Synthesis and photosensitized oxygenation of cyclopropylidenecyclobutenes

Cyclopropylidenecyclobutenes and -cyclobutanes were conveniently prepared using the Petasis titanocene approach. The cyclobutenes were unreactive to singlet oxygen, reacting sluggishly via a photoinitiated free radical autooxidative epoxidation process, to yield the corresponding spiroketones. By contrast, cyclopropylidenecyclobutanes react rapidly with ¹O₂, via an ‘ene’ process, initially generating a cyclopropyl hydroperoxide, which proceeds to products via Hock cleavage. The inertness of cyclopropylidenecyclobutenes to a ¹O₂ ‘ene’ reaction mode may be attributed to the fact that it would require the formation of the relatively high energy cyclobutadiene moiety.     

Exponential stability for nonlinear filtering

We study the a.s. exponential stability of the optimal filter w.r.t. its initial conditions. A bound is provided on the exponential rate (equivalently, on the memory length of the filter) for a general setting both in discrete and in continuous time, in terms of Birkhoff's contraction coefficient. Criteria for exponential stability and explicit bounds on the rate are given in the specific cases of a diffusion process on a compact manifold, and discrete time Markov chains on both continuous and discrete-countable state spaces. A similar question regarding the optimal smoother is investigated and a stability criterion is provided.     

Switchable Cucurbituril–Bipyridine Beacons

4‐Aminobipyridine derivatives form strong inclusion complexes with cucurbit[6]uril, exhibiting remarkably large enhancements in fluorescence intensity and quantum yields. The remarkable complexation‐induced pK_a shift (ΔpK_a=3.3) highlights the strong charge–dipole interaction upon binding. The reversible binding phenomenon can be used for the design of switchable beacons that can be incorporated into cascades of binding networks. This concept is demonstrated herein by three different applications: 1) a switchable fluorescent beacon for chemical sensing of transition metals and other ligands; 2) direct measurement of binding constants between cucurbit[6]uril and various nonfluorescent guest molecules; and 3) quantitative monitoring of biocatalytic reactions and determination of their kinetic parameters. The latter application is illustrated by the hydrolysis of an amide catalyzed by penicillin G acylase and by the elimination reaction of a β‐cabamoyloxy ketone catalyzed by aldolase antibody 38C2.     

Surface lattice solitons

We study theoretically nonlinear surface waves in optical lattices and show that solitons can exist at the heterointerface between two different semi-infinite 1D waveguide arrays, as well as at the boundaries of a 2D nonlinear lattice. The existence and properties of these surface soliton solutions are investigated in detail.     

Precise large deviation estimates for a one-dimensional random walk in a random environment

ω_x } (taking values in the interval [1/2, 1)), which serve as an environment. This environment defines a random walk {X _k } (called a RWRE) which, when at x, moves one step to the right with probability ω _x , and one step to the left with probability 1 −ωx. Solomon (1975) determined the almost-sure asymptotic speed (= rate of escape) of a RWRE, in a more general set-up. Dembo, Peres and Zeitouni (1996), following earlier work by Greven and den Hollander (1994) on the quenched case, have computed rough tail asymptotics for the empirical mean of the annealed RWRE. They conjectured the form of the rate function in a full LDP. We prove in this paper their conjecture. The proof is based on a “coarse graining scheme” together with comparison techniques. Received: 22 July 1997/Revised version: 15 June 1998     

Atomic volume dependence of the153Eu isomer shift in ScxY1−x

Mössbauer studies of dilute¹⁵³Eu in Sm_0.05Sc _x Y_0.95–x (0x0.95) reveal large changes in the isomer shift as a function ofx. The strong dependence of the isomer shift on alloy composition, is interpreted in terms of changes in the charge density at the Eu nucleus ((0)), which result from changes in atomic volume. The isomer shift was found to depend linearly on V/V (V/V changes between 0 and –0.3). A value of (–17.5±2.0)a ₀ ^–3 was obtained for d(0)/d lnV.This research was supported by a grant from the United States—Israel Binational Science Foundation (BSF), Jerusalem, Israel.     

On the Non-Adaptive Zero-Error Capacity of the Discrete Memoryless Two-Way Channel

We study the problem of communicating over a discrete memoryless two-way channel using non-adaptive schemes, under a zero probability of error criterion. We derive single-letter inner and outer bounds for the zero-error capacity region, based on random coding, linear programming, linear codes, and the asymptotic spectrum of graphs. Among others, we provide a single-letter outer bound based on a combination of Shannon’s vanishing-error capacity region and a two-way analogue of the linear programming bound for point-to-point channels, which, in contrast to the one-way case, is generally better than both. Moreover, we establish an outer bound for the zero-error capacity region of a two-way channel via the asymptotic spectrum of graphs, and show that this bound can be achieved in certain cases.     

Synthesis of novel, simplified, C-7 substituted eleutheside analogues with potent microtubule-stabilizing activity

The synthesis of a number of novel, simplified, C-7 substituted eleutheside analogues with potent tubulin-assembling and microtubule-stabilizing properties is described, using ring closing metathesis as the key-step for obtaining the 6-10 fused bicyclic ring system. The RCM precursors were synthesized starting from aldehyde 3 [prepared in six steps on a multigram scale from R-(−)-carvone in 30% overall yield] via multiple stereoselective Hafner-Duthaler allyltitanations and/or Brown allylborations. ‘Second generation’ RCM-catalyst 15 gave the desired ring closed ten-membered carbocycles as single Z stereoisomers in good yields. The RCM stereochemical course (100% Z) is likely to reflect thermodynamic control. Molecular mechanics and semi-empirical calculations also show that the Z stereoisomers of these ten-membered carbocycles are consistently more stable than the E. The crucial role of the homoallylic and allylic substituents and of their protecting groups for the efficiency of the RCM reactions is discussed. In particular, we have found that p-methoxyphenyl (PMP) protected allylic alcohols, the products of a stereoselective oxyallylation, are compatible with the RCM reaction and give better yields than the corresponding free allylic alcohols. One of the simplified analogues of the natural product (44, lacking inter alia the C-4/C-7 ether bridge) retains potent microtubule-stabilizing activity. However, the cytotoxicity tests did not parallel the potent tubulin-assembling and microtubule-stabilizing properties: limited cytotoxicity was observed against three common tumor cell lines (human ovarian carcinoma, human colon carcinoma and human leukemia cell lines, IC₅₀ in the μM range), approximately two orders of magnitude less than paclitaxel (IC₅₀ in the nM range). The mechanism of cell cycle arrest induced by compound 44 is similar to that obtained with paclitaxel.     

Mössbauer effect studies of excited states of 155Gd

Mössbauer effect studies of the 60.0, 86.5 and 105.3 keV transitions of ¹⁵⁵Gd, yield the following nuclear parameters: $\text{τ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(60}\text{keV level}\text{) = 194 ± 15}\text{ps}$, $\text{g(87)}\text{g(0)}\text{= 1.235 ± 0.008}$, $\text{g(105)}\text{g(0)}\text{= 2.01 ± 0.05 or ?0.55 ± 0.05}$; $\text{Q(87)}\text{Q(0)}\text{= +0.087 ± 0.006}$ and $\text{Q(105)}\text{Q(0)}\text{= 1.00 ± 0.03}$ or $\text{Q(87)}\text{Q(0)}\text{= ?0.083 ± 0.008}$ and $\text{Q(105)}\text{Q(0)}\text{= = 1.16 ± 0.03}$. Theoretical considerations favour the first set of values of $\text{Q(87)}\text{Q(0)}$ and $\text{Q(105)}\text{Q(0)}$.