2,940 research outputs found

    On a certain class of semigroups of operators

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    We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced by Kossakowski in the early 1970s. Each randomly generated semigroup is associated, in a natural way, with a pair formed by a representation or an antirepresentation of a locally compact group in a Banach space and by a convolution semigroup of probability measures on this group. Examples of randomly generated semigroups having important applications in physics are briefly illustrated.Comment: 11 page

    A homomorphism theorem and a Trotter product formula for quantum stochastic flows with unbounded coefficients

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    We give a new method for proving the homomorphic property of a quantum stochastic ow satisfying a quantum stochastic differential equation with unbounded coefficients, under some further hypotheses. As an application, we prove a Trotter product formula for quantum stochastic ows and obtain quantum stochastic dilations of a class of quantum dynamical semigroups generalizing results of [5

    A rigorous real time Feynman Path Integral and Propagator

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    We will derive a rigorous real time propagator for the Non-relativistic Quantum Mechanic L2L^2 transition probability amplitude and for the Non-relativistic wave function. The propagator will be explicitly given in terms of the time evolution operator. The derivation will be for all self-adjoint nonvector potential Hamiltonians. For systems with potential that carries at most a finite number of singularity and discontinuities, we will show that our propagator can be written in the form of a rigorous real time, time sliced Feynman path integral via improper Riemann integrals. We will also derive the Feynman path integral in Nonstandard Analysis Formulation. Finally, we will compute the propagator for the harmonic oscillator using the Nonstandard Analysis Feynman path integral formuluation; we will compute the propagator without using any knowledge of classical properties of the harmonic oscillator

    Modeling Adaptive Regulatory T-Cell Dynamics during Early HIV Infection

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    Regulatory T-cells (Tregs) are a subset of CD4+ T-cells that have been found to suppress the immune response. During HIV viral infection, Treg activity has been observed to have both beneficial and deleterious effects on patient recovery; however, the extent to which this is regulated is poorly understood. We hypothesize that this dichotomy in behavior is attributed to Treg dynamics changing over the course of infection through the proliferation of an ‘adaptive’ Treg population which targets HIV-specific immune responses. To investigate the role Tregs play in HIV infection, a delay differatial equation model was constructed to examine (1) the possible existence of two distinct Treg populations, normal (nTregs) and adaptive (aTregs), and (2) their respective effects in limiting viral load. Sensitivity analysis was performed to test parameter regimes that show the proportionality of viral load with adaptive regulatory populations and also gave insight into the importance of downregulation of CD4+ cells by normal Tregs on viral loads. Through the inclusion of Treg populations in the model, a diverse array of viral dynamics was found. Specifically, oscillatory and steady state behaviors were both witnessed and it was seen that the model provided a more accurate depiction of the effector cell population as compared with previous models. Through further studies of adaptive and normal Tregs, improved treatments for HIV can be constructed for patients and the viral mechanisms of infection can be further elucidated

    First order phase transition of the vortex lattice in twinned YBa2Cu3O7 single crystals in tilted magnetic fields

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    We present an exhaustive analysis of transport measurements performed in twinned YBa2Cu3O7 single crystals which stablishes that the vortex solid-liquid transition is first order when the magnetic field H is applied at an angle theta away from the direction of the twin planes. We show that the resistive transitions are hysteretic and the V-I curves are non-linear, displaying a characteristic s-shape at the melting line Hm(T), which scales as epsilon(theta)Hm(T,theta). These features are gradually lost when the critical point H*(theta) is approached. Above H*(theta) the V-I characteristics show a linear response in the experimentally accessible V-I window, and the transition becomes reversible. Finally we show that the first order phase transition takes place between a highly correlated vortex liquid in the field direction and a solid state of unknown symmetry. As a consequence, the available data support the scenario for a vortex-line melting rather than a vortex sublimation as recently suggested [T.Sasagawa et al. PRL 80, 4297 (1998)].Comment: 10 pages, 8 figures, submitted to PR

    An optimization model for metabolic pathways

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    This article is available open access through the publisher’s website through the link below. Copyright @ The Author 2009.Motivation: Different mathematical methods have emerged in the post-genomic era to determine metabolic pathways. These methods can be divided into stoichiometric methods and path finding methods. In this paper we detail a novel optimization model, based upon integer linear programming, to determine metabolic pathways. Our model links reaction stoichiometry with path finding in a single approach. We test the ability of our model to determine 40 annotated Escherichia coli metabolic pathways. We show that our model is able to determine 36 of these 40 pathways in a computationally effective manner. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online (http://bioinformatics.oxfordjournals.org/cgi/content/full/btp441/DC1)

    On the Global Existence of Bohmian Mechanics

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    We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the connection between the conditions necessary for global existence and the self-adjointness of the Schr\"odinger Hamiltonian.Comment: 35 pages, LaTe

    Rigorous Real-Time Feynman Path Integral for Vector Potentials

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    we will show the existence and uniqueness of a real-time, time-sliced Feynman path integral for quantum systems with vector potential. Our formulation of the path integral will be derived on the L2L^2 transition probability amplitude via improper Riemann integrals. Our formulation will hold for vector potential Hamiltonian for which its potential and vector potential each carries at most a finite number of singularities and discontinuities
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