A generalization of Vinograd's theorem for dynamical systems

The theory of dynamical systems has been expanded by the introduction of local dynamical systems [10, 4, 9] and local semidynamical systems [1]. Using integral curves of autonomous ordinary differential equations to illustrate these generalizations, we find that, roughly, the integral curves form a local dynamical system if solutions exist and are unique without requiring existence for all time, and the integral curves form a local semidynamical system if solutions exist and are unique in the positive sense but need not exist for all positive time. In addition to autonomous ordinary differential equations, the enlarged theory of dynamical systems has applications to nonautonomous ordinary differential equations, certain partial differential equations, functional differential equations, and Volterra Integral equations [9, 1, 2, 8], respectively. All of these have metric phase spaces. Since many dynamic considerations are invariant to reparameterizations, it is of interest to known when a local dynamical (or semidynamical) system can be reparameterized to yield a “global” dynamical (or semidynamical) system. For autonomous ordinary differential equations, Vinograd [7] has shown that the local dynamical system on an open subset ofRⁿ formed by integral curves is isomorphic (in the sense of Nemytskii and Stepanov) to a global dynamical system. In an extensive study of isomorphisms, Ura [12] has expanded the Gottschalk-Hedlund notion of an isomorphism and restated Vinograd's result in terms of a reparameterization. In this paper we study the problem of finding a global dynamical (or semidynamical) system which is isomorphic to a given local system. A necessary and sufficient condition is found which is then used to show that the Vinograd result holds on metric spaces.     

A facile synthesis of α-chloroboronic esters via the base induced reaction of α,α-dichloromethyl methyl ether with hindered borinic esters

Treatment of hindered borinic esters, R₂ BOR′; with an equimolar quantity of α,α-dichloromethyl methyl ether and lithium triethylcarboxide yields the α-chloroboronic esters, R₂ CHClB(OCH₃)OR′, in excellent yields. In cases where the steric requirements of R are not sufficient, the steric requirements of R′ can be increased to achieve the synthesis.     

Observation of radio-wave-induced red hydroxyl emission at low altitude in the ionosphere

We report the discovery of radio-wave-induced red emission of OH Meinel rotation-vibrational bands at 629.79 nm. These are the first measurements of artificial aurora below 100 km. We believe that the 629.79-nm OH emission was due to radio-wave focusing by sporadic ionization clouds near 80-85 km altitude, thus giving a technique to visualize the low-altitude sporadic ionization and providing insight into ionospheric interactions at these low altitudes.     

Constraints on proton structure from precision atomic-physics measurements

Ground-state hyperfine splittings in hydrogen and muonium are very well measured. Their difference, after correcting for magnetic moment and reduced mass effects, is due solely to proton structure-the large QED contributions for a pointlike nucleus essentially cancel. The rescaled hyperfine difference depends on the Zemach radius, a fundamental measure of the proton, computed as an integral over a product of electric and magnetic proton form factors. The determination of the Zemach radius, (1.019+/-0.016) fm, from atomic physics tightly constrains fits to accelerator measurements of proton form factors. Conversely, we can use muonium data to extract an experimental value for QED corrections to hydrogenic hyperfine data. There is a significant discrepancy between measurement and theory, in the same direction as a corresponding discrepancy in positronium.     

Martensitic fcc-to-hcp transformation observed in xenon at high pressure

Angle-resolved x-ray diffraction patterns of Xe to 127 GPa indicate that the fcc-to-hcp transition occurs martensitically between 3 and 70 GPa in diamond-anvil cells without an intermediate phase. These data also reveal that the transition occurs by the introduction of stacking disorder in the fcc lattice at low pressure, which grows into hcp domains with increasing pressure. The small energy difference between the hcp and the fcc structures may allow the two phases to coexist over a wide pressure range. Evidence of similar stacking disorder and incipient growth of an hcp phase are also observed in solid Kr.     

Highly optimized tolerance: robustness and design in complex systems

Highly optimized tolerance (HOT) is a mechanism that relates evolving structure to power laws in interconnected systems. HOT systems arise where design and evolution create complex systems sharing common features, including (1) high efficiency, performance, and robustness to designed-for uncertainties, (2) hypersensitivity to design flaws and unanticipated perturbations, (3) nongeneric, specialized, structured configurations, and (4) power laws. We study the impact of incorporating increasing levels of design and find that even small amounts of design lead to HOT states in percolation.     

Multiscale coherent structures and broadband waves due to parallel inhomogeneous flows

Linear theory analysis and particle-in-cell simulations show that a spatial transverse gradient in the ion drift parallel to the magnetic field, dV(di)/dxOmega(i). Nonlinearly, these waves lead to multiscale spatially coherent structures, substantial cross-field transport, ion energization, and phase-space diffusion. Large spikes are formed in the parallel electric field time series. These signatures are similar to the Fast Auroral Snapshot satellite observations in the upward current region.     

Nonlinear phase adjustment of selective excitation pulses

A continuous transformation of an RF waveform with a modified Korteweg-de Vries equation or generalization can be used to adjust the phase behavior of a selective excitation pulse while preserving the magnitude behavior of the spin response. This transformation has applications in removing or adding to the nonlinear phase properties of a selected region.