Bundles of Pseudodifferential Operators and Modular Forms

We describe connections between pseudodifferential operators and modular forms in terms of vector bundles over a Riemann surface whose fibers are the spaces of certain pseudodifferential operators.     

Holomorphic triples of genus 0

Here we study the relationship between the stability of coherent systems and the stability of holomorphic triples over a curve of arbitrary genus. Moreover we apply these results to study some properties and give some examples of holomorphic triples on the projective line.      

On the Construction of K-Operators in Field Theories as Sections Along Legendre Maps

The time-evolution K-operator (or relative Hamiltonian vector field) in mechanics is a powerful tool which can be geometrically defined as a vector field along the Legendre map. It has been extensively used by several authors for studying the structure and properties of the dynamical systems (mainly the nonregular ones), such as the relation between the Lagrangian and Hamiltonian formalisms, constraints, and higher-order mechanics. This paper is devoted to defining a generalization of this operator for field theories, in a covariant formulation. In order to do this, we use sections along maps, in particular multivector fields (skew-symmetric contravariant tensor fields of order greater than 1), jet fields and connection forms along the Legendre map. As a relevant result, we use these geometrical objects to obtain the solutions of the Lagrangian and Hamiltonian field equations, and the equivalence among them (specially for nonregular field theories).     

Double structures on rational space curves

There are very many non‐reduced schemes. In this paper, we consider two examples to back this statement: we give lists of double scheme structures on a twisted cubic, and we construct rank two bundles on projective 3‐space with prescribed Chern classes, from double structures on smooth rational curves. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identifying quadric bundle structures on complex projective varieties

In this paper we characterize smooth complex projective varieties that admit a quadric bundle structure on some dense open subset in terms of the geometry of certain families of rational curves.      

Measurements of turbulent flow in axially finned rod bundles

The hydraulic characteristics in subchannels of axially finned rod bundles installed in the Korea Multipurpose Research Reactor (KMRR) were measured using one-component laser-Doppler velocimetry (LDV). Pressure drops for each component, time mean axial velocity, and axial turbulent intensity were measured. Then the friction factors in rod bundles were estimated from the measured pressure drops. The turbulent crossflow mixing rate between neighboring subchannels was evaluated from the measured data. The results show that (1) the friction factors for axially finned rod bundles are less than those given by Moody's correlation for smooth tubes, and (2) as the flow develops, the turbulent crossflow mixing rate between neighboring subchannels decreases and, in the developed region, the values level out.     

U(1)-invariant current forms

Let λ : U(1) → GL (V) be a linear representation. Lagrangians defined on J¹(T*M × V)whose universal current form is gauge invariant, are described in terms of gauge invariant Lagrangians and invariant functions on V. A characterization of gauge invariant Lagrangians depending on matter fields only, that is, L : J¹V → ?, is also obtained.     

An extension of Cartan's method of equivalence to immersions: I. Necessary conditions

In this paper, we show that the existence of immersions preserving given geometric structures between manifolds can be expressed in terms of a relation between suitably constructed moving coframes on the manifolds, and we show that the key steps in Cartan's method of equivalence can be extended to yield necessary conditions for the existence of such immersions.     

Codes associated to the zero-schemes of sections of vector bundles

We consider the algebraic geometric codes associated to the zero-schemes of sections of vector bundles on a smooth projective variety. We give lower bounds for the minimum distances of the codes exploiting the Cayley–Bacharach property of zero-dimensional subschemes.     

On the conjecture of King for smooth toric Deligne-Mumford stacks

We construct full strong exceptional collections of line bundles on smooth toric Fano Deligne-Mumford stacks of Picard number at most two and of any Picard number in dimension two. It is hoped that the approach of this paper will eventually lead to the proof of the existence of such collections on all smooth toric nef-Fano Deligne-Mumford stacks.