Set-valued solutions to the Cauchy problem for hyperbolic systems of partial differential inclusions

We prove the existence of global set-valued solutions to the Cauchy problem for partial differential equations and inclusions, with either single-valued or set-valued initial conditions. The method is based on the equivalence between this problem and problem of finding viability tubes of the associated characteristic system of ordinary differential equations. As an application we construct the value function of the Mayer problem arising in control theory. Received August 25, 1995     

Stochastic Invariance for Differential Inclusions

The aim of this paper is to combine two ways for representing uncertainty through stochastic differential inclusions: a 'stochastic uncertainty", driven by a Wiener process, and a 'contingent uncertainty", driven by a set-valued map. The paper is also devoted to the invariance of closed under stochastic differential inclusions with a Lipschitz right-hand side, characterized in terms of stochastic tangent sets to closed subsets.     

Contents to Volume 8

Volume Contents

Contents to Volume 8     

Subpicosecond pulse generation from a 1.56 μm mode-locked VECSEL

Near-transform-limited subpicosecond pulses at 1.56 μm were generated from an optically pumped InP-based vertical-external-cavity surface-emitting laser (VECSEL) passively mode-locked at 2 GHz repetition rate with a fast InGaAsNSb/GaAs semiconductor saturable absorber mirror (SESAM). The SESAM microcavity resonance was adjusted via a selective etching of phase layers specifically designed to control the magnitude of both the modulation depth and the intracavity group delay dispersion of the SESAM. Using the same VECSEL chip, we observed that the mode-locked pulse duration could be reduced from several picoseconds to less than 1 ps with a detuned resonant SESAM.     

The electron mobility and the static dielectric constant of Cd3As2 at 4.2 K

The ionized-impurity mobility of Cd₃As₂ at 4.2 K with carrier concentration lying in the range 10¹⁸–10¹⁹ cm^?3 has been calculated taking into account the inverted HgTe-type energy band structure of this material. A comparison of the results with experimental mobility data leads to a static dielectric constant of ?₀ = 36. This value represents a lower limit since any compensation effects would increase the fitted estimate of ?₀.     

Finite-amplitude disturbances in self-gravitating media. II

This paper deals with finite-amplitude axisymmetric disturbances in a self-gravitating fluid column of finite radius R. It is shown that the cutoff wavelength λ_nl above which gravitational breakup occurs now depends on the relative amplitude $\text{?}\text{R}$ of the initial perturbation. Actually, for small-but finite-amplitude disturbances, $\text{λ}{}_{\mathrm{nl}}\text{=}\text{λ}{}_{\mathrm{l}}\text{(1 ? 0.34368}\text{?}{}^2\text{R}{}^2\text{)}$, where λ_l ( = 5.8898R) designates the cutoff wavelength predicted in the linear approximation.     

Peptides derived from two dynamically disordered proteins self-assemble into amyloid-like fibrils

Short peptides derived from p14ARF and Hdm2 (14 and 15 amino acids in length, respectively), two cancer associated proteins, have been found to co-assemble into amyloid-like structures. Larger protein domains containing these peptide segments interact in cells and also undergo a disorder-to-order transition upon binding in vitro. In contrast to the association of beta-strand assemblies with amyloid diseases, the system described herein utilizes the formation of binary, extended beta-strands as a novel mechanism of biomolecular assembly. The beta-strand-containing fibrils formed from these peptides may allow the directed assembly of decorated fibrils with applications as biological nanostructures.     

Perceptual salience of individually distinctive features in the calls of adult king penguins

In the king penguin, Aptenodytes patagonicus, incubation and brooding duties are undertaken alternately by both partners of a pair. Birds returning from foraging at sea find their mate in the crowded colony using acoustic signals. Acoustic recognition of the mate maintains and strengthens the mate's fidelity and favors synchronization in the different stages of reproduction. In this study it was found that the king penguin vocalizes in response to the mate's playback calls, but not to those of neighbors or unfamiliar conspecific individuals. To study individual features used by the birds for individual recognition of mates, various experimental signals consisting of synthesized modifications of the mate' s call were played back to the incubating bird. Results indicated that birds attend to the FM profile of the call, in particular its initial inflexion. The frequency modulation shape of the syllable can be assimilated to a vocal signature repeated though the different syllables of the call. King penguins pay little attention to the call' s AM envelope or its absolute frequency.     

Formation of the Main Cores Present in Natural Products by Tandem Additions

A rapid route to 5,5‐ and 5,6‐ bicyclic systems is provided by an 1,3‐alkyl‐shift process mediated by a hypervalent iodine reagent on aromatics. The structures obtained contain several unsaturations with different behaviors and reactivities. Such diversity allows further elaborations for the rapid formation of compact systems present in a variety of natural products. The potential for further transformations has been demonstrated by performing a double Michael addition. This cyclization process is regio‐ and stereoselective due to the presence of a former benzylic substituent. Furthermore, an extension of this approach has been accomplished on indole derivatives.     

Electron cotunneling transport in gold nanocrystal arrays

We describe current-voltage (I-V) characteristics of alkyl-ligated gold nanocrystals ~5 nm arrays in a long screening length limit. Arrays with different alkyl ligand lengths have been prepared to tune the electronic tunnel coupling between the nanocrystals. For long ligands, electronic diffusion occurs through sequential tunneling and follows activated laws, as a function of temperature σ∝e(-T(0)/T) and as a function of electric field I∝e(-E(0)/E). For better conducting arrays, i.e., with small ligands, the transport properties cross over to the cotunneling regime and follow Efros-Shklovskii laws as a function of temperature σ∝e(-(T(ES)/T)(1/2) and as a function of electric field I∝e(-(E)(ES)/E)(1/2). The data show that electronic transport in nanocrystal arrays can be tuned from the sequential tunneling to the cotunneling regime by increasing the tunnel barrier transparency.