On a semilinear Schrödinger equation with critical Sobolev exponent

We consider the semilinear Schrödinger equation , , where , are periodic in for , 0$">, is of subcritical growth and 0 is in a gap of the spectrum of . We show that under suitable hypotheses this equation has a solution . In particular, such a solution exists if and .

     

All-trans-1-acyloxy-1,3-pentadiene-5 ols as reactive dienes in new intramolecular diels-alder reactions

The high reactivity of the $\text{all-trans}$-1-acyloxy-1,3-pentadiene-5-ols as dienes in intramolecular Diels-Alder reactions with maleic anhydride and fumaric acid ethylester monochloride is discussed.     

Mapping of possible prion protein self-interaction domains using peptide arrays

Background  

The common event in transmissible spongiform encephalopathies (TSEs) or prion diseases is the conversion of host-encoded protease sensitive cellular prion protein (PrP^C) into strain dependent isoforms of scrapie associated protease resistant isoform (PrP^Sc) of prion protein (PrP). These processes are determined by similarities as well as strain dependent variations in the PrP structure. Selective self-interaction between PrP molecules is the most probable basis for initiation of these processes, potentially influenced by chaperone molecules, however the mechanisms behind these processes are far from understood. We previously determined that polymorphisms do not affect initial PrP^C to PrP^Sc binding but rather modulate a subsequent step in the conversion process. Determining possible sites of self-interaction could elucidate which amino acid(s) or amino acid sequences contribute to binding and further conversion into other isoforms. To this end, ovine – and bovine PrP peptide-arrays consisting of 15-mer overlapping peptides were probed with recombinant sheep PrP^C fused to maltose binding protein (MBP-PrP).     

Darstellung,Charakterisierung und Reaktionsverhalten von Natrium‐ und Kaliumhydridosilylamiden R2(H)Si—N(M)R′ (M = Na,K) — Kristallstruktur von [(Me3C)2(H)Si—N(K)SiMe3]2·THF

Preparation, Characterization and Reaction Behaviour of Sodium and Potassium Hydridosilylamides R₂(H)Si—N(M)R′ (M = Na, K) — Crystal Structure of [(Me₃C)₂(H)Si—N(K)SiMe₃]₂ · THF The alkali metal hydridosilylamides R₂(H)Si—N(M)R′ 1a‐Na — 1d—Na and 1a‐K — 1d‐K ( a : R = Me, R′ = CMe₃; b : R = Me, R′ = SiMe₃; c : R = Me, R′ = Si(H)Me₂; d : R = CMe₃, R′= SiMe₃) have been prepared by reaction of the corresponding hydridosilylamines 1a — 1d with alkali metal M (M = Na, K) in presence of styrene or with alkali metal hydrides MH (M = Na, K). With NaNH₂ in toluene Me₂(H)Si—NHCMe₃ ( 1a ) reacted not under metalation but under nucleophilic substitution of the H(Si) atom to give Me₂(NaNH)Si—NHCMe₃ ( 5 ). In the reaction of Me₂(H)Si—NHSiMe₃ ( 1b ) with NaNH₂ intoluene a mixture of Me₂(NaNH)Si—NHSiMe₃ and Me₂(H)Si—N(Na)SiMe₃ ( 1b‐Na ) was obtained. The hydridosilylamides have been characterized spectroscopically. The spectroscopic data of these amides and of the corresponding lithium derivatives are discussed. The ²⁹Si‐NMR‐chemical shifts and the ²⁹Si—¹H coupling constants of homologous alkali metal hydridosilylamides R₂(H)Si—N(M)R′ (M = Li, Na, K) are depending on the alkali metal. With increasing of the ionic character of the M—N bond M = K > Na > Li the ²⁹Si‐NMR‐signals are shifted upfield and the ²⁹Si—¹H coupling constants except for compounds (Me₃C)(H)Si—N(M)SiMe₃ are decreased. The reaction behaviour of the amides 1a‐Na — 1c‐Na and 1a‐K — 1c‐K was investigated toward chlorotrimethylsilane in tetrahydrofuran (THF) and in n‐pentane. In THF the amides produced just like the analogous lithium amides the corresponding N‐silylation products Me₂(H)Si—N(SiMe₃)R′ ( 2a — 2c ) in high yields. The reaction of the sodium amides with chlorotrimethylsilane in nonpolar solvent n‐pentane produced from 1a‐Na the cyclodisilazane [Me₂Si—NCMe₃]₂ ( 8a ), from 1b‐Na and 1‐Na mixtures of cyclodisilazane [Me₂Si—NR′]₂ ( 8b , 8c ) and N‐silylation product 2b , 2c . In contrast to 1b‐Na and 1c‐Na and to the analogous lithium amides the reaction of 1b‐K and 1c‐K with chlorotrimethylsilane afforded the N‐silylation products Me₂(H)Si—N(SiMe₃)R′ ( 2b , 2c ) in high yields. The amide [(Me₃C)₂(H)Si—N(K)SiMe₃]₂·THF ( 9 ) crystallizes in the space group C2/c with Z = 4. The central part of the molecule is a planar four‐membered K₂N₂ ring. One potassium atom is coordinated by two nitrogen atoms and the other one by two nitrogen atoms and one oxygen atom. Furthermore K···H(Si) and K···CH₃ contacts exist in 9 . The K—N distances in the K₂N₂ ring differ marginally.     

