Avoided level crossings and singular points

Avoided crossings of discrete states as well as of resonance states are traced back to the existence of branch points (BPs) which are singular points in the complex energy plane. They cannot be identified with exceptional points. At a BP width bifurcation occurs, different Riemann sheets evolve and the levels do not cross anymore when the system is still further opened. The BPs are physically meaningful: they influence the dynamics of open as well as of closed quantum systems. The geometric phase that arises by encircling a BP, is different from the phase that appears by encircling a diabolic point. This is found to be true even for the two BPs into which the diabolic point is unfolded by opening the system. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Stabilization of the Cauchy problem for integro-differential equations

In the present paper, we obtain a criterion for the stabilization of the Cauchy problem for an integro-differential equation in the class of functions of polynomial growth γ ≥ 0. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1571–1576, November, 2005.     

Stability of relative equilibria. Part I: The reduced energy-momentum method

Communicated by P.Holmes     

Carbon-13 spectral analysis,tautomeric structures and conformations of four two-ring methylene-bridged phloroglucinol derivatives

The ¹³C NMR spectra of phloropyron BB, desaspidin BB, albaspidin BB and margaspidin BB were recorded and the structures of the compounds investigated with the aid of chemical shifts and CH coupling constants. The filicinic acid ring of the first three compounds appeared to have a monoketonic structure with the carbonyl group in position 2 (acyl group in position 3). The pyronone ring of phloropyron BB also has a monoketonic structure, with the carbonyl function adjacent to the ring oxygen. The two rings of the first three compounds attain a conformation where a stabilizing hydrogen bond(s) is (are) formed between the two rings, as shown by the observed CH couplings to some of the hydroxyl protons. The spectrum of margaspidin BB, whichconsists of two aromatic acyl phloroglucinol rings, indicates less inter-ring hydrogen bonding interactions.     

Ionic conductivity of crystalline and glassy Mg4.5Na7(P2O7)4

In our work single crystals of Mg_4.5Na₇(P₂O₇)₄ were prepared, pulverized, pressed into pellets and sintered in order to measure the electrical conductivity of polycrystalline specimens. The conductivity was also measured on glassy specimens obtained by the melting of previously prepared crystals. The electrical conductivities at 25°C with values of the order of 10⁻¹⁶ Ω⁻¹ cm⁻¹ for polycrystalline samples and a value of the order of 10⁻¹⁴ Ω⁻¹ cm⁻¹ for glass, show that the glassy phase of Mg_4.5Na₇(P₂ because of its greater molar volume and loosely packed structure, is a better matrix for ionic motion.