On the topology of black holes

We establish from local hypotheses some results concerning the final state topology of black holes. We show that the surface of a black hole must have 2-sphere topology and that the topology of space in its vicinity is simple.Dedicated to Ted FrankelThis work has been partially supported by NSF grants DMS-8802877 and DMS-9006678     

Simple alkenes as substitutes for organometallic reagents: nickel-catalyzed, intermolecular coupling of aldehydes, silyl triflates, and alpha olefins

A nickel-catalyzed method for the three-component coupling of alkenes (ethylene and alpha olefins), aldehydes, and silyl triflates is described, and this process represents the first catalytic method for coupling aldehydes and alkenes to give allylic alcohol derivatives. Conceptually, the alkene functions as a replacement for an alkenylmetal reagent.     

Cobalt(II) halide complexes ofN-2-(4-picolyl)-,N-2-(6-picolyl)-andN-2-(4,6-lutidyl)-N′-phenylthioureas

Summary Co^II complexes of various stoichiometries have been isolated from reactions of the metal chlorides and bromides withN-2-(4-picolyl)-,N-2-(6-picolyl)- andN-2-(4,6-lutidyl)-N-phenylthioureas.     

Convergence of weighted sums of independent random variables

Let {X_k} be a sequence of i.i.d. random variables with d.f. F(x). In the first part of the paper the weak convergence of the d.f.'s F_n(x) of sums is studied, where 0<α≤2, a_nk>0, 1≤k≤m_n, and, as n→∞, bothmax _1≤k≤mn_{a nk}→0 and . It is shown that such convergence, with suitably chosen A_n's and necessarily stable limit laws, holds for all such arrays {α_nk} provided it holds for the special case α_nk=1/n, 1≤k≤n. Necessary and sufficient conditions for such convergence are classical. Conditions are given for the convergence of the moments of the sequence {F_n(x)}, as well as for its convergence in mean. The second part of the paper deals with the almost sure convergence of sums , where a_n≠0, b_n>0, andmax _1≤k≤n a_k/b_n→0. The strong law is said to hold if there are constants A_n for which S_n→0 almost surely. Let N(0)=0 and N(x) equal the number of n≥1 for which b_n/|a_n|<x if x>0. The main result is as follows. If the strong law holds,EN (|X₁|)<∞. If for some 0<p≤2, then the strong law holds with if 1≤p≤2 and A_n=0 if 0<p<1. This extends the results of Heyde and of Jamison, Orey, and Pruitt. The strong law is shown to hold under various conditions imposed on F(x), the coefficients a_n and b_n, and the function N(x). Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, 1993.     

Weighted composition operators on Hilbert spaces of vector-valued functions

In this paper we investigate criterion for the hyponormality, cohyponormality, and normality of weighted composition operators acting on Hilbert spaces of vector-valued functions.

     

Complex strict convexity of certain Banach spaces

Istratescu's characterization of complex strict convex (csc) Banach spaces is used to show that a modulared sum of a sequence ofcsc Banach spaces is again acsc Banach space. The equivalence of the Strong Maximum Modulus Property and complex strict convexity is used to show thatL ¹(,X) iscsc whenX is (real) strictly convex and thatl ¹(X _n) iscsc if and only if eachX _n iscsc.     

A comparative analysis of the total syntheses of the amphidinolide T natural products

In this article we compare and contrast the strategies and tactics used in the syntheses of the amphidinolide T family of natural products that have been reported by Fürstner, Ghosh and ourselves. Similar approaches to the trisubstituted THF ring present in the targets are utilized in all of the syntheses, but each strategy showcases a different means of macrocyclization.     

Ligand-switchable directing effects of tethered alkenes in nickel-catalyzed additions to alkynes

Nickel-catalyzed reductive couplings of aldehydes with alkynes that contain tethered olefins are described, in which the degree and sense of regioselectivity are controlled by the length of the tether and the presence or absence of an additive. When the alkyne and alkene are separated by four bonds, very high (>95:5) regioselectivities are observed. Use of a monodentate phosphine as an additive leads to formation of the opposite regioisomer in equal and opposite selectivity (5: >95). These results provide strong evidence for an interaction between the remote alkene and the metal center during the regioselectivity-determining step and suggest that reactions with and without an additive proceed via fundamentally distinct mechanisms.     

Characterizing the "shell phase" formed from amphiphilic picolinates

The shell phase forms when certain picolinates are subjected to energy input (via sonication or vortexing) while exposed to a water/toluene mixture. A shell, about 600 A thick and containing the picolinate and (very likely) toluene, surround the water droplets that are always produced during the mixing process. Solubility in either phase appears to be deleterious to shell formation. The shells, stable for months, are not easily distorted but can be punctured, even skewered, with a syringe needle without destroying the sphere, yet there is enough mobility among the molecules to repair the physical damage after the needle is removed. This, plus the absence of evidence for crystallinity, suggests a solid or semisolid film forms when picolinates, with the aid of an aromatic solvent, are provided the energy to rearrange themselves on water droplet surfaces. Structure-activity comparisons among the 10 compounds studied indicate that chain-chain association and intermolecular hydrogen bonding are dominant forces in a side-by-side self-assembly of the molecules within the shells.