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Notes: To check if the strong inhibition of N-acetyl-β-D-glucosaminidase by the tetrazole 8 and the imidazoles 9 and 10 correlates with the presence of a heteroatom corresponding to the glycosidic O-atom, we prepared the GlcNAc-derived pyrroles (tetrahydroindolizines) 18, 19, 27, 28, 34, and 35, lacking such a heteroatom. For this. the glucose-derived pyrroles 11-13 were treated with a Lewis acid in the presence of trimethylsilyl azide. Conditions of kinetic control favored the formation of the gluco-azides 14, 23, and 30, while thermodynamic control favoured the manno-azides 20, 29, and 36. Reduction of the azides 14, 20, 23, 30, and 36 by Pd/C-catalyzed hydrogenolysis or, better, with propanedithiol and Et3N, followed by acetylation or trifluoroacetylation and hydrogenolytic debenzylation, gave the deprotected acetamido- and trifluoroacetamido-pyrroles 18, 19, 22, 27, 28, 34, 35 40, and 41. As compared to the tetrazole 8 and the imidazole 9, the pyrroles 18, 19, 27, 28, 34, and 35 are only modest inhibitors of N-acetyl-β-D-glucosaminidase from bovine kidney (Ki values between 10 and 75 μM). indicating the necessity of a heteroatom at the glycosidic position. Ki Values between 100 and 160 μM for the inhibition of N-acetyl-β-D-glucosaminidase from jack beans were determined for the pyrroles 19, 34, and 35. The trifluoroacetamides inhibited both enzymes about twice as strongly as the corresponding acetamides.

Notes: Pirlindole is an antidepressant drug. It acts principally as reversible inhibitor of monoamine oxidase-A (RIMA) and appears relatively potent in comparison with reference drugs. Pirlindole possesses stereogenic center but is generally used as racemate. In this work, the first preparative resolution of its enantiomeric couple is described. Whereas selective crystallization of salts of chiral acid failed, two asymmetric synthetic pathways were also examined; however, without success. Finally separation and isolation of enantiomers of pirlindole was completed by using the derivatization method coupled with preparative HPLC. Optical purity of each isomer was determined by chiral HPLC. The specific rotation of each antipode was also determined.

Notes: The synthesis of new ‘bridged’ β-cyclodextrin (β-CD) ‘dimers’ 7-12 was successfully achieved by two one-pot reactions from β-CD (3) and 6A-azido-6A-deoxy-β-CD (4). The ‘phosphine imine’ reaction was shown to be a superior approach compared to the Mitsunobu reaction as coupling strategy for the preparation of these ‘dimers’. NMR Data, along with molecular-modelling calculations, suggest a ‘helical-like’ arrangement for the phenanthroline-diyl-linked ‘dimer’ derivative 9. Complexation properties of 9 were established by UV-VIS-spectrophotometric titration toward four metals. Among them CuII or EuIII ions were complexed selectively by 9, but no complexation occurred with LaIII and ZnII. In addition a specific and interesting esterase activity toward the phosphodiester bond of bis(4-nitrophenyl) phosphate anion was found in the case of the CuII complex of 9.

Notes: Three new derivatives of vitamin B12 with a pyrrole head group attached to the corrin ring have been prepared. Ligand-exchange reactions and reduction provided reactive CoIII and CoII complexes. Their electro-chemical properties and their potential for fixation at the surface of electrodes by electropolymerization were studied.

Notes: The kinetics of isomerization of deuterium and hydrogen oxoperoxonitrate, ONOOD and ONOOH, respectively, to trioxonitrate(1-), NO3-, and a deuteron or proton have been studied. Analysis of the pH-rate profiles result in a normal equilibrium isotope effect (KH/KD) of 3.3. The kinetic deuterium isotope effect for the isomerization reaction is 1.6 ± 0.2 between 5 and 55°. The activation enthalpies of isomerization of ONOOD and ONOOH are identical within the error of the measurement, 86.2 ± 0.5 and 86.5 ± 0.5 kJmol-1, respectively. A secondary kinetic isotope effect of 1.6 is compatible with a mechanism of isomerization where the terminal peroxide O-atom shifts to the N-atom.

Notes: The acid-catalyzed hydrolysis of (3S,5R,6S,3′S,5′R)-5,6-epoxycapsanthin (5) led to (3S,5R,6R,3′S,5′R)-(7) and (3S,5R,6S,3′S,5′R)-capsokarpoxanthin (8). In addition, (3S,5R,8R,3′S,5′R)- (9), (3S,5R,8S,3′S,5′R)-capsochrome (10), and (3S,5R,6R,3′S,5′R)-3,6-epoxycapsanthin (6) afforded (3S,5S,6R,3′S,5′R)-capsokarpoxanthin (12) (3S,5S,8S,3′S,5′R)- (13) and (3S,5S,8R,3′S,5′S)-capsochrome (14) as well as (3S,5S,6R,3′S,5′R)-3,6-epoxyepicapsanthin (15). Compounds 5-15 were isolated in crystalline form and characterized by their UV/VIS, CD, 1H- and 13C-NMR, and mass spectra.

Notes: Blood-protein adducts are used as dosimeter for modifications of macromolecules in the target organs where the disease develops. The functional groups of cysteine, tyrosine, serine, lysine, tryptophan, histidine and N-terminal amino acids are potential reaction sites for isocyanates. Especially the N-terminal amino acids, valine and aspartic acid of hemoglobin and albumin, respectively, are reactive towards electrophilic xenobiotics. To develop methods for the quantification of such blood-protein adducts, we treated 4-chlorophenyl isocyanate (1) with the tripeptide L-valyl-glycyl-glycine (2a) and with single amino acids yielding N-[(4-chlorophenyl)carbamoyl]valyl-glycyl-glycine (3a), N-[(4-chlorophenyl)carbamoyl]valine (3b), N-[(4-chlorophenyl)carbamoyl]aspartic acid (3c), N-(4-chlorophenyl)carbamoyl glutamic acid (3d), N-acetyl-S-[(4-chlorophenyl)carbamoyl]cysteine (3e), and N-acetyl-O-[(4-chlorophenyl)carbamoyl]serine (3f), Nα-acetyl-Nε-[(4-chlorophenyl)carbamoyl]lysine (3g). For several chemicals, it was shown that blood-protein adducts are good dosimeters of exposure and dosimeters for the target dose. The hydrolysis of the N-terminal adducts of isocyanates release hydantoins which can be separated from the rest of the protein and analyzed using GC/MS or HPLC. This was achieved with 3a. The released hydantoin could be analyzed using GC/MS. We propose to analyze the N-terminal adducts of isocyanates with blood protein to distinguish between arenamine and arylisocyanate exposure.

Notes: The synthesis of 3H-naphtho[2,1-b]pyrans 9-21 linked to a thiophene moiety is described. Two different synthetic approaches were applied to prepare these novel functionalized compounds, and their spectrokinetic properties in solution are reported.

Notes: The synthesis of oligonucleotides containing 2′-deoxy-5-methylisocytidine and 2′-deoxyisoguanosine using phosphoramidite chemistry in solid-phase oligonucleotide synthesis is described. Supporting previous observations, the N,N-diisobutylformamidine moiety was found to be a far superior protecting group than N-benzoyl for 2′-deoxy-5-methylisocytidine. 2′-Deoxy-N2-[(diisobutylamino)methylidene]-5′-(4,4′-dimethoxytityl)-5-methylisocytidine 3′-(2-cyanoethyl diisopropylphosphoramidite) (1c) incorporated multiple consecutive residues during a standard automated synthesis protocol with a coupling efficiency 〉 99% according to dimethoxytrityl release. Extending coupling times of the standard protocol to ≥ 600s using 2′-deoxy-N6-[(diisobutylamino)methylidene]-5′-O-(dimethoxytrityl)-O2-(diphenylcarbamoyl)isoguanosine, 3′-(2-cyanoethyl diisopropylphosphoramidite) (7e) led to successful incorporation of multiple consecutive 2′-deoxyisoguanosine bases with a coupling efficiency 〉 97% according to dimethoxytrityl release.

Notes: Studies towards the synthesis of a chiral primary α-phosphinoalkanamine 1a are reported. O-Activated. N-carbamate-protected phenylalaninol 3a did not undergo SN reaction with KPPh2: instead, after N-deprotonation, intramolecular substitution led to formation of the aziridine derivative 5a (Scheme 2). N-Phthalimido-protected, O-activated phenylalaninol 3b also underwent an intramolecular process on treatment with KPPh2, i.e., an unusual aryl-acyliminium cyclization furnishing the (epoxymethano)isoindolo[1,2-a]isoquinolinone 7 (Scheme 3). In a reaction with KPPh2, the N,N-dibenzyl-protected and activated phenylalaninol 3d finally yielded the intermolecular SN reaction product 2a (Scheme 4). However, debenzylation by catalytic hydrogenation turned out to be impossible.

