Asymptotic behavior of the solutions of certain parabolic equations

Some laws in physics describe the change of a flux and are represented by parabolic equations of the form (*) \documentclass{article}\pagestyle{empty}\begin{document}$$\frac{{\partial u}}{{\partial t}}=\frac{\partial}{{\partial x_j }}(\eta \frac{{\partial u}}{{ax_j}}-vju),$$\end{document} j≤m, where η and v_j are functions of both space and time. We show under quite general assumptions that the solutions of equation (*) with homogeneous Dirichlet boundary conditions and initial condition u(x, 0) = u_o(x) satisfy The decay rate d > 0 only depends on bounds for η, v and G § R^m the spatial domain, while the constant c depends additionally on which norm is considered. For the solutions of equation (*) with homogeneous Neumann boundary conditions and initial condition u₀(x) ≥ 0 we derive bounds d₁u₁ ≤ u(x, t) ≤ d₂u₂, Where d_i, i = 1, 2, depend on bounds for η, v and G, and the u_i are bounds on the initial condition u₀.     

Monophthalates with Oxidized C5-Carbon in the Ester Chain: A Simple Synthetic Access to Two Major Metabolites of Bis-(2-ethylhexyl)-phthalate

Summary.  The synthesis of two oxidized metabolites of bis-(2-ethylhexyl)-phthalate is described. The target structures were obtained by esterification of the appropriate alcohol carrying a protected hydroxy group with phthalic anhydride, followed by deprotection and further oxidation. Received February 26, 2002. Accepted March 6, 2002     

Kinetic energy and angular distributions of instantaneous fission fragments in a classical model

The process of instantaneous fission in deep inelastic collisions is investigated in a classical model. Kinetic energies and angular distributions of the fragments are calculated for the proposed reaction Pb+U atE _cm ^inc =750 MeV; an experimental setup for the separation of the fragments originating from instantaneous fission from the fragments of thermal fission is explained. We also discuss fusion following instantaneous fission as a mechanism for the production of superheavy elements and arrive at rather promising estimates.     

Iminophosphanes: Unconventional Compounds of Main Group Elements

The large number of known stable compounds in which phosphorus has a low coordination number makes it clear that such compounds can no longer be regarded as “exotic” in main group chemistry. While the rich chemistry of P? C multiply bonded systems makes clear their affinity to their organic congeners, iminophosphanes in particular are also of increasing importance. The linkage of a phosphinidine fragment with an imine fragment via a multiple bond gives rise to a class of compounds with an unusually wide range of structural types. This in turn leads to a broad spectrum of chemical behavior which makes iminophosphanes extremely useful synthetic building blocks in organoelement chemistry.     

HO2 ELIMINATION FROM α-HYDROXYALKYLPEROXYL RADICALS IN AQUEOUS SOLUTION

Abstract— In aqueous solutions α-hydroxyalkylperoxyl radicals undergo a spontaneous and a base catalysed HO₂ elimination. From kinetic deuterium isotope effects, temperature dependence, and the influence of solvent polarity it was concluded that the spontaneous reaction occurs via an HO₂ elimination followed by the dissociation of the latter into H⁺ and O₂^-. The rate constant of the spontaneous HO₂ elimination increases with increasing methyl substitution in α-position ( k (CH₂(OH)O₂) < 10s^-1 k (CH₃CH(OH)O₂) = 52s^-1 k ((CH₃)₂C(OH)O₂) = 665 s^-1). The OH^- catalysed reaction is somewhat below diffusion controlled. The mixture of peroxyl radicals derived from polyhydric alcohols eliminate HO₂ at two different rates. Possible reasons for this behaviour are discussed. The mixture of the six peroxyl radicals derived from d -glucose are observed to eliminate HO₂ with at least three different rates. The fastest rate is attributed to the HO₂ elimination from the peroxyl radical at C-l ( k > 7000s^-1). Because of the HO₂ eliminations the peroxyl radicals derived from d -glucose do not undergo a chain reaction in contrast to peroxyl radicals not containing an α-OH group. In competition with the first order elimination reactions the α-hydroxylalkylperoxyl radicals undergo a bimolecular decay. These reactions are briefly discussed.     

Chloro(η6‐p‐cymene)(phosphoramidite)ruthenium(II), a 16‐Electron Fragment Stabilized by an η2‐Aryl–Metal Interaction,and Its Use in Asymmetric Cyclopropanation

