Duality of osculating developables of projective curves

We give a description of the dual varieties of all developables of osculating linear spaces to a projective curve in terms of the higher order dual varieties of the curve, in arbitrary characteristic. We also determine for these varieties the inseparable degrees of the projections from the conormal varieties onto their dual varieties.

Higher grading conformal affine Toda theory and (generalized) sine-Gordon/massive Thirring duality

Some properties of the higher grading integrable generalizations of the conformal affine Toda systems are studied. The fields associated to the non-zero grade generators are Dirac spinors. The effective action is written in terms of the Wess-Zumino-Novikov-Witten (WZNW) action associated to an affine Lie algebra, and an off-critical theory is obtained as the result of the spontaneous breakdown of the conformal symmetry. Moreover, the off-critical theory presents a remarkable equivalence between the Noether and topological currents of the model. Related to the off-critical model we define a real and local lagrangian provided some reality conditions are imposed on the fields of the model. This real action model is expected to describe the soliton sector of the original model, and turns out to be the master action from which we uncover the weak-strong phases described by (generalized) massive Thirring and sine-Gordon type models, respectively. The case of any (untwisted) affine Lie algebra furnished with the principal gradation is studied in some detail. The example of s^l(n) (n = 2, 3) is presented explicitly. © SISSA/ISAS 2003.

A note on KKT-invexity in nonsmooth continuous-time optimization

We introduce the notion of KKT-inverity for nonsmooth continuous-time nonlinear optimization problems and prove that this notion is a necessary and sufficient condition for every KKT solution to be a global optimal solution.

Optimal control problems with nonsmooth mixed constraints

In this paper we present a weak maximum principle for optimal control problems involving mixed constraints and pointwise set control constraints. Notably such result holds for problems with possibly nonsmooth mixed constraints. Although the setback of such result resides on a convexity assumption on the extended velocity set, we show that if the number of mixed constraints is one, such convexity assumption may be removed when an interiority assumption holds. © 2008 IEEE.

Some remarks about Poincaré duality pairs

Bieri-Eckmann [6] introduced the concept of relative cohomology for a group pair (G, S), where G is a group and S is a family of subgroups of G and, by using that theory, they introduced the concept of Poincaré duality pairs (G, S) and provided a topological interpretation for such pairs through Eilenberg-MacLane pairs K(G, S, 1). A Poincaré duality pair is a pair (G, S) that satisfies two isomorphisms, one between absolute cohomology and relative homology and the second between relative cohomology and absolute homology. In this paper, we present a proof that those two isomorphisms are equivalent. We also present some calculations on duality pairs by using the cohomological invariant defined in [1] and studied in [2-4]. © 2012 Pushpa PublishingHouse.

New optimality conditions for nonsmooth control problems

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every MP-process is optimal necessarily obey our first optimality condition. The second condition is more natural, but it is only applicable to normal problems and the converse holds just for smooth problems. Nevertheless, it is proved that for the class of normal smooth optimal control problems the two conditions are equivalent. Some examples illustrating the features of these sufficient concepts are presented. © 2012 Springer Science+Business Media New York.

Birth of limit cycles bifurcating from a nonsmooth center

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The closed-string 3-loop amplitude and S-duality

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Particle-vortex and Maxwell duality in the AdS(4) x CP3/ABJM correspondence

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

THREE TIME SCALE SINGULAR PERTURBATION PROBLEMS AND NONSMOOTH DYNAMICAL SYSTEMS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Gaiotto duality for the twisted A(2N-1) series

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

N=1 SUSY backgrounds with an AdS factor from non-Abelian T duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Some aspects of abelian and nonabelian T-duality and the gauge/gravity correspondence

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Synthesis and Characterization of Ruteno-Cuprates by Solid State Reactions

A new class of hybrid ruteno-cuprates - such as Ru-1212 and Ru-1222 - was discovered in 1995 by Bauerfeind and collaborators. These materials present superconducting and magnetic states at low temperatures, an atypical duality in other superconductors. The superconductivity is more easily observed in Ru-1222, while Ru-1212 is a more problematic case, due to the strong effects of the preparation details in its superconducting properties, becoming the material superconductor or not. Ru-1212 presents a critical temperature that can vary between 0 and 46 K, depending on the preparation conditions, and a temperature of magnetic transition of around 132 K. The samples were prepared through solid state reactions, by using a mixture of high purity powders, followed by calcination and sinterization in the nitrogen and oxygen atmospheres. This paper shows the preparation process of Ru-1212 samples, followed by their structural and magnetic characterization.

On 3-Parameter Families of Piecewise Smooth Vector Fields in the Plane

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)