Semilinear parabolic equations involving measures and low regularity data

A detailed study of abstract semilinear evolution equations of the form is undertaken, where generates an analytic semigroup and is a Banach space valued measure depending on the solution. Then it is shown that the general theorems apply to a variety of semilinear parabolic boundary value problems involving measures in the interior and on the boundary of the domain. These results extend far beyond the known results in this field. A particularly new feature is the fact that the measures may depend nonlinearly and possibly nonlocally on the solution.

     

Neoglycoconjugates from synthetic tetra- and hexasaccharides that mimic the terminus of the O-PS of Vibrio cholerae O:1, serotype Inaba

A glycosyl acceptor and a glycosyl donor having the N-3-deoxy-L-glycero-tetronic acid side chain already attached have been prepared and used for the synthesis of the di-through to the hexasaccharide that mimic the upsteam terminus of the O-specific polysaccharide of Vibrio cholerae O:1, serotype Inaba. The target tetra- and the hexasaccharide, which were obtained in the form of 5-methoxycarbonylpentyl glycosides, were linked to BSA using squaric acid diester chemistry. The conjugation reactions were monitored by surface enhanced laser desorption ionization-time of flight mass spectrometry (SELDI-TOF MS). This allowed the progression of the conjugation of the synthetic oligosaccharides in a controlled way and termination of the reaction when the desired molar hapten/BSA ratio had been reached, yielding neoglycoconjugates with predetermined carbohydrate/carrier ratios. The ability to monitor the conjugation by the SELDI-TOF MS technique made it possible to prepare, from one hapten in a one-pot reaction, several neoglycoconjugates having different, predetermined carbohydrate/carrier ratios.     

Generic hyperbolicity for reaction diffusion equations on symmetric domains

Summary The problem of generic hyperbolicity for reaction diffusion equations with Dirichlet boundary conditions on a ball inR ⁿ is studied. It is proved that while hyperbolicity is not a generic property, radially symmetric solutions are generically hyperbolic.

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Zusammenfassung Das Problem der generischen Hyperbolizität für Reaktion-Diffusionsgleichungen mit Dirichletschen Randbedingungen in einer Kugel imR ⁿ wird betrachtet. Es wird bewiesen, daß radialsymmetrische Lösungen generisch symmetrische sind, während Hyperbolizität nicht eine generische Eigenschaft ist.

     

Di­methyl 2‐{[2‐(methoxy­carbonyl)‐1‐(methoxy­carbonyl­methyl)pyrrol‐4‐yl]­methyl­ene}propane­dioate

The title compound, C₁₅H₁₇NO₈, is a pyrrole–ethene derivative with potential biological activity. Although a large part of the mol­ecule is planar, there is no structural evidence for any conjugation push–pull effect across the ethyl­enic bond, which is usually observed for substituted ethyl­enes; π‐electron delocalization appears to be restricted to the 2‐(methoxy­carbonyl)­pyrrole moiety.     

Effect of dielectric medium on angiotensin converting enzyme inhibitors binding to Zn<Superscript>2+</Superscript>

The Becke3LYP density functional was used to study structural and thermodynamic parameters of bivalent zinc cation complexes with selected substrates and ACE inhibitors (H₂O/OH⁻, neutral forms of captopril, zofenoprilat, omapatrilat, CH₃CONHCH₃, and N-terminal anions of captopril, zofenoprilat, omapatrilat, enalaprilat, perindoprilat, trandolaprilat, and fosinoprilat). The combination of DFT and the conductor-like polarizable continuum model (CPCM) were employed to compute the Gibbs interaction energies (ΔG) between Zn²⁺ and the selected ACE inhibitors for dielectric media with ɛ = 5 (to simulate the protein environment) and for water media (ɛ = 78.39) for comparison purposes. The results show that ΔG is sensitive to the dielectric constant of the environment and that lower dielectric medium favors the binding of inhibitors to the zinc cation.     

