Search results for "Commutation"
showing 10 items of 21 documents
Automated simultaneous triple dissolution profiles of two drugs, sulphamethoxazole-trimethoprim and hydrochlorothiazide-captopril in solid oral dosag…
2003
This article deals with the simultaneous determination of three dissolution profiles with the aid of the new and emerging continuous-flow methodology known as multicommutation. This methodology is based on a flow network of a set of solenoid valves controlled by the computer and acting as independent multicommutators to allow the easy and automated control of flowing solutions. The obtained three dissolution profiles from one dosage form are the whole formulation profile or "global profile" recommended by pharmacopoeias, and, at same time, are recorded two "individual" profiles from two drugs present in the formulation. This is the second attempt to obtain simultaneously three dissolution p…
Stochastic anticipative calculus on the path space over a compact Riemannian manifold
1998
Abstract In this paper, we shall first give another expression for Cruzeiro-Malliavin structure equation, by means of the Skorohod integral. The torsion tensor with respect to the Markovian connection used in [CF] is computed. This is the key step to establish a Stroock-like formula of commutation on the derivative of the Skorohod integral, which enables us to prove an Ito formula. As an application, we shall give a maximal inequality for Skorohod integrals following [AN2].
An operator-like description of love affairs
2010
We adopt the so--called \emph{occupation number representation}, originally used in quantum mechanics and recently considered in the description of stock markets, in the analysis of the dynamics of love relations. We start with a simple model, involving two actors (Alice and Bob): in the linear case we obtain periodic dynamics, whereas in the nonlinear regime either periodic or quasiperiodic solutions are found. Then we extend the model to a love triangle involving Alice, Bob and a third actress, Carla. Interesting features appear, and in particular we find analytical conditions for the linear model of love triangle to have periodic or quasiperiodic solutions. Numerical solutions are exhibi…
Pseudobosons, Riesz bases, and coherent states
2010
In a recent paper, Trifonov suggested a possible explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. Although being rather intriguing, in his treatment many mathematical aspects of the model have just been neglected, making most of the results of that paper purely formal. For this reason we are re-considering the same model and we repeat and extend the same construction paying particular attention to all the subtle mathematical points. From our analysis the crucial role of Riesz bases clearly emerges. We also consider coherent states associated to the model.
A Tutorial Approach to the Renormalization Group and the Smooth Feshbach Map
2006
2.1 Relative Bounds on the Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 The Feshbach Map and Pull-Through Formula . . . . . . . . . . . . . . . . . 4 2.3 Elimination of High-Energy Degrees of Freedom . . . . . . . . . . . . . . . . 5 2.4 Normal form of Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Banach Space of Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 The Renormalization Map Rρ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Weak commutation relations of unbounded operators: Nonlinear extensions
2013
We continue our analysis of the consequences of the commutation relation $[S,T]=\Id$, where $S$ and $T$ are two closable unbounded operators. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. {We also consider what we call, adopting a physical terminology}, a {\em nonlinear} extension of the above commutation relations.
Construction of pseudo-bosons systems
2010
In a recent paper we have considered an explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. We have introduced the so-called {\em pseudo-bosons}, and the role of Riesz bases in this context has been analyzed in detail. In this paper we consider a general construction of pseudo-bosons based on an explicit {coordinate-representation}, extending what is usually done in ordinary supersymmetric quantum mechanics. We also discuss an example arising from a linear modification of standard creation and annihilation operators, and we analyze its connection with coherent states.
Multi-commutation in spectrometry
2009
We review recent developments in manifold components and the introduction of light-emitting-diode technology in spectroscopic detection in order to evaluate the tremendous possibilities offered by multi-commutation for in-field and in-situ measurements, based on the use of multi-pumping and low-voltage, portable batteries, which make possible a dramatic reduction in size, weight and power requirements of spectrometric devices.
Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons
2010
In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a different class of examples arising from a classical system, i.e. a damped harmonic oscillator.
Pseudo-Bosons, So Far
2011
In the past years several extensions of the canonical commutation relations have been proposed by different people in different contexts and some interesting physics and mathematics have been deduced. Here, we review some recent results on the so-called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. We start discussing some of their mathematical properties and then we discuss several examples.