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.

     

Optical characterization and composition of abdominal wall muscle from rat

Complete optical characterization of biological tissue is desirable to develop clinical methods using optical technologies. Particularly, to develop optical clearing methods in biological tissues, it is necessary to know the composition of the tissue, the percentage of each constituent and corresponding refractive indexes. To obtain such information for rat muscle, we used a simple method to characterize tissue constituents for both content percentage and refractive index. The study consisted on measuring mass with a precision weighting scale and the refractive index with an Abbe refractometer during tissue dehydration. With the collected data, we used a theoretical model to calculate the refractive index and percentage for both interstitial fluid and solid part of the rat muscle. The results obtained are in good agreement with data published by other authors, and were considered of vital information for the optical clearing studies that we planned to perform.     

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.     

Coercivity of Combined Boundary Integral Equations in High‐Frequency Scattering

We prove that the standard second‐kind integral equation formulation of the exterior Dirichlet problem for the Helmholtz equation is coercive (i.e., sign‐definite) for all smooth convex domains when the wavenumber k is sufficiently large. (This integral equation involves the so‐called combined potential, or combined field, operator.) This coercivity result yields k‐explicit error estimates when the integral equation is solved using the Galerkin method, regardless of the particular approximation space used (and thus these error estimates apply to several hybrid numerical‐asymptotic methods developed recently). Coercivity also gives k‐explicit bounds on the number of GMRES iterations needed to achieve a prescribed accuracy when the integral equation is solved using the Galerkin method with standard piecewise‐polynomial subspaces. The coercivity result is obtained by using identities for the Helmholtz equation originally introduced by Morawetz in her work on the local energy decay of solutions to the wave equation. © 2015 Wiley Periodicals, Inc.     

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.     

Hydrophilic sulfonated bis-1,2,4-triazine ligands are highly effective reagents for separating actinides(iii) from lanthanides(iii) via selective formation of aqueous actinide complexes

We report the first examples of hydrophilic 6,6′-bis(1,2,4-triazin-3-yl)-2,2′-bipyridine (BTBP) and 2,9-bis(1,2,4-triazin-3-yl)-1,10-phenanthroline (BTPhen) ligands, and their applications as actinide(iii) selective aqueous complexing agents. The combination of a hydrophobic diamide ligand in the organic phase and a hydrophilic tetrasulfonated bis-triazine ligand in the aqueous phase is able to separate Am(iii) from Eu(iii) by selective Am(iii) complex formation across a range of nitric acid concentrations with very high selectivities, and without the use of buffers. In contrast, disulfonated bis-triazine ligands are unable to separate Am(iii) from Eu(iii) in this system. The greater ability of the tetrasulfonated ligands to retain Am(iii) selectively in the aqueous phase than the corresponding disulfonated ligands appears to be due to the higher aqueous solubilities of the complexes of the tetrasulfonated ligands with Am(iii). The selectivities for Am(iii) complexation observed with hydrophilic tetrasulfonated bis-triazine ligands are in many cases far higher than those found with the polyaminocarboxylate ligands previously used as actinide-selective complexing agents, and are comparable to those found with the parent hydrophobic bis-triazine ligands. Thus we demonstrate a feasible alternative method to separate actinides from lanthanides than the widely studied approach of selective actinide extraction with hydrophobic bis-1,2,4-triazine ligands such as CyMe₄-BTBP and CyMe₄-BTPhen.     

Kinetics and mechanism of free-surface vaporization of zinc, cadmium and mercury oxides analyzed by the third-law method

On the basis of critical comparison of experimental and theoretical values of the E parameter and investigation of the retardation effect of oxygen on the evaporation rate of ZnO, CdO and HgO, it was concluded that the dissociative evaporation of ZnO and HgO proceeds with releasing of atomic oxygen (O) as a primary product of decomposition. By contrast, the mechanism of dissociative evaporation of CdO corresponds to the equilibrium reaction with releasing of molecular oxygen (O₂) as a primary product of decomposition. As was shown, this difference in mechanisms is not related with interatomic OO distances in these oxides. From the analysis of crystal structure for 12 different oxides, which evaporate with releasing of atomic oxygen, and for 13 compounds, which evaporate with releasing of molecular oxygen, it was revealed that the first mechanism is observed for all oxides with the cubic crystal structure. It was proposed that a decisive role in this difference belongs to a local symmetry in the position of O atoms.     

Two-state irreversible thermal denaturation of anionic peanut (Arachis hypogaea L.) peroxidase

Detailed differential scanning calorimetry (DSC), steady-state tryptophan fluorescence and far-UV circular dichroism (CD) studies, together with enzymatic assays, were carried out to monitor the thermal stability of anionic peanut peroxidase (aPrx) at pH 3.0. The spectral parameters were seen to be good complements to the highly sensitive but integral method of DSC. Thus, changes in far-UV CD corresponded to changes in the overall secondary structure of the enzyme, while changes in intrinsic tryptophan fluorescence emission corresponded to changes in the tertiary structure of the enzyme. The results, supported with data concerning changes in enzymatic activity with temperature, show that thermally induced transitions for aPrx are irreversible and strongly dependent upon the scan rate, suggesting that denaturation is under kinetic control. It is shown that the process of aPrx denaturation can be interpreted with sufficient accuracy in terms of the simple kinetic scheme, , where k is a first-order kinetic constant that changes with temperature, as given by the Arrhenius equation; N is the native state, and D is the denatured state. On the basis of this model, the parameters of the Arrhenius equation were calculated.     

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.