Synthesis of unique cagelike thiacalix[4]arene derivatives in a 1,3-alternate conformation

A novel type of doubly bridged thiacalix[4]arenes in the 1,3-alternate conformation has been prepared by direct aminolysis reaction of easily accessible thiacalix[4]arene tetraacetates with alpha,omega-diamines. Despite the high excess of diamine, both sites of a 1,3-alternate conformer can be intramolecularly bridged to form the cagelike structures in high yields. Optimum results were obtained using 1,2-ethanediamine as bridging units. X-ray analysis of the novel cagelike molecules revealed a highly preorganized array of -C(O)-NH- bonds pointing to the interior of the cavity.     

DFT-calculated structure of protonated tetraphenyl p - tert -butylcalix[4]arene tetraketone

Using DFT calculations, two of the most probable structures (A, B) of the tetraphenyl p-tert-butylcalix[4]arene tetraketone·H₃O⁺ cationic complex species were derived. The hydroxonium ion H₃O⁺, placed in the coordination cavity formed by the calix[4]arene lower-rim groups, is bound by strong hydrogen bonds to the phenoxy oxygen atoms of the calix[4]arene ligand (structures A, B) and also to one carbonyl oxygen (structure B).     

Synthesis and Molecular Structure of [Ru3(CO)10(μ-dppa)] (dppa = Ph2PN(H)PPh2) Provided by Its Dioxane Solvate

The sodium benzophenone ketyl-induced reaction of [Ru₃(CO)₁₂] with bis(diphenylphosphanyl)amine Ph₂PN(H)PPh₂ (dppa) in THF resulted in the formation of the expected metal cluster [Ru₃(CO)₁₀(μ-dppa)] ( 1 ) in high yield. 1 was fully characterized by spectroscopic means and crystals of the compound suitable for X-ray diffraction were obtained from dichloromethane/dioxane. The molecular structure of 1 as its dioxane solvate was determined by X-ray crystallography. The compound crystallized in a new crystal structure of [Ru₃(CO)₁₀(μ-dppa)] in the triclinic space group P1 , whereas that compound was described in an earlier report crystallizing from chloroform in the monoclinic space group P2₁/c.     

Physical Properties and Erosion Behavior of Poly(trimethylene carbonate‐co‐ε‐caprolactone) Networks

Form‐stable resorbable networks are prepared by gamma irradiating trimethylene carbonate (TMC)‐ and ε‐caprolactone (CL)‐based (co)polymer films. To evaluate their suitability for biomedical applications, their physical properties and erosion behavior are investigated. Homopolymer and copolymer networks that are amorphous at room temperature are flexible and rubbery with elastic moduli ranging from 1.8 ± 0.3 to 5.2 ± 0.4 MPa and permanent set values as low as 0.9% strain. The elastic moduli of the semicrystalline networks are higher and range from 61 ± 3 to 484 ± 34 MPa. The erosion behavior of (co)polymer networks is investigated in vitro using macrophage cultures, and in vivo by subcutaneous implantation in rats. In macrophage cultures, as well as upon implantation, a surface erosion process is observed for the amorphous (co)polymer networks, while an abrupt decrease in the rate and a change in the nature of the erosion process are observed with increasing crystallinity. These resorbable and form‐stable networks with tuneable properties may find application in a broad range of biomedical applications.

     

NiCl(2)(dppe)-catalyzed cross-coupling of aryl mesylates, arenesulfonates, and halides with arylboronic acids

An investigation of the NiCl(2)(dppe)-, NiCl(2)(dppb)-, NiCl(2)(dppf)-, NiCl(2)(PCy(3))(2)-, and NiCl(2)(PPh(3))(2)-catalyzed cross-coupling of the previously unreported aryl mesylates, and of aryl arenesulfonates, chlorides, bromides, and iodides containing electron-withdrawing and electron-donating substituents with aryl boronic acids, in the absence of a reducing agent, is reported. NiCl(2)(dppe) was the only catalyst that exhibited high and solvent-independent activity in the two solvents investigated, toluene and dioxane. NiCl(2)(dppe) with an excess of dppe, NiCl(2)(dppe)/dppe, was reactive in the cross-coupling of electron-poor aryl mesylates, tosylates, chlorides, bromides, and iodides. This catalyst was also efficient in the cross-coupling of aryl bromides and iodides containing electron-donating substituents. Most surprisingly, the replacement of the excess dppe from NiCl(2)(dppe)/dppe with excess PPh(3) generated NiCl(2)(dppe)/PPh(3), which was found to be reactive for the cross-coupling of both electron-rich and electron-poor aryl mesylates and chlorides. Therefore, the solvent-independent reactivity of NiCl(2)(dppe) provides an inexpensive and general nickel catalyst for the cross-coupling of aryl mesylates, tosylates, chlorides, bromides, and iodides with aryl boronic acids.