The problem of the diagonalization of the flavor-neutrino propagator matrix is investigated in the theory with flavor-mixing mass terms in Lagrangian. For this purpose we examine one-pole structures of flavor-neutrino propagators, leading to physical neutrino masses, and discuss the relation of the propagator diagonalizaion to the diagonalizaion of the mass matrix in Lagrangian. In connection w...

We show that the Bruschlinsky group with the winding order is a homeomorphism invariant for a class of one-dimensional inverse limit spaces. In particular we show that if a presentation of an inverse limit space satisfies the Simplicity Condition, then the Bruschlinsky group with the winding order of the inverse limit space is a dimension group and is a quotient of the dimension group with the ...

Entangled quantum states are an important component of quantum computing techniques such as quantum error-correction, dense coding and quantum teleportation. We describe how to generate fully entangled states in the Hilbert space C N C N starting from a unitary matrix and show that they form an orthonormal basis in this space. Disentanglement is also discussed. Moreover we also calculate the Wi...

A Filbert matrix is a matrix whose (i, j) entry is 1/Fi+j−1, where Fn is the n Fibonacci number. The inverse of the n × n Filbert matrix resembles the inverse of the n× n Hilbert matrix, and we prove that it shares the property of having integer entries. We prove that the matrix formed by replacing the Fibonacci numbers with the Fibonacci polynomials has entries which are integer polynomials. W...

In a deformable template representation of observed images fundamental to mod-eling the variability of target pose is the action of the matrix Lie groups (such as SO(n)) on rigid templates. For the problem of target identiication using remote sensors , a Bayesian approach constructs a posterior distribution on the rotation group from which the conditional expectations can be generated. Due to t...

We consider the general problem of learning an unknown functional dependency, f : X !→ Y, between a structured input space X and a structured output space Y, from labeled and unlabeled examples. We formulate this problem in terms of data-dependent regularization in Vector-valued Reproducing Kernel Hilbert Spaces (Micchelli & Pontil, 2005) which elegantly extend familiar scalarvalued kernel meth...

In this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of 4n-dimensional operator Hilbert space (Liouville space). It allows to use a quantum computer model with four-valued logic....

It is often the case that the moments of a distribution can be readily determined, while its exact density function is mathematically intractable. We show that the density function of a continuous distribution defined on a closed interval can be easily approximated from its exact moments by solving a linear system involving a Hilbert matrix. When sample moments are being used, the same linear s...

In this paper we generalize the usual model of quantum computer to a model in which the state is an operator of density matrix and the gates are general superoperators (quantum operations), not necessarily unitary. A mixed state (operator of density matrix) of n twolevel quantum system (open or closed n-qubit system) is considered as an element of 4dimensional operator Hilbert space (Liouville ...

We consider polynomials orthogonal on [0,∞) with respect to Laguerre-type weights w(x) = xe, where α > −1 and where Q denotes a polynomial with positive leading coefficient. The main purpose of this paper is to determine Plancherel-Rotach type asymptotics in the entire complex plane for the orthonormal polynomials with respect to w, as well as asymptotics of the corresponding recurrence coeffic...