Coherent states on Hilbert modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.

Contractive Hilbert modules and their dilations

In this note, we show that a quasi-free Hilbert module R defined over the polydisk algebra with kernel function k(z,w) admits a unique minimal dilation (actually an isometric co-extension) to the Hardy module over the polydisk if and only if S (-1)(z, w)k(z, w) is a positive kernel function, where S(z,w) is the Szego kernel for the polydisk. Moreover, we establish the equivalence of such a factorization of the kernel function and a positivity condition, defined using the hereditary functional calculus, which was introduced earlier by Athavale [8] and Ambrozie, Englis and Muller [2]. An explicit realization of the dilation space is given along with the isometric embedding of the module R in it. The proof works for a wider class of Hilbert modules in which the Hardy module is replaced by more general quasi-free Hilbert modules such as the classical spaces on the polydisk or the unit ball in a'', (m) . Some consequences of this more general result are then explored in the case of several natural function algebras.

Unitary invariants for Hilbert modules of finite rank

We associate a sheaf model to a class of Hilbert modules satisfying a natural finiteness condition. It is obtained as the dual to a linear system of Hermitian vector spaces (in the sense of Grothendieck). A refined notion of curvature is derived from this construction leading to a new unitary invariant for the Hilbert module. A division problem with bounds, originating in Douady's privilege, is related to this framework. A series of concrete computations illustrate the abstract concepts of the paper.

Hilbert W*-modules and coherent states

Hilbert C*-module valued coherent states was introduced earlier by Ali, Bhattacharyya and Shyam Roy. We consider the case when the underlying C*-algebra is a W*-algebra. The construction is similar with a substantial gain. The associated reproducing kernel is now algebra valued, rather than taking values in the space of bounded linear operators between two C*-algebras.

Performance of telecommunication modules to 0.5µS-100kHz ring wave surges

This paper presents an experimental investigations performed on various electronic components used in telecommunication networks and those used in avionics for the ring wave surge voltages. IEEE Std C 62.41.1-2002 specifies a stringent requirement of waveforms to be applied for the evaluation of telecom components. To meet the necessary requirements in the absence of commercial equipment for generating the required waveforms, special efforts were made to fabricate a ring wave surge generator as per prescribed standards. The developed surge generator is capable of delivering an output of 0.5 mu s-100kHz which meets the requirements of telecom standards prescribed for evaluation of various modules used in low voltage ac power circuits used in communication networks. The results of the experimental investigations obtained on various modules used in communication networks are presented.

Resolution of Singularities for a Class of Hilbert Modules

Let M be the completion of the polynomial ring C(z) under bar] with respect to some inner product, and for any ideal I subset of C (z) under bar], let I] be the closure of I in M. For a homogeneous ideal I, the joint kernel of the submodule I] subset of M is shown, after imposing some mild conditions on M, to be the linear span of the set of vectors {p(i)(partial derivative/partial derivative(w) over bar (1),...,partial derivative/partial derivative(w) over bar (m)) K-I] (., w)vertical bar(w=0), 1 <= i <= t}, where K-I] is the reproducing kernel for the submodule 2] and p(1),..., p(t) is some minimal ``canonical set of generators'' for the ideal I. The proof includes an algorithm for constructing this canonical set of generators, which is determined uniquely modulo linear relations, for homogeneous ideals. A short proof of the ``Rigidity Theorem'' using the sheaf model for Hilbert modules over polynomial rings is given. We describe, via the monoidal transformation, the construction of a Hermitian holomorphic line bundle for a large class of Hilbert modules of the form I]. We show that the curvature, or even its restriction to the exceptional set, of this line bundle is an invariant for the unitary equivalence class of I]. Several examples are given to illustrate the explicit computation of these invariants.

