Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation

Applying the method of normalized systems of functions we construct solutions of the generalized Dirichlet problem for the iterated slice Dirac operator in Clifford analysis. This problem is a natural generalization of the Dirichlet problem.

     

Open Sets Avoiding Integral Distances

We study open point sets in Euclidean spaces $\mathbb{R }^d$ R d without a pair of points an integral distance apart. By a result of Furstenberg, Katznelson, and Weiss such sets must be of Lebesgue upper density $0$ 0 . We are interested in how large such sets can be in $d$ d -dimensional volume. We determine the exact values for the maximum volumes of the sets in terms of the number of their connected components and dimension. Here techniques from diophantine approximation, algebra and the theory of convex bodies come into play. Our problem can be viewed as a counterpart to known problems on sets with pairwise rational or integral distances. It possibly opens a new research direction with strong links to topology and measure theory.     

Surprisingly slow reaction of dimethylsilylene with dimethylgermane: time-resolved kinetic studies and related quantum chemical calculations

Time-resolved studies of silylene, SiH2, and dimethylsilylene, SiMe2, generated by the 193 nm laser flash photolysis of appropriate precursor molecules have been carried out to obtain rate constants for their bimolecular reactions with dimethylgermane, Me2GeH2, in the gas phase. SiMe2 + Me2GeH2 was studied at five temperatures in the range 299-555 K. Problems of substrate UV absorption at 193 nm at temperatures above 400 K meant that only three temperatures could be used reliably for rate constant measurement. These rate constants gave the Arrhenius parameters log(A/cm3 molecule(-1) s(-1)) = -13.25 +/- 0.16 and E(a) = -(5.01 +/- 1.01) kJ mol(-1). Only room temperature studies of SiH2 were carried out. These gave values of (4.05 +/- 0.06) x 10(-10) cm3 molecule(-1) s(-1) (SiH2 + Me2GeH2 at 295 K) and also (4.41 +/- 0.07) x 10(-10) cm3 molecule(-1) s(-1) (SiH2 + MeGeH3 at 296 K). Rate constant comparisons show the surprising result that SiMe2 reacts 12.5 times slower with Me2GeH2 than with Me2SiH2. Quantum chemical calculations (G2(MP2,SVP)//B3LYP level) of the model Si-H and Ge-H insertion processes of SiMe2 with SiH4/MeSiH3 and GeH4/MeGeH3 support these findings and show that the lower reactivity of SiMe2 with Ge-H bonds is caused by a higher secondary barrier for rearrangement of the initially formed complexes. Full details of the structures of intermediate complexes and the discussion of their stabilities are given in the paper. Other, related, comparisons of silylene reactivity are also presented.     

Spectroscopic detection of DNA quadruplexes by vibrational circular dichroism

The four-stranded G-quadruplex motif is a conformation frequently adopted by guanine-rich nucleic acids that plays an important role in biology, medicine, and nanotechnology. Although vibrational spectroscopy has been widely used to investigate nucleic acid structure, association of particular spectral features with the quadruplex structure has to date been ambiguous. In this work, experimental IR absorption and vibrational circular dichroism (VCD) spectra of the model quadruplex systems d(G)(8) and deoxyguanosine-5'-monophosphate (5'-dGMP) were analyzed using molecular dynamics (MD) and quantum-chemical modeling. The experimental spectra were unambiguously assigned to the quadruplex DNA arrangement, and several IR and VCD bands related to this structural motif were determined. Involvement of MD in the modeling was essential for realistic simulation of the spectra. The VCD signal was found to be more sensitive to dynamical structural variations than the IR signal. The combination of the spectroscopic techniques with multiscale simulations provides extended information about nucleic acid conformations and their dynamics.     

Kinetics of swelling of polyether-modified poly(acrylic acid) microgels with permanent and degradable cross-links

Spherical particles of 50-100 mum size composed of poly(acrylic acid) networks covalently bonded to Pluronic polyether copolymers were tested for swelling in aqueous media. The microgels were cross-linked either by permanent ethylene glycol dimethacrylate (EGDMA) cross-links alone or by EDGMA together with reversible disulfide or biodegradable azoaromatic cross-links. Optimum conditions for a rapid, diffusion-limited swelling of the pH- and temperature-sensitive microgels with nondegradable cross-links were found. The microgels cross-linked by disulfide groups and equilibrium-swollen in the buffer solution exhibited degradation-limited kinetics of swelling under physiological conditions, with a first-order reaction constant, k(1), linearly proportional to the concentration of reducing agents such as dithiotreitol and tris(2-carboxyethyl)phosphine (TCEP). A severalfold faster swelling in the presence of more powerful reducing agent, TCEP, was observed, indicating the chemical specificity of the microgel swelling. The reoxidation of the thiol groups into disulfide cross-links by sodium hypochlorite led to the restoration of the microgels' diameter measured prior to the reduction-reoxidation cycle, which confirms the shape memory of the microgels. Enzymatically degradable azoaromatic cross-links enabled slow microgel swelling due to degradation of the cross-links by azoreductases from the rat intestinal cecum. The low rate of swelling of the Pluronic-containing microgels can enable sustained drug release in colon-specific drug delivery.     

Polyfunctional activity of metal complexes containing 2,6-Di-tert-butylphenol in catalytic oxidation

The results of the investigations of metal complexes containing 2,6-di-tert-butilphenol in the ligand environment in catalytic homogeneous oxidation of organic compounds are reviewed. The liquid-phase oxidation of hydrocarbons, olefins, aminophenol and unsaturated fatty acids by molecular oxygen in the presence of phthalocyanines, porphyrins, σ-aryl and π-allyl transition metal complexes is described. The change of the reactivity of organometallic and coordination compounds by oxidation of the redox active phenolic group opens up the possibility to use them as polyfunctional catalytic systems showing positive and/or negative catalytic effects.     

Electron Capture,Collision-Induced,and Electron Capture-Collision Induced Dissociation in Q-TOF

Recently, we demonstrated that a radio-frequency-free electromagnetostatic (rf-free EMS) cell could be retrofitted into a triple quad mass spectrometer to allow electron-capture dissociation (ECD) without the aid of cooling gas or phase-specific electron injection into the cell (Voinov et al., Rapid Commun Mass Spectrom 22, 3087–3088, 2008; Voinov et al., Anal Chem 81, 1238–1243, 2009). Subsequently, we used our rf-free EMS cell in the same instrument platform to demonstrate ECD occurring in the same space and at the same time with collision-induced dissociation (CID) to produce golden pairs and even triplets from peptides (Voinov et al., Rapid Commun Mass Spectrom 23, 3028–3030, 2009). In this report, we demonstrate that ECD and CID product-ion mass spectra can be recorded at high resolution with flexible control of fragmentation processes using a newly designed cell installed in a hybrid Q-TOF tandem mass spectrometer.