Notes: Selective NMR decoupling and nuclear Overhauser effect (NOE) experiments with phycocyanobilin (PCB) show proton-proton interactions between the terminal rings A and D, viz. the chiral C(2) methine center and the ethyl substituent at C(18), as a result of the helical conformation of this open-chain tetrapyrrole in solution. Quantitative NOE measurements and a combination of force-field and semiempirical calculations (FSC) afford inter-proton distances across the helical gap of 4.2-4.6 (NOE) and 3.2-4.2 A° (FSC). The NOE and FSC, in conjuction with a qualitative evaluation of the steric interactions in the two optimized helices, suggest furthermore that, in solution, the helix M is somewhat more stable than P. The coexistence of at least two diastereoisomers is corroborated also by the circular dichroism (CD) spectra of PCB in MeOH/EtOH which point to a temperature-dependent equilibrium in solution, and by a considerable increase of this CD upon changing the solvent from the achiral alcohols to ethyl (-)-(S)-lactate which reflects a selective solvent-induced CD differentiating between diastereoisomers.

Notes: Enantiomerically pure β-amino-acid derivatives with the side chains of Ala, Val, and Leu in the 2- or 3-position (β2- and β3-amino acids, resp.), as well as with substituents in both the 2- and 3-positions (β2,3-amino acids, of like-configuration) have been prepared (compounds 8-17) and incorporated (by stepwise synthesis and fragment coupling, intermediates 24-34) into β-hexa-, β-hepta-, and β-dodecapeptides (1-17). The new and some of the previously prepared β-peptides (35-39) showed NH/ND exchange rates (in MeOH at room temperature) with τ1/2 values of up to 60 days, unrivalled by short chain α-peptides. All β-peptides 1-7 were designed to be able to attain the previously described 31-helical structure (Figs. 1 and 2). CD Measurements (Fig. 4), indicating a new secondary structure of certain β-peptides constructed of β2- and β3-amino acids, were confirmed by detailed NMR solution-structure analyses: a β2-heptapeptide (2c) and a β2,3-hexapeptide (7c) have the 31-helical structure (Figs. 6 and 7), while to a β2/β3-hexapeptide (4) with alternating substitution pattern H-(β2-Xaa-β3-Xaa)3-OH a novel, unusual helical structure (in (D5)pyridine, Fig. 8; and in CD3OH, Figs. 9 and 10) was assigned, with a central ten-membered and two terminal twelve-membered H-bonded rings, and with C=O and N—H bonds pointing alternatively up and down along the axis of the helix (Fig. 11). Thus, for the first time, two types of β-peptide turns have been identified in solution. Hydrophobic interactions of and hindrance to solvent accessibility by the aliphatic side chains are discussed as possible factors influencing the relative stability of the two types of helices.

Notes: Tetraepoxy[22]annulene(2.2.2.0): a Tetraepoxy-Bridged Neutral Aromatic [22]Annulene of a New TypeWe describe the synthesis of tetraepoxy[22]annulene(2.2.2.0) 4, the first aromatic annulene of type B by a cyclizing twofold Wittig reaction of 2,2′-bifuran-5,5′-dicarbaldehyde (5) and the bis[phosphonium] salt 8. The configuration of 4, mainly determined by NMR spectroscopy is (Z,E,Z). According to the UV/VIS spectrum and the 1H-NMR data, the electronic situation in 4 is quite different from that of tetraepoxy[22]annulene(3.0.3.0) 2 and tetraepoxy[22]annulene(2.1.2.1) 3. According to variable-temperature 1H-NMR spectroscopy, 4 is a highly dynamic system, where the (E)-double bond rotates around the adjacent σ-bonds. At ca. -130°, this dynamic process is frozen, and 4 appears as a diatropic aromatic system; the free activation energy of the rotation ΔG≠ is ca. 8.75 kcal/mol.

Notes: In the center of the immune system, there are major histocompatibility (MHC) protein/nonapeptide complexes which are recognized by T cell. The nonapeptides consist of three regions, an N-terminal one containing three amino-acid residues with a mandatory arginine in position 2, a C-terminal one with a lysine or arginine in position 9, and a central, variable one of five residues (cf. Fig. 1). We have now synthesized the first conjugates (1-4) of oligopeptides with oligo[(R)-3-hydroxybutanoates] (OHB) as analogs of MHC-binding peptides. Of the approaches chosen (Scheme 1), a fragment coupling of a hydroxy-butanoyl-amido ester (17 and 19) with an [(aminoalkanoyl)oxy]butanoyl chloride (27; Scheme 3), followed by two peptide-coupling steps (Scheme 4), turned out to be most efficient. The conjugates H-Gln-Arg-Leu-(HB)3,4-Lys-OH (1 and 2) and H-Ala-Arg-Leu-(HB)3,4-Lys-OH (3 and 4) were thus obtained in pure form. The conjugates 1 and 2 with N-terminal glutamine have a tendency to undergo cyclization with formation of a pyroglutamate residue (ef. Fig. 2). CD Measurements at different temperatures and so-called epitope-stabilization assays show that the complexes of the conjugates 2 and 4, containing four HB units, with the HLA-B27 class-I-MHC protein are more stable than those of a model nonapeptide (C50 values of 2.25 and 1.60 μM vs. 10 μM), while the conjugates 1 and 3 with three HB units incorporated form less stable complexes (C50 values of 30 and 21 μM). The tetra(hydroxybutanoate)-peptide conjugates 2 and 4 are the first nonapeptide analogs for which the modification of the central part leads to increased affinities for a class-I-MHC protein, as compared to a model nonapeptide.

Notes: 6-Epikarpoxanthin ((all-E,3S,5R,6S,3′R)-5,-6-dihydro-β,β-carotene-3,5,6,3′-tetrol, 5), 5,6-diepikarpoxanthin ((all-E,3S,5S,6S,3′R)-5,6-β,β-carotene-3,5,6,3′-tetrol, 13), 5,6-diepilatoxanthin ((all-E,3S,5S,6S,3′S5′R,6′S)-5,6′-epoxy-5,6,5′,6′-tetrahydro-β,β-carotene-3,5,6,3′-tetrol, 14), and 5,6-diepicapsokarpoxanthin ((all-E,3S,5S,6S,3′S,5′R)-5,6-dihydro-3,5,6,3′-tetrahydroxy-β,κ-caroten-6′-one, 15) were isolated from red spice paprika (Capsicum annuum var. longum) and characterized by their UV/VIS, CD, 1H- and 13C-NMR, and mass spectra. Our investigations demonstrate that the configuration of the 3,5,6-trihydroxy-5,6-dihydro-β-end group may differ depending on the biological source.

Notes: The X-ray analyses of (η3-allyl){4-benzyl-2-[2-(diphenylphosphino-κP)phenyl]-4,5-dihydro-4-4-methyloxazole-κN}palladium(II) hexafluorophosphate (5) and the analogous [Pd(η3-1,3-diphenylallyl)] complex 6 are presented. A comparison with the (η3-allyl)- and (η-1,3-diphenylallyl)palladium complexes 2 and 3, respectively, containing the 4-monosubstituted 4,5-dihydro-2-(phosphinoaryl)oxazole ligand 1a reveals important structural differences (Fig. 3). 1H-NMR Spectroscopic investigation confirm that the 4,4-disubstituted 4,5-dihydro-2-(phosphinoaryl)oxazole ligand 4 of 5 and 6 shows the same conformation in solution as in the solid state (Table 2). The application of ligand (S)-4 in the Pd-catalyzed allylic substitution demonstrates a configurational relationship between the orientation of the allyl ligand in the intermediate (cf. complex 6) and the absolute configuration of the allylic-substitution product (Table 3).

Notes: Some new (2′-5′)triadenylates 13-16, containing at the 2′-terminal end 3′-fluoro-2′,3′-dideoxyadenosine derivatives, have been synthesized by the phosphotriester method. The selectively blocked nucleosides 2, 4, 5, and 7, were synthesized from the corresponding unprotected nucleosides 1, 3, and 6. The synthesized trimers 13, and 14 were 4- and 8-fold, respectively, more stable towards phosphodiesterase from Crotalus durissus than the natural trimer 17. In comparison to trimer 17 the new compounds 13-15 inhibit HIV-1 reverse transcriptase (RT) activity, and 15 and 16 the HIV-1 induced syncytia formation 2-3 fold whereas none of 13-16 can improve R Nase L activity.

