Orderings of uniquely colorable hypergraphs

For a mixed hypergraph H=(X,C,D), where C and D are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’ such that every C∈C meets some class in more than one vertex, and every D∈D has a nonempty intersection with at least two classes. A vertex-orderx₁,x₂,…,x_n on X (n=|X|) is uniquely colorable if the subhypergraph induced by {x_j:1?j?i} has precisely one coloring, for each i (1?i?n). We prove that it is NP-complete to decide whether a mixed hypergraph admits a uniquely colorable vertex-order, even if the input is restricted to have just one coloring. On the other hand, via a characterization theorem it can be decided in linear time whether a given color-sequence belongs to a mixed hypergraph in which the uniquely colorable vertex-order is unique.     

Twin Paradox and the Logical Foundation of Relativity Theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND.     

Calculation of cyclodextrin-mediated enantiomer ratio shifting of racem norgestrel in aqueous solutions

Enantioselective solubility of rac-norgestrel was found in the presence of γ-cyclodextrin or hydroxypropyl-γ-cyclodextrin. In both cases the efficacious enantiomer was dissolved in greater extent. Calculating the molar absorptivity and molar ellipticity spectra of the γ- and hydroxypropyl-γ-cyclodextrin aqueous complexes, a simple and rapid direct circular dichroism (CD) spectrometric method was obtained for the determination of the enantiomer ratio in aqueous solutions.     

An additive problem in the Fourier coefficients of cusp forms

 We establish an estimate on sums of shifted products of Fourier coefficients coming from holomorphic or Maass cusp forms of arbitrary level and nebentypus. These sums are analogous to the binary additive divisor sum which has been studied extensively. As an application we derive, extending work of Duke, Friedlander and Iwaniec, a subconvex estimate on the critical line for L-functions associated to character twists of these cusp forms. Received: 2 October 2001 / Revised version: 9 September 2002 / Published online: 28 March 2003 Mathematics Subject Classification (2000): Primary 11F30, 11F37; Secondary 11M41.     

Liquid phase oxidation of alcohols with oxygen: in situ monitoring of the oxidation state of Bi-promoted Pd/Al2O3

In situ, time-resolved XAS studies on a Bi-Pd/Al2O3 catalyst indicate that Pd, and Bi located on the Pd surface, are in a reduced, metallic state during the oxidation of 1-phenylethanol with molecular oxygen--a key for understanding the role of promoter in the reaction mechanism.     

Unexpected valence bond isomerization of [1,2,4]triazolo[3,4-c][1,2,4]benzotriazines under flash vacuum pyrolytic (fvp) conditions

Flash vacuum pyrolysis (fvp) of some substituted [1,2,4]triazolo[3,4-c][1,2,4]benzotriazine derivatives (1a-d) has been studied between 450 and 600 °C. The only transformation observed up to 525 °C was the unexpected valence bond isomerization of the angularly fused starting compounds to the isomeric linearly fused [1,2,4]triazolo[4,3-b][1,2,4]benzotriazine derivatives (9a-d), whereas at higher temperatures fragmentation products such as aromatic nitriles were also formed. Kinetic measurements revealed negative entropies of activation in the isomerization process, which suggest a concerted ring closure reaction to an intermediate antiaromatic diazirine. Reversibiblity of the title isomerization reaction was also proved by FVP experiments.     

A fluorescent molecular imaging probe with selectivity for soluble tau aggregated protein

Soluble forms of aggregated tau misfolded protein, generally termed oligomers, are considered to be the most toxic species of the different assembly states that are the pathological components of neurodegenerative disorders. Therefore, a critical biomedical need exists for imaging probes that can identify and quantify them. We have designed and synthesized a novel fluorescent probe, pTP-TFE for which binding and selectivity profiles towards aggregated tau and Aβ proteins were assessed. Our results have shown pTP-TFE to be selective for early forms of soluble tau aggregates, with high affinity of dissociation constants (K_d) = 66 nM, and tenfold selectivity over mature tau fibrils. Furthermore, we found that pTP-TFE is selective for tau over Aβ aggregates and had good cell permeability. This selectivity of pTP-TFE towards early forms of aggregated tau protein ex vivo was also supported with studies on human brain tissue containing tau and Aβ pathology. To the best of our knowledge, this is the first fluorescent molecule to be reported to have this form of selectivity profile, which suggests that pTP-TFE is a unique probe candidate for imaging-based detection of early stages of Alzheimer''s disease and other tauopathies.

pTP-TFE imaging probe can distinguish soluble tau aggregated proteins from other aggregated proteins enabling earlier detection of neurodegenerative diseases.     

Copper(II) complexes of N-terminal protected tri- and tetra-peptides containing histidine residues

Copper(II) complexes of peptides containing two or three histidyl residues (Ac-HisGlyHis-OH, Ac-HisGlyHis-NHMe, Ac-HisHisGlyHis-OH and Ac-HisHisGlyHis-NHMe) have been studied by potentiometric, UV-Vis, EPR and CD spectroscopic measurements. The imidazole nitrogen atoms are described as the primary metal binding sites of all ligands resulting in the formation of various macrochelates in the pH range 4 to 7. The (Nim, N-, Nim)-co-ordinated [CuH-1L]0+ complexes were mainly detected in samples containing free carboxylates at the C-termini, whilst the [CuH-2L]-(0) complexes were the predominant species in slightly alkaline solution and their binding modes were described via 4N-co-ordination (Nim, N-, N-, Nim) in (7,5,6)-membered fused chelate rings. Deprotonation and co-ordination of the third amide nitrogens were detected above pH approximately 9 in all cases.     

Oxygen quenching of tris(2,2′-bipyridine) ruthenium(II) complexes in thin organic films

A study is presented of the quenching, by oxygen, of the luminescence of tris(2,2′-bipyridine) ruthenium(II) complexes immobilized in thin, transparent, polymer-based films. The film media consist of a water-insoluble linear polymer plasticized with a trialkylphosphate ester, in which the complex ruthenium cations are solubilized by ion pairing with organophilic anions such as tetraphenylborate.

Luminescence lifetimes were studied in relation oxygen concentration in a gas stream contiguous with the film medium, film thickness and concentration of the metal complex within the film medium. It is shown that the microheterogeneous environment of the luminescent complex, which has recently been implicated in the non-linear quenching responses of polymer-immobilized, transition metal complex oxygen sensors, may arise simply as a consequence of the limited solubility of the complex in the film medium. When solubility is limited, the partial precipitation of the complex results in a colloidal of luminescent particles which exhibit non- uniform susceptibilities to quenching by oxygen. Good solubility, and therefore linear quenching characteristics, are promoted by methyl substitution of the bipyridyl ligand and by use of a plasticizer (tributylphosphate) with marked cation solvating powers.