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.     

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.     

Structure of slope-critical configurations

In 1970, P. R. Scott conjectured, and recently P. Ungar proved, that n noncollinear points in the plane determine at least n–1 directions. The goal here is to obtain information on the structure of the critical sets where the minimum of n–1 is attained. Such a set is distributed in a rather regular way onto spokes radiating out from a centrex point. If the number of spoke-pairs is even, the set must be centrally symmetric. Moreover, some bounds on the number of points per spoke are obtained. These results lead to the characterization, for small n, of certain types of slope-critical configurations.Dedicated to M. S. Irani on his 90th birthday 25 February, 1984Research supported in part by NSF EPSCoR Grant IPS-80-11451.     

Nickel‐Catalyzed Mizoroki–Heck Reaction of Aryl Sulfonates and Chlorides with Electronically Unbiased Terminal Olefins: High Selectivity for Branched Products

Achieving high selectivity in the Heck reaction of electronically unbiased alkenes has been a longstanding challenge. Using a nickel‐catalyzed cationic Heck reaction, we were able to achieve excellent selectivity for branched products (≥19:1 in all cases) over a wide range of aryl electrophiles and aliphatic olefins. A bidentate ligand with a suitable bite angle and steric profile was key to obtaining high branched/linear selectivity, whereas the appropriate base suppressed alkene isomerization of the product. Although aryl triflates are traditionally used to access the cationic Heck pathway, we have shown that, by using triethylsilyl trifluoromethanesulfonate, we can effect a counterion exchange of the catalytic nickel complex, such that cheaper and more stable aryl chlorides, mesylates, tosylates, and sulfamates can be used to yield the same branched products with high selectivity.     

Deuteriodifluoromethylation and gem‐Difluoroalkenylation of Aldehydes Using ClCF2H in Continuous Flow

The deuteriodifluoromethyl group (CF₂D) represents a challenging functional group due to difficult deuterium incorporation and unavailability of precursor reagents. Herein, we report the use of chlorodifluoromethane (ClCF₂H) gas in the continuous flow deuteriodifluoromethylation and gem‐difluoroalkenylation of aldehydes. Mechanistic studies revealed that the difluorinated oxaphosphetane (OPA) intermediate can proceed via alkaline hydrolysis in the presence of D₂O to provide α‐deuteriodifluoromethylated benzyl alcohols or undergo a retro [2+2] cycloaddition under thermal conditions to provide the gem‐difluoroalkenylated product.