A simple proof of Sanov’s theorem*

A simple self-contained proof of Sanov's theorem in τ-topology is given, well suited for a first course on large deviations. *This work was supported by the Hungarian National Foundation for Scientific Research under Grant T046376     

Multiple recurrence and nilsequences

Aiming at a simultaneous extension of Khintchine(X,X,m,T)(X,\mathcal{X},\mu,T) and a set A ? XA\in\mathcal{X} of positive measure, the set of integers n such that A T^2nA T^knA)(A)^k+1-\mu(A{\cap} T^{n}A{\cap} T^{2n}A{\cap} \ldots{\cap} T^{kn}A)>\mu(A)^{k+1}-\epsilon is syndetic. The size of this set, surprisingly enough, depends on the length (k+1) of the arithmetic progression under consideration. In an ergodic system, for k=2 and k=3, this set is syndetic, while for kòf(x)f(Tⁿx)f(T²ⁿx)? f(T^knx)  dm(x)\int{f(x)f(T^{n}x)f(T^{2n}x){\ldots} f(T^{kn}x) \,d\mu(x)} , where k and n are positive integers and f is a bounded measurable function. We also derive combinatorial consequences of these results, for example showing that for a set of integers E with upper Banach density d^*(E)>0 and for all {n ? \mathbbZ\colon d^*(E?(E+n)?(E+2n)?(E+3n)) > d^*(E)⁴-e}\big\{n\in\mathbb{Z}{\colon} d^*\big(E\cap(E+n)\cap(E+2n)\cap(E+3n)\big) > d^*(E)^4-\epsilon\big\}     

Mimicking catalase and catecholase enzymes by copper(II)-containing complexes

An imidazolate-bridged copper(II)-zinc(II) complex (Cu(II)-diethylenetriamino-μ-imidazolato-Zn(II)-tris(2-aminoethyl)amine perchlorate (denoted as “Cu,Zn complex”) and a simple copper(II) complex (Cu(II)-tris(2-aminoethyl) amine chloride (“Cu-tren”) were prepared and immobilised on silica gel (by hydrogen or covalent bonds) and montmorillonite (by ion exchange). The immobilised substances were characterised by FT-IR spectroscopy and their thermal characteristics were also studied. The obtained materials were tested in two probe reactions: catalytic oxidation of 3,5-di-tert-butyl catechol (DTBC) (catecholase activity) and the decomposition of hydrogen peroxide (catalase activity). It was found that the catecholase activity of the Cu,Zn complex increased considerably upon immobilization on silica gel via hydrogen bonds and intercalation by ion exchange among the layers of montmorillonite. The imidazolate-bridged copper(II)-zinc(II) complex and its immobilised versions were inactive in hydrogen peroxide decomposition. The Cu(II)-tris(2-aminoethyl)amine chloride complex displayed good catalase activity; however, immobilisation could not improve it.     

X-ray investigation of the role of the mixed emulsifier in the structure formation in o/w creams

The aim of this research work was to clarify the role of the mixed emulsifier in the structure formation and water binding mode in the case of o/w creams prepared with different surfactants. The swelling behavior of mixed emulsifiers was examined by means of direct investigation methods such as transmission electron microscopy (TEM) and X-ray diffraction. The detailed structure image of the creams was created with the help of the latter. The influence of the structure of the hydrophilic gel phase, and the structural changes during storage were studied with rheological methods. On the basis of the results, it can be stated that the investigated creams had different structures from those mentioned in the literature: surfactant did not create a mixed bilayer with the structure to furnish fatty amphiphile; instead, micelles were formed. These results correlated well with the results of the rheological tests.     