Moduli of equivariant sheaves and Kronecker-McKay modules

We extend Alvarez-Consul and King description of moduli of sheaves over projective schemes to moduli of equivariant sheaves over projective Gamma-schemes, for a finite group Gamma. We introduce the notion of Kronecker-McKay modules and construct the moduli of equivariant sheaves using a natural functor from the category of equivariant sheaves to the category of Kronecker-McKay modules. Following Alvarez-Consul and King, we also study theta functions and homogeneous co-ordinates of moduli of equivariant sheaves.

Quaternary cocrystals: combinatorial synthetic strategies based on long-range synthon Aufbau modules (LSAM)

A synthetic strategy is outlined whereby a binary cocrystal may be developed in turn into a ternary and finally into a quaternary cocrystal. The strategy hinges on the concept of the long-range synthon Aufbau module (LSAM) which is a large supramolecular synthon containing more than one type of intermolecular interaction. Modulation of these interactions may be possible with the use of additional molecular components so that higher level cocrystals are produced. We report six quaternary cocrystals here. All are obtained as nearly exclusive crystallization products when four appropriate solid compounds are taken together in solution for crystallization.

Semi-automatic generation of learning domain modules for technology supported learning systems

In a time when Technology Supported Learning Systems are being widely used, there is a lack of tools that allows their development in an automatic or semi-automatic way. Technology Supported Learning Systems require an appropriate Domain Module, ie. the pedagogical representation of the domain to be mastered, in order to be effective. However, content authoring is a time and effort consuming task, therefore, efforts in automatising the Domain Module acquisition are necessary.Traditionally, textbooks have been used as the main mechanism to maintain and transmit the knowledge of a certain subject or domain. Textbooks have been authored by domain experts who have organised the contents in a means that facilitate understanding and learning, considering pedagogical issues.Given that textbooks are appropriate sources of information, they can be used to facilitate the development of the Domain Module allowing the identification of the topics to be mastered and the pedagogical relationships among them, as well as the extraction of Learning Objects, ie. meaningful fragments of the textbook with educational purpose.Consequently, in this work DOM-Sortze, a framework for the semi-automatic construction of Domain Modules from electronic textbooks, has been developed. DOM-Sortze uses NLP techniques, heuristic reasoning and ontologies to fulfill its work. DOM-Sortze has been designed and developed with the aim of automatising the development of the Domain Module, regardless of the subject, promoting the knowledge reuse and facilitating the collaboration of the users during the process.

Development of catalytic methane reforming systems integrating hydrogen selective PdCu membrane modules

En la presente tesis doctoral se ha estudiado la integración del proceso de producción de hidrógeno con su purificación mediante el empleo de membranas selectivas de hidrógeno. La producción de hidrógeno se realiza empleando catalizadores no convencionales de níquel soportado sobre magnesia y alúmina en un reactor catalítico. Se analiza la actividad de los catalizadores y la producción de hidrógeno mediante distintos procesos con metano como son la oxidación parcial catalítica (OPC), OPC húmeda y reformadoLa purificación de hidrógeno se realiza en un módulo provisto de una membrana selectiva de hidrógeno de PdCu depositado en un soporte poroso cerámico. Una vez optimizada su preparación mediante deposición no electrolítica se caracterizan. Para ello se determina su permeabilidad a distintas temperaturas y realizando ciclos térmicos en atmósferas inerte y de hidrógeno, que puede fragilizar el metal. Una vez preparados los catalizadores y las membranas se integran los dos sistemas y se determinan los parámetros de operación óptimos como la presión de la línea de alimentación y el caudal de gas de arrastre en el módulo de membrana. Ambos parámetros se optimizan para lograr la máxima recuperación de hidrógeno en el módulo de membrana. Por últimos se realizan ensayos completos de producción y purificación, que permiten observar el rendimiento del sistema y también el efecto que los compuestos de la mezcla compleja alimentada a las membranas tienen en su comportamiento. Para concluir la integración de procesos se realizan ensayos añadiendo azufre de forma que el sistema sea más similar al proceso real. Esto permite también analizar el efecto del azufre tanto en los catalizadores como en las membranas.