Semisimplicity of indefinite extrinsic symmetric spaces and mean curvature

Improving a result of Eschenburg and Kim we give a criterion for semisimplicity of pseudo-Riemannian extrinsic symmetric spaces in terms of the shape operator with respect to the mean curvature vector.     

Analysis of enhanced-power solitons in dispersion-managed optical fibers

We analyze pulse propagation in an optical fiber employing a periodic dispersion map. Second-order averaging is used to determine a general evolution equation valid for both return-to-zero and non-return-to-zero pulses in dispersion-managed systems. The equation is then applied to the case of solitons, and an analytic expression for the power enhancement arising from the dispersion management is obtained.     

Improvement of the performance of cw CO lasers by using externally ribbed wall cooled discharge tubes

 We describe a modified design of a continuous-flow cw CO laser with longitudinal electric discharge using an externally ribbed wall cooled discharge tube. The transverse ribbed discharge tube provides a more intense heat exchange of the CO-laser gas with the walls. With this configuration it was possible to obtain about 50% more output power from an all-line CO Δv=1 laser. For a CO-overtone Δv=2 laser we were able to improve both the output power and the number of lines as compared to a conventional smooth tube. Received: 23 April 1996     

Normally hyperbolic operators, the Huygens property and conformal geometry

In this paper we give a review on normally hyperbolic operators of Huygens type. The methods to determine Huygens operators we explain here were essentially influenced and developed by Paul Günther.     

Hydrogenation of sorbic acid in mono- and biphasic systems catalyzed by Rh(I)- phosphine complexes

Hydrogenation of sorbic acid in ethyl acetate with [RhCl(PPh₃)₃] was studied and compared to the hydrogenation of its K-salt in water catalyzed by [RhCl(mtppms)₃]. Aqueous biphasic hydrogenation of sorbic acid with [RhCl(mtppms)₃] as catalyst proceeded faster and more selectively than that in homogeneous solutions and afforded trans-hex-2-enoic acid with 80% selectivity.     

Pseudo-RiemannianT-duals of compact Riemannian homogeneous spaces

The first part of this paper describes the construction of pseudo-Riemannian homogeneous spaces with special curvature properties such as Einstein spaces, using corresponding known compact Riemannian ones. This construction is based on the notion of a certain duality between compact and non-compact homogeneous spaces. In the second part we apply this method to obtain pseudo-Riemannian homogeneous manifolds with real Killing spinors. We will prove that under a certain additional condition a dual pseudo-Riemannian space (G/H, g) of a compact Riemannian homogeneous space (G/H, g) with homogeneousSpin-structure admits a homogeneousSpin ⁺-structure and theG_invariant Killing spinors on (G/H, g) correspond toG-invariant Killing spinors on (G/H, g). We can ensure that in most cases the hypothesis onG-invariance is satisfied.     

Optimal dispersion maps for wavelength-division-multiplexed soliton transmission

We propose an advantageous dispersion-management scheme for wavelength-division-multiplexed soliton transmission in which optimal launch points are obtained whose locations are independent of the fibers' dispersion parameters. Inasmuch as using such optimal launch points minimizes dispersively shed radiation, it is possible to optimize the transmission simultaneously in several different channels. For the particular case of a two-step dispersion map we demonstrate that this result can be achieved by proper choice of the fiber lengths.     

7-Dimensional compact Riemannian manifolds with Killing spinors

Using a link between Einstein-Sasakian structures and Killing spinors we prove a general construction principle of odd-dimensional Riemannian manifolds with real Killing spinors. In dimensionn=7 we classify all compact Riemannian manifolds with two or three Killing spinors. Finally we classify nonflat 7-dimensional Riemannian manifolds with parallel spinor fields.     

Waiting-Time Behavior in a Nonlinear Diffusion Equation

We study the nonlinear diffusion equation u_t*=(uⁿu_x)_x, which occurs in the study of a number of problems. Using singular-perturbation techniques, we construct approximate solutions of this equation in the limit of small n. These approximate solutions reveal simply the consequences of this variable diffusion coefficient, such as the finite propagation speed of interfaces and waiting-time behavior (when interfaces wait a finite time before beginning to move), and allow us to extend previous results for this equation.     

A Path‐Based Method for Simulating Large Deviations and Rare Events in Nonlinear Lightwave Systems

Errors in nonlinear lightwave systems are often associated with rare, noise‐induced, large deviations of the signal. We present a method to determine the most probable manner in which such rare events occur by solving a sequence of constrained optimization problems. These results then guide importance‐sampled Monte Carlo simulations to determine the events' probabilities. The method applies to a general class of intensity‐based optical detectors and to arbitrarily shaped and multiple pulses.