Notes: The first asymmetric α-alkylations of lithiated sulfonamides bearing the chirality information within the amine moiety under high asymmetric inductions (de 83-95%) are described. Racemization-free acidic hydrolysis led to the title compounds 11 in acceptable overall yields and with high enantiomeric purity (ee 91- ≥ 98%; Scheme 2). As a novel chiral auxiliary, the primary amine (S,S)-or (R,R)-2 was synthesized employing the classical Erlenmeyer phenylserine synthesis (Scheme 1).

Notes: This theoretical study focuses on two indole derivatives, melatonin (1) and carvedilol (8), with the objective of improving our understanding of the molecular mechanisms underlying their radical-scavenging activity. Quantum-mechanical calculations were carried out using the AM1 semi-empirical method, some results being confirmed by ab initio (3-21G) calculations. The quantum-chemical descriptor Δ Hox (relative adiabatic oxidation potential) and the shape of the SOMO (singly occupied molecular orbital) indicate that the stabilization of its radical cation can partially explain the well-documented antioxidant efficacy of melatonin. This stablization may result from electrostatic interactions and from a hyperconjugative effect existing in a family of conformers of the melatonin radical cation having the side chain almost perpendicular to the plane of the aromatic rings. Furthermore, 6-hydroxymelatonin (7) appears to be a better free-radical scavenger than melatonin (1) in agreement with experimental results. According to the theoretical parameters Δ Hox and Δ Habs (relative bond dissociation enthalpy), carvedilol (8) is not a good antioxidant, in contrast to its ring-hydroxylated metabolites whose powerful antioxidant effects are explained by the formation of an oxyl radical stabilized by delocalization over the carbazole nucleus.

Notes: The reaction of α-nitro ketones to the corresponding α-hydroxy ketones under basic aqueous conditions, a novel transformation, was studied. The investigation revealed that the reaction is only possible with α-nitro ketones that are CH-acidic in the α′-position and readily deprotonated under the reaction conditions. The NO2/OH exchange was established to proceed with retention of configuration at the stereogenic center, and labeling experiments have shown that the OH O-atom originates, to a great extent, from the solvent. In particular, the stereochemical course of the reaction and the incorporation of external nucleophiles led us to propose a mechanism that involves neighboring-group participation. The product formation is explained by a double SN2 reaction, which proceeds via a Favorskii-like cyclopropanone intermediate.

Notes: We report on the synthesis of a receptor 4 for β,β-carotene (1), and on the binding interaction between the two which yields inclusion complex 5. The cyclodextrin ‘dimer’ 4 was obtained via condensation of the corresponding 4,4′-(porphyrin-5,15-diyl)bis phenol 8 with 6A-deoxy-6A-iodo-β-cyclodextrin (6) in the presence of Cs2CO3. Fluorescence studies of the binding interaction between ‘dimer’ 4 and β,β-carotene (1) gave a binding constant Ka of (2.4 ± 0.1) · 106 M-1.

Notes: The lithium enolate of (±)-6-endo-chloro-5-exo-(phenylseleno)-7-oxabicyclo[2.2.1]heptan-2-one (16) added to furan-2-carboxaldehyde giving a single aldol 19 (Schemes 1 and 2) that was converted with high stereoselectivity into (±)-(1RS,3SR,4SR,5RS,6SR)-5-exo-{(RS)-[(tert-butyl)dimethylsilyloxy](furan-2-yl)methyl}-6-endo-(methoxymethoxy)-2-oxo-7-oxabicyclo[2.2.1]hept-3-exo-yl 4-bromobenzenesulfonate (46). Highly regioselective Baeyer-Villiger oxidation of 46 provided the corresponding β-DL-altrofuranurono-6,1-lactone 49, the methanolysis of which gave (±)-methyl 1,5-anhydro-3-{(SR)-[(tert-butyl)dimethylsiloxy](furan-2-yl)methyl}-3-deoxy-2-O-(methoxymethyl)-α-DL-galactofuranuronate (51). Reduction of 51 followed by protection furnished (±)-1,4-anhydro-3-{(SR)-[(tert-butyl)dimethylsilyoxy](furan-2-yl)methyl}-3-deoxy-2,6-bis-O-(methoxymethyl)-α-DL-galactopyranose (54). Clean oxidation of the furan unit in (54). Clean oxidation of the furan unit in 54 was possible with dimethyldioxirane, giving the corresponding (Z)-4-oxoenal 59 that was converted into pyrroles such as (±)-1,4-anhydro-3-{(SR)-[(tert-butyl)dimethylsilyloxy](1-benzyl-1 H-pyrrol-2-yl)methyl}-3-deoxy-2,6-bis-O-(methoxymethyl)-α-DL-galactopyranose (58; Scheme 5), or into pyrrolidin-3,4-diols by dihydroxylation of (±)-1,4-anhydro-3-{(1′RS,2′RS,Z)-1′-[(tert-butyl)-dimethylsilyloxy]-2′,5′-bis[(methylsulfonyl)oxy]pent-3′-enyl}-3-deoxy-2,6-bis-O-(methoxymethyl)-α-DL-galactopyranose (70; Schemes 6 and 7). After adequate protection (→ 70), selective displacement of one of the mesylate moieties with LiN3, followed by hydrogenation of the corresponding primary azide and intramolecular substitution, led to four protected, stereoisomeric C-linked imino disaccharides (Scheme 7); the latter were deprotected under acidic conditions to give (±)-3-deoxy-3-[(1′SR)-2′,5′-dideoxy-2′,5′-imino-α-LD-ribitol-1′-C-yl]-DL-galactose (3), (±)-3-deoxy-3-[(1′SR)-2′,5′-dideoxy-2′,5′-imino-α-DL-arabinitol-1′-C-yl]-DL-galactose (4), (±)-3-deoxy-3-[(1′SR)-2′,5′-dideoxy-2′,5′-imino-β-DL-ribitol-1′-C-yl]-DL-galactose (5), and (±)-3-deoxy-3-[(1′SR)-2′,5′-dideoxy-2′,5′-imino-β-DL-arabinitol-1′-C-yl]-DL-galactose (6). These unprotected C-linked imino disaccharides were more stable as ammonium chlorides in H2O. Neutralization of 4 · HCl, followed by NaBH4 reduction, gave (±)-(1RS,2SR,6SR,7RS,8RS,8aSR)-1,2,3,5,6,7,8,8a-octahydro-7-[(1SR,2SR)-1,2,3-trihydroxypropyl]indolizine-1,2,6,8-tetrol (14), a new octahydroindolizinepolyol (Scheme 8). Methyl glycosides of C-linked imino disaccharides 3-6 were also obtained, such as (±)-methyl 3-deoxy-3-[(1′SR)-2′,5′-dideoxy-2′,5′-imino-α-LD-ribitol-1′-C-yl]-β-DL-galactofuranoside (7), (±)-methyl 3-deoxy-3-[(1′SR)-2′,5′-dideoxy-2′,5′-imino-β-LD-arabinitol-1′-C-yl]-β-DL-galactofuranoside (8) and -α-DL-galactofuranoside (9), (±)-methyl 3-deoxy-3-[(1′SR)-2′,5′-dideoxy-2′,5′-imino-α-DL-arabinitol-1′-C-yl]-β-DL-galactofuranoside (11) and -α-DL-galactopyranoside (10), and (±)-methyl 3-deoxy-3-[(1′SR)-2′,5′-dideoxy-2′,5′-imino-β-DL-ribitol-1′-C-yl]-β-DL-galactofuranoside (13) and -α-DL-galactopyranoside (12). All these new C-linked imino disaccharides can be obtained in their enantiomerically pure form either starting with enantiomerically pure 7-oxabicyclo[2.2.1]heptain-2-one derivatives (‘naked sugars of the first generation’) or using the method of Johnson and Zeller applied to the racemic protected aldol 3-exo-{[(tert-butyl)dimethylsiloxy](furan-2-yl)methyl}-6-endo-chloro-5-exo-(phenylseleno)-7-oxabicyclo[2.2.1]heptan-2-one (22; see Scheme 2). The unprotected C-linked imino disaccharides 3-13 and octahydroindolzinetetrol 14 were tested for their inhibitory activity toward 25 commercially available glycohydrolases. Only compound 3 which mimics the mannopyranosyl-cation intermediate during the hydrolysis of an α-mannopyranosyl-(1 → 3)-galactose has a weak, but specific α-mannosidase inhibitory activity.

