On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem. *Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2. Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA.     

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.     

Preparation of a novel molecularly imprinted polymer using a water-soluble crosslinking agent

A molecularly imprinted polymer was prepared using a water-soluble crosslinking agent. An ionic complex was utilized as the assembly for the template molecule and the functional monomer, and water as porogenic solvent during preparation of the imprinted polymer. The results of chromatographic evaluations for the prepared polymer suggested that the polymer had much lower hydrophobicity compared with usual octadecyl group bonded silica or the usual molecular imprinted polymer prepared from ethyleneglycol dimethacrylate, and the selective recognition ability for template molecule in the completely aqueous condition.     

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.     

Synthesis and characterization of oligo-4-[(pyridin-3-ylimino)methyl]phenol

The oxidative polycondensation of 4-[(pyridin-3-ylimino)methyl]phenol (4-PIMP) with O₂, H₂O₂, and NaOCl was studied in an aqueous alkaline medium between 50°C and 90°C. Oligo-4-[(pyridin-3-ylimino)methyl]phenol (O-4-PIMP) prepared was characterized by ¹H-NMR, ¹³C-NMR, FT-IR, UV-VIS, size-exclusion chromatography, and elemental and thermal analyses techniques. At the optimum reaction conditions, the yield of O-4-PIMP was 18.9%, 39.4%, and 46.8% using H₂O₂, O₂, and NaOCl oxidant, respectively. According to the TG analysis, the initial degradation temperature of O-4-PIMP was 218°C, which was by 50°C higher than that of 4-PIMP. Thermal analyses of 4-PIMP and O-4-PIMP were carried out in N₂ atmosphere at 15–1000°C. The highest occupied molecular orbital, the lowest unoccupied molecular orbital, and electrochemical energy gaps of 4-PIMP and O-4-PIMP were determined from the onset potentials for n-doping and p-doping, respectively. Also, optical band gaps of 4-PIMP and O-4-PIMP were determined according to UV-VIS measurements.