Search results for "Geometric"
showing 10 items of 652 documents
Orbiting Orbitals: Visualization of Vi-Bronic Motion at a Conical Intersection
2013
The Jahn-Teller (JT) active unpaired electron of single metalloporphyrin radical anions is imaged through scanning tunneling microscopy. It is demonstrated that the electron is delocalized over the porphyrin macrocycle and its topographic image is determined by vibronic motion: the orbital of the electron adiabatically follows the zero-point pseudorotation of skeletal deformations. Transformation of the polar graphs of the observed images allows visualization of the adiabatic vibrational density to which the electron is coupled. The vibronic potential at the conical intersection is visualized and the half-integer angular momentum characteristic of the Berry phase is revealed in the radial f…
Evaluation of several global resolution functions for liquid chromatography
1999
Abstract An interpretative approach, that makes use of the overlapped fraction of each chromatographic peak as elementary resolution criterion, was applied to the separation of mixtures of compounds. The elementary resolution measurements for all peaks in the chromatogram were reduced to a single numerical value using several functions: normalised by the mean resolution product, unnormalised product, geometrical mean of the unnormalised product, and worst elementary resolution value. The descriptive capability of these reduction functions was evaluated through the observation of global resolution diagrams and the change in the shape of the chromatograms in the selected factor space. michrom…
On deformation of Poisson manifolds of hydrodynamic type
2001
We study a class of deformations of infinite-dimensional Poisson manifolds of hydrodynamic type which are of interest in the theory of Frobenius manifolds. We prove two results. First, we show that the second cohomology group of these manifolds, in the Poisson-Lichnerowicz cohomology, is ``essentially'' trivial. Then, we prove a conjecture of B. Dubrovin about the triviality of homogeneous formal deformations of the above manifolds.
Roots in the mapping class groups
2006
The purpose of this paper is the study of the roots in the mapping class groups. Let $\Sigma$ be a compact oriented surface, possibly with boundary, let $\PP$ be a finite set of punctures in the interior of $\Sigma$, and let $\MM (\Sigma, \PP)$ denote the mapping class group of $(\Sigma, \PP)$. We prove that, if $\Sigma$ is of genus 0, then each $f \in \MM (\Sigma)$ has at most one $m$-root for all $m \ge 1$. We prove that, if $\Sigma$ is of genus 1 and has non-empty boundary, then each $f \in \MM (\Sigma)$ has at most one $m$-root up to conjugation for all $m \ge 1$. We prove that, however, if $\Sigma$ is of genus $\ge 2$, then there exist $f,g \in \MM (\Sigma, \PP)$ such that $f^2=g^2$, $…
Knot Theory, Jones Polynomial and Quantum Computing
2005
Knot theory emerged in the nineteenth century for needs of physics and chemistry as these needs were understood those days. After that the interest of physicists and chemists was lost for about a century. Nowadays knot theory has made a comeback. Knot theory and other areas of topology are no more considered as abstract areas of classical mathematics remote from anything of practical interest. They have made deep impact on quantum field theory, quantum computation and complexity of computation.
Automorfismi di Codici Algebrico-Geometrici Generalizzati
2008
In questo lavoro si studiano gli automorfismi di codici algebrico geometrici generalizzati costruiti a partire da campi di funzione razionali, ellittici o iperellittici.
A cognitive architecture for artificial vision
1997
Abstract A new cognitive architecture for artificial vision is proposed. The architecture, aimed at an autonomous intelligent system, is cognitive in the sense that several cognitive hypotheses have been postulated as guidelines for its design. The first one is the existence of a conceptual representation level between the subsymbolic level, that processes sensory data, and the linguistic level, that describes scenes by means of a high level language. The conceptual level plays the role of the interpretation domain for the symbols at the linguistic levels. A second cognitive hypothesis concerns the active role of a focus of attention mechanism in the link between the conceptual and the ling…
KNOTS WITH UNKNOTTING NUMBER ONE AND GENERALISED CASSON INVARIANT
1996
We extend the classical notion of unknotting operation to include operations on rational tangles. We recall the “classical” conditions (on the signature, linking form etc.) for a knot to have integral (respectively rational) unknotting number one. We show that the generalised Casson invariant of the twofold branched cover of the knot gives a further necessary condition. We apply these results to some Montesinos knots and to knots with less than nine crossings.
On orderability of fibred knot groups
2003
It is known that knot groups are right-orderable, and that many of them are not bi-orderable. Here we show that certain bred knots in S 3 (or in a homology sphere) do have bi-orderable fundamental group. In particular, this holds for bred knots, such as 41, for which the Alexander polynomial has all roots real and positive. This is an application of the construction of orderings of groups, which are moreover invariant with respect to a certain automorphism.
A knot without tritangent planes
1991
We show, with computations aided by a computer, that the (3,2)-curve on some standard torus (which topologically is the trefoil knot) has no tritangent planes, thus answering in the negative a conjecture of M. H. Freedman.