Using the notion of fading memory we prove very strong versions of two folk theorems. The first is that any time-invariant (TI) continuous nonlinear operator can be approximated by a Volterra series operator, and the second is that the approximating operator can be realized as a finite-dimensional linear dynamical system with a nonlinear readout map. While previous approximation results are valid over finite time intervals and for signals in compact sets, the approximations presented here hold for all time and for signals in useful (noncompact) sets. The discretetime analog of the second theorem asserts that any TI operator with fading memory can be approximated (in our strong sense) by a nonlinear moving- average operator. Some further discussion of the notion of fading memory is given.

Laser targets, created by fast optical breakdown of shock fronts produced in an electrothermal shock tube filled with D2 or H2, have been used for studies of resonance absorption of CO2 laser light. In these targets, the critical-surface density-gradient vector always points along the shock-tube axis, leading to reproducible hot-electron emission by plasma wave breaking. The angular distribution and energy spectrum of this emission have been studied. For 200 psec risetime laser pulses, the measured scaling of hot-electron temperature with laser pulse energy agrees with predictions of models of profile steepening by the ponderomotive force of the laser light. For 20 psec risetime laser pulses, the results are consistent with a model in which the detected electron emission is dominated by a ’’chirped’’ monoenergetic burst lasting only 1 to 2 psec. In this model, the electron energy spectrum is due to the integrated temporal variation of the enery of the burst, and the hot-electron temperature is practically independent of laser pulse energy.

We adopt a statistical mechanical approach toward the optics of textured and inhomogeneous optical sheets. As a general rule, the local light intensity in such a medium will tend to be <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 n^{2}(x)</tex> times greater than the externally incident light intensity, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n(x)</tex> is the local index of refraction in the sheet. This enhancement can contribute toward a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4 n^{2}(x)</tex> increase in the effective absorption of indirect-gap semiconductors like crystalline silicon.

We have found that a thin silicon dioxide skin stabilizes the float zone in ribbon-to-ribbon single crystal growth. 40-μm-thick single crystal ribbons, oriented 〈100〉 and scanned in the 〈011〉 direction, were grown completely free of subgrain as well as grain boundaries. This surprising suppression of low angle grain boundaries may be related to a similar effect which has been seen in supported thick silicon on SiO2 films.

A facile patterning method for the functionalization of vertically aligned carbon nanotubes is described. Modification of the surface of nanotube forests with hydrophilic, hydrophobic, or polymerizable small molecules was achieved via UV-triggered attachment of perfluoroarylazides. Multiple functionalizations of the tube surface can be achieved. Macro- and micropatterning of forest substrates were demonstrated. Superhydrophobic surfaces containing superhydrophilic regions were prepared.

This paper describes the geometric structure of a strange attractor observed from the simplest known chaotic electronic circuit which the author conceived and proposed to Professor Matsumoto from Waseda University in 1983. Computer simulation of this circuit by Professor Matsumoto in October 1983 confirmed its rich chaotic dynamics [1]. Subsquent laboratory experiments using an operational amplifier circuit further confirmed the robust nature of the chaotic attractor [2], and its rich bifurcation phenomena [3]. The strange attractor is now widely known as the double scroll [4] because it resembles, from a distance, a pair of Saturn plants attached to the opposite ends of a tube formed by rolling two long strips of paper together into a scroll whose cross section consists of two tightly wound spirals.

Abstract The inherent saturation non‐linearity of the op amp is used to design circuits having a wide variety of useful non‐linear v‐i characteristics. These circuits are made of one op amp and 3 or 4 linear resistors which are passive under a rather mild assumption derived from the 3‐port paramountcy condition. Explicit design formulae are given for each prototype circuit and numerous examples are given and validated by actual measurements.

Department of Electrical Engineering and Computer Science Nagasaki University 1-14, Bunkyo-machi, Nagasaki-shi, 852 Japan E-mail: itoh@itoh.ec.nagasaki-u.ac.jp Department of Electrical Engineering and Computer Sciences University of California, Berkeley CA 94720, USA The communication systems via chaos synchronization are experimentally demonstrated using Chua's circuit.

A fundamental chemoselectivity challenge that remains intrinsically unsolved in aldol-type reactions is the suppression of self-aldol reactions with enolizable aldehydes in reactions such as cross-aldol processes. Contrasting with the usual practice of using large excesses of one component to compete with the undesired self-aldehyde condensation reactions, we have developed an enzyme-like polymer catalyst consisting of a hyperbranched polyethyleneimine derivative and proline that can eliminate the self-aldol reactions by suppressing an irreversible aldol condensation pathway. Control experiments and preliminary mechanistic studies suggest that the polymer catalyst provides an optimum environment for the aldol reaction to proceed selectively in water, and the catalytic conditions provided by the polymer are difficult to duplicate with typical small molecule analogues. This polymer catalyst system or its modified version has potential applications in developing a new or more efficient synthesis, as demonstrated in a dynamic catalytic process for the preparation of alpha,beta-unsaturated ketones using cross ketone/aldehyde reactions without the need for excess substrates.

Experimental confirmation has been made on a negativeresistance oscillator circuit which exhibits the new period-adding route to chaos recently reported by Kaneko on a discrete map. The nonlinear element in the circuit is a negative-resistance device synthesized by using two bipolar transistors and four positive linear resistors. This circuit exhibits a new route to chaos; namely, through period-adding where the periods of two successive periodic waveforms belonging to each periodadding sequence differ by one; i.e., from period <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n - 1</tex> or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n + 1</tex> . The transition to chaos (after one or more periodic states) resulted directly from a loss of stability of a periodic state at a bifurcation point. Several general features of the periodic-chaotic transition sequence have been observed and presented.

The synthesis of a variety of core functionalized PEGylated polyester dendrimers and their in vitro and in vivo properties are described in this report. These water-soluble dendrimers have been designed to carry eight functional groups on their dendritic core for a variety of biological applications such as drug delivery and in vivo imaging as well as eight solubilizing groups. Using a common symmetrical aliphatic ester dendritic core and trifunctional amino acid moieties, a library of dendrimers with phenols, alkyl alcohols, alkynes, ketones, and carboxylic acid functionalities has been synthesized without the need for column chromatography. The amines were PEGylated, leaving the other functionality of the amino acid available for further manipulation such as the attachment of drugs and/or labels. Radiolabeling experiments with the PEGylated dendrimers showed that they had a long circulation half-life in mice, confirming the potential of this class of dendrimers for therapeutic and/or diagnostic applications. A carboxylic acid functionalized dendrimer was elaborated to carry doxorubicin bound via a hydrazone bond. The drug-loaded carrier accumulated more in tumors and less in healthy organs than the clinically used PEGylated liposomal formulation Doxil. The efficient synthesis, high versatility, and favorable biological properties make these PEGylated polyester dendrimers promising structures for therapeutic and/or imaging applications.

A polarity-directed organocatalytic cascade reaction of two different aldehydes with nitromethane in biphasic systems is reported. Since the involved aliphatic aldehydes exhibit similar reactivities, the predominantly formed cross-products of the reaction can be explained by slight differences in polarity. Most likely the proline (1)-catalyzed condensation of the more polar aldehyde with nitromethane succeeds first in the aqueous phase, thus releasing a nitroalkene intermediate. This species enriches in the organic phase consisting of the neat aldehydes, where it undergoes conjugate addition preferred with the less polar aldehyde, accelerated by secondary amine catalyst 2, respectively.

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