Notes: We study the large time asymptotics of solutions u(x, t) of the wave equation with time-harmonic force density f(x)e-iωt, ω≥0, in the semi-strip Ω= (0, ∞)×(0, 1) for a given f∊C∞0(Ω). We assume that u satisfies the initial condition u=(∂/∂t)u=0 for t=0 and the boundary conditions u=0 for x2=0 and x2=1, and (∂/∂x1)u=αu for x1=0, with given α, -π≤α〈∞. Let Dα be the self-adjoint realization of -Δ in Ω with this boundary condition. For -π≤α〈0, Dα has eigenvalues λj=π2j2-α2, j=1, 2, … For j≥2 these eigenvalues are embedded in the continuous spectrum of Dα, σc(Dα)=[π2, ∞]. For α≥0, Dα has no eigenvalues. We consider the asymptotic behaviour of u(x, t), t→∞, as a function of α. In the case α=0 resonances of order √t at ω=πj, j=1, 2, …, were found in References 5 and 10. We prove that for α=-π there is a resonance of order t2 for ω=0 and resonances of order t for every ω〉0 (note that 0 is an eigenvalue of D-π). Moreover, for -π〈α〈0 there are resonances of order t at ω=√λj. The resonance frequencies are continuous functions of α for -π〈α〈0 and tend to πj, j=1, 2, … as α goes to zero.On the contrary in the case α〉0 there are no real resonances in the sense that the solution remains bounded in time as t→∞. Actually in this case, the limit amplitude principle is valid for all frequencies ω≥0. This rather striking behaviour of the resonances is explained in terms of the extension of the resolvent R(κ)=(Dα-κ2)-1 as a meromorphic function of κ into an appropriate Riemann surface. We find that as α crosses zero the real poles of R(κ) associated with the eigenvalues remain real, but go into a second sheet of the Riemann surface. This behaviour under perturbation is rather different from the case of complex resonances which has been extensively studied in the theory of many-body Schrödinger operators where the (real) eigenvalues embedded in the continuous spectrum turn under a small perturbation into complex poles of the meromorphic extension of the resolvent, as a function of the spectral parameter κ2. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The global existence and uniqueness of classical solution of steady motions of a third-grade fluid provided assumptions on positivness of μ (coefficient of viscosity) and α1, γ (material coefficients) is proved. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: Integral equations associated with the basic boundary value problems for the Laplace and Stokes equations are considered. The integral operators for these integral equations are interpreted as the pseudodifferential operators, and their principal symbols are calculated. The symbols are obtained in terms of the principal curvatures and the coefficients of the first quadratic form of the boundary. As a consequence, the initial approximation is suggested for the iterative methods solving the integral equations. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The boundary integral equation method is used to prove the convergence of the Drude-Born-Fedorov equations with variable coefficients, possibly non-smooth, to Maxwell's equations as chirality admittance tends to zero. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: New explicit stability conditions are derived for a linear integro-differential equation with periodic operator coefficients. The equation under consideration describes oscillations of thin-walled viscoelastic structural members driven by periodic loads. To develop stability conditions two approaches are combined. The first is based on the direct Lyapunov method of constructing stability functionals. It allows stability conditions to be derived for unbounded operator coefficients, but fails to correctly predict the critical loads for high-frequency excitations. The other approach is based on transforming the equation under consideration in such a way that an appropriate ‘differential’ part of the new equation would possess some reserve of stability. Stability conditions for the transformed equation are obtained by using a technique of integral estimates. This method provides acceptable estimates of the critical forces for periodic loads, but can be applied to equations with bounded coefficients only. Combining these two approaches, we derive explicit stability conditions which are close to the Floquet criterion when the integral term vanishes. These conditions are applied to the stability problem for a viscoelastic bar compressed by periodic forces. The effect of material and structural parameters on the critical load is studied numerically. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In order to maintain spectrally accurate solutions, the grids on which a non-linear physical problem is to be solved must also be obtained by spectrally accurate techniques. The purpose of this paper is to describe a pseudospectral computational method of solving integro-differential systems with quadratic performance index. The proposed method is based on the idea of relating grid points to the structure of orthogonal interpolating polynomials. The optimal control and the trajectory are approximated by the m th degree interpolating polynomial. This interpolating polynomial is spectrally constructed using Legendre-Gauss-Lobatto grid points as the collocation points, and Lagrange polynomials as trial functions. The integrals involved in the formulation of the problem are calculated by Gauss-Lobatto integration rule, thereby reducing the problem to a mathematical programming one to which existing well-developed algorithms may be applied. The method is easy to implement and yields very accurate results. An illustrative example is included to confirm the convergence of the pseudospectral Legendre method, and a comparison is made with an existing result in the literature. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: This article establishes the existence of a trapped-mode solution to a linearized water-wave problem. The fluid occupies a symmetric horizontal channel that is uniform everywhere apart from a confined region which either contains a thin vertical plate spanning the depth of the channel or has indentations in the channel walls; the forces of gravity and surface tension are operative. A trapped mode corresponds to an eigenvalue of the composition of an inverse differential operator and a Neumann-Dirichlet operator for an elliptic boundary-value problem in the fluid domain. The existence of such an eigenvalue is established by extending previous results dealing with the case when surface tension is absent. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notes: In this paper an initial-boundary-value problem in one-space dimension is studied for the Broadwell model extended to a gas mixture undergoing bimolecular reactions. Techniques of semigroup of bounded positive operators in a suitable Banach space are used to prove existence and uniqueness of the solution on bounded time intervals whose length depends on the initial data. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In the present work, the problem of electromagnetic wave propagation in three-dimensional stratified media is studied. The method of decoupling the electric and magnetic fields is implemented, and the spectral approach is adopted, componentwise, to the vector equation involving the electric field. Operational calculus of self-adjoint, positive operators in suitable Hilbert spaces is used to solve the corresponding initial value problems. The spectral families of these operators for the cases of the whole space and of a finite layer are constructed. A discussion on the applicability of the obtained results to physical problems is also included. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In this paper we prove under the assumption of small initial data the global existence of a classical solution to the equations in viscoelasticity, associated with a free damping boundary condition. We also show that if we choose the initial data large enough, blow up will occur in finite time. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We consider the thermoelastic plate system,utt-γΔutt+Δ2u+αΔθ=0,θt-κΔθ-αΔut=0 and we make a comparison between the models in which γ=0 and γ〉0. We conclude that in the first case the plate system is of a parabolic type, while when γ〉0 the corresponding system has a hyperbolic behaviour. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: This paper concerns the orbital stability for solitary waves of the Long Wave-Short Wave resonance equations. Since the abstract results of Grillakis et al. [7, 8] cannot be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain the stability of the solitary waves. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: We consider particle transport in a three-dimensional convex region V, bounded by the regular surface ∂V. We assume that particles are specularly reflected by ∂V and that a source q is assigned on ∂V; more general non-homogeneous boundary conditions are also discussed. The problem is non-linear because the boundary condition is not homogeneous. We prove existence of a unique strict solution and by using the theory of semigroups we derive the explicit expression of such a solution in terms of the boundary source q. In the appendix, we indicate how some properties of affine operators can be used to derive the solution. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: A phase-field model based on the Coleman-Gurtin heat flux law is considered. The resulting system of non-linear parabolic equations, associated with a set of initial and Neumann boundary conditions, is studied. Existence, uniqueness, and regularity results are proved. An asymptotic analysis is also carried out, in the case where the coefficient of the interfacial energy term tends to 0. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: We apply the Child-Langmuir asymptotics of the Vlasov-Poisson system to the case of a bipolar diode, i.e. a vacuum diode where two species of particles of opposite electric charge are flowing. This leads to a simplified model which, if at least one of the two injected currents is not too large, has a unique solution. Moreover, in that case, the currents flowing inside the diode are limited by the so-called bipolar Child-Langmuir currents. In the case of large currents, other solutions may appear, and the formation of virtual electrodes may occur inside the diode. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: In this paper we consider the Cauchy problem for the equation∂u/∂t + u ∂u/∂x + u/x = 0 for x 〉 0, t ≥ 0, with u(x, 0) = u0-(x) for x 〈 x0, u(x, 0) = u0+(x) for x 〉 x0, u0-(x0) 〉 u0+(x0). Following the ideas of Majda, 1984 and Lax, 1973, we construct, for smooth u0- and u0+, a global shock front weak solution u(x, t) = u-(x, t) for x 〈 φ(t), u(x, t) = u+(x, t) for x 〉 φ(t), where u- and u+ are the strong solutions corresponding (respectively) to u0- and u0+ and the curve t → φ(t) is defined by dφ/dt (t) = 1/2[u-(φ(t), t) + u+(φ(t), t)], t ≥ 0 and φ(0) = x0.© 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: A variational approach to a non-linear non-local identification problem related to the non-linear transport equation is studied. Introducing a similarity transformation, the problem is formulated as an identification problem for a non-linear differential equation of second order with an additional non-local condition. For the solution of the forward problem stability in H1-norm with respect to the identification parameter is obtained. Using this result the existence of a solution to the identification problem is proved. Some results of computational experiments are given. