Variational resolution for some general classes of nonlinear evolutions. Part II

Using our results in [11], we provide existence theorems for general classes of nonlinear evolutions. Then we give examples of applications of our results to parabolic, hyperbolic, Schr¨odinger, Navier-Stokes and other time-dependent systems of equations.     

Synthetic,structural and binding studies of the 4,6-dimethyldibenzothiophene complex [(eta(5)-C(5)Me(5))Ru(CO)(2)(eta(1)(S)-4,6-Me(2)DBT)]BF(4): toward an understanding of deep hydrodesulfurization

The synthesis of the first completely characterized transition-metal complex containing a sulfur-bound 4,6-dimethyldibenzothiophene (4,6-Me(2)DBT) ligand, [CpRu(CO)(2)(eta(1)(S)-4,6-Me(2)DBT)]BF(4) (1) (Cp = eta(5)-C(5)Me(5)), is reported. X-ray studies of 1 and its 4-methyldibenzothiophene and dibenzothiophene analogues, [CpRu(CO)(2)(eta(1)(S)-4-MeDBT)]BF(4) (2) and [CpRu(CO)(2)(eta(1)(S)-DBT)]BF(4) (3), show that the Ru-S bond distances increase in the order, 3 < 2 < 1. Equilibrium studies on the series of [CpRu(CO)(2)(eta(1)(S)-DBTh)](+) compounds, where DBTh = DBT, 4-MeDBT, 4,6-Me(2)DBT, and 2,8-Me(2)DBT, show that the relative binding strengths of the dibenzothiophene ligands increase in the order 4,6-Me(2)DBT (1) < 4-MeDBT (20.2(1)) < DBT (62.7(6)) < 2,8-Me(2)DBT (223(3)). These results are the first to quantify the steric effect of 4- and 6-methyl groups on the sulfur-coordinating ability of dibenzothiophenes to transition-metal centers. They are also consistent with the proposal that 4- and 6-methyl groups reduce the coordination of dibenzothiophenes to active metal sites on hydrodesulfurization catalysts, which could account for the slow rate of 4-MeDBT and 4,6-Me(2)DBT hydrodesulfurization in petroleum feedstocks.     

Reduction of the allylic substituents in Ni(I)(1,8-dipropenyl-1,4,8,11-tetraazacyclotetradecane)+ by the central Ni(I) in aqueous solutions

The complex Ni(II)(1,8,-di-2-propenyl-1,4,8,11-tetraazacyclotetradecane)(2+), (NiL(1))(2+), was synthesized. X-ray crystallography demonstrates that the complex obtained is the trans-III isomer. The allylic substituents shift the redox couples (NiL(1))(3+/2+) and (NiL(1))(2+/+) anodically relative to the corresponding couples for Ni(II)(1,4,8,11-tetraazacyclotetradecane)(2+), (NiL(2))(2+), as expected. Surprisingly, the lifetime of (NiL(1))(+) in neutral aqueous solutions is shorter than that of (NiL(2))(+). Pulse radiolysis experiments reveal that the allylic substituents are reduced by the central Ni(I) ion. The first step in this reduction is a general acid catalyzed process. The results suggest that this step involves schematically the reaction Ni(I)[bond]NCH(2)CH[double bond]CH(2)(+) + H(+) --> Ni(III)[bond]NCH2CH2CH(2)(2+). The latter transient decomposes slowly with a half-life time of several minutes. Preliminary results support the suggestion that (NiL(2))(+), or other Ni(I)L complexes of this family, might reduce many alkenes present in the solution.     

Convenient magnesiation of aromatic and heterocyclic rings bearing a hydroxy group in presence of LiCl

The reaction of various iodophenols with MeMgCl in presence of LiCl followed by the addition of i-PrMgCl provides the corresponding magnesiated magnesium phenolates as THF soluble reagents; this approach can be extended to heterocyclic compounds bearing a hydroxy group like pyridines and quinolines.     

Facile methods of the synthesis of S-trialkylstannyl esters of dithio- and tetrathiophosphoric acids

S-Trialkylstannyl dialkyldithiophosphates 3 and tetrathiophosphates 6 were easily obtained in the reaction of tetraphosphorus decasulfide 1 with trialkylalkoxystannanes 2 or alkylthiostannanes 5 under mild conditions. Tetraphosphorus decasulfide 1 and hexaalkyl distannylsulfides 4 produce tris(trialkylstannyl) tetrathiophosphates 9 .     

