196,886 research outputs found
Michael Polyak
No full text. The classical Whitney formula relates the algebraic number of selfintersections of a generic plane curve to its winding number. We generalize it to an infinite family of identities, expressing the winding number in terms of the internal geometry of a plane curve. This enables us to split the Whitney formula by some characteristic of double points. It turns out, that only crossings of a very specific type contribute to the computation of the winding number. We also provide a "difference integration" of these formulae, establishing a new family of simple formulae with the base point pushed off the curve. Similar new identities are obtained for Arnold's invariant Strangeness of plane curves. 1. Whitney formula and its generalizations 1.1. Introduction. The classical Whitney formula [4] relates the algebraic number of times that a generic immersed plane curve intersects itself to the Whitney index, or winding number, of this curve. Since it was discovered in 1937, this formula remained m..
Michael Polyak
No full text: Bennequin invariant l() of a Legendrian curve in the space of cooriented contact elements of the plane counts its self-linking number. We present a new formula for computation of this invariant via a state summation over crossings of the corresponding Legendrian front. Using this state sum we obtain a quantization l q () 2 Z[q;q \Gamma1 ] of l(). Other generalizations of l() are discussed. SUR L'INVARIANT DE BENNEQUIN DES COURBES LEGENDRIENNES ET SA QUANTIFICATION R' esum' e: L'invariant de Bennequin l() d'une courbe de Legendre dans l'espace des 'el'ements de contact coorient'es du plan est un nombre d'auto-enlacement de . Nous pr'esentons une nouvelle formule de calcul de cet invariant utilisant une somme statistique sur les croisements du front legendrien correspondant. Une quantification l q () 2 Z[q;q \Gamma1 ] de l() est d'eduite de cette somme statistique. D'autres g'en'eralisations de l() sont consid'er'ees. Version francaise abr'eg'ee. 1. Consid'erons l'espace M =..
Toward Accurate QM/MM Reaction Barriers with Large QM Regions Using Domain Based Pair Natural Orbital Coupled Cluster Theory
No full textThe hydroxylation reaction catalyzed by p-hydroxybenzoate hydroxylase and the Baeyer-Villiger reaction catalyzed by cyclohexanone monooxygenase are investigated by means of quantum mechanical/molecular mechanical (QM/MM) calculations at different levels of QM theory. The geometries of the stationary points along the reaction profile are obtained from QM/MM geometry optimizations, in which the QM region is treated by density functional theory (DFT). Relative energies are determined from single-point QM/MM calculations using the domain-based local pair natural orbital coupled cluster DLPNO-CCSD(T) method as QM component. The results are compared with single-point DFT/MM energies obtained using popular density functionals and with available experimental and computational data. It is found that the choice of the QM method strongly affects the computed energy profiles for these reactions. Different density functionals provide qualitatively different energy barriers (variations of the order of 10 kcal/mol in both reactions), thus limiting the confidence in DFT/MM computational predictions of energy profiles. On the other hand, the use of the DLPNO-CCSD(T) method in conjunction with large QM regions and basis sets makes it possible to achieve high accuracy. A critical discussion of all the technical aspects of the calculations is given with the aim of aiding computational chemists in the application of the DLPNO-CCSD(T) methodology in QM/MM calculations
Polyak type equations for virtual arrow diagram formulas in the annulus
No full text21 pages, 15 figuresInternational audienceWe describe the space of arrow diagram formulas for virtual knot diagrams in the annulus as the kernel of a linear map, inspired from a conjecture due to M. Polyak. As a main application, we slightly improve Grishanov-Vassiliev's theorem for planar chain invariants
Purification, crystallization and preliminary crystallographic analysis of biotin protein ligase from Staphylococcus aureus
No full textBiotin protein ligase from Staphylococcus aureus catalyses the biotinylation of acetyl-CoA carboxylase and pyruvate carboxylase. Recombinant biotin protein ligase from S. aureus has been cloned, expressed and purified. Crystals were grown using the hanging-drop vapour-diffusion method using PEG 8000 as the precipitant at 295 K. X-ray diffraction data were collected to 2.3 A resolution from crystals using synchrotron X-ray radiation at 100 K. The diffraction was consistent with the tetragonal space group P4₂2₁2, with unit-cell parameters a = b = 93.665, c = 131.95.N. R. Pendini, S. W. Polyak, G. W. Booker, J. C. Wallace and M. C. J. Wilc
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
"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
Sulphuric acid speleogenesis and landscape evolution: Montecchio cave, Albegna river valley (Southern Tuscany, Italy)
No full textMontecchio cave (Grosseto province, Tuscany, Italy) opens at 320 m asl, in a small outcrop of Jurassic limestone
(Calcare Massiccio Fm.), close to the Albegna river. This area is characterised by the presence of several thermal
springs and the outcropping of travertine deposits at different altitudes. The Montecchio cave, with passage
length development of over 1700 m, is characterised by the presence of several sub-horizontal passages and
many medium- and small-scale morphologies indicative of sulphuric acid speleogenesis (SAS). The thermal
aquifer is intercepted at a depth of about 100 m below the entrance: the water temperature exceeds 30 °C and
sulphate content is over 1300mg l−1. The cave hosts large gypsumdeposits from40 to 100mbelowthe entrance
that are by-products of the reaction between sulphuric acid and the carbonate host rock. The lower part of the
cave hosts over 1 m thick calcite cave raft deposits, which are evidence of long-standing, probably thermal,
water in an evaporative environment related to significant air currents.
Sulphur isotopes of gypsumhave negative δ34S values (from−28.3 to−24.2‰), typical of SAS. Calcite cave rafts
and speleogenetic gypsumboth yield young U/Th ages varying from68.5 ka to 2 ka BP, indicating a rapid phase of
dewatering followed by gypsumprecipitation in aerate environment. This fastwater table lowering is related to a
rapid incision of the nearby Albegna river, andwas followed by a 20–30mfluctuation of the thermalwater table,
as recorded in the calcite raft deposits and gypsum crusts
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
Invariants of plane curves and Polyak-Viro type formulas for Vassiliev invariants
No full textThe Kontsevich integral is decomposed into two parts; one part depends on overpass or underpass of the crossing of a knot while the other depends only on the plane curve obtained by projecting the knot to the plane. In this paper, firstly, we express the latter part in terms of Arnold\u27s invariants of plane curves , and up to degree three. Secondly, we show that the Gauss diagram formulas for the Kontsevich integral agree with other types of formulas for Vassiliev invariants which are introduced by M. Polyak and O. Viro
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