Intramolecular sulfur-ylide additions to ketones. A cyclopentane annulation1

Various 2-(3′-phenylthiopropyl)cycloalkanones were prepared from the corresponding cyclic ketones and subjected to S-alkylation by triethyloxonium tetrafluoroborate followed by potassium $\text{tert}$-butoxide treatment to give bicyclic epoxides with new five-membered carbocycles. A related cyclization to a six-membered ring was also observed.     

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.     

On viscosity solutions of fully nonlinear equations with measurable ingredients

We study fully nonlinear, uniformly elliptic equations with measurable ingredients. Caffarelli's recent work on W^2,p estimates for viscosity solutions has led to significant progress in this area. Here we present a unified treatment of this theory based on an appropriate notion of viscosity solution. For instance, it is shown that strong solutions are viscosity solutions, that viscosity solutions are twice differentiable a.e., and that the pointwise derivatives satisfy the equation a.e. An important consequence of our approach is the possibility of passage to various kinds of limits in fully nonlinear equations. This extends results of this type due to Evans and Krylov. Our work is to some extent expository, the main purpose being to provide an easily accessible set of tools and techniques to study equations with measurable ingredients. © 1996 John Wiley & Sons, Inc.     

The twenty-fourth Fermat number is composite

We have shown by machine proof that is composite. The rigorous Pépin primality test was performed using independently developed programs running simultaneously on two different, physically separated processors. Each program employed a floating-point, FFT-based discrete weighted transform (DWT) to effect multiplication modulo . The final, respective Pépin residues obtained by these two machines were in complete agreement. Using intermediate residues stored periodically during one of the floating-point runs, a separate algorithm for pure-integer negacyclic convolution verified the result in a ``wavefront' paradigm, by running simultaneously on numerous additional machines, to effect piecewise verification of a saturating set of deterministic links for the Pépin chain. We deposited a final Pépin residue for possible use by future investigators in the event that a proper factor of should be discovered; herein we report the more compact, traditional Selfridge-Hurwitz residues. For the sake of completeness, we also generated a Pépin residue for , and via the Suyama test determined that the known cofactor of this number is composite.

     

Apparate

Ohne Zusammenfassung     

Regularizing effects for ut + Aϑ(u) = 0 in L1

Various initial-boundary value problems and Cauchy problems can be written in the form $\text{du}\text{dt}\text{+ A?(u) = 0}$, where ?:R→$\text{R}$ is nondecreasing and A is the linear generator of strongly continuous nonexpansive semigroup e^?tA in an L¹ space. For example, if A = ?Δ (subject, perhaps, to suitable boundary conditions) we obtain equations arising in flow in a porous medium or plasma physics (depending on the choice of ?) while if $\text{A =}\text{?}\text{?x}$ acting in L¹($\text{R}$) we have a scalar conservation law. In this paper we show that if M, m > 0 and m?′² ? ν??′' ? M?′², where ν ? {1,?1}, then (roughly speaking), the norm of $\text{t}\text{du}\text{dt}$ may be estimated in terms of the initial data u₀ in L¹. Such estimates give information about the regularity of solutions, asymptotic behaviour, etc., in applications. Side issues, such as the introduction of sufficiently regular approximate problems on which estimates can be made and the assignment of a precise meaning to the operator A?, are also dealt with. These considerations are of independent interest.