Sign changes in the prime number theorem

The Ramanujan Journal - Let V(T) denote the number of sign changes in $$\psi (x) - x$$ for $$x\in [1, T]$$ . We show that $$\liminf _{T\rightarrow \infty } V(T)/\log T\ge \gamma _{1}/\pi +...     

ON QUOTIENTS OF BRAID GROUPS

ABSTRACT.

Let G be the group ?[t, t ^?1] x ?. By studying the action of the braid group B_n on the set Gⁿ , we obtain representations of B_n into a wreath product of the symmetric group and the general linear group over ?[t, t ^?1]. This in particular recovers the Burau representation of the braid group. Furthermore, some quotients of the braid group are obtained by using the representations found.     

Organocatalytic functionalization of carboxylic acids: isothiourea-catalyzed asymmetric intra- and intermolecular Michael addition--lactonizations

Tetramisole promotes the catalytic asymmetric intramolecular Michael addition-lactonization of a variety of enone acids, giving carbo- and heterocyclic products with high diastereo- and enantiocontrol (up to 99:1 dr, up to 99% ee) that are readily derivatized to afford functionalized indene and dihydrobenzofuran carboxylates. Chiral isothioureas also promote the catalytic asymmetric intermolecular Michael addition-lactonization of arylacetic acids and α-keto-β,γ-unsaturated esters, giving anti-dihydropyranones with high diastereo- and enantiocontrol (up to 98:2 dr, up to 99% ee).     

Synthesis of 4-arylpiperidines from 1-benzyl-4-piperidone: application of the Shapiro reaction and alkenylsilane cross-coupling

[reaction: see text] 1-Benzyl-3,4-unsaturated-4-piperidinyl benzyldimethylsilane has been prepared and observed to readily undergo palladium-catalyzed cross-coupling reactions with a variety of aryl iodides and aryl bromides to generate 3,4-unsaturated 4-arylpiperidines, often at ambient temperature.     

Rhenium-catalyzed 1,3-isomerization of allylic alcohols: scope and chirality transfer

The scope of the triphenylsilyl perrhennate (O3ReOSiPh3, 1) catalyzed 1,3-isomerization of allylic alcohols has been thoroughly explored. It was found to be effective for a wide variety of secondary and tertiary allylic alcohol substrates bearing aryl, alkyl, and cyano substituents. Two general reaction types were found which gave high levels of product selectivity: those driven by formation of an extended conjugated system and those driven by selective silylation of a particular isomer. The efficiency of chirality transfer with various substrates was investigated, and conditions were found in which secondary and tertiary allylic alcohols could be formed with high levels of enantioselectivity. Consideration of selectivity trends with respect to the nature of the substituents around the allylic system revealed that this is a reliable and predictable method for allylic alcohol synthesis.     

DETECTION OF DNA-PSORALEN PHOTOADDUCTS in situ

Abstract— An immunological method, with the use of specific immune serum, has been developed for detection of 8-methoxypsoralen (8-MOP) photoadducts to DNA, formed in situ in cell nuclei, after combined treatment with 8MOP and UV-A irradiation (Zarçbska et al. , 1978). Lymphocytes fixed on slides or in suspension, and cryostat sections of different mammalian tissues, served as antigenic substrate, after treatment with 8-MOP and UV-A in vitro. Specific fluorescence in these substrates was detected in the nuclei after treatment with 30 ˜ 140 kJ/m² UV-A in the presence of 0.1-0.3 μg/cm² 8-MOP. PHA-stimulated-lymphocytes appeared to be the most sensitive substrate.
However, hairless mice treated with high doses of UV-A in vivo , 70 ˜ 360 kJ/m² did not reveal a specific fluorescence of epidermal nuclei, unless a high local concentration of 8-MOP was attained.
The apparent discrepancy in the level of photoadduct detection between the in vitro and in vivo treated specimens was explained by the low number of DNA-8-MOP-photoadducts formed in vivo under these experimental conditions. The relevance of these findings to the role of DNA-8-MOP-photoadducts formed during PUVA photochemotherapy is discussed.     

Magnetic circular dichroism studies—XLVI: Structure and the magnetic circular dichroism of trans-2-decalones and bicyclo[2.2.2]octan-2-ones

The magnetic CD spectra of a number of Me substituted trans-2-decalones and bicyelo[2.2.2]octan-2-ones were measured. The results showed a large, and sometimes dominant, contribution to the MCD intensity which could be correlated with the presence of α-substituents lying outside of the plane of the carbonyl chromophore.