Search results for "OPF"
showing 10 items of 89 documents
The hidden group structure of quantum groups: strong duality, rigidity and preferred deformations
1994
A notion of well-behaved Hopf algebra is introduced; reflexivity (for strong duality) between Hopf algebras of Drinfeld-type and their duals, algebras of coefficients of compact semi-simple groups, is proved. A hidden classical group structure is clearly indicated for all generic models of quantum groups. Moyal-product-like deformations are naturally found for all FRT-models on coefficients andC∞-functions. Strong rigidity (H bi 2 ={0}) under deformations in the category of bialgebras is proved and consequences are deduced.
THE ZONE MODULUS OF A LINK
2005
In this paper, we construct a conformally invariant functional for two-component links called the zone modulus of the link. Its main property is to give a sufficient condition for a link to be split. The zone modulus is a positive number, and its lower bound is 1. To construct a link with modulus arbitrarily close to 1, it is sufficient to consider two small disjoint spheres each one far from the other and then to construct a link by taking a circle enclosed in each sphere. Such a link is a split link. The situation is different when the link is non-split: we will prove that the modulus of a non-split link is greater than [Formula: see text]. This value of the modulus is realized by a spec…
On the Computational Complexity of Binary and Analog Symmetric Hopfield Nets
2000
We investigate the computational properties of finite binary- and analog-state discrete-time symmetric Hopfield nets. For binary networks, we obtain a simulation of convergent asymmetric networks by symmetric networks with only a linear increase in network size and computation time. Then we analyze the convergence time of Hopfield nets in terms of the length of their bit representations. Here we construct an analog symmetric network whose convergence time exceeds the convergence time of any binary Hopfield net with the same representation length. Further, we prove that the MIN ENERGY problem for analog Hopfield nets is NP-hard and provide a polynomial time approximation algorithm for this p…
Minimal unit vector fields
2002
We compute the first variation of the functional that assigns each unit vector field the volume of its image in the unit tangent bundle. It is shown that critical points are exactly those vector fields that determine a minimal immersion. We also find a necessary and sufficient condition that a vector field, defined in an open manifold, must fulfill to be minimal, and obtain a simpler equivalent condition when the vector field is Killing. The condition is fulfilled, in particular, by the characteristic vector field of a Sasakian manifold and by Hopf vector fields on spheres.
A natural and rigid model of quantum groups
1992
We introduce a natural (Frechet-Hopf) algebra A containing all generic Jimbo algebras U t (sl(2)) (as dense subalgebras). The Hopf structures on A extend (in a continuous way) the Hopf structures of generic U t (sl(2)). The Universal R-matrices converge in A\(\hat \otimes \)A. Using the (topological) dual of A, we recover the formalism of functions of noncommutative arguments. In addition, we show that all these Hopf structures on A are isomorphic (as bialgebras), and rigid in the category of bialgebras.
Minimal Morse flows on compact manifolds
2006
Abstract In this paper we prove, using the Poincare–Hopf inequalities, that a minimal number of non-degenerate singularities can be computed in terms only of abstract homological boundary information. Furthermore, this minimal number can be realized on some manifold with non-empty boundary satisfying the abstract homological boundary information. In fact, we present all possible indices and types (connecting or disconnecting) of singularities realizing this minimal number. The Euler characteristics of all manifolds realizing this minimal number are obtained and the associated Lyapunov graphs of Morse type are described and shown to have the lowest topological complexity.
A Survey of Continuous-Time Computation Theory
1997
Motivated partly by the resurgence of neural computation research, and partly by advances in device technology, there has been a recent increase of interest in analog, continuous-time computation. However, while special-case algorithms and devices are being developed, relatively little work exists on the general theory of continuous- time models of computation. In this paper, we survey the existing models and results in this area, and point to some of the open research questions. Final Draft peerReviewed
Dracocephalum ruyschiana L. (Numerne, 1888)
1888
Nordischer Drachenkopf finden in lichte Kieferwaldhouge Nemerno. /// Ruiša pūķgalve, atradne: gaiša priežu meža nogāne Numernē. /// Northern Dragon-head, deposit: light pine forest slope in Numerne. [Attēls no LU Muzeja kolekcijas Herbarium Balticum (RIG I); (BOT2791_12)]
Dracocephalum ruyschiana L. (Ogres Kangari pie Ikšķiles)
1923
Nordischer Drachenkopf finden in sonnigers Abhang des Grandhügels am Ogre - Kanger bei Üxküll. /// Ruiša pūķgalve, atradne: liela kalna saulaina nogāze Ogres Kangaros pie Ikšķiles. /// Northern Dragon-head, deposit: sunny slope of the grand hill on the Ogre - Kanger near Ikskil. [Attēls no LU Muzeja kolekcijas Herbarium Balticum (RIG I); (BOT 2791_7)]
Dracocephalum ruyschiana L. (Grants-kalns pie Ogres Kangariem, Rīgas apriņķis)
1895
Nordischer Drachenkopf finden in Livland, Kreis Riga, Hügel, genannt "Grant-kalns" am Oger Kanger zwischen Üxkull und Oger. /// Ruiša pūķgalve, atradne: Livlande, Rīgas apriņķis, tā sautā "Grants-kalns" pie Ogres Kangariem starp Ikšķili un Ogri. /// Northern Dragon-head, deposit: Riga district, hill, called "Grant-kalns" on the Ogres Kangar between Ikskil and Ogre. [Attēls no LU Muzeja kolekcijas Herbarium Balticum (RIG I); (BOT2791_11)]