Ont ∞ quasi-similarity of linear systems

Summary Conti defined t similarity of systems (1)x=tA(t)xand (2)y=B(t)y, and showed that it is an equivalence relation which preserves uniform and strict stability. Here the definition is weakened by imposing less stringent integrability conditions, some in terms of perhaps conditionally convergent improper integrals, on the matrix function relating A and B. The extended relation, t quasi-similarity, is not symmetric or transitive; however, it is shown that if (2) is t quasi-similar to (1)and (1)is uniformly, uniformly asymptotically, or strictly stable, then so is (2).Results are also given concerning linear asymptotic equilibrium of (2)in the case where (1)is stricly stable or has linear asymptotic equilibrium.     

The physics of detecting torsion and placing limits on its effects

We present the essential principles of torsion-detection physics and evaluate several conceivable types of experiments and observations for actually detecting torsion fields, reemphasizing also the evident impossibility of successfully searching for its manifestations among cosmological relics. In particular, a polarized body, with net intrinsic (fundamental-particle) spin, is essential for detecting a torsion field. One which possesses only orbital angular momentum—rotation—or an unpolarized intrinsic spin density will not feel torsion. The fundamental problem in searching for such fields is the extremely small basic unit of the coupling or interaction energy between the torsion field and spin,(8G/c ²)( ²/4). The best way of maximizing the total interaction energy is to increase the spin density of the source _s, and, at the same time the spin numberS _D of the detector.This essay was awarded an honorable mention in 1984 by the Gravity Research Foundation—Ed.     

Very long-lived doubly vibrationally excited states above dissociation threshold: non-RRKM behavior in model triatomic systems

For couplings and mass ratios appropriate to molecules such as H₂O, D₂O, and CH₂ large volumes of the classical vibrational phase space are found to be non-dissociating even well above threshold. Fully quantum calculations yield families of exceptionally long-lived quantum states corresponding to these trapped volumes.     

Facile homogeneous hydrogenations of hindered olefins with [Ir(cod)py(PCy3)]PF6

The title complex readily hydrogenates a number of hindered steroidal olefin groups from the α face, without reducing ketone carbonyl groups, carbon—halogen bonds or cyclopropane rings.     

Observations on the reduction of aryl nitro groups with palladium-sodium borohydride

The reduction of aryl nitro groups by the palladium-sodium borohydride system can be controlled in some instances to give products differing from those of catalytic hydrogenation. With six equivalents of borohydride added to the catalyst 2,2′-dinitrobiphenyl formed only 2,2′-diaminobiphenyl. With added sodium hydroxide and varying amounts of borohydride and catalyst, the reduction can be controlled to give benzo[c]cinnoline, benzo[c]cinnoline 5-oxide or benzo[c]cinnoline 5,6-dioxide. In a closed system, the reagents reduce both the nitro and olefin functional groups in 6-nitro-5,8-dimethoxy-1,4-dihydro-1,4-ethano-naphthalene. In an open flask flushed with argon, the reduction is confirmed to the nitro group. Reduction of 2-chloro and 4-chloronitrobenzene with palladium-borohydride gives substantial yields of the appropriate chloroanilines. In contrast, hydrogen and palladium give aniline as the major product from each of these. These results suggest that the addition of sodium borohydride to palladium on carbon produces a reductive entity differing from that of catalytic hydrogenation.     

Stereoelective polymerization of D,L-lactide using N-heterocyclic carbene based compounds

A new Zn alkoxide catalyst supported by an N-heterocyclic carbene rapidly polymerizes D,L-lactide (D,L-LA) to heterotactic enriched poly(lactide)(PLA), while the free carbene and analogs instead yield highly isotactic enriched PLA.     

Uses and analyses of curtin-hammett/winstein-holness systems involving second order reactions

The Curtin-Hammett (C-H) principle and the Winstein-Holness (W-H) equation approximate the product ratio and overall rate constant of reaction for systems involving a starting material which exists in two forms, each of which reacts via first-order kinetics to give a different product. The C-H/W-H approximations are valid when the rates of isomer interconversion are significantly faster than the rates of product formation. The present treatment encompasses non-first-order reactions to product. A numerical predictor-corrector technique is used to show (1) that relative reagent concentration can affect both the product ratio and the observed rates of product formation; (2) that the absolute concentration of reagent and substrate can affect the kinetics; and (3) that factors (1) and (2) above can affect the validity of the C-H/W-H approximations for non-first-order C-H/W-H schemes.     

A new short synthesis of 3-substituted 5-amino-1-(chloromethyl)-1,2-dihydro-3H-benzo[e]indoles (amino-CBIs)

A new short synthesis of 3-substituted 5-amino-1-(chloromethyl)-1,2-dihydro-3H-benzo[e]indoles from Martius Yellow is disclosed. The key steps of the synthesis were three efficient regioselective reactions (iodination, 5-exo-trig aryl radical-alkene cyclization and carboxylation).     

Synthesis of 1-Aza-8-thiabicyclo[4.2.1]nona-2,4-diene 8,8-dioxide and its conversion to a strained spirocycle via photoinduced SO2-N bond cleavage

A route to the doubly unsaturated bridgehead sultam 12 has been developed. When irradiated at 350 nm, this conjugated diene is isomerized via a two-photon process to the structurally novel spiro heterocycle 17 constituted of cyclobutene, thietane dioxide, and pyrrolidine rings. A probable mechanism for the generation of 17 and select reactions thereof are reported. [reaction: see text]     

The reaction of 1,2-dilithiotetrafluorobenzene with group V halides

Although the arsenic containing analogue of triptycene, 5,10-$\text{o}$-benzenoarsanthrene $\text{A}$ (E=As) was isolated some time ago [1] the related derivatives of antimony and bismuth are unknown. We now find that when 1,2-diiodotetrafluorobenzene is treated with methyllithium at -78/dg, to afford the little studied dilithiotetrafluorobenzene [2], and the appropriate metal chloride is added to the resulting solution, perfluorinated analogues of $\text{A}$ (E = As, Sb, or Bi) are obtained in good yield. These are stable volatile solids.