Stability radii of positive linear Volterra-Stieltjes equations

We study stability radii of linear Volterra-Stieltjes equations under multi-perturbations and affine perturbations. A lower and upper bound for the complex stability radius with respect to multi-perturbations are given. Furthermore, in some special cases concerning the structure matrices, the complex stability radius can precisely be computed via the associated transfer functions. Then, the class of positive linear Volterra-Stieltjes equations is studied in detail. It is shown that for this class, complex, real and positive stability radius under multi-perturbations or multi-affine perturbations coincide and can be computed by simple formulae expressed in terms of the system matrices. As direct consequences of the obtained results, we get some results on robust stability of positive linear integro-differential equations and of positive linear functional differential equations. To the best of our knowledge, most of the results of this paper are new.     

Diffraction by a wedge at skew incidence: integral representations of Cauchy-Carleman for the electromagnetic fields

An electromagnetic diffraction problem in a wedge shaped region is reduced to a system of coupled functional difference equations by means of Sommerfeld integrals and Malyuzhinets theorem. By introducing an integral operator it is shown that the solutions of this system of functional equations can be defined in terms of integral representations whose kernels are solutions of a singular integral equation of Cauchy-Carleman type for which an explicit solution is given.     

Determination of uranium and thorium isotopes in soil samples by coprecipitation

Summary The paper presents a procedure to prepare soil samples for U and Th isotope measurement by alpha-spectrometry after coprecipitation with LaF₃. In this procedure the reduction of U(VI) to U(IV) was performed by Zn metal in 4M HCl solution. The recoveries of chemical separation equal to e_U-chemistry = 78±4% for uranium and e_Th-chemistry = 82±4% for thorium. Canberra alpha-spectrometer was used with PIPS detectors of A-1200-37-AM Model of 1200 mm² active area. The counting efficiency of the measuring system equals to e_counting = 18% and the total efficiencies were e_U = e_counting ^.e_U-chemistry = 14.0±0.7% for uranium and e_Th = e_counting ^.e_Th-chemistry = 14.7±0.7% for thorium. The recoveries of chemical separation were rather high (about 80%), that leads to the use of a small weight of soil sample (about 0.5 g). The efficiencies were also stable, that allows analyzing the soil sample without using radiotracers. They are advantages of the sample preparation procedure of this work.     

Chemical isolation of element 106 from aqueous solutions according to model experiments with short-lived tungsten isotopes

The short-lived isotopes of W and their descendants have been isolated from the products of the bombardment of¹⁴⁴Sm with²⁴Mg by a fast continuous ion-exchange method, using HF solution media. The feasibility of this method for isolation of element 106 is discussed.     

Renormalization Effects in the Spectrum of a Coherently Driven Exciton–Biexciton System

Starting from the total Hamiltonian of an excited exciton–biexciton system, nonresonant renormalizations in the electronic spectrum of a coherently driven direct semiconductor are considered. Stringent group-theoretical inclusion of the particle spin in the Hamiltonian allows one to account for the dependence of different renormalization effects on polarizations of the incident laser fields. On the example of circularly polarized driving and probing pulses it is shown that the kind of observed renormalization is defined by the pump-and-probe polarization geometry. Thus, the exciton optical Stark effect must appear in the case of co-circular pump-and-probe, whereas a mixing of the polariton and biexciton spectra is possible only in the case of counter-circular pump-and-probe. The polariton--biexciton dispersion renormalization may manifest itself as synchronous splittings of the exciton--polariton and biexciton spectra under resonant pumping at a frequency of the polariton--biexciton transition, or in their shifts in opposite directions under near-resonant pumping. The mechanisms of both kinds of renormalization effects are analyzed, and the dependence of their characteristics on the pump parameters and microscopic parameters of the exciton–biexciton–photon system is established. An evaluation of the characteristics shows that the effect of polariton–biexciton dispersion renormalization dominates in the spectra of semiconductors with stable biexciton formation. Results of the theoretical study provide an adequate explanation of available experimental data.     

Synthesis and orientation study of a magnetically aligned liquid‐crystalline chitin/poly(acrylic acid) composite

A high magnetic field of 5 T was used to fabricate a magnetically aligned, optically anisotropic, liquid‐crystalline chitin/poly(acrylic acid) composite. The aligned mesophase was fixed by photoinitiated free‐radical polymerization. From an examination of polarized optical micrographs and an X‐ray diffraction study, a high degree of orientation of 0.70 was observed for the composite with a higher liquid‐crystalline chitin concentration (10.70 wt %); the orientation was reduced with a decreased chitin concentration at a given acrylic acid concentration. The X‐ray data for the developed composite showed a uniplanar orientation for the chitin crystallites, with its molecular long axes perpendicular to the direction of the magnetic field. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 711–714, 2003     

Excitation functions for some output channels following the p +55Mn interaction atE p=1·3–2·0 MeV

Excitation functions for the⁵⁵Mn(p, p )⁵⁵Mn,⁵⁵Mn(p, n )⁵⁵Fe and⁵⁵Mn(p, )⁵⁶Fe reactions are studied for proton beam energyE _p=1·3–2 MeV. The excitation functions are established from yield functions for -rays emitted from the first excited states of final nuclei. Many resonances are observed and competition of their decay into all three output channels is analysed. Spin-parity assignment for some resonant states in the⁵⁶Fe compound nucleus is deduced.Participated partly in the course of his work on a Thesis.The authors wish to thank the staff of the Van de Graaff accelerator at Charles University in Prague for the efficient operation of the machine and dr. I. Wilhelm for the valuable technical help in the early period of the experimental work. One of us (N. A. N.) acknowledges the staff of the Dept. of Nuclear Physics of Charles University in Prague for the excellent working conditions.     

Fast and continuous chemical isolation of short-lived isotopes of Hf,Ta and W as homologs of elements 104, 105 and 106

Some short-lived isotopes of Hf, Ta and W, synthesized at the U-400 cyclotron of JINR-Dubna, have been isolated using a previously elaborated fast continuous method of chemical isolation of element 104 from nuclear reaction products. The products were transported by a NaCl aerosol jet, from the irradiated targets to a separation device in which Hf, Ta and W were isolated by using three coupled ion-exchange columns.     

Neosappanone A, a xanthine oxidase (XO) inhibitory dimeric methanodibenzoxocinone with a new carbon skeleton from Caesalpinia sappan

A novel dimeric methanodibenzoxocinone, named neosappanone A (1), possessing a unique unprecedented novel carbon framework, has been isolated from the heartwood of Caesalpinia sappan L. of Vietnam, and its structure was elucidated on the basis of spectroscopic analysis. Neosappanone A (1) competitively inhibited xanthine oxidase in a concentration-dependent manner (IC₅₀, 29.7 μM; K_i, 16.3 μM).