Functional linear regression has been widely used to model the relationship between a scalar response and functional predictors. If the original data do not satisfy the linear assumption, an intuitive solution is to perform some transformation such that transformed data will be linearly related. The problem of finding such transformations has been rather neglected in the development of function...

We prove that any gauged WZNW model has a Lax pair representation, and give explicitly the general solution of the classical equations of motion of the SL(2,R)/U(1) theory. We calculate the symplectic structure of this solution by solving a differential equation of the Gelfand-Dikii type with initial state conditions at infinity, and transform the canonical physical fields non-locally onto cano...

Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body Toda equation are also found. The derivation of these representations motivate the form of a two-dimensional generalized hypergeometric equation which contains...

This paper is concerned with the stabilization of nonholonomic systems in port-controlled Hamiltonian formulae via generalized canonical transformations. A special class of timevarying generalized canonical transformations are introduced which preserves the passivity property. Utilizing this transformation timevarying asymptotically stabilizing controllers for the nonholonomic Hamiltonian syste...

We investigate two methods of constructing a solution of the Schrödinger equation from the canonical transformation in classical mechanics. One method shows that we can formulate the solution of the Schrödinger equation from linear canonical transformations, the other focuses on the generating function which satisfies the Hamilton-Jacobi equation in classical mechanics. We also show that these ...

We examine a classical and quantum dynamics of systems described by the DBItype Lagrangian with tachyon-like potentials and corresponding DBI Lagrangians on (non-)Archimedean spaces. The dynamic of tachyon fields in spatially homogeneous and in zero-dimensional limits is analysed. A formalism for connecting a wide class of potentials and DBI Lagrangians with the locally equivalent canonical Lag...

This paper introduces generalized canonical transformations for generalized Hamiltonian systems which convert a generalized Hamiltonian system into another one, and preserve the generalized Hamiltonian structure of the original. As in classical mechanics it is expected that canonical transformations will provide new insights and fundamental tools for both analysis and synthesis of those systems...

We apply the “consistent discretization” technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well defined canonical theory that is free of constraints and where the dynamics is implemented as a canonical transformation. In the Lorentzian case, the framework appears to be naturally free of the “spikes” that plague tra...

The proliferation of database systems based on diierent data models and query languages has created the need for techniques that support interoperability so that information may be shared among the database systems. This dissertation proposal describes a technique to support interoperable query processing when multiple heterogeneous databases are accessed. We will focus on the problem of suppor...

As a prosecution of a preceeding paper, a canonical set of classical observables for the open Nambu string is determined. As a byproduct, a local involutory set of constants of motion is found. This result is obtained by determining a canonical transformation to a new set of variables, of which the constraints of the string are a subset. The Poincare’ algebra is analyzed in terms of the new var...