The Modern Methods of Quarantine.

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Non-positivity of Groenewold operators

A central feature in the Hilbert space formulation of classical mechanics is the quantisation of classical Liouville densities, leading to what may be termed term Groenewold operators. We investigate the spectra of the Groenewold operators that correspond to Gaussian and to certain uniform Liouville densities. We show that when the classical coordinate-momentum uncertainty product falls below Heisenberg's limit, the Groenewold operators in the Gaussian case develop negative eigenvalues and eigenvalues larger than 1. However, in the uniform case, negative eigenvalues are shown to persist for arbitrarily large values of the classical uncertainty product.Comment: 9 pages, 1 figures, submitted to Europhysics Letter

Conservation laws for invariant functionals containing compositions

The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains a new term involving inverse images of the minimizing trajectories. In this work we prove a generalization of the necessary optimality condition of DuBois-Reymond for variational problems with compositions. With the help of the new obtained condition, a Noether-type theorem is proved. An application of our main result is given to a problem appearing in the chaotic setting when one consider maps that are ergodic.Comment: Accepted for an oral presentation at the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), to be held in Pretoria, South Africa, 22-24 August, 200

Group Theory and Quasiprobability Integrals of Wigner Functions

The integral of the Wigner function of a quantum mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0,1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric disks and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in Hilbert space carrying the positive discrete series representations of the algebra su(1,1)or so(2,1). The explicit relation between the spectra of operators associated with disks and circles with proportional radii, is given in terms of the dicrete variable Meixner polynomials.Comment: 11 pages, latex fil

Bulletin No. 230 - San Juan County Experimental Farm: Progress Report, 1925-30, Inclusive

San Juan County, located in the southeast corner of the state, has a dry-farm area of approximately 600,000 acres extending from Monticello 26 miles south to Blanding and 6 miles north to Peter\u27s Hill and stretching from the Blue Mountains east 30 miles to the Colorado line. One-fourth to one-third of this area is covered with timber consisting mainly of pinion pine, oak brush, and juniper commonly called cedar. Both the juniper and pinion are of value as fuel and building material, and the juniper has an additional value for fence posts. While small areas have been cleared of timber for farm purposes with favorable results in respect to yield of crops, most of the tillable land was or is now in sagebrush. The sagebrush consists of two types: the common type (Artemesia tridentata) and a dwarf brush, compact, and dark in color. The latter type is found growing usually on the poorer soils, shallow in depth, and of a heavy, clayey type. Bluestem wheat grass, another native plant of this area commonly found growing in association with sagebrush, is of economic value in that it serves as summer pasturage for stock

Discrepancies in Written Versus Calculated Durations in Opioid Prescriptions: Pre-Post Study.

BACKGROUND: The United States is in the midst of an opioid epidemic. Long-term use of opioid medications is associated with an increased risk of dependence. The US Centers for Disease Control and Prevention makes specific recommendations regarding opioid prescribing, including that prescription quantities should not exceed the intended duration of treatment. OBJECTIVE: The purpose of this study was to determine if opioid prescription quantities written at our institution exceed intended duration of treatment and whether enhancements to our electronic health record system improved any discrepancies. METHODS: We examined the opioid prescriptions written at our institution for a 22-month period. We examined the duration of treatment documented in the prescription itself and calculated a duration based on the quantity of tablets and doses per day. We determined whether requiring documentation of the prescription duration affected these outcomes. RESULTS: We reviewed 72,314 opioid prescriptions, of which 16.96% had a calculated duration that was greater than what wasdocumented in the prescription. Making the duration a required field significantly reduced this discrepancy (17.95% vs 16.21%,P CONCLUSIONS: Health information technology vendors should develop tools that, by default, accurately represent prescription durations and/or modify doses and quantities dispensed based on provider-entered durations. This would potentially reduce unintended prolonged opioid use and reduce the potential for long-term dependence

The quantum state vector in phase space and Gabor's windowed Fourier transform

Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed `window state vector'. Here aspects of this construction are explored, with emphasis on the connection with Gabor's `windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of window are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schr\"odinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.Comment: 36 pages, 6 figures. Revised in light of referees' comments, and further references adde

Phase space spinor amplitudes for spin 1/2 systems

The concept of phase space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin-\half is treated in detail, and it is shown that phase space amplitudes on the sphere transform correctly as spinors under under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-\half magnetic dipole in a time-dependent magnetic field.Comment: 19 pages, added new results, fixed typo

Quantum integrability and exact solution of the supersymmetric U model with boundary terms

The quantum integrability is established for the one-dimensional supersymmetric $U$ model with boundary terms by means of the quantum inverse scattering method. The boundary supersymmetric $U$ chain is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. This provides us with a basis for computing the finite size corrections to the low lying energies in the system.Comment: 4 pages, RevTex. Some cosmetic changes. The version to appear in Phys. Rev.

A symmetry reduction technique for higher order Painlev\'e systems

The symmetry reduction of higher order Painlev\'e systems is formulated in terms of Dirac procedure. A set of canonical variables that admit Dirac reduction procedure is proposed for Hamiltonian structures governing the ${A^{(1)}_{2M}}$ and ${A^{(1)}_{2M-1}}$ Painlev\'e systems for $M=2,3,...$.Comment: to appear in Phys. Lett.