Study of fragmentation pattern and adsorption of 9-O-(triphenylsilyl)-10,11-dihydrocinchonidine on platinum by hydrogen/deuterium exchange using electrospray ionization ion-trap tandem mass spectrometry

We have studied the adsorption on a platinum (Pt) catalyst of two compounds utilizable as a chiral basic catalyst and a chiral modifier, dihydrocinchonidine (DHCD), and a new cinchona alkaloid derivative containing a bulky group, the Ph3SiO-DHCD molecule. The method of choice was the detection by electrospray ionization (ESI) ion-trap tandem mass spectrometry (MS/MS) of hydrogen/deuterium (H/D) exchange at room temperature, in tetrahydrofuran, at a D2 pressure of 1 bar. Based on the ESI-MS/MS spectrum of the new compound, we propose a mechanism for the formation of the silatropylium cation containing a Si-O bond. From the fragmentation pattern of Ph3SiO-DHCD it was confirmed that ESI-ion-trap MS/MS can be used to study the adsorption processes of complicated carbon compounds by investigating their H/D exchange reactions. In the case of Ph3SiO-DHCD, the results demonstrate that H/D exchange takes place mainly on the quinoline skeleton. However, the strong pi-bonded adsorption of the quinoline skeleton parallel with the imaginary plane of Pt is not preferred because the bulky Ph3Si group inhibits the multiple pi-bonded adsorption of the Ph3SiO-DHCD. Because of this hindrance the molecule was adsorbed tilted via the nonbonding electron pair of the N atom and C2' atom of the quinoline skeleton; consequently, mainly alkaloid-d1 and alkaloid-d2 are formed.     

Relative stability of major types of beta-turns as a function of amino acid composition: a study based on Ab initio energetic and natural abundance data

Folding properties of small globular proteins are determined by their amino acid sequence (primary structure). This holds both for local (secondary structure) and for global conformational features of linear polypeptides and proteins composed from natural amino acid derivatives. It thus provides the rational basis of structure prediction algorithms. The shortest secondary structure element, the beta-turn, most typically adopts either a type I or a type II form, depending on the amino acid composition. Herein we investigate the sequence-dependent folding stability of both major types of beta-turns using simple dipeptide models (-Xxx-Yyy-). Gas-phase ab initio properties of 16 carefully selected and suitably protected dipeptide models (for example Val-Ser, Ala-Gly, Ser-Ser) were studied. For each backbone fold most probable side-chain conformers were considered. Fully optimized 321G RHF molecular structures were employed in medium level [B3LYP/6-311++G(d,p)//RHF/3-21G] energy calculations to estimate relative populations of the different backbone conformers. Our results show that the preference for beta-turn forms as calculated by quantum mechanics and observed in Xray determined proteins correlates significantly.     

Detection of Amadori compounds by capillary electrophoresis coupled to tandem mass spectrometry

Capillary electrophoresis coupled to mass spectrometry (CE-MS) is reported for the first time as an alternative and powerful analytical method for the characterization and monitoring of N-substituted 1-amino-1-deoxyketoses (Amadori compounds). It allows rapid separation and identification of Amadori compounds, while benefiting from the well-known advantages of MS, such as specificity and sensitivity. Amadori compounds of several amino acids, such as glycine, valine, isoleucine, methionine, proline, and phenylalanine, as well as a cysteine-derived compound, were separated and/or discriminated using CE-MS/MS under standard conditions. The technique may also be useful to study the stability and degradation kinetics of other labile charged Maillard intermediates that play an important role in food and medical science.     

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.     

Theoretical conformational analysis of a simple sulphilimine model

The topomerization (bond rotation andS-pyramidal inversion) of a simple sulphilimine model, H₂SNH has been studied with the aid ofab initio SCF MO calculations. The highest rotation barrier occurs when the H₂SN moiety is planar, < HSN = 120 °. The maxima of the inversion crossections occur at the planar conformation for all rotation angles α as expected, however, the minima belong to different values when α is varied. The minimum energy path between the two lowest minima of the conformational energy surface consists of a pure inversion section and a section which is mostly rotation. The optimum values of the < HSN bond angles are significantly smaller than the corresponding < RSN bond angles of sulphilimines of bulkierR substituents.     

A study of molecular one-electron properties in terms of localized molecular orbital components

A number of molecular one-electron progperties have been analyzed by partitioning their electronic components over energy localized molecular orbitals (LMO ). The ammonia and ethane molecules, calculated in an Approximately double zeta qualtiy basis set, were considered. The partitioning of the electronic components of certain one-electron properteies over LMO allows a quantitative rationalization of the sensitivity of certain properties to basis set effects due to the differeing degree of difficulty of accurately determining different LMO as measures of the molecular electron density.