Degenerate billiards in celestial mechanics

In an ordinary billiard trajectories of a Hamiltonian system are elastically reflected after a collision with a hypersurface (scatterer). If the scatterer is a submanifold of codimension more than one, we say that the billiard is degenerate. Degenerate billiards appear as limits of systems with singularities in celestial mechanics. We prove the existence of trajectories of such systems shadowing trajectories of the corresponding degenerate billiards. This research is motivated by the problem of second species solutions of Poincaré.     

Liquid-crystal 2-aroylaminopyridines

A number of 2-aroylaminopyridines that have mesogenic properties were synthesized. The relationship between the mesogenic character and the structure was traced on the basis of data from x-ray diffraction analysis and IR spectroscopy.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1079–1082, August, 1992.     

Measured lifetimes of states in 197Au and a critical comparison with the weak-coupling core-excitation model

The lifetimes of five excited states in ¹⁹⁷Au up to an excitation energy of 885 keV were measured by the recoil-distance method (RDM). These levels were populated by Coulomb excitation using both 90 MeV ²⁰Ne and 120 MeV ³⁵Cl ion beams. The experimentally determined spectroscopy of the low-lying levels $\text{3}\text{2}{}^{\mathrm{+}}$ (ground state) and $\text{1}\text{2}{}^{\mathrm{+}}$, $\text{3}\text{2}{}_2{}^{\mathrm{+}}$, $\text{5}\text{2}{}^{\mathrm{+}}$, and $\text{7}\text{2}{}^{\mathrm{+}}$ at 77.3, 268.8, 278.9, and 547.5 keV excitation energy, respectively, has been critically compared with the detailed predictions of the de-Shalit weak-coupling core-excitation model. When the model is taken to represent the case of a $\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ proton hole coupled to a ¹⁹⁸Hg core, the model parameters obtained are in accord with the criteria implicit for weak core coupling and, at the same time, are in remarkably good agreement with virtually all measured E2 and M1 transition rates.     

Investigation of electronic structure in chlorine-substituted methanes

The electronic structure, dipole moments, and nuclear magnetic resonance and nuclear quadrupole resonance constants of the CH₄, CCl₄, CHCl₃, CH₂Cl₂, and CH₃Cl molecules were calculated by the Parr-Pariser-Pople (PPP) and Wolfsberg-Helmholz (WH) methods, with self-consistency of the charges on the atoms. Conclusions were reached on the applicability limits of these methods. The calculated values were compared with experimental data.     

Level structure and lifetimes of low-excitation states in 63Cu

The lifetimes of 9 states in ⁶³Cu up to an excitation energy of 2092 keV have been determined by means of the Doppler-shift attenuation method using the ${}^{60}\text{Ni}\text{(α,}\text{p}\text{γ)}$ reaction. A search was made for a suitable set of M1 and E2 single-particle matrix elements for use with shell-model eigenstates throughout the Ni, Cu and Zn isotopes. The theoretical predictions for the level spectroscopy and electromagnetic transitions and static moments in ⁶³Cu are in satisfactory agreement with the experimental findings.     

Influence of the method of synthesis on the composition and structure of copper(II) complexes with galactaric acid

The influence of the conditions and the method of synthesis on the composition of copper(II) complexes with galactaric acid (H₂Gala) has been studied. In aqueous and water-DMSO solutions, 1 : 1 complexes are formed. Depending on the procedure and conditions of the synthesis, CuGala · 4H₂O, Cu(HGala)₂ · 4H₂O, and (CuOH)₂Gala · 2H₂O compounds have been obtained. The structure of the coordination environment of the metal ion has been identified by IR spectroscopy.     

Disparity of measured gyromagnetic ratios of ground- and excited-band states in184W

Gyromagnetic ratios of levels in the ground-band and of the 2 ₂ ⁺ state in¹⁸⁴W were measured by means of the transient magnetic field perturbedγ-ray angular distribution technique. The levels of interest were Coulomb excited by beams of 220-MeV⁵⁸Ni and⁶³Cu ions. The results show theg-factor of the 2 ₂ ⁺ state to be approximately half the effectively constant value found for the ground-band levels. This disparity is compared with those previously obtained for the corresponding states in^188–192Os and¹⁸⁶W; these are discussed in the context of the interacting boson model.     

On the Influence of the Kinetic Energy¶on the Stability of Equilibria¶of Natural Lagrangian Systems

Natural Lagrangian systems (T,Π) on R ² described by the equation are considered, where is a positive definite quadratic form in and Π(q) has a critical point at 0. It is constructively proved that there exist a C ^∞ potential energy Π and two C ^∞ kinetic energies T and such that the equilibrium q(t)≡ 0 is stable for the system (T,Π) and unstable for the system . Equivalently, it is established that for C ^∞ natural systems the kinetic energy can influence the stability. In the analytic category this is not true. Accepted: October 20, 1999     

1H NMR study of the interaction between ethidium bromide and self-complementary and self-complementary deoxytetranucleotide 5′-d(CpGpCpG) in an aqueous solution

Complexation of the ethidium bromide (3,8-diamino-6-phenyl-5-ethylphenanthridine) dye with self-complementary deoxytetraribonucleoside triphosphate 5′-d(CpGpCpG) in a water-salt solution is studied by one- and two-dimensional¹H NMR spectroscopy (500 MHz). Two-dimensional PMR spectroscopy (2D-COSY and 2D-NOESY) is used for the full assignment of proton signals of the molecules in the solution and for the qualitative analysis of the interaction between ethidium bromide and the tetranucleotide. The concentration dependences of the proton chemical shifts of the molecules at a fixed temperature (T=308 K) are measured. Different schemes of the formation of the dye complexes with the tetranucleotide, taking into account various molecular associations in the solution are considered. The equilibrium constants of the reactions and the limiting chemical shifts of ethidium bromide protons in the complexes are determined. The relative contents of different complexes in the solution are analyzed, and the dynamic equilibrium is studied as a function of the dye-tetranucleotide ratio in the solution. The data obtained suggest that ethidium bromide (like the acridine dye proflavine) is intercalated predominantly into the pyrimidine-purine sections (CG sites) of the tetranucleotide duplex. However, ethidium bromide is intercalated on the side of the narrow slot of the duplex, while proflavine intercalation occurs through the broad slot of the double helix. The most likely structures of the 1∶2 and 2∶2 dye-tetranucleotide complexes in the solution are constructed using the calculated values of the induced chemical shifts of ethidium bromide protons and 2D NOESY spectroscopy data. Sevastopol State Technical University. Berkbeck College, London University. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 1, pp. 75–87, January–February, 1996. Translated by I. Izvekova