Largest known twin primes

The numbers are twin primes.

     

On the variance of the number of pivot steps required by the simplex algorithm

The article provides an asymptotic probabilistic analysis of the variance of the number of pivot steps required by phase II of the shadow vertex algorithm — a parametric variant of the simplex algorithm, which has been proposed by Borgwardt [1]. The analysis is done for data which satisfy a rotationally invariant distribution law in then-dimensional unit ball.     

Mechanisms of mass spectrometric fragmentations: X–Interaction between remote or-groups in decalin-1,5-diols and their dimethyl ethers

The mass spectra of the five stereoisomers of decalin-1,5-diol and its dimethyl ether have been investigated. The differences in the mass spectra of stereoisomers I to III with a trans- decalin ting system are small. The differences are much larger in the mass spectra of the two isomers IV and V of the cis-decalin series and the elimination of CH₂O, formed by interaction between the two methoxy groups, from the molecular ion is only observed in the mass spectrum of Vb.     

Insertion reactions of thermally generated stannylenes R2Sn into Sn-X (X = Cl,Br, SPh) and Sn-Sn bonds

Thermally generated stannylenes R₂Sn insert efficiently into Sn-X bonds (X  Cl, 3r, SPh) as well as into electron deficient SnSn bonds e.g. in Me₂(Hal)SnSn(Hal)Me₂, but not into hexaalkyldistannanes R₆Sn₂ under the same conditions; stannylenes R₂Sn always behave as nucleophiles here.     

Tunnel effect on the kinetics of hydrogen shifts. The enol-ketone transformation of 2′-methylacetophenone

A large isotope effect on the enol—keto transition of 2′-methylacetophenone and a temperature-dependent activation energy for this process have been observed in flash experiments. A tunnel process and the existence of two metastable rotamers of the enol are proposed to describe the kinetcis of the reketonization process.     

Darstellung,Eigenschaften und Molekülstruktur eines Titan-tris(diazadien)-Komplexes

Preparation, Properties, and Molecular Structure of a Titanium-tris(diazadiene) Complex (R = i-C₃H₇) 1 was obtained by reaction of TiCl₄ · 2 THF with Li₂(NR? CH = CH? NR) in the presence of the ligand molecules. The compound was characterized by ¹H-, ¹³C-n.m.r., and mass spectroscopy. The molecular structure was determined by X-ray diffraction. The bonding distances in the identically coordinated diazadiene ligands are similar to those of radical.     

Darstellung und Molekülstruktur des (μ-Alkylidenamido)titanocenkomplexes [(C5H5)2TiCl]2[μ-{N=C(CH2C6H5)C(CH2C6H5)=N}]

Reduction of (C₅H₅)₂TiCl₂ with Zn in presence of benzyl cyanide gives the (μ-alkyl-ideneamido)titanocene complex [(C₅H₅)₂TiCl]₂[μ-{N=C(CH₂C₆H₅)---C(CH₂C₆H₅)=N}] with C---C bond formation between two benzyl cyanide molecules.

X-ray structure investigation indicates a symmetrical structure. The C=N distances are smaller than usual, the Ti---N distances are very short, and the Ti---N---C angle differs only a little from 180°, which infers a heteroallene structure of the complex.     

Sequence dependence of secondary-structure formation part IV Helix-forming potential of amphiphilic oligopeptides containing aib residues

The conformational properties of Aib-containing oligopeptides having the propensity to adopt amphiphilic helical conformations were investigated by CD spectroscopy in solution. The peptides CF₃COOH.H-Pro-Glu-[Ala-Aib-Glu-Aib-]₄Gly-OH ( I ), HCl.H-Pro-Ala-Aib-[Gul-Ala-Ala-Aib-]₂Glu-Ala-Aib-Gly-PEGM ( II ), and CF₃COOH.H-Ala-Aib-[Glu-Glu-Ala-Aib-]₃PEGM ( III ) were synthesized according to the general principles of the liquid-phase method for peptide synthesis. Peptides I-III exhibit helical conformations in CF₃CH₂OH, MeOH, and in H₂O at acidic pH; however, at pH 7, only II forms a stable helix, whereas I and III are predominantly in an unordered conformation. Some general features for the construction of amphiphilic helices are discussed in the light of the experimental data.     

Herstellung der 1H-Indazole durch Photolyse von 2-Aminophenylketon-O-(äthoxycarbonyl)oximen und von 3,1,4-Benzoxadiazepin-2 (1H)-onen

1H-Indazoles Obtained by Photolysis of 2-Aminophenylketon-O-(ethoxycarbonyl)oximes and of 3, 1, 4-Benzoxadiazepine-2(1 H)-ones Irradiation of (E)- and (Z)-O-(ethoxycarbonyl)oximes 1 of 2-aminophenyl ketones in solution with UV, and/or visible light gives 1 H-indazole derivatives 2 in high yields (Scheme 1). For this reaction the amino group must be un- or mono substituted. With the N, N-disubstituted (E)- 1d (Scheme 2) no 1 H-indazole formation is observed, because the radicals formed by its photolysis react in an unspecific manner with each other and with the solvent. From the behaviour of (E)- 1d and from the lack of any E/Z-isomerization of 1 we conclude that the photoreaction starts with a splitting of the N, O-bond in two separate radicals, whereas the radical pair produced by the also studied photolysis of 3,1,4-benzoxadiazepine-2(1 H)-one derivatives 3 is fixed in the parent molecule, and therefore tends to recombine. This makes a prolonged irradiation necessary to convert the benzoxadiazepinones 3 into the 1 H-indazoles 2 . The different reaction rates of the (E) and (Z)-isomers of 1 (provided R⁴ = H) are understood by means of different intramolecular H-bridges.