A note on compact elements in the lattice of radicals

An example of radical compact ring A whose Dorroh extension A¹ is not radical compact is constructed.     

Fold‐2‐covering triangular embeddings

For a graph G and a positive integer m, G_(m) is the graph obtained from G by replacing every vertex by an independent set of size m and every edge by m² edges joining all possible new pairs of ends. If G triangulates a surface, then it is easy to see from Euler's formula that G_(m) can, in principle, triangulate a surface. For m prime and at least 7, it has previously been shown that in fact G_(m) does triangulate a surface, and in fact does so as a “covering with folds” of the original triangulation. For m = 5, this would be a consequence of Tutte's 5‐Flow Conjecture. In this work, we investigate the case m = 2 and describe simple classes of triangulations G for which G₍₂₎ does have a triangulation that covers G “with folds,” as well as providing a simple infinite class of triangulations G of the sphere for which G₍₂₎ does not triangulate any surface. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 79–92, 2003     

Three-dimensional structure of Saccharomyces cerevisiae inorganic pyrophosphatase complexed with cobalt and phosphate ions

Crystals of Saccharomyces cerevisiae inorganic pyrophosphatase suitable for X-ray diffraction study were grown by cocrystallization of the enzyme with cobalt chloride and imidodiphosphate. Saccharomyces cerevisiae is a metal-dependent enzyme which catalyzes hydrolysis of inorganic pyrophosphate to orthophosphate. The three-dimensional structure of this enzyme was solved by the molecular-replacement method and refined at 1.8 Å resolution to an R factor of 19.5%. Cobalt and phosphate ions were revealed in the active centers of both identical subunits (A and B) of the pyrophosphatase molecule. In subunit B, a water molecule was found between two cobalt ions. It is believed that this water molecule acts as an attacking nucleophile in the enzymatic cleavage of the pyrophosphate bond. It was demonstrated that cobalt ions and a phosphate group occupy only part of the potential binding sites (two chemically identical and crystallographically independent subunits have different binding sites). The arrangement of ligands and the structure of the nucleophile-binding site are discussed in relation to the mechanism of action of the enzyme and the nature of the metal activator.     

Determination of flutter derivatives via a neural network approach

A neural-network-based method is offered to determine the flutter derivatives of section models under smooth and turbulent flows. The approach uses the observed dynamic responses to train an appropriate neural network. Subsequently, the modal parameters of the model for different mean velocities of wind flow are directly estimated using weight matrices in the neural network. The flutter derivatives can then be determined accurately. The validity of the present method is verified through numerical studies. Finally, the procedure is employed to process experimental data from an inverted-U-type section model, obtained from wind tunnel tests.     

A note on the necessary conditions for the algebraic Riccati equation

We derive some useful and easily computable necessary conditionsfor the existence of a positive semi-definite solution to thealgebraic Ricatti equation (ARE). A motivating example is givento highlight the usefulness of the conditions for controllerand observer designs for nonlinear systems. Further, an upperbound on the trace of the solution to the ARE is also derived.     

Comments on `Semianalytic BER evaluation by simulation for noisynonlinear bandpass channels'

Pent et al. (see ibid., vol.SAC-6, no.1, p.34-41, 1988) proposed a semianalytic method for performance evaluation of communication channels with a bandpass nonlinearity. This method is based on a decomposition of the composite signal at the output of the nonlinear device which leads to the definition of an equivalent nonlinearity. In Pent et al. such an equivalent model is evaluated via numerical integration. In the present comment it is shown that a suitable series expansion of the nonlinearity characteristic yields to an evaluation of the equivalent nonlinearity in closed form     

Analysis and synthesis of on-chip spiral inductors

This paper presents a physically based compact model for estimating high-frequency performance of spiral inductors. The model accurately accounts for skin and proximity effects in the metal conductors as well as eddy current losses in the substrate. The model shows excellent agreement with measured data mostly within 10% across a variety of inductor geometries and substrate dopings up to 20 GHz. A web-based spiral inductor synthesis and analysis tool COILS, which makes use of the compact models, is presented. An optimization algorithm using binary searches speeds up the synthesis of inductor designs.     

Karhunen–Loeve representations of turbulent channel flows using the method of snapshots

For three‐dimensional flows with one inhomogeneous spatial coordinate and two periodic directions, the Karhunen–Loeve procedure is typically formulated as a spatial eigenvalue problem. This is normally referred to as the direct method (DM). Here we derive an equivalent formulation in which the eigenvalue problem is formulated in the temporal coordinate. It is shown that this so‐called method of snapshots (MOS) has some numerical advantages when compared to the DM. In particular, the MOS can be formulated purely as a matrix composed of scalars, thus avoiding the need to construct a matrix of matrices as in the DM. In addition, the MOS avoids the need for so‐called weight functions, which emerge in the DM as a result of the non‐uniform grid typically employed in the inhomogeneous direction. The avoidance of such weight functions, which may exhibit singular behaviour, guarantees satisfaction of the boundary conditions. The MOS is applied to data sets recently obtained from the direct simulation of turbulence in a channel in which viscoelasticity is imparted to the fluid using a Giesekus model. The analysis reveals a steep drop in the dimensionality of the turbulence as viscoelasticity is increased. This is consistent with the results that have been obtained with other viscoelastic models, thus revealing an essential generic feature of polymer‐induced drag reduced turbulent flows. Published in 2006 by John Wiley & Sons, Ltd.     

Comparison of the effects of nonlinear gain and weak opticalfeedback on the dynamics of semiconductor lasers

The influence of nonlinear gain and optical feedback on the dynamics of single-mode semiconductor lasers are numerically investigated based on the Lang and Kobayashi model. It is well known that the nonlinear gain tends to stabilize the dynamics, while the optical feedback tends to increase the instabilities. In this paper, we study the behavior of the attractors when the feedback level k and the gain saturation coefficient ε vary and show that the effects of these parameters are surprisingly opposite. For example, we find that the route to chaos that the external cavity modes follow for increasing k is reversed for increasing ε in an almost identical manner. When the feedback increases the modes follow the usual quasi-periodic route and turn into torus. If k continues to increase, the torus become chaotic attractors as the result of several period-doubling bifurcations or a third Hopf bifurcation. Further increase of k causes the chaotic attractors to lose stability, Contrarily, if the value of the parameter ε is increased, the attractors recover their stability and reverse the route becoming simple torus again. If ε is increased further, the torus reverse the quasi-periodic route and turn into stable modes again. We also find that on the contrary to k, the parameter ε enhances the stability region of an attractor. We show that the feedback level above which a limit cycle emerges from a stable mode, the feedback level above which a torus emerges from a limit cycle, and the feedback level above which a chaotic attractor loses stability are all increasing functions of ε