Dielectric investigations of associate formation process in thin nitrobenzene interlayers formed between metal substrates

Studies of thickness and temperature dependencies of the dielectric susceptibility of nitrobenzene interlayers formed on conductive substrates were carried out. The obtained data were processed under the assumption of the existence of dimers (with opposite directions of molecular dipole moments) in orientationally ordered wall-adjacent layers. The results were treated on the basis of Lifshits theory.     

Line graphs of bipartite graphs with Hamiltonian paths

It is shown that, if t is an integer ≥3 and not equal to 7 or 8, then there is a unique maximal graph having the path P_t as a star complement for the eigenvalue ?2. The maximal graph is the line graph of K_m,m if t = 2m?1, and of K_m,m+1 if t = 2m. This result yields a characterization of L(G ) when G is a (t + 1)‐vertex bipartite graph with a Hamiltonian path. The graphs with star complement P_r ∪ P_s or P_r ∪ C_s for ?2 are also determined. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 137–149, 2003     

Acoustic waves in random fields

The effect of space- and time-dependent random mass density, velocity, and pressure fields on frequencies and amplitudes of acoustic waves is considered by means of the analytical perturbative method. The analytical results, which are valid for weak fluctuations and long wavelength sound waves, reveal frequency and amplitude alteration, the effect of which depends on the type of random field. In particular, the effect of a random mass density field is to increase wave frequencies. Space-dependent random velocity and pressure fields reduce wave frequencies. While space-dependent random fields attenuate wave amplitudes, their time-dependent counterparts lead to wave amplification. In another example, sound waves that are trapped in the vertical direction but are free to propagate horizontally are affected by a space-dependent random mass density field. This effect depends on the direction along which the field is varying. A random field, which varies along the horizontal direction, does not couple vertically standing modes but increases their frequencies and attenuates amplitudes. These modes are coupled by a random field which depends on the vertical coordinate, but the dispersion relation remains the same as in the case of the deterministic medium.     

Puzzles in astrophysics in the past and present

About 400 years have passed since the great discoveries by Galileo, Kepler, and Newton, but astronomy still remains an important source of discoveries in physics. They start with puzzles, with phenomena difficult to explain, and phenomena which in fact need new physics for explanation. Do such puzzles exist now? There are at least three candidates: absence of absorption of TeV gamma radiation in extragalactic space (violation of Lorentz invariance?), absence of GZK cutoff in the spectrum of ultrahigh-energy cosmic rays (new particle physics?), tremendous energy (up to 10⁵⁴ erg) released in gamma ray bursts on a time scale of a second (collapsing stars or sources of a new type?). Do these puzzles really exist? A critical review of these phenomena is given.     

Derivations in Commutative Regular Algebras

Mathematical Notes -