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: We consider the plate equation in a polygonal domain with free edges. Its resolution by boundary integral equations is considered with double layer potentials whose variational formulation was given in Reference 25. We approximate its solution (u, (∂u/∂n)) by the Galerkin method with approximated spaces made of piecewise polynomials of order 2 and 1 for, respectively, u and (∂u/∂n). A prewavelet basis of these subspaces is built and equivalences between some Sobolev norms and discrete ones are established in the spirit of References 14, 16, 30 and 31. Further, a compression procedure is presented which reduces the number of nonzero entries of the stiffness matrix from O(N2) to O(N log N), where N is the size of this matrix. We finally show that the compressed stiffness matrices have a condition number uniformly bounded with respect to N and that the compressed Galerkin scheme converges with the same rate than the Galerkin one. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: The relativistic Vlasov-Maxwell-Fokker-Planck system is used in modelling distribution of charged particles in plasma. It consists of a transport equation coupled with the Maxwell system. The diffusion term in the equation models the collisions among particles, whereas the viscosity term signifies the dynamical frictional forces between the particles and the background reservoir. In the case of one space variable and two momentum variables, we prove the existence of a classical solution when the initial density decays fast enough with respect to the momentum variables. The solution which shares this same decay condition along with its first derivatives in the momentum variables is unique. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: We consider reactive mixtures of dilute polyatomic gases in full vibrational non-equilibrium. The governing equations are derived from the kinetic theory and possesses an entropy. We recast this system of conservation laws into a symmetric conservative form by using entropic variables. Following a formalism developed by the authors in a previous paper, the system is then rewritten into a normal form, that is, in the form of a quasilinear symmetric hyperbolic-parabolic system. Using a result of Vol'pert and Hudjaev, we prove local existence and uniqueness of a bounded smooth solution to the Cauchy problem. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: Approximate solutions of the non-linear Boltzmann equation, which have the structure of the linear combination of three global Maxwellians with arbitrary hydrodynamical parameters, are considered. Some sufficient conditions which allow the error between the left- and the right-hand sides of the equation tend to zero, and which are calculated either in the mixed metric or in the pure integral metric, are obtained. The class of the distributions, which minimized this error for the arbitrary Knudsen number, is found. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: The paper considers a system of partial differential equations of convection dispersion type, modelling a stratified two-phase fluid flow. Local existence in time is proved for a sufficiently smooth initial data, given in the set of physically admissible states. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: In this paper we study the motion of an elastic conducting wire in a magnetic field. The motion of the conductor induces a current in the wire (Faraday's law) which, in turn produces a force on the wire. We consider the linear equation obtained by linearizing the resulting equations of motion about an equilibrium solution. This is a hyperbolic partial differential equation with a non-local term. We prove existence and uniqueness of a weak solution of an initial-boundary value problem for this equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: In this paper we are concerned with a weighted least-squares finite element method for approximating the solution of boundary value problems for 2-D viscous incompressible flows. We consider the generalized Stokes equations with velocity boundary conditions. Introducing the auxiliary variables (stresses) of the velocity gradients and combining the divergence free condition with some compatibility conditions, we can recast the original second-order problem as a Petrovski-type first-order elliptic system (called velocity-stress-pressure formulation) in six equations and six unknowns together with Riemann-Hilbert-type boundary conditions. A weighted least-squares finite element method is proposed for solving this extended first-order problem. The finite element approximations are defined to be the minimizers of a weighted least-squares functional over the finite element subspaces of the H1 product space. With many advantageous features, the analysis also shows that, under suitable assumptions, the method achieves optimal order of convergence both in the L2-norm and in the H1-norm. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: We consider the two-parameter non-linear Sturm-Liouville problems. By using the variational method on general level sets, the variational eigenvalues are obtained. The purpose of this paper is to study the properties of these variational eigenvalues with respect to the parameter of general level sets. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: We study the limit behaviour of solution of Poisson's equation in a class of thin two-dimensional domains, both simply connected or single-hollowed, as its thickness becomes very small. The method is based on a transformation of the original problem into another posed on a fixed domain, obtention of a priori estimates and convergence results when thickness parameter tends to zero. As an important application of abstract results we obtain the limit expressions for functions appearing in elastic beam theories as torsion and warping functions. In this way, we provide a mathematical justification and a correct definition of torsion, warping and Timoshenko functions and constants that should be used in the open and closed thin-walled elastic beam theories. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The generalized Möbius function and Möbius inversion formula are applied to a multiplicative semigroup. A general mathematical method based on this Möbius inversion is presented to solve inversion problems of expansions with unequally weighted terms. By this method, all the inverse lattice problems in physics can be solved concisely. The solutions of four inverse lattice problems: the Fibonacci structure, the square lattice structure, the bcc and the hcp lattice structures are given. These are difficult to be solved by other methods. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We use the eigenfunction expansion of Green's function of Dirichlet problems to obtain sampling theorems. The analytic properties of the sampled integral transforms as well as the uniform convergence of the sampling series are proved without any restrictions on the integral transforms. We obtain a one- and multi-dimensional versions of sampling theorems. In both cases the sampling series are written in terms of Lagrange-type interpolation expansions. Some examples and the truncation error as well as the stability of the obtained sampling expansions are discussed at the end of the paper. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We consider a dynamical von Kármán system in the presence of thermal effects. Our model includes the possibility of a rotational inertia term in the system. We show that the total energy of the solution of such system decays exponentially as t→+∞. The decay rates we obtain are uniform on bounded sets of the energy space. The main ingredients of our method of proof are suitable properties of a decoupled system, the energy method and the compactness of the nonlinear map associated to the von Kármán system. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: This short article discusses the spectrum of the Neumann Laplacian in the infinite domain Ω⊂∝n, n ≥2 created by inserting a compact obstacle P into the uniform cylinder Ω0 =(-∞, ∞)×Ω′. The main result is the existence of at least one embedded eigenvalue when P is an (n -2)-dimensional surface whose unit normal is parallel to Ω′ at each point of P . The special case when P is symmetric about {0}×Ω′ is also treated. It is shown that there is at least one symmetric eigenvector and, when P is sufficiently long, at least one antisymmetric eigenvector. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We prove the existence of solutions to the three-dimensional elastoplastic problem with Hencky's law and Neumann boundary conditions by elliptic regularization and the penalty method, both for the case of a smooth boundary and of an interior two dimensional crack. It is shown, in particular, that the variational solution satisfies all boundary conditions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The propagation of Hölder regularity of the solutions to the 3D Euler equations is discussed. Our method is a special semi-linearization of the vorticity equation combined with the classical Schauder interior estimates. © 1998 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: This paper is concerned with the solution of Maxwell equations in the modelling of the scattering of a time-harmonic electromagnetic wave by an obstacle located in a two-layered medium. The use of the Silver-Müller radiation condition in each layer is shown to provide a well-posed scattering problem. The analysis is based on the study of the Green tensor, which allows to relate the radiation condition to an integral representation formula. The analyticity properties of the scattering problem with respect to the frequency are then investigated. This gives rise to a limiting absorption principle and furnishes a characterization of the resonances. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We apply our recently developed distributional technique [2, 3] to study time-domain asymptotics. This enables us to present a rigorous mathematical discussion and extensions of the results given by Chapman [1] and subsequent workers in this field. The present analysis is facilitated by defining functions which are distributionally small at infinity. We find that one of the advantages of using this technique is that multidimensional extensions can be derived very easily. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: This paper is concerned with a specific finite element strategy for solving elliptic boundary value problems in domains with corners and edges. First, the anisotropic singular behaviour of the solution is described. Then the finite element method with anisotropic, graded meshes and piecewise linear shape functions is investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates for functions from anisotropically weighted spaces are derived. