196,192 research outputs found
Arnol′d tongues arising from a grazing-sliding bifurcation
No full textThe Neımark–Sacker bifurcation, or Hopf bifurcation for maps, is a well-known bifurcation for smooth dynamical systems. At this bifurcation a periodic orbit loses stability, and, except at certain “strong” resonances, an invariant torus is born. The dynamics on the torus is organized by Arnol'd tongues in parameter space; inside the Arnol'd tongues phase-locked periodic orbits exist that disappear in saddle-node bifurcations on the tongue boundaries, and outside the tongues the dynamics on the torus is quasi-periodic. In this paper we investigate whether a piecewise-smooth system with sliding regions may exhibit an equivalent of the Neımark–Sacker bifurcation. The vector field defining such a system changes from one region in phase space to the next, and the dividing (or switching) surface contains a sliding region if the vector fields on both sides point toward the switching surface. We consider the grazing-sliding bifurcation at which a periodic orbit becomes tangent to the sliding region and provide conditions under which it can be thought of as a Neımark– Sacker bifurcation. We find that the normal form of the Poincar´e map derived at the grazing-sliding bifurcation is, in fact, noninvertible. The resonances are again organized in Arnol'd tongues, but the associated periodic orbits typically bifurcate in border-collision bifurcations that can lead to more complicated dynamics than simple quasi-periodic motion. Interestingly, the Arnol'd tongues of piecewise-smooth systems look like strings of connected sausages, and the tongues close at double border-collision points. Since in most models of physical systems nonsmoothness is a simplifying approximation, we relate our results to regularized systems. As one expects, the phase-locked solutions deform into smooth orbits that, in a neighborhood of the Ne˘ımark–Sacker bifurcation, lie on a smooth torus. The deformation of the Arnol'd tongues is more complicated; in contrast to the standard scenario, we find several coexisting pairs of periodic orbits near the points where the Arnol'd tongues close in the piecewise-smooth system. Nevertheless, the unfolding near the double border-collision points is also predicted as a typical scenario for nondegenerate smooth systems
The use of L-serine in the construction of carboalkoxy-substituted delta��-oxazoline, oxazole, delta��-thiazoline, and thiazole heterocyclic ring systems
No full textTypescript (photocopy).An (alpha)-amino acid was used in the preparation of non-peptide materials. The use of the (beta)-hydroxy-(alpha)-amino acid serine (14) was demonstrated to be effective in the construction of 2-substituted-4-carboxy-(DELTA)('2)-oxazolines (5), 2-substituted-4-carboxyoxazoles (4), 2-substituted-4-carboxy-(DELTA)('2)-thiazolines (13), and 2-substituted-4-carboxythiazoles (12). Starting from L-serine (14), stable crystalline O-tosyl-L-serine esters 25 and 30 were prepared in 65% and 34% overall yields, respectively. Acylation of these serine synthons (25 and 30) gave N-acyl-O-tosyl-L-serine esters (28 and 34), which underwent cyclization upon treatment with pyridine in methylene chloride at reflux to provide 2-substituted-4-carboxy-(DELTA)('2)-oxazolines (5). Subsequent oxidation with NiO(,2) yielded the corresponding 2-substituted-4-carboxyoxazoles (4). The L-serine methyl ester hydrochloride salt (20), which was prepared from L-serine in 95% yield, allowed for the rapid construction of 2-substituted-4-carboxy-(DELTA)('2)-thiazolines (13) and 2-substituted-4-carboxythiazoles (12) by three different routes. First, the serine synthon 20 underwent thioacylation to give N-thioacyl-L-serine methyl esters (50), which were then ring cyclized under basic sulfonate ester preparation conditions to 2-substituted-4-carbomethoxy-(DELTA)('2)-thiazolines (48). Second, the serine synthon 20 was acylated to give N-acyl-L-serine methyl ester 38, which underwent direct thiation and ring cyclization to give 2-substituted-4-carbomethoxy-(DELTA)('2)-thiazolines (48). Third, carboxymethyldithiobenzoate (46a) was coupled with the O-tosyl-L-serine ester 25 to give the (DELTA)('2)-thiazoline 48a in 34% yield. Subsequent oxidation yielded the corresponding 2-substituted-4-carboxythiazole (12). For both the heterocyclic ring systems, the methodology allows for the incorporation of a wide array of alkyl and aryl groups at the C-2 position, introduction of the C-2 position substituent in a common intermediate before ring cyclization, and basic ring cyclization conditions to accommodate acid sensitive C-2 position substituents
Dr. Duane M. Jackson, Morehouse College, July 2011
No full textThis video is a conversation with Dr. Duane M. Jackson. Dr. Jackson talks about his paper, "Recall and the Serial Position Effect: The Role of Primacy and Recency on Accounting Students' Performance." Jackie Daniel, AUC Woodruff Library, is the interviewer
New views on an old move: hominin migration into Eurasia
No full textAbstract not availableJ.M. Parés, M. Duval, L.J. Arnol
"Reflections on the subject of Emigration from Europe with a view to Settlement in the United States" By M. Carey.
No full text"Reflections on the subject of Emigration from Europe with a view to Settlement in the United States: containing bried sketches of the moral and political character of those states.
By M. Carey, member of the American philosophical, and of the American Antiquarian Society, and author of The Olive Branch, Cindiciae Hibernicae, essays on banking, on political economy, and on internal improvement.
To which are now added the English editor's comments on the subject; together with Important Advice to Emigrants, and Cautions Against Impositions Practiced in the Outports
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Kevin M. Garza, Orchestral Conducting
No full textOuverture Die Weihe des Hauses Op. 124 / Ludwig van Beethoven; Symphony no. 35 in D major Haffner K. 385 / W.A. Mozart; Pastoral / Karel Husa; Four Irish Dances, Op. 126 / Malcolm Arnol
Dr. Glendon Swarthout
No full textHosted by Roger M. Busfield, MSU Assistant Professor of Speech and Theater, Meet the Author is designed to introduce a general audience to a contemporary author and their work through in-depth interviews. This episode features a conversation between Dr. Glendon Swarthout, prolific author and English professor at MSU, and assistant professors Sam S. Baskett and Theodore B. Strandness
Efficient computation of quasiperiodic oscillations in nonlinear systems with fast rotating parts
No full textWe present a numerical method for the investigation of quasiperiodic oscillations in applications modeled by systems of ordinary differential equations. We focus on systems with parts that have a significant rotational speed. An important element of our approach is to change coordinates into a co-rotating frame. We show that this leads to a dramatic reduction of computational effort in the case that gravitational forces can be neglected. As a practical example we study a turbocharger model for which we give a thorough comparison of results for a model with and without gravitational forces
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