Aspects of proton transport in calix[6]arene sulfonic acid

The features of proton transport and proton hydration shell structure of calix[6]arene sulfonic acid were studied. XRD and NMR data indicate the existence of crystalline and amorphous phases and various conformations in the acid structure. The hydration process occurs in three stages by thermal analysis and IR spectroscopy. The change in the composition of the hydrate affected the conductivity only at low humidity; an inverse relationship between the water uptake and the activation energy of conductivity is observed in the entire investigated range of humidity.     

Encapsulation of a guest sodium cation by iron(III) tris-(hydroxamate)s

An unprecedented encapsulation of an exogenous sodium ion by iron(III) tris(hydroxamate)s was observed upon crystallization of an iron(III) complex with isonicotinylhydroxamic acid. The sodium cation is bound by bridging coordination of the amide oxygen atoms from two mononuclear iron(III) fac-tris(hydroxamate)s.     

On non-normal arc-transitive 4-valent dihedrants

Let X be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group Dn such that X is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within Dn. It is shown that X is isomorphic either to the lexicographic product Cn[2K1] with n 〉 4 even, or to one of the five sporadic graphs on 10, 14, 26, 28 and 30 vertices, respectively.     

Constrained topological degree and positive solutions of fully nonlinear boundary value problems

In the first part of the paper we provide a construction of an abstract homotopy invariant detecting zeros of maps of the form −A+F where is a densely defined m-accretive operator in a Banach space E and is a tangent field defined on an open subset U of a neighborhood retract M being invariant with respect to the resolvents of A. The construction is performed under the assumption that resolvents of A are completely continuous. In the second part we derive index formulae for isolated zeros and apply them to show the existence of nontrivial positive steady state solutions for a class of nonlinear reaction-diffusion equations and equations with one-dimensional p-Laplacian with possibly non-positive perturbations as well as some controlled Neumann-like problems.     

Tempered relaxation with clustering patterns

This work is motivated by the relaxation data for materials which exhibit a change of the relationship between the fractional power-law exponents when different relaxation peaks in their dielectric susceptibility are observed. Within the proposed framework we derive a frequency-domain relaxation function fitting the whole range of the two-power-law dielectric spectroscopy data with independent low- and high-frequency fractional exponents γ and −α, respectively. We show that this effect results from a contribution of different processes. For high frequencies it is determined by random stops and movement of relaxing components, and the low-frequency slope is caused by clustering in their temporal changes.     

Solitons generated by self-organization in bismuth germanium oxide single crystals during the interaction with laser beam

We present here the experimental, theoretical, and numerical investigations of Kerr solitons generated by self-organization in black and yellow high quality bismuth germanium oxide (Bi₁₂GeO₂₀) single crystals. A picosecond laser beam of increasing power induces competing cubic and quintic nonlinearities. The numerical evolution of two-dimensional complex cubic-quintic nonlinear Schrödinger equation with measured values of nonlinearities shows the compensation of diffraction by competing cubic and quintic nonlinearities of opposite sign, i.e., the self-generation and stable propagation of solitons. Experiments as well as numerical simulations show higher nonlinearity in the black Bi₁₂GeO₂₀ than in the more transparent yellow one.     

Recombination of hydrogen atoms on fine-grain graphite

The probability of recombination of hydrogen atoms on surfaces of fine-grain graphite EK98 was investigated as a function of surface roughness. The source of hydrogen atoms used in this experiment was weakly ionised plasma created with an inductively coupled radiofrequency generator at pressures from 30 Pa to 175 Pa in hydrogen. Hydrogen atom density was measured by means of fibre optic catalytic probes. The recombination coefficient of the graphite samples was determined by observing their impact on the spatial distribution of the atom density in a closed side-arm of the reactor. Smith's diffusion model was used to calculate the values of the recombination coefficient. The measured recombination coefficient was found to increase much faster than the measured effective surface. This discrepancy is explained by the fact that on a surface which is not perfectly flat, there is a finite probability for multiple collisions. Impinging atoms collide more than once with the surface before they are reflected into the surface, which results in a larger probability of recombination.     

Cores,cutsets and the fixed point property

The purpose of this paper is the analysis and application of the concepts of a core (a pair of chains) and cutset in the fixed point theory for posets. The main results are:

1. (Theorem 3) If P is chain-complete and (*), it contains a cutset S such that every nonempty subset of S has a join or a meet in P, then P has the fixed point property (FPP),
2. (Theorem 5) If P or Q is chain-complete, Q satisfies (*) and both P and Q have the FPP, then P x Q has the FPP.
3. (Theorem 6) Let P or Q be chain-complete and there exist p∈P and a finite sequence f ₁, f ₂, ..., f _n of order-preserving mappings of P into P such that $$\left( {\forall x\varepsilon P} \right)x \leqslant f_1 \left( x \right) \geqslant f_2 \left( x \right) \leqslant \cdots \geqslant f_n \left( x \right) \leqslant p$$ If P and Q have the FPP then P x Q has the FPP.
4. (Theorem 7) If T is an ordered set with the FPP and {P _t :t∈T} is a disjoint family of ordered sets with the FPP then its ordered sum ∪{P _t :t∈T} has the FPP.

     

On the error term in the mean square formula for the Riemann zeta-function in the critical strip

For 1/2<<1 fixed, letE (T) denote the error term in the asymptotic formula for . We obtain some new bounds forE (T), and an _-result which is the analogue of the strongest _-result in the classical Dirichlet divisor problem.