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: This paper presents a general method of analysis for investigating the whirl stability of a rotor-bearing system whose appendage is flexibly attached to the spinning shaft. Sufficient conditions of asymptotic stability involving system different parameters are derived based on Liapunov's theory. An inclusive analysis of the effect of the combined flexibilities of the elastic attachment of the appendage to the shaft and the two end bearings coupled with the other various parameters of the system on the dynamic stability is presented. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We investigate the steady compressible Navier-Stokes equations near the equilibrium state v = 0, ρ = ρ0 (v the velocity, ρ the density) corresponding to a large potential force. We introduce a method of decomposition for such equations: the velocity field v is split into a non-homogeneous incompressible part u (div (ρ0u) = (0) and a compressible (irrotational) part ∇φ. In such a way, the original complicated mixed elliptic-hyperbolic system is split into several ‘standard’ equations: a Stokes-type system for u, a Poisson-type equation for φ and a transport equation for the perturbation of the density σ = ρ - ρ0. For ρ0 = const. (zero potential forces), the method coincides with the decomposition of Novotny and Padula [21]. To underline the advantages of the present approach, we give, as an example, a ‘simple’ proof of the existence of isothermal flows in bounded domains with no-slip boundary conditions. The approach is applicable, with some modifications, to more complicated geometries and to more complicated boundary conditions as we will show in forthcoming papers. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We consider acoustic scattering from an obstacle inside an inhomogeneous structure. We prove in the paper that if the outside inhomogeneity is known then the obstacle and possible inside inhomogeneity are uniquely determined by the fixed energy far field data. The proof is based on new mapping properties of layer potentials in spaces that specify one point. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The linear problem for the velocity potential around a slightly curved thin finite wing is considered under the Joukowskii-Kutta hypothesis. The exponents of possible singularities of solutions at angular points on wing's trailing edge are expressed in terms of eigenvalues of mixed boundary value problems for the Beltrami-Laplace operator on the hemisphere and the semicircle. These singularities have a structure such that the circulation function turns out to be continuous in interior angular points of the trailing edge. In the case of trapezoidal shape of the wing ends there occur square-root singularities of the velocity field at the trailing edge endpoints and the same singularities, of course, are extended along the lateral sides of the wake behind the wing. It is proved that for any angular point on the trailing edge the exponents of all above-mentioned singularities form a countable set in the upper complex half-plane with the only accumulation point at infinity. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: We study the long-time behaviour of solutions of the Vlasov-Poisson-Fokker-Planck equation for initial data small enough and satisfying some suitable integrability conditions. Our analysis relies on the study of the linearized problems with bounded potentials decaying fast enough for large times. We obtain global bounds in time for the fundamental solutions of such problems and their derivatives. This allows to get sharp bounds for the decay of the difference between the solutions of the Vlasov-Poisson-Fokker-Planck equation and the solution of the free equation with the same initial data. Thanks to these bounds, we get an explicit form for the second term in the asymptotic expansion of the solutions for large times. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: An initial-value problem modelling coagulation and fragmentation processes is studied. The results of earlier papers are extended to models where either one or both of the rates of coagulation and fragmentation depend on time. An abstract integral equation, involving the solution operator to the linear fragmentation part, is investigated via the contraction mapping principle. A unique global, non-negative, mass-conserving solution to this abstract equation is shown to exist. The latter solution is used to generate a global, non-negative, mass-conserving solution to the original non-autonomous coagulation and multiple-fragmentation equation. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In this paper we prove the global existence and study decay property of the solutions to the initial boundary value problem for the quasi-linear wave equation with a dissipative term without the smallness of the initial data. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: Reaction random-walk systems are hyperbolic models to describe spatial motion (in one dimension) with finite speed and reactions of particles. Here we present two approaches which relate reaction random-walk equations with reaction diffusion equations. First, we consider the case of high particle speeds (parabolic limit). This leads to a singular perturbation analysis of a semilinear damped wave equation. A initial layer estimate is given. Secondly, we consider the case of a transcritical bifurcation. We use techniques similar to that of the Ginzburg-Landau method to find a modulation equation for the amplitude of the first unstable mode. It turns out that the modulation equation is Fisher's equation, hence near the bifurcation point travelling wave solutions are obtained. The approximation result and the corresponding estimate is given in terms of the bifurcation parameter. Both results are based on an a priori estimate for classical solutions which follows from explicit representations of the solution of the linear telegraph equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: In the article the problem of regulation of the cardiovascular system is investigated from the point of view of control process theory. This problem was reduced to finding the optimal control in the sense of speed in a bilinear system. In the first part of the article the possibility of applying Saburov's method for the solution to bilinear control problems is considered. The second part of the article is devoted to the application of this method to a concrete problem from practical medicine. The method has allowed the complete synthesis of an optimal control to be carried out  -  the sliding mode takes place and it was investigated completely. The results obtained are interesting from the point of view of control process theory, and testify to the high efficiency of the method. The final results allow concrete recommendations about the regulation of the cardiovascular system. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: The steady-state equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear elliptic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet-Neumann boundary conditions are prescribed. The existence of generalized solutions is proven. The key of the proof is a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrize the equations. The uniqueness of weak solutions is shown under the assumption that the boundary data are not far from the thermal equilibrium. A general uniqueness result cannot be expected for physical reasons. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: We consider an elastic plate with the non-deformed shape ΩΣ := Ω \ Σ, where Ω is a domain bounded by a smooth closed curve Γ and Σ ⊂ Ω is a curve with the end points {γ1, γ2}. If the force g is given on the part ΓN of Γ, the displacement u is fixed on ΓD := Γ \ ΓN and the body force f is given in Ω, then the displacement vector u(x) = (u1(x), u2(x)) has unbounded derivatives (stress singularities) near γk, k = 1, 2   u(x) = ∑2k, l=1 Kl(γk)r1/2kSCkl(θk) + uR(x)     near γk.Here (rk, θk) denote local curvilinear polar co-ordinates near γk, k = 1, 2, SCkl (θk) are smooth functions defined on [-π, π] and uR(x) ∊ {H2(near γk)}2. The constants Kl(γk),   l = 1, 2, which are called the stress intensity factors at γk (abbr. SIFs), are important parameters in fracture mechanics. We notice that the stress intensity factors Kl(γk) (l = 1, 2;  k = 1, 2) are functionals Kl(γk) = Kl(γk; L, Ω, Σ) depending on the load L, the shape of the plate Ω and the shape of the crack Σ. We say that the crack Σ is safe, if Kl(γk; Ω)2 + K2(γk; Ω)2 〈 RẼ. By a small change of Ω the shape Σ can change to a dangerous one, i.e. we have K1(γk; Ω)2 + K2(γk; Ω)2 ≥ RẼ. Therefore it is important to know how Kl(γk) depends on the shape of Ω.For this reason, we calculate the Gâteaux derivative of Kl(γk) under a class of domain perturbations which includes the approximation of domains by polygonal domains and the Hadamard's parametrization Γ(τ) := {x + τφ(x)n(x);  x ∊ Γ}, where φ is a function on Γ and n is the outward unit normal on Γ. The calculations are quite delicate because of the occurrence of additional stress singularities at the collision points {γ3, γ4} = ΓD ∩ ΓN.The result is derived by the combination of the weight function method and the Generalized J-integral technique (abbr. GJ-integral technique). The GJ-integrals have been proposed by the first author in order to express the variation of energy (energy release rate) by extension of a crack in a 3D-elastic body. This paper begins with the weak solution of the crack problem, the weight function representation of SIF's, GJ-integral technique and finish with the shape sensitivity analysis of SIF's. GJ-integral Jω(u; X) is the sum of the P-integral (line integral) Pω(u, X) and the R-integral (area integral) Rω(u, X). With the help of the GJ-integral technique we derive an R-integral expression for the shape derivative of the potential energy which is valid for all displacement fields u ∊ H1. Using the property that the GJ-integral vanishes for all regular fields u ∊ H2 we convert the R-integral expression for the shape derivative to a P-integral expression. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: It is shown that a stochastic system of N interacting particles in a slab approximates, in the Boltzmann-Grad limit, a one-dimensional Boltzmann equation with diffusive boundary conditions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notes: The asymptotic behaviour of solutions of certain semilinear elliptic Dirichlet boundary value problems defined on a semi-infinite cylinder is investigated by means of energy arguments and maximum principles. Various hypotheses are made on the form of the semilinear term, and in some cases it is found that the rate of decay of solutions is faster than the optimal decay rate for harmonic functions. