Global solutions of the Laplace equation with a nonlinear dynamical boundary condition

We study the boundedness and a priori bounds of global solutions of the problem Δu=0 in Ω×(0, T), (∂u/∂t) + (∂u/∂ν) = h(u) on ∂Ω×(0, T), where Ω is a bounded domain in ℝ^N, ν is the outer normal on ∂Ω and h is a superlinear function. As an application of our results we show the existence of sign-changing stationary solutions. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.     

Biodegradable hybrid polymer films based on poly(vinyl alcohol) and collagen hydrolyzate

Hybrid blends of poly(vinyl alcohol) (PVA) and collagen hydrolyzate (CH), an added value waste from leather indutry, have been converted by blown molding extrusion, to environmentally degradable films. Blown extruded films comprising 5-15% of CH, were tested as sel fertilizing mulching films and analyzed for their propensity to enviromental degradation. PVA/CH films rapidly disintegrate when buried in soil, and resulted promising for application such as transplanting films, with additional fertilizing action of CH.     

A new approach to nickel electrolytic colouring of anodised aluminium

Energy dispersive X-ray spectroscopy and scanning electron microscopy were used to analyse nickel on anodic aluminium surfaces after stripping the anodic aluminium oxide. The metal was electroplated at the bottom of the pores of anodised aluminium during electrolytic colouring in solutions without (Watts) and with (citrate) complexing agents, respectively. A relation between the anodic-cathodic processes, changes of the structure and composition of the coating in dependence on the used solution were studied. A morphology study performed after stripping the anodic aluminium oxide revealed the crucial influence of the anodic process/cycle and the complexing agent on the nickel structure on the aluminium surface. Off-time of half-way rectified current influenced the nickel deposition in the pores of anodic alumina negatively.     

On complexity of round transformations

A modern block cipher consists of round transformations, which are obtained by alternatively applying permutations (P-boxes) and substitutions (S-boxes). Clearly, the most important attribute of a block cipher is its security. However, with respect to the hardware implementation, a good block cipher has to have a reasonable complexity as well. In this paper, we study complexity of round transformations satisfying some basic security criteria. There are several ways to define the complexity of a round transformation, and to choose “necessary” security criteria. It turns out, that for our purpose, it is suitable to view a round transformation as a single Boolean function, not separating it into S-boxes and P-boxes. We require that the Boolean function F possesses some fundamental properties imposed on each block cipher for security reasons; namely, we require that the function is a strictly non-linear bijection and that it has a good diffusion. The total number of variables in the normal algebraic form of the component functions of F is taken as its complexity. We find the minimum complexity of such functions, and this way we establish a lower bound on complexity of all round transformations. To show that the lower bound is the best possible, we construct a round transformation F^′ attaining the bound. We stress that it is not an aspiration of this paper to construct a round transformation which would be of practical use; F^′ is useful only from the theoretical point of view.     

Peculiarities of the Interaction of Short Oligonucleotides with Supported Lipid Films and Langmuir Monolayers

Summary.  The method of electrostriction was applied to supported bilayer lipid membranes (sBLM) and Langmuir monolayers with the aim to study the peculiarities of the interaction of short oligonucleotides with lipid films and of the duplex formation between complementary oligonucleotides. The bilayer lipid membranes (sBLM) were formed on an agar support, whereas Langmuir monolayers were generated on the air-water interface. As an oligonucleotide, the 15-mer 5^′-cholesterolphosphoryl-dT15 (CHpdT15) was synthesized. We could show that the interaction of CHpdT15 with sBLM resulted in a considerable increase of the elasticity modulus perpendicular to the membrane plane (E _⊥) and an increase of the surface potential. Interaction of complementary oligodeoxyadenylate (dA15) with sBLM modified by CHpdT15 resulted in a slight increase of the surface potential whereas E _⊥ slightly decreased. CHpdT15 forms monomolecular layers on the air/water interface. Interaction of dA15 with such monolayers resulted in an increase of the surface pressure, probably due to an increase of the surface charge of the monolayer; similar effects were observed for lipid monolayers modified by CHpdT15. Prospects of using such interactions for detecting DNA hybridization are discussed. Received June 23, 2000. Accepted (revised) September 19, 2000     