Influence of polarity of solvents on the spectral properties of bichromophoric coumarins

Absorption and fluorescence spectra of bichromophoric coumarins were investigated in different solvents and in polymer matrices. These bichromophoric coumarins were composed of a coumarin dimethylamino-substituted at position 7 or unsubstituted coumarin and phthalimide or a 1,8-naphthylimide linked with an iminomethyl bridge to the position 3 or 8 of the coumarin ring. Absorption spectra of 7-dimethylamino derivatives in position 3 of coumarin were quite similar, exhibiting broad bands around 430-440 nm like the parent compound 7-dimethylaminocoumarin-3-carbaldehyde. For coumarin derivatives substituted in position 8, the absorption maximum was shifted to shorter wavelength as for derivatives without position 7 dimethylamino substitution. The most intense fluorescence was observed for 7-(N,N-dimethylamino)-3-[(N-phtalimidoyl)iminomethyl]coumarin in polar solvent, while intense fluorescence was observed for 7-(N,N-dimethylamino)-3-[N-(1,3-dioxobenz[de]isoquinolinyl)iminomethyl]-coumarin in non polar solvent (chloroform), comparable with the fluorescence of 7-amino-4-methylcoumarin. Spectral measurements of bichromophoric coumarins in polymer matrices revealed that the maxima lies in between those for chloroform and methanol yielding more intense fluorescence then in solutions. Completely different solvent effects were observed for 7-(N,N-dimethylamino)-3-[N-(1,3-dioxobenz[de]isoquinolinyl)imino-methyl]coumarin and 7-(N,N-dimethylamino)-3-[(N-phtalimidoyl)iminomethyl]coumarin. With addition of polar methanol the intensity of fluorescence decreases, yielding a Stern-Volmer-like constant of 0.54 dm3 mol?1 for 7-(N,N-dimethylamino)-3-[N-(1,3-dioxo-benz[de]isoquinolinyl)iminomethyl]coumarin and an even higher one of 1.08 dm3·mol?1 for 7-dimethylaminocoumarin-3-carbaldehyde compared to the rather low one of 0.024 dm3 mol?1 for 7-amino-4-methylcoumarin. Contrary to this, addition of methanol under identical conditions brings about an increase in fluorescence intensity of 7-(N,N-dimethylamino)-3-[(N-phtalimidoyl)iminomethyl]coumarin (about 60-fold). The reasons for these different solvent effects are discussed.     

On some consequences of an external magnetic field applied to HTS coils

A computational model which enables to evaluate the distribution of the critical currents, electric fields and the voltage in the winding of a solenoidal high temperature superconducting (HTS) magnets subjected to an external magnetic field parallel with the magnet axis, was developed. The model comes out from the well-known power law between the electric field and the transport current of the HTS tape short sample. It allows to predict the voltage–current V(I) characteristics of both the pancake coils and the complete magnet. The model was applied to the magnet system consisting of 22 pancake coils made of multifilamentary Bi(2223)/Ag tape at 20 K, which is subjected to an external uniform magnetic field parallel with the coil axis. A rather unexpected behavior of the magnet at different operating conditions (operating current and external magnetic field strength) is predicted, analyzed and reported together with a theoretical explanation. On one hand, the external uniform magnetic field parallel with the coil axis increases the resulting magnetic field strength, however, on the other hand it simultaneously decreases the angle between the resulting magnetic field and the tape surface. Thus, the effect of higher magnetic loading caused by the presence of an external magnetic field strength which is acting on individual turns located close to the coil’s flanges is compensated by more favorable orientation of the tape with respect to the resulting magnetic field. As a result, increase in the critical currents of these turns is expected. Further, the results indicate, that in case of the high field HTS insert coils the anisotropy in the I_c(B) characteristic does not play a substantial role. As a consequence, the technology of the production of the tapes for high field insert HTS coils should concentrate rather on the tapes having the current carrying capacity as high as possible, than on the attempt how to decrease the anisotropy in the I_c(B) by changing the architecture of the filaments in the tape.