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: In this paper the problem of collision analysis for a mobile robot operating in a planar environment with moving objects (obstacles) is addressed. The pattern of motion of the potential obstacles cannot be predicted; only a bound on their maximum velocity is available. Based on this information, at its current position the robot constructs the Hazard Region that corresponds to the path it contemplates. If the Hazard Region contains at least one obstacle, then there is a potential for this obstacle to collide with the robot (in which case perhaps another path should be planned). We first derive the solution for Hazard Region for two standard path primitives, a straight line segment and a circular arc segment; the solution is exact, except for one special case (for which the approximation error is estimated). This result is then applied to a more complex case when the path presents a combination of those primitives. Such are, for example, the optimal (shortest) paths with constrained curvature (known as Dubins paths [3]), which connect two points, each with a prescribed direction of motion. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: We consider the acoustic propagator A=-∇·c2∇ in the strip Ω={(x, z)∊∝2∣0〈z〈H} with finite width H〉0. The celerity c depends for large ∣x∣ only on the variable z and describes the stratification of Ω: it is assumed to be in L∞(Ω), bounded from below by cmin〉0, such that there exists M〉0 with c(x, z)=c1(z) if x〈 -M and c(x, z)=c2(z) if x〉M. We look at the propagator A as a ‘perturbation’ of the free propagators Aj in Ω associated to the velocities cj, j=1, 2, and implement a ‘perturbative’ method, adapting ideas of Majda and Vainberg. The spectrum of A is defined in section 2, a limiting absorption principle is proved in section 3 outside of a countable set Γ(A). The points of Γ(A) can only accumulate at the left of the thresholds of the free propagators. The needed material about Aj, j=1, 2, and some technical estimates for A are given in Appendix. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: Considered is the rotation of a robot arm or rod in a horizontal plane about an axis through the arm's fixed end and driven by a motor whose torque is controlled. The model was derived and investigated computationally by Sakawa and co-authors in [7] for the case that the arm is described as a homogeneous Euler beam. The resulting equation of motion is a partial differential equation of the type of a wave equation which is linear with respect to the state, if the control is fixed, and non-linear with respect to the control.Considered is the problem of steering the beam, within a given time interval, from the position of rest for the angle zero into the position of rest under a certain given angle.At first we show that, for every L2-control, there is exactly one (weak) solution of the initial boundary value problem which describes the vibrating system without the end condition.Then we show that the problem of controllability is equivalent to a non-linear moment problem. This, however, is not exactly solvable. Therefore, an iteration method is developed which leads to an approximate solution of sufficient accuracy in two steps. This method is numerically implemented and demonstrated by an example. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: A time-dependent Ginzburg-Landau-type model of a superconducting-normal-superconducting junction is presented. The existence and the uniqueness of the solutions are proved. When the data of the model are symmetric of some kinds, the solutions turns out to be symmetric of some kinds. In this symmetric case, an approximate model with the small thickness of the normal material in the middle of the junction as coefficients of a differential system is established for the sake of numerical computations. And also the existence and the uniqueness of the solution to this approximate model are set up. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We consider the problem of a polygonal plate with free edges. It is a boundary value problem for the biharmonic operator on a polygon with Neumann boundary conditions. Its resolution is studied via boundary integral equations. A variational formulation of the boundary problem obtained by a double-layer potential is given. Finally, we implement the method and give numerical results. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: Wavelets on closed surfaces in Euclidean space ∝3 are introduced starting from a scale discrete wavelet transform for potentials harmonic down to a spherical boundary. Essential tools for approximation are integration formulas relating an integral over the sphere to suitable linear combinations of function values (resp. normal derivatives) on the closed surface under consideration. A scale discrete version of multiresolution is described for potential functions harmonic outside the closed surface and regular at infinity. Furthermore, an exact fully discrete wavelet approximation is developed in case of band-limited wavelets. Finally, the role of wavelets is discussed in three problems, namely (i) the representation of a function on a closed surface from discretely given data, (ii) the (discrete) solution of the exterior Dirichlet problem, and (iii) the (discrete) solution of the exterior Neumann problem. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We state a 1D model with quasi-stationary gas flows approximation for a carbon reactivity test in the production of silicon. The mathematical problem we formulate is a non-linear boundary value problem for a third-order ordinary differential equation with non-linear boundary conditions, which are non-local in time. We prove existence and uniqueness of a classical solution and provide a numerical example. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We present a bending model for a shallow arch, namely the type of curved rod where the curvature is of the order of the diameter of the cross section. The model is deduced in a rigorous mathematical way from classical tridimensional linear elasticity theory via asymptotic techniques, by taking the limit on a suitable re-scaled formulation of that problem as the diameter of the cross section tends to zero. This model is valid for general cases of applied forces and material, and it allows us to calculate displacements, axial stresses, bending moments and shear forces. The equations present a more general form than in the classical Bernoulli-Navier bending theory for straight slender rods, so that flexures and extensions are proved to be coupled in the most general case. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In this work we analyse a model for radiative heat transfer in materials that are conductive, grey and semitransparent. Such materials are for example glass, silicon, water and several gases. The most important feature of the model is the non-local interaction due to exchange of radiation. This, together with non-linearity arising from the well-known Stefan-Boltzmann law, makes the resulting heat equation non-monotone. By analysing the terms related to heat radiation we prove that the operator defining the problem is pseudomonotone. Hence, we can prove the existence of weak solution in the cases where coercivity can be obtained. In the general case, we prove the solvability of the system using the technique of sub and supersolutions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In the paper we study the problem of control by means of a heat source g for a thermoelastic system of equationsutt - ρ∇·p(θ, ∇u) - νΔut + DΔ2 u = f, cv(θ, ∇u)θt - κΔθ - ρθ[pθ (θ, ∇u)·∇ut] - ν∣∇ut∣2 = g, in a two-dimensional domain, where both viscosity ν and rigidity D are positive. Such a system has been considered in our former papers, and existence of solutions as well as uniqueness have been obtained. Here we prove the continuity and differentiability of solutions under somewhat stronger assumptions. An example of a control problem and necessary optimality conditions are presented. The system has an interpretation as a plate reinforced with shape memory alloy (SMA) wire mesh. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The exact solutions for the KdV and the Calogero-Degasperis-Fokas mKdV equations can be obtained by the AKNS class. The technique developed relies on the construction of the wave functions which are solutions of the associated AKNS system; that is, a linear eigenvalue problem in the form of a system of first order partial differential equations. The method of characteristics is used and Bäcklund transformations (BTs) are employed to generate two new solutions from the old. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In this paper we consider the boundary value problem for a semilinear equation□u(t, x)-μu(t, x)+aum(t, x)=0, μ〉0, a∊ℜ in the interior domain. We find a time global classical solution with exponential decay property by using singular hyperbolic equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: This paper deals with the detection of emergent plane cracks, by using boundary measurements. An identifiability result (uniqueness of the solution) is first proved. Then, we look at the stability of this solution with respect to the measurement. A weak stability result is proved, as well as a Lipshitz stability result for straight cracks, by using domain-derivative techniques. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: In this paper, the existence, both locally and globally in time, the uniqueness of solutions and the non-existence of global solutions to the initial boundary value problem of a generalized Modification of the Improved Boussinesq equation utt-uxx-uxxtt=σ(u)xx are studied and a few examples are discussed. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: In this paper we study the following problem:ut-Δu=-f(u) in Ω×(0, T)≡QT,∂u ∂n=g(u) on ∂Ω×(0, T)≡ST,u(x, 0)=u0(x) in Ω, where Ω⊂∝N is a smooth bounded domain, f and g are smooth functions which are positive when the argument is positive, and u0(x)〉0 satisfies some smooth and compatibility conditions to guarantee the classical solution u(x, t) exists. We first obtain some existence and non-existence results for the corresponding elliptic problems. Then, we establish certain conditions for a finite time blow-up and global boundedness of the solutions of the time-dependent problem. Further, we analyse systems with same kind of boundary conditions and find some blow-up results. In the last section, we study the corresponding elliptic problems in one-dimensional domain. Our main method is the comparison principle and the construction of special forms of upper-lower solutions using related equations. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notes: The rate data for the Menschutkin reaction between strongly activated Z-substituted benzyl p-toluenesulfonates and Y-substituted N,N-dimethylanilines in acetonitrile at 35 °C fit the equation, kobs  =  k1 + k2 [DMA], which is consistent with concurrent first- and second-order processes. The k1 and k2 values for each substrate were separated based on the above equation. The SN1 rate constant, k1, is unaffected by the nature of the nucleophile, whereas the SN2 rate constant, k2, increased with the electron-donating substituent of the N,N-dimethylaniline. The substituent effect on the k1 values is linearly correlated by the Yukawa-Tsuno equation with ρ  =  -5.2 and r  =  1.3. The unimolecular reaction can be regarded as a classical SN1 mechanism. In contrast, that on the k2 values shows an upward curvature when analyzed by the Brown σ+ treatment. These results are ascribed to the simultaneous and independent occurrence of SN1 and SN2 mechanisms in the present Menschutkin reaction. © 1998 John Wiley & Sons, Ltd.

