An electronic instrument for displaying any perspective of a three-dimensional surface S generated by three time-varying (not necessarily periodic) signals is described. The surface S is a three-dimensional Lissajous figure which need not be a closed curve as is typical of all strange attractors. This analog (not digital) instrument is designed to rotate S along any axis (not just the X-, Y-, Z-axis) through any prescribed solid angles (0°-360°) in the three-dimensional coordinate system in real time. The instrument works as a preprocessor for a standard oscilloscope and is built with components capable of displaying time-varying signals with a frequency spectrum from 0 to 20 kHz. To illustrate some immediate applications of this instrument, strange attractors associated with both autononmus and nonautonomous circuits are presented in many different perspectives and cross sections. In particular, numerous cross sections of these strange attractors which have never been seen before can be easily displayed in any desired perspective in real time. Such cross sections have proved to be most revealing and invaluable in dissecting and uncovering the fine structures of strange attractors.

Die Polarität ist es, die den Unterschied zwischen Substraten mit sonst fast identischer chemischer Reaktivität macht. Eine Eintopf-Kaskadenreaktion von Nitromethan und zwei aliphatischen Aldehyden ähnlicher Reaktivitäten wurde entwickelt (siehe Schema). Die Verwendung eines zweiphasigen Reaktionsmediums mit zwei verschiedenen organischen Katalysatoren führte zur hochselektiven Bildung eines einzigen von vier möglichen Produkten. Detailed facts of importance to specialist readers are published as ”Supporting Information”. Such documents are peer-reviewed, but not copy-edited or typeset. They are made available as submitted by the authors. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

Abstract Necessary and sufficient conditions are given for resistive circuits containing both monotone‐increasing non‐linear resistors and monotone‐decreasing non‐linear resistors (called negative non‐linear resistors), in addition to controlled sources and op‐amps, to have a unique solution for all circuit parameters. Several theorems are given for various classes of circuits containing different combinations of active circuit elements. the theorems are couched mostly in topological terms and can therefore be checked by inspection.

We illustrate how to form the Taylor polynomial for a stable or unstable manifold when considered as a curve in the plane. Our method does not use power series or assume that the manifold is analytic as is done in the method of Poincaré. Instead we use simple calculus to obtain closed form expressions for the Taylor coefficients.

Abstract This paper describes the dynamics of the simplest physical system known to date whose chaotic dynamics and rich bifurcation phenomena have been observed not only in the laboratory, but also reconfirmed by extensive computer simulation of its associated mathematical model: a 3rd‐order autonomous ordinary differential equation. The physical system is a 5‐element electrical circuit whose only non‐linearity is a non‐linear resistor characterized by a 3‐segment piecewise‐linear voltage‐current characteristic. Despite the simplicity of the circuit, however, it is imbued with an extremely rich variety of bifurcation phenomena. By changing the capacitance values, many phenomena, including Hopf bifurcation, period‐doubling cascades, Rössler's spiral‐type and screw‐type attractors, 4 periodic windows, ‘double‐scroll’ attractor, 1 boundary crisis, 5 Shilnikov‐type phenomenon, 6 etc. have been observed experimentally and confirmed by computer simulation. Other attractors and periodic windows have also been observed by varying the conductance values. In addition, Rössler's spiral‐type and screw‐type attractors have been observed from the same circuit, where the non‐linear resistor has only one break point, i.e. it is described by a 2‐ segment piecewise‐linear v ‐ i characteristic. This means that extremely complicated non‐periodic (chaotic) waveforms can arise in the simplest third‐order uncoupled electrical circuit in which all elements except one (a resistor ) are linear and passive, and in which the constitutive relation of the non‐linear resistor is made of the simplest conceivable non‐linearity, namely 2 straight‐line segments.

Acid-degradable particles containing a model protein antigen, ovalbumin, were prepared from a polyurethane with acetal moieties embedded throughout the polymer, and characterized by dynamic light scattering and transmission electron microscopy. The small molecule degradation byproduct of the particles was synthesized and tested in vitro for toxicity indicating an LC 50 of 12,500 microg/mL. A new liquid chromatography-mass spectrometry technique was developed to monitor the in vitro degradation of these particles. The degradation byproduct inside RAW macrophages was at its highest level after 24 h of culture and was efficiently exocytosed until it was no longer detectable after 4 days. When tested in vitro, these particles induced a substantial increase in the presentation of the immunodominant ovalbumin-derived peptide SIINFEKL in both macrophages and dendritic cells. In addition, vaccination with these particles generated a cytotoxic T-lymphocyte response that was superior to both free ovalbumin and particles made from an analogous but slower-degrading acid-labile polyurethane polymer. Overall, we present a fully degradable polymer system with nontoxic byproducts, which may find use in various biomedical applications including protein-based vaccines.

We report chaotic phenomena observed from a simple nonlinear switched-capacitor circuit. The experimentally measured bifurcation tree diagram reveals a period-doubling route to chaos. This circuit is described by a first-order discrete equation which can be transformed into the logistic map whose chaotic dynamics is well known.

The synthesis and characterization of platinum-containing conjugated polymers in which the platinum atom is attached to the conjugated backbone via a C∧N ligand is presented. The newly designed platinum-containing monomer can be polymerized under both Stille and Suzuki conditions. The polymers exhibit optical bandgaps between 2.1 and 1.65 eV depending on the choice of comonomer. Triplet exciton formation is detected indirectly by measuring photosensitized emission of singlet oxygen in both solution and in film. The ability of the materials to sensitize formation of singlet oxygen varies both with excitation wavelength and with the change from solution to solid state. This study provides design principles for developing conjugated polymers with significant triplet yields in the solid state. The photovoltaic performance of these polymers was also evaluated in preliminary experiments with power conversion efficiencies as high as 1.3% obtained for a bulk heterojunction cell with PCBM.

We have investigated the temperature-dependent behavior of thiolated azobenzene molecules on Au(111) using scanning tunneling microscopy. The addition of a thiol functional group to azobenzene molecules leads to increased surface anchoring of single azobenzene molecules to gold. Thiolated azobenzene shows diverse surface morphology and does not form well-ordered structures at low coverage. At elevated temperatures, anchored molecules are observed to spin in place via hindered rotation. By measuring the number of rotating molecules as a function of temperature and using a simple model, we are able to estimate the energy barrier and attempt frequency for thermally induced hindered rotation to be 102±3 meV and 110±2 GHz, respectively.

Abstract As an extension to the breakpoint hopping algorithm developed in reference 1, the algorithm presented in this paper efficiently solves the d.c. problem for finding the d.c. operating point(s) and for tracing the driving‐point and transfer characteristics of an extremely broad class of non‐linear resistive circuits. In particular, bipolar and MOS transistor circuits are included. A user‐friendly C program has been written to implement this algorithm where the input format for describing the circuit is compatible with the SPICE program.

A crossing between phases: Polarity makes a difference in distinguishing substrates of otherwise nearly identical chemical reactivities. A one-pot cascade reaction involving nitromethane and two aliphatic aldehydes with similar reactivities has been developed (see scheme). The use of a biphasic reaction medium with two different organic catalysts results in the controlled incorporation of both aldehyde substrates into a single major cross-product.

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.