Acidity of montmorillonite pillared by alumina, zirconia and chromia

Acidic properties of Al-, Zr- and Cr- pillared montmorillonites prepared from Jelšovy Potok bentonite (Central Slovakia) have been investigated using temperature-programmed desorption of ammonia. The number of acid sites varied with different interlayer cations from 0.06 to 0.23 mmol g⁻¹. The character of acid sites was similar in the case of Al- and Zr- forms. It is obvious that the chromium analogue contains fewer acid sites, nevertheless, they seem to be stronger compared to Al- and Zr- pillared montmorillonites.     

Electronic phase transitions in the spinless Falicov-Kimball model

We have studied thedV/dI vs.V characteristics of point contacts between the heavy fermion superconductor URu₂Si₂ and the conventional superconductors Zn and NbTi. Contacts between URu₂Si₂ and Zn do not show Josephson effects; instead Andreev reflection type structures occur, which are related to both, the heavy fermion and the conventional superconductor. In contrast, contacts between URu₂Si₂ and NbTi become superconducting at low currents. A closed-loop setup with two NbTi contacts on URu₂Si₂ showed SQUID oscillations in a small magnetic field. Our data give evidence that the contacts should be described as superconductor/normal/superconductor junctions with a thick normal layer on the URu₂Si₂ side of the contact with proximity induced superconductivity in theN-layer in the case of NbTi. With such a model the occurrence or absence of superconductivity can be explained and also the suppression of Andreev-scattering which is frequently observed for contacts between heavy fermion superconductors and normal metals.     

The two-dimensional Falicov-Kimball model at finite temperatures: numerical studies

The finite temperature properties of the spinless Falicov-Kimball model are studied in two dimensions using small-cluster exact-diagonalization calculations. The resultant exact solutions are used to examine the f-state occupation (n _f), the specific heat (C) and the density of doubly occupied sites (d) as functions of temperature (τ), f-level energy (E _f) and the interaction strength U. A number of remarkable results are found. (i) In all cases nf and d are smooth functions of τ and E _f. No discontinuous transitions occur at finite temperatures. (ii) The specific-heat curves exhibit a broad single-peak structure of Shottky form (‖E _f‖ large), as well as a two-peak structure consisting of a sharp peak of Ising type followed by a broad peak of Shottky type (‖E _f‖ small). (iii) The specific-heat coefficient is extremely enhanced at low temperatures for some values of E _f. (iv) Depending on a range of parameters used, the system exhibits intermediate-valence behavior as well as some features of heavy-fermion behavior. The results are independent of the size of clusters for a wide range of parameters and can be used to interpret much of the experimental data of rare-earth compounds. Finally, the f-electron density-density correlation functions are calculated and the U-dependence of the critical temperature is discussed.     

Network formation of a phenyl vinyl ketone copolymer with 4-vinylbenzil and its photodecrosslinking in films

The irradiation (λ > 400 nm) in air of a copolymer of phenyl vinyl ketone with 4-vinylbenzil (VBZ) containing 1.5 wt % VBZ structural units in film, followed by the thermal decomposition of the resulting pendant benzoyl peroxide groups, leads to crosslinking. The subsequent irradiation of the crosslinked polymer at 366 nm results in the cleavage of the poly(phenyl vinyl ketone) chain between the junction points of the polymer network through a Norrish type II reaction. Therefore, poly(phenyl vinyl ketone-co-4-vinylbenzil) represents a novel type of photoresist based on polymer network decrosslinking. The process involves three steps: photogeneration of peroxide, crosslinking by its thermal decomposition, and subsequent photodecrosslinking of the polymer network. This material provides positive-tone images after UV exposure (λ > 330 nm) and development in an organic medium such as isopropyl methyl ketone. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 765–771, 2004