A relaxation approach to hencky’s plasticity

Givenμ, κ, c>0, we consider the functional

Eigenfunctions of the hyperbolic composition operator

Letu inH ² be zero at one of the fixed points of a hyperbolic Möbius transform of the unit diskD. We will show, under some additional conditions onu, that the doubly cyclic subspaceS _u =V _n=– C ⁿ u contains nonconstant eigenfunctions of the composition operatorC . This implies that the cyclic subspace generated byu is not minimal. If there is an infinite dimensional minimal invariant subspace ofC (which is equivalent to the existance of an operator with only trivial invariant subspaces), then it is generated by a function with singularities at the fixed points of .     

A commonly used spin label: S‐(2,2,5,5‐tetramethyl‐1‐oxyl‐Δ3‐pyrrolin‐3‐ylmethyl) methanethiosulfonate

The title compound, C₁₀H₁₈NO₃S₂, which finds application as a spin label, has triclinic (P) symmetry at 100 (2) K with two independent molecules in the asymmetric unit. Both molecules are very similar with respect to bond lengths and angles, but molecule 2 shows disordering of its side chain. The pyrroline rings differ slightly with respect to the position of the NO group, which in both cases are sterically shielded by the surrounding methyl groups. The crystal structure of the title compound represents the first example of a 2,2,5,5‐tetramethyl‐1‐oxyl‐Δ³‐pyrroline derivative with a side chain at the double bond which is linked to it through an sp³‐hybridized C atom. In the solid state, the side chain adopts a conformation with the methyl group above/below the pyrroline ring and a H atom directed towards a C atom of the double bond. The disordered side chain of molecule 2 represents a second conformation with low potential energy. Both molecules exhibit planar chirality, but in the solid state both pairs of stereoisomers are present. These four stereoisomers are stacked one behind the other in four different columns, denoted A, A′, B and B′, the angle between the vectors of the N—O bonds in columns A and B being 80.38 (8)°.     

Characterization of the inhibition of enveloped virus infectivity by the cationic acrylate polymer eudragit E100

The antiviral effects of the cationic acrylate polymer E100 on a panel of lipid-enveloped viruses and the interactions involved are studied. The treatment of several common viruses with E100 induced a dose-dependent inhibition of the infectivity of viruses below the detection limit of the assays employed. Similarly, the treatment of human sera infected with HIV or HCV reduced virus RNA plasma levels to undetectable values. This implies that Eudragit E100 can interact with enveloped viruses, even in the presence of proteins, through a mechanism that is not reversed by titration of the positively charged groups of the polymer, opening the possibility to remove viral particles with the polymer as it is eliminated.     

Computational study of thioflavin T torsional relaxation in the excited state

Quantum-chemical calculations of the Thioflavin T (ThT) molecule in the ground S0 and first excited singlet S1 states were carried out. It has been established that ThT in the ground state has a noticeable nonplanar conformation: the torsion angle phi between the benzthiazole and the dimethylaminobenzene rings has been found to be approximately 37 degrees. The energy barriers of the intramolecular rotation appearing at phi = 0 and 90 degrees are quite low: semiempirical AM1 and PM3 methods predict values approximately 700 cm-1 and ab initio methods approximately 1000-2000 cm(-1). The INDO/S calculations of vertical transitions to the S1(abs) excited state have revealed that energy ES1(abs) is minimal for the twisted conformation with phi = 90 degrees and that the intramolecular charge-transfer takes place upon the ThT fragments' rotation from phi = 0 to 90 degrees. Ab initio CIS/RHF calculations were performed to find optimal geometries in the excited S1 state for a series of conformers having fixed phi values. The CIS calculations have predicted a minimum of the S1 state energy at phi approximately 21 degrees; however, the energy values are 1.5 times overestimated in comparison to experimental data. Excited state energy dependence on the torsion angle phi, obtained by the INDO/S method, reveals that ES1(fluor) is minimal at phi = approximately 80-100 degrees, and a plateau is clearly observed for torsion angles ranging from 20 to 50 degrees. On the basis of the calculation results, the following scheme of photophysical processes in the excited S1 state of the ThT is suggested. According to the model, a twisted internal charge-transfer (TICT) process takes place for the ThT molecule in the excited singlet state, resulting in a transition from the fluorescent locally excited (LE) state to the nonfluorescent TICT state, accompanied by torsion angle phi growth from 37 to 90 degrees. The TICT process effectively competes with radiative transition from the LE state and is responsible for significant quenching of the ThT fluorescence in low-viscosity solvents. For viscous solvents or when the ThT molecule is located in a rather rigid microenvironment, for example, when it is bound to amyloid fibrils, internal rotation in the dye molecule is blocked due to steric hindrance, which results in suppression of the LE --> TICT quenching process and in a high quantum yield of fluorescence.     

Competitive solubilization of cholesterol and phytosterols in nonionic microemulsions

It is well documented that phytosterols inhibit the uptake of exogenic cholesterol and do not interfere with cholesterol synthesis or cause side effects. The mechanism by which phytosterols interfere with cholesterol absorption is not completely clear and there are at least three hypotheses for their beneficial activity. Among these is that of competitive solubilization of phytosterols and cholesterol in dietary mixed micelles. In the present study we investigated the competitive solubilization of phytosterols (approximately 50% beta-sitosterol) and cholesterol in a nonionic microemulsion system constructed as a model for the dietary mixed micelles. We studied the effect of the competitive solubilization of cholesterol and phytosterols on the structural transformations and physical properties of the microemulsion and evaluated the locus of the solubilizates within the nanodroplets of each sterol separately and when they are loaded together at different weight ratios along one dilution line. Our results show that chemical and structural differences between cholesterol and phytosterols significantly influence the solubilization capacity of the nonionic microemulsion. Cholesterol, being more amphiphilic, is solubilized more efficiently at the W/O microemulsion interface, while in the O/W microemulsion phytosterols are dissolved somewhat more efficiently in the droplet core.     

Harnack inequality and continuity of solutions to quasi-linear degenerate parabolic equations with coefficients from Kato-type classes

For a general class of divergence type quasi-linear degenerate parabolic equations with measurable coefficients and lower order terms from nonlinear Kato-type classes, we prove local boundedness and continuity of solutions, and the intrinsic Harnack inequality for positive solutions.