Brouwer-Livsey groups

Translated from Matematicheskie Zametki, Vol. 51, No. 3, pp. 122–127, March, 1992.     

On continuous dependence of solutions of linear differential equations on a parameter in a Banach space

We prove the reduction theorem for linear differential equations in a Banach space in the case where the convergence is strong. This result is used to obtain the necessary and sufficient conditions for continuous dependence of solutions on a parameter. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 275–280, February, 1999.     

3,5-Di-<Emphasis Type="Italic">tert</Emphasis>-butyl-1,2-benzoquinone in the synthesis of quinolino[4,5-<Emphasis Type="Italic">bc</Emphasis>][1,5]benzoxazepines,aminophenols, and phenoxazines

Reaction of 3,5-di-tert-butyl-1,2-benzoquinone with 5-amino-4-chloroquinolines gave derivatives of a new fused heterocyclic system, substituted quinolino[4,5-bc][1,5]benzoxazepines. The molecular structure of 9,11-di-tert-butyl-2,4,6-trimethyl-7H-quinolino[4,5-bc][1,5]benzoxazepine was determined by X-ray analysis. 3,5-Di-tert-butyl-1,2-benzoquinone reacted with o-nitro-, o-acyl-, and o-methoxycarbonylanilines and some amino-substituted nitrogen-containing heterocycles to form the corresponding sterically hindered N-aryl-(hetaryl)-o-aminophenols. Di-tert-butyl-substituted phenoxazines were obtained as a result of thermal cyclization of intermediately formed quinone imines.     

Quantitative isoperimetric inequalities for a class of nonconvex sets

Quantitative versions (i.e., taking into account a suitable “distance” of a set from being a sphere) of the isoperimetric inequality are obtained, in the spirit of Fuglede (Trans Am Math Soc 314:619–638, 1989) and Fusco et al. (Ann Math 168:941–980, 2008) for a class of not necessarily convex sets called φ-convex sets. Our work is based on geometrical results on φ-convex sets, obtained using methods of both nonsmooth analysis and geometric measure theory.     

The isomeric ratios in photonuclear reactions of natural strontium induced by bremsstrahlungs in the giant dipole resonance region and by 65 MeV bremsstrahlung

We have determined the isomeric ratio of ^85m,gSr in photonuclear reactions of natural strontium induced by bremsstrahlungs with end-point energies in the giant dipole resonance (GDR) region as well as the isomeric ratios of ^85m,gSr and ^84m,gRb produced at 65 MeV bremsstrahlung. In GDR region the target was irradiated at electron accelerator Microtron MT-25 of the Flerov Laboratory of Nuclear Reaction, Joint Institute for Nuclear Research, Dubna, Russia. The target irradiation with 65 MeV bremsstrahlung was performed at the linear electron accelerator of the Pohang Neutron Facility, Pohang, South Korea. The gamma spectra of the samples irradiated in both cases were measured with spectroscopic systems consisting of 8192 channel analyzer and high-energy resolution (180 keV at gamma ray 1332 keV of ⁶⁰Co) HP(Ge) semiconductor detector Canberra. The GENIE2000 (Canberra) computer program was used for data processing. The results were discussed and compared with those of other authors.     

Hypographs satisfying an external sphere condition and the regularity of the minimum time function

We prove that if the hypograph of a continuous function f admits at every boundary point a supporting ball then it has “essentially” positive reach, i.e. the hypograph of the restriction of f outside a closed set of zero measure has (locally) positive reach. Hence such a function enjoys some properties of a concave function, in particular a.e. twice differentiability. We apply this result to a minimum time problem in the case of a nonlinear smooth dynamics and a target satisfying internal sphere condition.     

Elastic scattering for the system 11Be + 209Bi at Coulomb barrier energies

The elastic scattering process for ¹¹Be ions impinging on a ²⁰⁹Bi target was studied in the energy range around the Coulomb barrier. The angular distributions of the ¹¹Be scattered particles were analyzed within the optical model framework in order to evaluate the reaction cross section, which turned out to be much larger than the fusion one, especially in the sub-barrier region. The comparison with the system ⁹Be + ²⁰⁹Bi showed that the reaction cross section is larger for the reaction ¹¹Be + ²⁰⁹Bi in the energy range around the Coulomb barrier, while they are rather similar at higher bombarding energies. This result suggests that direct processes related to the ¹¹Be halo structure and lower binding energy are more relevant at near-barrier energies.     

Structure of argentamine

Chemistry of Natural Compounds - On the basis of chemical transformations and the UV, IR, and mass spectra of argentamine, isolated from the epigeal part ofAmmodendron argenteum O. Ktze, the...     

Scattering of harmonic waves by a disk-shaped rigid inclusion in a three-dimensional elastic matrix

We consider a three-dimensional problem on the interaction of harmonic waves with a thin rigid movable inclusion in an infinite elastic body. The problem is reduced to solving a system of two-dimensional boundary integral equations of Helmholtz potential type for the stress jump functions on the opposite surfaces of the inclusion. We propose a boundary element method for solving the integral equations on the basis of the regularization of their weakly singular kernels. Using the asymptotic relations between the amplitude-frequency characteristics of the wave farzone field and the obtained boundary stress jump functions, we determine the amplitudes of the shear plane wave scattering by a circular disk-shaped inclusion for various directions of the wave incident on the inclusion and for a broad range of wave numbers.