Note on regular subgraphs

Let f(n, γ) denote the largest integer r such that any graph G on n vertices with γn² edges contains an r-regular subgraph. In this paper we prove that © 1997 John Wiley & Sons, Inc.     

Non-Covalent Interactions in the Biphenyl Crystal: Is the Planar Conformer a Transition State?

A combined experimental and theoretical study of the biphenyl (BP) crystal is presented. The X-ray diffraction data collected at 100 K were subjected to Hirshfeld atom and multipole refinements of the electron density, ρ(r). A theoretical exploration of the potential energy surface (PES) of the crystal was also carried out. This investigation challenges the common assumption that the planar structure of BP in the phase I crystal is an average of two twisted configurations in a double-well potential. The theoretical computations provide compelling evidence that this structure corresponds to a minimum on the PES hence to a stable molecular arrangement. Consistently, the experiment showed no evidence of positional or dynamic disorder. The intramolecular hydrogen-hydrogen bonds detected are not repulsive. The topological analysis of the experimental and theoretical ρ(r) reveals that both the intra- and intermolecular H⋅⋅⋅H and the C−H⋅⋅⋅π contacts stabilize the BP crystal.     

Divisibility classes are seldom closed under flat covers

We show that the class of all divisible modules over an integral domain R is closed under flat covers if and only if R is almost perfect. Also, we show that if the class of all s-divisible modules, where s is a regular element of a commutative ring R, is closed under flat covers then the quotient ring $R/sR$ satisfies some rather restrictive properties. The question is motivated by the recent classification [11] of tilting classes over commutative rings.     

Linear and Multi-Photon Fluorescence of Thiophene Based Copolymer with Electron-Accepting Side Chains

A novel copolymer poly(thiophene-2,5-diyl-2,5-di-n-octyloxycarbonyl-1,4-phenylene), denoted as P33, is introduced as potential material for photovoltaics, polymer light-emitting diodes, and/or organic transistors. P33 dissolved in chloroform is investigated by steady-state absorption, linear/non-linear fluorescence spectroscopies and time-resolved fluorescence spectroscopy. Molar extinction coefficient, fluorescence quantum yield, and singlet fluorescence lifetime of P33 are determined to be 18,315 M^?1 cm^?1, 0.4, and 810 ps, respectively. The P33 fluorescence fast components of decay times are 1.2 ps, 2.0 ps, and 0.5 ps for increasing wavelengths of 480 nm, 500 nm, and 520 nm, respectively. The fast component is attributed to a transport of nearly instantaneously formed excitons to localized states known as downhill energy transfer. Additionally multi-photon excited fluorescence is observed for pumping with wavelengths of 800 nm and 1200 nm. Two-photon absorption cross-section is determined to be 6.9 GM. These spectroscopic studies provide basic fluorescence characteristics of the novel thiophene copolymer P33.     

Effect of nonadiabaticity on the Fermi-edge photoemission and tunneling spectra of superconductors

Temperature dependence of the experimental photoemission spectra of the high-T_c superconductors have been interpreted and simulated by the recently formulated molecular nonadiabatic theory of the electron-vibrational interaction. The change of the spectral feature below T_c, particularly formation of the narrow, near Fermi surface (FS) edge, peak separated by the dip from a broad spectral band at higher binding energies has been shown to be the consequence of the nonadiabatic electron-phonon coupling and corresponding properties of the nonadiabatic polarons. Simulation yields very good fit to the experimental temperature-dependent spectra, with the calculated value of the gap 30.5 meV. © 1996 John Wiley & Sons, Inc.     

On p-intersection representations

For a graph G = (V,E) and integer p, a p-intersection representation is a family F = {S_x: × E V} of subsets of a set S with the property that |S_u ∩ S_ν| ≥ p ∩ {u, ν} E E. It is conjectured in [1] that θ_p(G) ≤ θ (K_n/2,n/2) (1 + o(1)) holds for any graph with n vertices. This is known to be true for p = 1 by [4]. In [1], θ (K_n/2,n/2) ≥ (n² + (2p− 1n)n)/4p is proved for any n and p. Here, we show that this is asymptotically best possible. Further, we provide a bound on θp(G) for all graphs with bounded degree. In particular, we prove θp(G) ≤ O(n^1/p) for any graph Gwith the maximum degree bounded by a constant. Finally, we also investigate the value of θ_p for trees. Improving on an earlier result of M. Jacobson, A. Kézdy, and D. West, (The 2-intersection number of paths and bounded-degree trees, preprint), we show that θ₂(T) ≤ O(d√n) for any tree T with maximum-degree d and θ₂(T) ≤ O(n^3/4) for any tree on n vertices. We conjecture that our results can be further improved and that θ₂(T) ≤ O(d√n) as long as Δ(T) ≤ √n. If this conjecture is true, our method gives θ₂(T) ≤ O(n^3/4) for any tree T which would be the best possible. © 1996 John Wiley & Sons, Inc.     

Effect of drying methods on the content of natural pigments and antioxidant capacity in extracts from medicinal plants: a spectroscopic study

Medicinal plants are a significant source of biological active and health protective compounds. Post-harvest treatments can affect, in different ways, the content and biological activity of such compounds. One of the most common post-harvesting methods is drying. In this study, we investigated the effect of drying method on the content of natural pigments (chlorophylls, carotenoids and anthocyanins) and on the antioxidant capacity of two traditionally used herbs, the Melissa officinalis (lemon balm) and the Urtica dioica (stinging nettle) both of them landraces collected from plants grown in Nitra region, West of Slovakia. The freeze-dried samples of both herbs exhibited the highest content of chlorophyll a (7.55 ± 0.13 mg/g dry mass for lemon balm and 9.41 ± 0.17 mg/g dry mass for stinging nettle), chlorophyll b (3.12 ± 0.28 mg/g dry mass for lemon balm and 3.34 ± 0.24 mg/g dry mass for stinging nettle) and carotenoids (2.11 ± 0.24 mg/g dry mass for lemon balm and 2.62 ± 0.06 mg/g dry mass for stinging nettle). The content of chlorophylls and carotenoids correlated with the DPPH antioxidant (radical scavenging) capacity. Higher antioxidant capacity of the lemon balm extracts compared to nettle samples was attributed to the higher content of polyphenol compounds anthocyanins. Despite the higher cost, the freeze drying (lyophilisation) was recommended as the most suitable drying method, mainly for reasons of preserving maximum pigment content and antioxidant capacity.     

Regularly weakly based modules over right perfect rings and Dedekind domains

A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contains a weak basis. We study

1. (1)
   rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and
    
2. (2)
   regularly weakly based modules over Dedekind domains.