediate pressures between 4 and 6 GPa as an indication of the pressure induced two stage order-disorder transition observed in these materials. In addition, we include results of a low temperature Raman study of CdAl₂S₄ and CdAl₂Se₄, which shows a very weak temperature dependence of the Raman-active phonon modes.