Reduction of Deuterium Level Supports Resistance of Neurons to Glucose Deprivation and Hypoxia: Study in Cultures of Neurons and on Animals

The effect of a reduced deuterium (D) content in the incubation medium on the survival of cultured neurons in vitro and under glucose deprivation was studied. In addition, we studied the effect of a decrease in the deuterium content in the rat brain on oxidative processes in the nervous tissue, its antioxidant protection, and training of rats in the T-shaped maze test under hypoxic conditions. For experiments with cultures of neurons, 7–8-day cultures of cerebellar neurons were used. Determination of the rate of neuronal death in cultures was carried out using propidium iodide. Acute hypoxia with hypercapnia was simulated in rats by placing them in sealed vessels with a capacity of 1 L. The effect on oxidative processes in brain tissues was assessed by changes in the level of free radical oxidation and malondialdehyde. The effect on the antioxidant system of the brain was assessed by the activity of catalase. The study in the T-maze was carried out in accordance with the generally accepted methodology, the skill of alternating right-sided and left-sided loops on positive reinforcement was developed. This work has shown that a decrease in the deuterium content in the incubation medium to a level of −357‰ has a neuroprotective effect, increasing the survival rate of cultured neurons under glucose deprivation. When exposed to hypoxia, a preliminary decrease in the deuterium content in the rat brain to −261‰ prevents the development of oxidative stress in their nervous tissue and preserves the learning ability of animals in the T-shaped maze test at the level of the control group. A similar protective effect during the modification of the ²H/¹H internal environment of the body by the consumption of DDW can potentially be used for the prevention of pathological conditions associated with the development of oxidative stress with damage to the central nervous system.     

Synthesis and Properties of Some Derivatives of Chloromethylphosphonic and Bis(Chloromethyl) Phosphinic Acids

Abstract

Reactions of chloromethylchlorophosphonates with heptamethyldisilazane(1 : 1 ratio]proceed with the formation of silylamidophosphonates, while with bis(chloromethy1)phosphinate P-N-P compounds were formed.     

Experimental study of aortic flow in the ascending aorta via Particle Tracking Velocimetry

A three-dimensional, pulsatile flow in a realistic phantom of a human ascending aorta with compliant walls is investigated in vitro. Three-Dimensional Particle Tracking Velocimetry (3D-PTV), an image-based, non-intrusive measuring method is used to analyze the aortic flow. The flow velocities and the turbulent fluctuations are determined. The velocity profile at the inlet of the ascending aorta is relatively flat with a skewed profile toward the inner aortic wall in the early systole. In the diastolic phase, a bidirectional flow is observed with a pronounced retrograde flow developing along the inner aortic wall, whereas the antegrade flow migrates toward the outer wall of the aorta. The spatial and temporal evolution of the vorticity field shows that the vortices begin developing along the inner wall during the deceleration phase and attenuate in the diastolic phase. The change in the cross-sectional area is more distinct distal to the inlet cross section. The mean kinetic energy is maximal in the peak systole, whereas the turbulent kinetic energy increases in the deceleration phase and reaches a maximum in the beginning of the diastolic phase. Finally, in a Lagrangian analysis, the temporal evolution of particle dispersion was studied. It shows that the dispersion is higher in the deceleration phase and in the beginning of the diastole, whereas in systole, it is smaller but non-negligible.     

Modeling spurt and stress oscillations in flows of molten polymers

The paper presents an approach for modeling polymer flows with non-slip, slip and changing non-slip — slip boundary conditions at the wall. The model consists of a viscoelastic constitutive equation for polymer flows in the bulk, prediction of the transition from non-slip to sliding boundary conditions, a wall slip model, and a model for the compressibility effects in capillary polymer flows. The bulk viscoelastic constitutive equation contains a hardening parameter which is solely determined by the polymer molecular characteristics. It delimits the conditions for the onset of solid, rubber-like behavior. The non-monotone wall slip model introduced for polymer melts, modifies a slip model derived from a simple stochastic model of interface molecular dynamics for cross-linked elastomers. The predictions for the onset of spurt, as well as the numerical simulations of hysteresis, spurt, and stress oscillations are demonstrated. They are also compared with available data for a high molecular weight, narrow distributed polyisoprene. By using this model beyond the critical conditions, many of the qualitative features of the spurt and oscillations observed in capillary and Couette flows of molten polymers, are described.Notations upper convected derivative of elastic strain tensor - f, f_m, f_min dimensionless (sliding) shear friction characteristics, and its maximum and minimum - G Hookean elastic modulus - G_p plateau modulus - G, G storage and loss moduli - I₁, I₂ first and second invariant of strain tensor - I₁, I₀ capillary and barrel lengths - M non-dimensional mass flow rate - M_C critical molecular weight - M^*, M_e molecular weights of a statistical segment, and of polymer chain between entanglements - M_n, M_W number average and weight average molecular weights - m, k two fitting parameters of slip model - _s , _s ^o nominal and characteristic sliding velocities - u non-dimensional sliding velocity - u _sc initial (infinitesimal) slip velocity - u ₁ upper limit of u on the lower branch - u ₂ lower limit of u on the upper branch - u _max value of u corresponding to f_min - u _min value of u corresponding to f_max - U piston speed - Q nominal volumetric flow rate - q non-dimensional volumetric flow rate - R, R_o capillary and barrel radii - M non-dimensional mass flow rate