Examples for the Infinite Dimensional Morse Lemma

Examples are presented which show how to use the Morse lemma in specific infinite dimensional examples and what can go wrong if various hypotheses are dropped. One of the examples shows that the version of the Morse lemma using singularity theory can hold, yet the hypotheses of the Morse–Palais and Morse–Tromba lemmas fail. Another example shows how to obtain a concrete normal form in infinite dimensions using the splitting lemma and hypotheses related to those in the Morse–Tromba lemma. An example of Dancer is given which shows that for the validity of the Morse lemma in Hilbert space, some hypotheses on the higher order terms must be made in addition to smoothness, if the quadratic term is only weakly nondegenerate. A general conjecture along these lines is made

A parametric LQ approach to multiobjective control system design

The synthesis of a constant parameter output feedback control law of constrained structure is set in a multiple objective linear quadratic regulator (MOLQR) framework. The use of intuitive objective functions such as model-following ability and closed-loop trajectory sensitivity, allow multiple objective decision making techniques, such as the surrogate worth tradeoff method, to be applied. For the continuous-time deterministic problem with an infinite time horizon, dynamic compensators as well as static output feedback controllers can be synthesized using a descent Anderson-Moore algorithm modified to impose linear equality constraints on the feedback gains by moving in feasible directions. Results of three different examples are presented, including a unique reformulation of the sensitivity reduction problem

A Search for a Surviving White Dwarf Companion in SN 1006

Multiple channels have been proposed to produce Type Ia supernovae, with many scenarios suggesting that the exploding white dwarf accretes from a binary companion pre-explosion. In almost all cases, theory suggests that this companion will survive. However, no such companion has been unambiguously identified in ancient supernova remnants -- possibly falsifying the accretion scenario. Existing surveys, however, have only looked for stars as faint as $\approx 0.1 L_\odot$ and thus would have missed a surviving white dwarf companion. In this work, we present very deep DECAM imaging $(u, g, r, z)$ of the Type Ia supernova remnant SN 1006 specifically to search for a potential surviving white dwarf companion. We find no object within the inner third of the SN 1006 remnant that is consistent with a relatively young cooling white dwarf. We find that if there is a companion white dwarf, it must have formed long ago and cooled undisturbed for $> 10^8$ yr to be consistent with the redder objects in our sample. We conclude that our findings are consistent with the complete destruction of the secondary (such as in a merger) or an unexpectedly cool and thus very dim surviving companion white dwarf.Comment: 9 pages, 5 figure, submitted to MNRAS - comments welcom

X-ray bolometric corrections for Compton-thick active galactic nuclei

We present X-ray bolometric correction factors, $\kappa_{Bol}$ ($\equiv L_{Bol}/L_X$), for Compton-thick (CT) active galactic nuclei (AGN) with the aim of testing AGN torus models, probing orientation effects, and estimating the bolometric output of the most obscured AGN. We adopt bolometric luminosities, $L_{Bol}$, from literature infrared (IR) torus modeling and compile published intrinsic 2--10 keV X-ray luminosities, $L_{X}$, from X-ray torus modeling of NuSTAR data. Our sample consists of 10 local CT AGN where both of these estimates are available. We test for systematic differences in $\kappa_{Bol}$ values produced when using two widely used IR torus models and two widely used X-ray torus models, finding consistency within the uncertainties. We find that the mean $\kappa_{Bol}$ of our sample in the range $L_{Bol}\approx10^{42}-10^{45}$ erg/s is log$_{10}\kappa_{Bol}=1.44\pm0.12$ with an intrinsic scatter of $\sim0.2$ dex, and that our derived $\kappa_{Bol}$ values are consistent with previously established relationships between $\kappa_{Bol}$ and $L_{Bol}$ and $\kappa_{Bol}$ and Eddington ratio. We investigate if $\kappa_{Bol}$ is dependent on $N_H$ by comparing our results on CT AGN to published results on less-obscured AGN, finding no significant dependence. Since many of our sample are megamaser AGN, known to be viewed edge-on, and furthermore under the assumptions of AGN unification whereby unobscured AGN are viewed face-on, our result implies that the X-ray emitting corona is not strongly anisotropic. Finally, we present $\kappa_{Bol}$ values for CT AGN identified in X-ray surveys as a function of their observed $L_X$, where an estimate of their intrinsic $L_{X}$ is not available, and redshift, useful for estimating the bolometric output of the most obscured AGN across cosmic time.Comment: Accepted for publication in Ap

Patient-Reported Side Effects of Intradetrusor Botulinum Toxin Type A for Idiopathic Overactive Bladder Syndrome

Objective: The aim of the study was a prospective assessment of patient-reported side effects in an open-label study after intradetrusor botulinum toxin injections for idiopathic overactive bladder (OAB). Patients and Methods: Botulinum toxin A injection was performed in 56 patients with idiopathic OAB. Patients were followed up for 6 months concerning side effects and patients' satisfaction. Results: Different types of side effects were assessed such as dry mouth (19.6%), arm weakness (8.9%), eyelid weakness (8.9%), leg weakness (7.1%), torso weakness (5.4%), impaired vision (5.4%) and dysphagia (5.4%). In all cases, symptoms were mild and transient. Urological complications such as gross hematuria (17.9%), acute urinary retention (8.9%) and acute urinary tract infection (7.1%) were noticed. In all cases, acute urinary retention was transient and treated with temporary intermittent self-catheterization. There was no statistically significant correlation between dosage and observed side effects. Patients' satisfaction rate was high (71.4%). Conclusion: Intradetrusor injection of botulinum toxin was associated with a high rate of neurourological side effects. In general, side effects were transient, mild and did not require special treatment. Copyright (C) 2010 S. Karger AG, Base

Growing Stronger: Strength Training for Older Adults

In choosing to read this book, you have taken the first step on a journey toward greater strength and vitality. Growing Stronger was written for you—the older adult who wants to grow stronger, healthier, more active, and more independent. You may be inactive or only mildly active at the moment. You may know that regular exercise is important for your health and well-being and want to get started on a program of physical activity. But you may feel that you don’t have the necessary information. Perhaps you are concerned that because of your age or health problems physical activity may not be safe for you. Or perhaps you have had trouble finding or staying with a suitable program. This book gives you a safe, simple, and highly effective exercise program based on the principles of strength training. Studies at laboratories around the world have shown that strength training benefits women and men of all ages and all levels of fitness. According to Physical Activity and Health: A Report of the Surgeon General (1996), experts agree that aerobic activities should be supplemented with strength-developing exercises at least twice per week

Geometric approach to the dynamic glass transition

We numerically study the potential energy landscape of a fragile glassy system and find that the dynamic crossover corresponding to the glass transition is actually the effect of an underlying geometric transition caused by a qualitative change in the topological properties of the landscape. Furthermore, we show that the potential energy barriers connecting local glassy minima increase with decreasing energy of the minima, and we relate this behaviour to the fragility of the system. Finally, we analyze the real space structure of activated processes by studying the distribution of particle displacements for local minima connected by simple saddles