Chloride abstraction from the half‐sandwich complexes [RuCl₂(η⁶‐p‐cymene)(P*‐κP)] ( 2a : P* = (S_a,R,R)‐ 1a = (1S_a)‐[1,1′‐binaphthalene]‐2,2′‐diyl bis[(1R)‐1‐phenylethyl)]phosphoramidite; 2b : P* = (S_a,R,R)‐ 1b = (1S_a)‐[1,1′‐binaphthalene]‐2,2′‐diyl bis[(1R)‐(1‐(1‐naphthalen‐1‐yl)ethyl]phosphoramidite) with (Et₃O)[PF₆] or Tl[PF₆] gives the cationic, 18‐electron complexes dichloro(η⁶‐p‐cymene){(1S_a)‐[1,1′‐binaphthalene]‐2,2′‐diyl {(1R)‐1‐[(1,2‐η)‐phenyl]ethyl}[(1R)‐1‐phenylethyl]phosphoramidite‐κP}ruthenium(II) hexafluorophosphate ( 3a ) and [Ru(S)]‐dichloro(η⁶‐p‐cymene){(1S_a)‐[1,1′‐binaphthalene]‐2,2′‐diyl {(1R)‐1‐[(1,2‐η)‐naphthalen‐1‐yl]ethyl}[(1R)‐1‐(naphthalen‐1‐yl)ethyl]phosphoramidite‐κP)ruthenium(II) hexafluorophosphate ( 3b ), which feature the η²‐coordination of one aryl substituent of the phosphoramidite ligand, as indicated by ¹H‐, ¹³C‐, and ³¹P‐NMR spectroscopy and confirmed by an X‐ray study of 3b . Additionally, the dissociation of p‐cymene from 2a and 3a gives dichloro{(1S_a)‐[1,1′‐binaphthalene]‐2,2′‐diyl [(1R)‐(1‐(η⁶‐phenyl)ethyl][(1R)‐1‐phenylethyl]phosphoramidite‐κP)ruthenium(II) ( 4a ) and di‐μ‐chlorobis{(1S_a)‐[1,1′‐binaphthalene]‐2,2′‐diyl [(1R)‐1‐(η⁶‐phenyl)ethyl][(1R)‐1‐phenylethyl]phosphoramidite‐κP}diruthenium(II) bis(hexafluorophosphate) ( 5a ), respectively, in which one phenyl group of the N‐substituents is η⁶‐coordinated to the Ru‐center. Complexes 3a and 3b catalyze the asymmetric cyclopropanation of α‐methylstyrene with ethyl diazoacetate with up to 86 and 87% ee for the cis‐ and the trans‐isomers, respectively.     

Two-dimensional condensation in camphor-10-sulphonic acid films at the mercury/electrolyte interface

The electrosorption properties of camphor-10-sulphonic acid (CS) in different electrolytes (Na₂SO₄, LiClO₄, KNO₃, KCl, KBr, KJ) were investigated experimentally by ac polarographic measurements at different temperatures. Depending on the type of electrolyte and on the temperature, film condensation was observed.The Frumkin interaction coefficient, determined from the critical degree of coverage, does not depend linearly on the reciprocal temperature as would be the case in correspondence to the temperature dependence of the pit width. This contradiction does not occur if the interaction coefficient is determined from the critical degree of coverage using the lattice gas model. The temperature dependence of the pit width of the differential capacity-potential curves, found in the experiment, can be theoretically described by both these models. The interaction coefficient in the models is inversely proportional to the temperature. Furthermore, the parameters of the standard free energy of adsorption, the interaction energy, the interaction coefficient of the Frumkin isotherm, the adsorption coefficient, and the maximal surface concentration of CS in the film were estimated and compared.     

Phosphonio‐benzophospholide Zwitterions as Bridging 8e‐Donor Ligands: Synthetic and Mechanistic Studies

Reactions of the phosphonio‐benzophospholide π‐complexes 3a, b[Cr] with [M(CO)₅(olefin)] or of the σ‐complexes 2a, b[M] (M = Cr, Mo, W) with [M(CO)₃(aren)] lead to the first binuclear complexes 4a, b[CrM] featuring phosphonoio‐benzophospholides as μ‐bridging 8e‐donor ligands to two group 6 metal atoms. The constitution of the products was determined by spectroscopic and X‐ray diffraction studies. Mixed complexes with both group 6 and 7 metals were not accessible. Mechanistic studies showed that the reactions follow a complicated mechanism whose single steps may involve transfer of either M(CO)_n fragments or single CO ligands between complexes; the latter are associated with a σ/π‐coordination isomerization of the benzophospholide unit. Competition between both reaction channels can lead to the formation of product mixtures whose composition is controlled by the relative thermodynamic stabilities of the products. Computational studies suggest that in the more stable isomer of heterobimetallic complexes 4a, b[MM′] end‐on coordination to the heavier and side‐on coordination to the lighter metal atom is preferred.     

Cytochemical differences in bacterial glycocalyx.

To examine new cytochemical aspects of the bacterial adhesion, a strain 41452/01 of the oral commensal Streptococcus sanguis and a wild strain of Staphylococcus aureus were grown with and without sucrose supplementation for 6 days. Osmiumtetraoxyde (OsO4), uranyl acetate (UA), ruthenium red (RR), cupromeronic blue (CB) staining with critical electrolytic concentrations (CECs), and the tannic acid-metal salt technique (TAMST) were applied for electron microscopy. Cytochemically, only RR-positive fimbriae in S. sanguis were visualized. By contrast, some types of fimbriae staining were observed in S. aureus glycocalyx: RR-positive, OsO4-positive, tannophilic and CB-positive with ceasing point at 0.3 M MgCl2. The CB staining with CEC, used for the first time for visualization of glycoproteins of bacterial glycocalyx, also reveals intacellular CB-positive substances-probably the monomeric molecules, that is, subunits forming the fimbriae via extracellular assembly. Thus, glycosylated components of the biofilm matrix can be reliably related to single cells. The visualization of intracellular components by CB with CEC enables clear distinction between S. aureus and other bacteria, which do not produce CB-positive substances. The small quantities of tannophilic substances found in S. aureus makes the use of TAMST for the same purpose difficult. The present work protocol enables, for the first time, a partial cytochemical differentiation of the bacterial glycocalyx.