Self-similarities in the frequency-amplitude space of a loss-modulated CO2 laser

We show the standard two-level continuous-time model of loss-modulated CO2 lasers to display the same regular network of self-similar stability islands known so far to be typically present only in discrete-time models based on mappings. Our results suggest that the two-parameter space of class B laser models and that of a certain class of discrete mappings could be isomorphic.     

On the Rubin–Stark Conjecture for a special class of CM extensions of totally real number fields

We use Greithers recent results on Brumers Conjecture to prove Rubins integral version of Starks Conjecture, up to a power of 2, for an infinite class of CM extensions of totally real number fields, called nice extensions under the assumption that a certain Iwasawa –invariant vanishes. As a consequence and under the same assumption, we show that the Brumer–Stark Conjecture is true for nice extensions, up to a power of 2.Mathematical Subject Classification (1991): 11R42, 11R58, 11R27Research on this project was partially supported by NSF grants DMS–9801267 and DMS–0196340.in final form: 16 July 2003     

Characterization of the time dependence of polarization mode dispersion

We elaborate on a recently proposed model of the temporal dependence of polarization mode dispersion in long fiber links. We evaluate the probability that a channel of a wavelength-division multiplexed system never incurs an outage, and the range of frequency over which the parameters that characterize the temporal statistics of the differential group delay are correlated.     

Two-phase channel structures based on alpha-cyclodextrin-polyethylene glycol inclusion complexes

Wide-angle X-ray scattering observations of alpha-cyclodextrin (CD)-poly(ethylene glycol) (PEG) inclusion complexes (ICs) have shown for the first time that two crystalline columnar modifications (forms I and II) are produced in the process of their formation. This was made possible by precise azimuthal X-ray diffraction scanning of oriented IC samples. Form I is characterized by CDs threaded onto PEG chains and arranged along channels in the order head-to-head/tail-to-tail, while form II is formed by unbound CDs also arranged into columns in a head-to-tail and also possibly a head-to-head/tail-to-tail manner, probably as a result of template crystallization on the form I IC crystals. It was shown that similar structural peculiarities are inherent for channel structures based on ICs obtained with PEG with a wide range of molecular weights (MWs). The characteristic feature of ICs based on PEG, especially with MW > 8000, is the presence of unbound polymer in the composition of the complex. The amount of unbound PEG was shown to rise with increasing MW of PEG, resulting in greater imperfections in the IC crystalline structure. The polyblock structure of ICs based on alpha-CD and PEG was therefore proposed.     

Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings

We demonstrate edge-enhanced imaging produced by volume phase gratings recorded on a polyvinyl alcohol/acrylamide photopolymer. Bragg diffraction, exhibited by volume gratings, modifies the impulse response of the imaging system, facilitating spatial filtering operations with no need for a physical Fourier plane. We demonstrate that Kogelnik's coupled-wave theory can be used to calculate the transfer function for the transmitted and the diffracted orders. The experimental and simulated results agree, and they demonstrate the feasibility of our proposal.     

Geometric properties of the sections of solutions to the Monge-Ampère equation

In this paper we establish several geometric properties of the cross sections of generalized solutions to the Monge-Ampère equation , when the measure satisfies a doubling property. A main result is a characterization of the doubling measures in terms of a geometric property of the cross sections of . This is used to obtain estimates of the shape and invariance properties of the cross sections that are valid under appropriate normalizations.

     

The Ghirlanda-Guerra Identities

If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.     

Regulating complex dynamics in firms and economic systems

The decisions of economic firms are often guided by simple routines. We demonstrate that such a routine may generate suboptimal chaotic dynamics, where the suboptimality is due to the fact that decision outcomes are in regions of low performance. We discuss a simple, but effective, method to regulate such dynamics in order to improve the performance. The method works as follows: In a first step, from time series information one has to identify critical starting areas which may lead to a crash or an outcome with low performance. In a second step, one has to perturb the system when it enters these critical areas. Due to sensitive dependence on initial conditions, already minor interventions suffice to prevent harmful events and to obtain better results.     

Vibrational Spectra of Dimethyldithiophosphinate Anion: (CH3)2PS2

Abstract

The infrared and Raman spectra of dimethyldithiophosphinate anion (CH₃)₂PS₂ were measured and the vibrational modes for the anion complex were assigned. A Normal Coordinate Analysis in the Modified General Valence Force Field (MGVFF) approximation was carried out assuming C_2v symmetry. Ab Initio Calculations at RHF and MP2 level were also carried out for the anion geometry as well as for its frequencies, intensities and force constants.