Nonstationary curves in Hilbert spaces and their correlation functions II

Partially supportted by Grant MM-22/1991 of MESC     

Rotational tunneling dynamics of methyl groups inn-alkane host lattices: An optical investigation of the internal and external isotope effect

We exploited the slow relaxation of methyl group rotational tunneling states to perform optical hole burning inn-alkane crystals. The dye probe used was dimethyl-s-tetrazine and its perdeuterated derivative. We investigatedn-octane, perdeuteratedn-octane andn-hexane as host crystals. By comparing the experimentally observed hole-antihole splitting of the protonated and perdeuterated dye probe, all parameters, i.e. the tunneling splitting in the ground-and in the electronically excited state as well as the respective heights of the potential can be determined, assuming a threefold rotational symmetry axis. We found that matrix deuteration has a severe influence on the potential heights, which increase by a factor of two. With these parameters determined, many features of the complex relaxation behavior of the tunneling states can be qualitatively understood: We found Raman-type conversion processes inn-octane-h ₁₈, Orbach-type processes inn-octane-d ₁₈ and inn-hexane we found, in addition, a relaxation regime governed by a Direct process. The experimental activation energies as well as the cross-over temperatures are in satisfying agreement with current theories.     

Boundary slip phenomena in a binary gas mixture

The slip phenomena in gas mixtures are of fundamental significance in the specification of boundary conditions for flows in the slip regime. In a recent paper, new explicit results for the slip coefficients appropriate to binary gas mixtures were reported. The present work being reported extends the previous work to a higher level of accuracy by involving a higher order Chapman-Enskog expansion. In particular, new expressions for the slip coefficients are presented which are applicable for arbitrary models of the intermolecular interaction. Limiting expressions for the slip coefficients are given (for a simple gas) and the accuracy of the theory is discussed. Numerical calculations of the slip coefficients for different binary gas mixtures using the first and second order Chapman-Enskog approximations and the rigid sphere and Lennard-Jones (12-6) potential models have been carried out. The thermal creep and diffusion slip coefficients are found to be sensitive to the order of the approximation and to the potential model used. A comparison of the new higher order results with some of our previously obtained experimental data for the thermal transpiration effect has also been carried out and shows excellent agreement between the theory and the experiments which confirms the accuracy of the theory.     

Optimal control problems with applications to the elimination of substrate diffusing and convecting through immobilized enzyme

Some optimization problems concerning a substrate in a fluid are considered. The concentration of the substrate is affected by diffusion, convection, and elimination by enzymes, and the problem is to find the optimal distribution of enzymes. In this paper, the rate of elimination and the transmission coefficient are optimized. Mathematically, these problems are optimal control problems, and they are analyzed by means of Pontryagin's maximum principle.     

Identification of low-energy light nuclei recorded by means of an ionizational mass spectrometer

A method of identifying low-energy nuclei from the readings of an ionizational mass spectrometer is considered. The identification principles for particles recorded by a multilayer detector are discussed, together with the fundamentals of a probabilistic approach to the solution of this problem. The method permits correct analysis of the experimental data obtained. The determination of the charge and isotopic composition of radiation consisting of a mixture of different nuclei is considered. The results of calculations by the given method which permit the determination of the optimal detector parameters for the solution of the specific physical problem are outlined. This approach is also applicable for the analysis of data from other types of measuring apparatus.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 84–88, July, 1991.     

An automated laboratory EXAFS spectrometer of Johansson type: indigenous development and testing

An automated linear laboratory EXAFS spectrometer of the Johansson type has been indigenously developed. Only two translational motions are required to achieve the necessary Rowland circle configuration for the (fixed) X-ray source, the dispersing and focusing bent crystal and the receiving slit. With the available crystals the spectral region from 5 to 25 keV can be scanned. The linear motions of the crystal and receiving slit including the detector assembly are achieved by employing software-controlled DC motors and utilizing optical encoders for position sensing. The appropriate rotation of the crystal is achieved by the geometry of the instrument. There is a facility to place the sample alternately in the path of the X-ray beam and out of the path to record both the incident X-ray intensityI ₀ and the transmitted intensityI employing the scintillation detector. An arrangement with a two-window proportional detector before the sample to measureI ₀ and the scintillation detector to recordI is also developed; in this case it is not necessary to oscillate the sample. Fast electronic circuits are employed to minimize counting errors. The instrument is user-friendly and it is operated through a menu-driven IBM compatible PC. EXAFS spectra of high resolution have been recorded using the spectrometer and employing the Si(111) reflecting planes; the X-ray source being a Rigaku 12 kW rotating anode with Cu target. We describe the spectrometer and discuss its performance with a few representative spectra.     

Quantitative dependence of MR signal intensity on tissue concentration of Gd(HP-DO3A) in the nephrectomized rat.

Cardiac-gated SE 20/224 +/- 20 MR images were obtained from nephrectomized rats before and after intravenously administering 153Gd-Gd(HP-DO3A). The concentration of Gd, [Gd], was linear in dose in myocardium, skeletal muscle, and blood. Under steady-state conditions, where d[Gd]/dt = 0, image intensities (IIN) in regions of interest were compared with the measured [Gd]. IIN was linear in myocardium at less than or equal to 0.61 mumol/g-myocardium (less than or equal to 0.5 mmol/kg dose) and in skeletal muscle at less than or equal to 0.63 mumol/g-muscle (less than or equal to 0.75 mmol/kg). Above 0.6 mumol Gd/g-tissue, IIN did not increase further. The in vivo data were consistent with measured ex vivo and in vivo relaxivities. A 29% greater slope for IIN versus [Gd] in myocardium [14,439 +/- 4350 IIN (mumol/g)] than in muscle [10,258 +/- 5,296 IIN/(mumol/g)] was attributed to a significant difference in blood content: 25% versus 2% weight blood in myocardium and skeletal muscle, respectively. Two components were apparent from plots of ex vivo 1/T1 versus [Gd] in myocardium and muscle, and only one for blood.     

Conflict Analysis in the Politico-Military Environment of a New World Order

A methodology is developed to analyse present and future crisis and conflict potentials of small or large geopolitical regions. A set of criteria is used to describe the present economic, social, political and military conditions of a country and the future criteria trends. A multi-criteria decision analysis model is invoked to compute the crisis and conflict potentials under simultaneous consideration of all other countries in that region. The methodology is demonstrated in the crisis and conflict potentials analysis of the former Soviet republics including bordering countries.     

On composition of some general fractional integral operators

In the present paper we derive three interesting expressions for the composition of two most general fractional integral oprators whose kernels involve the product of a general class of polynomials and a multivariableH-function. By suitably specializing the coefficients and the parameters in these functions we can get a large number of (new and known) interesting expressions for the composition of fractional integral operators involving classical orthogonal polynomials and simpler special functions (involving one or more variables) which occur rather frequently in problems of mathematical physics. We have mentioned here two special cases of the first composition formula. The first involves product of a general class of polynomials and the Fox’sH-functions and is of interest in itself. The findings of Buschman [1] and Erdélyi [4] follow as simple special cases of this composition formula. The second special case involves product of the Jacobi polynomials, the Hermite polynomials and the product of two multivariableH-functions. The present study unifies and extends a large number of results lying scattered in the lierature. Its findings are general and deep.