Wave optics of Liesegang rings

Liesegang rings refract and reflect at the interface between the regions of the same gel but of different thickness. The incident and the refracted rings obey a refraction law analogous to the Snell's law of classical optics, with a reverse of the spacing coefficient being a counterpart of the refraction index. The wavelike behavior of the rings at the interface is explained by geometrical arguments derived from the Jablczynski's spacing principle, and is reproduced in numerical simulations based on a three-dimensional minimalistic version of the nucleation-growth model.     

Iron and copper complexes of tetraphenyl-m-benziporphyrin: reactivity of the internal C-H bond

Iron and copper complexes of tetraphenyl-m-benziporphyrin (TPmBPH)H have been prepared and structurally characterized. The iron system, (TPmBPH)Fe(II)Br, contains a high-spin Fe(II) center. In the solid state the complex forms dimeric units linked by weak CH.Br hydrogen bonds. The Cu complex contains a tetrameric copper cluster with a Cu(2)Cl(4)(2)(-) unit bridging two [(TPmBPCl)Cu(II)](+) fragments. The formation of (TPmBPCl)H represents an example of copper-catalyzed chlorination on the internal carbon atom of (TPmBPH)H.     

Degrees of logics with Henkin quantifiers in poor vocabularies

We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L–tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L* is of degree 0. We show that the same holds also for some weaker logics like L(H) and L(E). We show that each logic of the form L^(k)(Q), with the number of variables restricted to k, is decidable. Nevertheless – following the argument of M. Mostowski from [Mos89] – for each reasonable set theory no concrete algorithm can provably decide L^(k)(Q), for some (Q). We improve also some results related to undecidability and expressibility for logics L(H₄) and L(F₂) of Krynicki and M. Mostowski from [KM92].Mathematics Subject Classification (2000): 03C80, 03D35, 03B25Revised version: 28 August 2003     

Vortex fluctuations in underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) crystals

Vortex thermal fluctuations in heavily underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) (T(c)=69.4 K) are studied using Josephson plasma resonance. From the zero-field data, we obtain the c-axis penetration depth lambda(L,c)(0)=230+/-10 micrometer and the anisotropy ratio gamma(T). The low plasma frequency allows us to study phase correlations over the whole vortex solid state and to extract a wandering length r(w) of vortex pancakes. The temperature dependence of r(w) as well as its increase with dc magnetic field is explained by the renormalization of the vortex line tension by the fluctuations, suggesting that this softening is responsible for the dissociation of the vortices at the first order transition.     

Synthesis of twist-twist pi-conjugated di-sec-alkylstilbenes and stilbene polymers

Twist-twist pi-conjugated (TTPC) pi systems promise unique properties with their 90 degrees twist angles. Di-sec-alkyl substituted stilbenes, 5, were prepared by low-valent titanium coupling of phenyl ketones, 4. Long alkyl chains stopped the coupling reaction. Stilbenes 5 were shown to be approximately 90% TTPC. Inserting TTPC units into poly(p-phenylene) polymers created highly fluorescent, soluble, TTPC pi systems with weak electronic segmentation for organic light emitting diode (OLED) studies.     

A numerical test of analytical methods for reduction of IR and MW spectra of NaCl chi1sigma+ to parameters of radial functions

Two methods for direct inversion of IR and MW spectra of diatomic molecules--a deformational self-consistent procedure (DS-cP) and a computer program RADIATOM based on hypervirial perturbation theory are tested numerically. The test calculations for NaCl chi1sigma+ confirm that the RADIATOM program does not produce sufficiently accurate radial parameters and energy term values for their export to other utilities employed in the spectral analysis of diatomic systems.     

The Gold Partition Conjecture for 6-Thin Posets

We consider the Gold Partition Conjecture (GPC) that implies the 1/3–2/3 Conjecture. We prove the GPC in the case where every element of the poset is incomparable with at most six others. The proof involves the extensive use of computers. This paper contains results obtained using computer resources of the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM), University of Warsaw.     

Die Destillation von Ammoniak bei der Stickstoffbestimmung

Ohne Zusammenfassung