Integrability of a system of two nonlinear Schrödinger equations

P. P. Shirshov Institute of Oceanology, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 79, No. 2, pp. 180–184, May, 1989.     

Parametric and Non Homogeneous Semi-Markov Process for HIV Control

In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed. A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct times and follow-up has an impact on the evolution of patients.      

Ultrashort-pulse dual-wavelength source for digital holographic two-wavelength contouring

Digital holographic shape measurements using femtosecond laser pulses are reported. For contouring of very fast moving objects, the simultaneous generation of at least two spectrally separated ultrashort pulses is required. To deliver this particular spectral signature at high pulse energies, a chirped-pulse Ti:sapphire laser amplifier was modified to emit two spectrally separated pulses with energies above 1 μJ each. The wavelength separation of these pulses was adjustable within the 50 nm gain bandwidth, cutting out two distinct wavelength peaks by a variable double-slit assembly in a prism sequence. A Michelson-type interferometer was employed to perform the two-wavelength contouring. The phases of the holograms and the phase differences are calculated numerically, which allow us to deduce the contour lines of the topology of the object. The suitability of the light source for digital holography is demonstrated with contouring of stationary objects and the potential for high-speed applications is indicated. PACS 42.40.-i; 42.60.By     

Research,teaching, and social activities of academician Sergey Alekseevich Khristianovich

Sergey Alekseevich Khristianovich is one of the famous Russian mechanical engineers of the 20th century together with N.E. Zhukovsky, S.A. Chaplygin, N.E. Kochin, and others. He made an immense contribution to some aspects of mechanics, such as aerogasdynamics, rock mechanics, theory of plasticity, filtration theory, and environmental power engineering. All this was preceded by a long, hard, and fruitful life full of outstanding events.     

Speedup estimates for some variants of the parallel implementations of the branch-and-bound method

The efficiency of parallel implementations of the branch-and-bound method in discrete optimization problems is considered. A theoretical analysis and comparison of two parallel implementations of this method is performed. A mathematical model of the computation process is constructed and used to obtain estimates of the maximum possible speedup. Examples of problems in which none of these two parallel implementations can speed up the computations are considered.     

Acoustic properties of the disordered relaxor ferroelectric PbSc1/2Ta1/2O3

The behavior of acoustic phonons in crystals of a relaxor ferroelectric, namely, the lead scandium tantalate PbSc_1/2Ta_1/2O₃ (PST), is studied in the vicinity of the diffuse phase transition. The behavior of longitudinal and transverse acoustic phonons in a PST single crystal is examined using Brillouin scattering. The phonon subsystem is found to behave anomalously in the vicinity of T = 297 K, which can probably be assigned to the existence of a phase transition. Analysis of the results obtained yields the values of the elastic moduli C₁₁, C₁₂, and C₄₄ for the cubic phase of the crystal over a wide temperature range.     

Structural phase transformations and physical properties of intercalation compounds in the Cr0.5Ti(Se1−x Tex)2 system

The atomic structure and magnetic and electric properties of the Cr_0.5TiSe₂-Cr_0.5TiTe₂ system of intercalated phases were studied in detail by gradually replacing selenium by tellurium. It was revealed that this replacement changes the crystalline structure from monoclinic in the initial compounds to hexagonal in the compounds containing various types of chalcogen atoms; this is accompanied by disordering of chromium atoms in the van der Waals gaps. The electrical resistance and magnetic characteristics vary nonmonotonically on replacement of selenium by tellurium, which is associated with a change in the degree of atomic disordering during the transition from Cr_0.5TiSe₂ to Cr_0.5TiTe₂.     

Kinetics of polarization reversal in irradiated thin PZT films

The effect of irradiation with electrons and neutrons and of exposure to synchrotron radiation on cyclic switching of polarization in thin films of lead zirconate titanate Pb(Zr,Ti)O₃ (PZT) was studied. It is shown that variations in the shape of switching currents are due to the generation of a spatially nonuniform bound internal field with account for an increase in the rate of bulk screening caused by irradiation. A correlation between structural variations and the evolution of the switching current measured during and after irradiation is established.