Notes: No Abstract

Notes: Solution enthalpies of n-hexane, acetone, butan-2-one and octan-2-one in a series of tetrachloromethane-acetonitrile mixtures and the carbonyl stretching absorption frequencies in the IR spectra of these ketones were determined. It was found that over the whole range of concentrations (varying from neat tetrachloromethane up to neat acetonitrile) the solvation enthalpy of these compounds can be obtained additively from the contributions of the alkyl and carbonyl fragments. The solvent effect on the solvation enthalpy of the carbonyl group was found to be satisfactorily correlated with the corresponding IR frequency shifts of the C=O group. It was also found that the sensitivities of the carbonyl IR frequencies to the solvent composition are different for various ketones. From both IR and calorimetric data, the preferential solvation parameters were evaluated. The differences between the IR spectroscopic and calorimetric data are discussed. © 1998 John Wiley & Sons, Ltd.

Notes: In an effort to model solute-solvent interactions, the C=O stretching frequencies of five 1-substituted 2-pyrrolidinones and four other carbonyl-containing compounds were measured for 30 common solvents. These were then correlated with four empirical parameter sets and one theoretical (computational) parameter set. While an empirical parameter set gave the best correlation equations, the theoretical parameter equations are physically and statistically significant. Solvent volume, polarizability and hydrogen bond donor acidity (capacity) terms are significant in the correlation equations. © 1998 John Wiley & Sons, Ltd.

Notes: The P - S bond cleavage process in the hydroperoxidolysis of a model system for the nerve agent VX was studied using ab initio and semiempirical molecular orbital methods. Aqueous solvation effects were included through single-point calculations using the semiempirical SM5.2PD/A continuum solvation model and geometries optimized at the HF/MIDI! level of theory. The predominant pathway for P - S bond cleavage involves pseudorotation of a low-energy trigonal bipyramidal intermediate followed by apical ligand ejection. In aqueous solution, the free energy barriers for these processes are found to be 14.3 and 4.6 kcal mol-1, respectively, with electronic energies calculated at the MP2/cc-pVDZ//HF/MIDI! level of theory. By comparison with another continuum model of solvation (PCM), it is concluded that the SM5.2PD/A model performs well even for hypervalent phosphorus species, in spite of not having included any such molecules in the model's parameterization set. © 1998 John Wiley & Sons, Ltd.

Notes: N-Methyl-N-phenyl-tert-butylsulfenamide (MPSA) and morpholinyl-tert-butylsulfenamide (MOSA) were thermolyzed in a stirred-flow reactor at temperatures of 340-390 °C and pressures of 7-13 Torr, using toluene as carrier gas, at residence times of 0.3-1.3 s. Isobutene was formed in 99% yield through first-order reactions having the following Arrhenius parameters (A,s-1, Ea, kJ mol-1): MPSA, log A  =  12.41 ± 0.02, Ea  =  158.8 ± 0.2; MOSA, log A  =  12.91 ± 0.22, Ea  =  159 ± 3. It is proposed that the elimination of isobutene takes place by unimolecular reaction mechanisms involving polar, four-center cyclic transition states, forming S-unsubstituted thiohydroxylamines as co-products. Thermochemical parameters, estimated by semiempirical AM1 calculations, are reported for the latter and for the parent molecules. © 1998 John Wiley & Sons, Ltd.

Notes: A dynamic NMR study of the tautomerism of 2,2′-bisbenzimidazolyl in DMSO-d6 and a mechanistic interpretation of the process, based on a stepwise, single-proton transfer and formation of a zwitterionic intermediate, are presented. This interpretation is substantiated by semi-empirical calculations of the postulated intermediate and transition state, that yield results which are compared with previous studies on related aliphatic systems. © 1998 John Wiley & Sons, Ltd.

Notes: Acidities and bond dissociation energies (BDEs) of the N-H bond in two phenylsulfenylamides, PhSNHBz and PhSNH-t-Bu, and four phenylsulfenylanilides, 4-GC6H4NHSPh, where G  =  MeO, H, Br and CN, were measured in order to compare the effects of substituents on acidities and BDEs of N - H bonds with those of C - H bonds. The effects of PhS groups on acidities and BDEs in a series of C - H acids were found to be comparable to those on acidities and BDEs of PhS in a similar series of N - H acids. Comparisons were also made of the effects of changing the oxidation state of sulfur in the series PhS, PhSO and PhSO2 on the acidities and BDEs of adjacent N - H and C - H bonds in weak acids. Hammett-type plots of pKHA values for phenyl benzyl sulfones (4-GC6H4CH2SO2Ph) and phenylsulfenylanilides (4-GC6H4NHSPh) were linear vs σp- values. A linear plot was obtained and explained for a plot of BDE of the N - H bonds in remotely substituted phenylsulfonylanilides with σ+ values. Plots of BDEs vs Eox(A-) were also linear for 4-substituted phenylsulfenylanilides (4-GC6H4NHSPh), phenylsulfonylanilides (4-GC6H4NHSO2Ph) and phenyl benzyl sulfones (4-GC6H4CH2SO2Ph). © 1998 John Wiley & Sons, Ltd.

Notes: 17O NMR spectra of several α-diamides were obtained at natural isotopic abundance in acetonitrile solution in order to study the conformations of these compounds in solution. The 17O NMR shifts vary with the intercarbonyl dihedral angle α in a sense opposite to that observed for α-diketones. © 1998 John Wiley & Sons, Ltd.

Notes: The prototropic tautomerism of 8-azaadenine (azaade) was studied theoretically by means of ab initio methods, in both the gas phase and aqueous solution. A number of tautomeric forms were not included in the calculations after applying a stepwise elimination procedure based on both AM1 and HF/6-31G* energy values. The tautomers 9H-azaade, 8H-azaade and 7H-azaade survived to this elimination and their optimized geometries and energies were calculated at the MP2/6-31*//HF/6-31G* level. To include the solvent effects, two self-consistent reaction field method were used: (1) Onsager's SCRF with multipolar expansion up to the hexadecapolar term and (2) the isodensity polarizable continuum method (IPCM). Both methods produce similar results, although the latter represents better the situation in aqueous solution. The stability order in solution, 8H- 〉 9H- 〉 7H-azaade, differs slightly from that found in the gas phase, implying that in general the electrostatic effects in solution are important, but the intrinsic stability of these species in the gas phase overcomes the solvent effect. © 1998 John Wiley & Sons, Ltd.

Notes: No abstract.

Notes: Cyclic voltamograms of the solvatochromic dye 5-nitro-5′-dimethylamino-2,2′-bisthiophene (1), introduced recently as a sensitive π* probe, were recorded in different solvents. An EPR spectrum of the anionic radical of 1 in DMSO was obtained and compared with other spectra of analogous substituted bisthiophene radicals. It was found that the presence of a donor- acceptor pair of substituents in 1-⋅ reduces significantly the rotational barrier of the radical compared with the unsubstituted bithienyl radical anion 2-⋅. This is the result of an electronic repulsion between the donor ring fragment and the added electron in the coplanar radical, which does not exist in 2-⋅. © 1998 John Wiley & Sons, Ltd.

Notes: Reversed-phase high-performance liquid chromatography [LiChrosorb RP-18,UV detection at 254 nm and acetonitrile-water (86:14,v/v) as mobile phase] was applied to studies of the host-guest complexation of tetraalkylcalix[4]resorcinareneoctols and their upper rim phosphoryl, sulfonyl and dialkylaminomethyl derivatives with some aromatic guests in the mobile phase. It was shown that the formation of the inclusion complexes results in changes in the retention of aromatic guests and improves their separation. Stability constants of the complexes were calculated from the dependences of the l/k′ values of the aromatic guest on the concentration of the calix[4]resorcinarene in the mobile phase. The molecular structure of 4,6,16,18-tetrahydroxy-10,12,22,24-tetrakis(dipropoxyphosphoryloxy)-2,8,14,20-tetramethylcalix[4]resorcinarene (12) was determined. Crystal data for 12 are P21/n, a  =  16.708(9) Å, b  =  18.683(6) Å, c  =  20.243(5) Å, β  =  95.75(3)°, V  =  6287(4) Å3 and Z  =  4. Compound 12 exists in a boat conformation, in which two opposite unsubstituted resorcinol rings of the macrocyclic skeleton lie in the plane formed by four methine bridges and two diphosphorylated rings are perpendicular to the plane. © 1998 John Wiley & Sons, Ltd.

Notes: The boronic acid functional group has been incorporated into various biologically important compounds. In order to study this class of compounds better with molecular mechanics, five alkyl- and arylboronic acids were calculated using ab initio methods (Spartan) at the RHF/6-31G* level. MM3 force field parameters were developed based on the theoretically calculated geometries, vibrational spectra, and torsional profiles. © 1998 John Wiley & Sons, Ltd.