On strongly stable normal operators in Krein spaces

For bounded normal operators in Krein spaces we give a necessary and sufficient condition for strong stability. The same result for unitary operators was obtained by M.G.Krein [1] (see also [2]). For selfadjoint operators we refer to the papers of P.Jonas, H.Langer [3] and H.Langer [4].     

Gas chromatographic quantitation of underivatized amines in the determination of their octanol-0.1 M sodium hydroxide partition coefficients by the shake-flask method

The elution behaviour of a selection of sequence variant and modified insulins has been compared on a C18 reversed-phase column. Observed elution times were compared with those expected from the nature of the differences from bovine insulin. In some cases prediction rules established for peptides are adequate to explain the observed elution and in others detailed knowledge of the structure of the protein is of considerable importance in understanding elution behaviour.     

Collisional cooling enhances the ability to observe non-covalent interactions within the inducible nitric oxide synthase oxygenase domain: Dimerization,complexation, and dissociation

The investigation of protein quaternary structure, protein-cofactor, and protein-ligand interactions by mass spectrometry is often limited by the fragility of such interactions under experimental conditions. To develop more gentle conditions of perhaps general use, we used as a model for study the oxygenase domain of murine inducible nitric oxide synthase (iNOS), which is homodimeric, binds heme and tetrahydrobiopterin H(4)B cofactors, and the substrate L-arginine. The energetics of the collisions in q2 and in the lens region of the mass spectrometer were manipulated for varying the degree of solvation around the non-covalently bound ions. Furthermore, the number of low-energy collisions in the collision cell of the instrument was varied, focusing and dampening the ion beam. Under gentle source collision conditions, and using multiple low-energy collisions in the collision cell of the mass spectrometer, dimers of the iNOS oxygenase domain containing heme, H(4)B, and arginine were observed intact after electrospraying at pH values near neutrality; a mutant of this protein (Trp188 --> Phe) was monomeric and did not bind cofactors. The pH dependence of the iNOS oxygenase domain under acidic conditions was also studied; while heme remained bound to the protein between pH 2.5 and 4.0, the dimeric structure was disrupted. Our findings confirm that non-covalently bound macromolecular complexes are retained and observable using electrospray mass spectrometry under the appropriate experimental conditions.     

Electrospray ionization tandem mass spectrometric study of salt cluster ions. Part 1--investigations of alkali metal chloride and sodium salt cluster ions

Salt cluster ions of alkali metal chlorides ACl (A = Li(+), Na(+), K(+), Rb(+) and Cs(+)) and sodium salts NaB (B = I(-), HCOO(-), CH(3)COO(-), NO(2)(-), and NO(3)(-)), formed by electrospray ionization, were studied systematically by mass spectrometry. The influences on the total positive ion and negative ion currents of variation of solvent, solution concentration, desolvation temperature, solution flow-rate, capillary voltage and cone voltage were investigated. Only cone voltage was found to influence dramatically the distribution of salt cluster ions in the mass spectra observed. Under conditions of normal cone voltage of approximately 70 V, cluster ions having magic numbers of molecules are detected with high relative signal intensity. Under conditions of low cone voltage of approximately 10 V, the distribution of cluster ions detected is characterized by a relatively low average mass/charge ratio due to the presence of multiply charged cluster ions; in addition, there is a marked reduction in cluster ions having a magic number of molecules. Product ion mass spectra obtained by tandem mass spectrometry of cluster ions are characterized by a base peak having a magic number of molecules that is less than and closest to the number of molecules in the precursor ion. Structures have been proposed for some dications and some quadruply charged ions. At pH 3 and 11, the mass spectra of NaCl clusters show the presence of mixed clusters of NaCl with HCl and NaOH, respectively. The effects of ionic radius on 20 distributions of cluster ions for 10 salts were investigated; however, the fine structure of these effects is not readily discerned.     

The synthesis of annulated pyridazines by cycloaddition of azodicarboxylates to vinyl heterocycles

Reaction between 2-vinyl pyridine and azodicarboxylates 2 or 5 gives N,N'-disubstituted tetrahydropyrido[3,2-c]pyridazines 3 and 6, and dihydro-3H-pyrido[1,2-c]triazines 4 and 7; 2-(prop-1-en-1-yl)-pyridine 8 gives hydropyridopyridazines 10 and 11 but 2-(prop-1-en-2-yl)pyridine 9 gives mainly the ‘ene’ addition product 12. From 4-vinyl-pyridine and esters 2 or 5 diesters of tetrahydropyrido[3,4-c]pyridazine-1,2-dicarboxylic acid, 25 and 26 are obtained, and from 2-methyl-5-vinylpyridine both possible cyclisation products, the tetrahydro-pyrido[2,3-c]pyridazines 33 and 36, and -pyrido[4,3-c]pyridazines 34 and 37. The di-t-butyl esters 6, 11, 26, and 37 are quantitatively decarbalkoxylated in TFA, giving tetrahydropyridopyridazines 16, 18, 27, and 41; of these, the first three were oxidized to give pyrido[2,3-c]-pyridazine 15, its 3-methyl derivative 19, and pyrido[3,4-c]pyridazine 28 respectively. A dihydropyrido[4,3-c]-pyridazine 42 was obtained from compound 41. Thieno[2,3-c]-pyridazine 48 has been similarly prepared from 2-vinylthiophen, but 2-(prop-1-en-2-yl)thiophen gave an ene addition compound 51 and a dihydrothienopyridazine 50. Reactions with other vinylpyridines, and with vinylfurans, were unsuccessful.     

Holographic Roberge-Weiss transitions

We investigate \( \mathcal{N} = 4 \) SYM coupled to fundamental flavours at nonzero imaginary quark chemical potential in the strong coupling and large N limit, using gauge/gravity duality applied to the D3-D7 system, treating flavours in the probe approximation. The interplay between \( {\mathbb{Z}_N} \) symmetry and the imaginary chemical potential yields a series of first-order Roberge-Weiss transitions. An additional thermal transition separates phases where quarks are bound/ unbound into mesons. This results in a set of Roberge-Weiss endpoints: we establish that these are triple points, determine the Roberge-Weiss temperature, give the curvature of the phase boundaries and confirm that the theory is analytic in μ ² when μ ² ≈ 0.     

Synthetic studies towards lagunamide C: Polyketide assembly investigations

Lagunamide C is a depsipeptide natural product with low nM cytotoxicity towards numerous cancer cell lines. Synthetically, it is disconnected to a pentapeptide backbone and polyketide unit that possesses four stereogenic centers, of which two of centers are in question (C38 & 40). Our model system highlights a high-selective aldol addition via a Crimmin’s auxiliary setting the C40 ester linkage, and a non-facially selective cyclopropanation with subsequent ring opening for the installation of the C38 methyl center.