WorldWideScience

Sample records for liouville billiard tables

  1. Billiards

    Kozlov, V V; Ivanov, Simeon; Schulenberger, J R

    1991-01-01

    Starting with the work of G. D. Birkhoff, billiards have been a popular research topic drawing on such areas as ergodic theory, Morse theory, and KAM theory. Billiard systems are also remarkable in that they arise naturally in a number of important problems of mechanics and physics. This book is devoted to mathematical aspects of the theory of dynamical systems of billiard type. Focusing on the genetic approach, the authors strive to clarify the genesis of the basic ideas and concepts of the theory of dynamical systems with impact interactions and also to demonstrate that these methods are natural and effective. Recent limit theorems, which justify various mathematical models of impact theory, are key features. Questions of existence and stability of periodic trajectories of elastic billiards occupy a special place in the book, and considerable attention is devoted to integrable billiards. A brief survey is given of work on billiards with ergodic behavior. Each chapter ends with a list of problems.

  2. Billiards in L-shaped tables with barriers

    Bainbridge, Matthew

    2010-01-01

    We compute the volumes of the eigenform loci in the moduli space of genus-two Abelian differentials. From this, we obtain asymptotic formulas for counting closed billiards paths in certain L-shaped polygons with barriers.......We compute the volumes of the eigenform loci in the moduli space of genus-two Abelian differentials. From this, we obtain asymptotic formulas for counting closed billiards paths in certain L-shaped polygons with barriers....

  3. Nontrivial paths and periodic orbits of the T-fractal billiard table

    Lapidus, Michel L.; Miller, Robyn L.; Niemeyer, Robert G.

    2016-07-01

    We introduce and prove numerous new results about the orbits of the T-fractal billiard. Specifically, in section 3, we give a variety of sufficient conditions for the existence of a sequence of compatible periodic orbits. In section 4, we examine the limiting behavior of particular sequences of compatible periodic orbits. Additionally, sufficient conditions for the existence of particular nontrivial paths are given in section 4. The proofs of two results of Lapidus and Niemeyer (2013 The current state of fractal billiards Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics (Contemporary Mathematics vol 601) ed D Carfi et al (Providence, RI: American Mathematical Society) pp 251-88 (e-print: arXiv:math.DS.1210.0282v2, 2013) appear here for the first time, as well. In section 5, an orbit with an irrational initial direction reaches an elusive point in a way that yields a nontrivial path of finite length, yet, by our convention, constitutes a singular orbit of the fractal billiard table. The existence of such an orbit seems to indicate that the classification of orbits may not be so straightforward. A discussion of our results and directions for future research is then given in section 6.

  4. Shaping old age: Innovation partnerships, senior centres and billiards tables as active ageing technologies

    Lassen, Aske Juul

    2017-01-01

    During the past decade active ageing has been positioned as a solution to the problem of global ageing. While the scientific, economic and even moral arguments for pursuing a more active old age has been many, the integration of active ageing in everyday practices face challenges. This chapter...... explores the ways that active ageing policies become part of everyday practices, by proposing the concept of active ageing technologies. Active ageing technologies are material and immaterial condensations of knowledge that form old age in specific ways. Through the cases of an innovation partnership, two...... activity centres and a billiards table, the author explores how active ageing policies are transformed in practice. The chapter draws on an ethnographic study of active ageing conducted at the two activity centres, as well as the author’s participation in the innovation partnership. The author uses...

  5. Integrable topological billiards and equivalent dynamical systems

    Vedyushkina, V. V.; Fomenko, A. T.

    2017-08-01

    We consider several topological integrable billiards and prove that they are Liouville equivalent to many systems of rigid body dynamics. The proof uses the Fomenko-Zieschang theory of invariants of integrable systems. We study billiards bounded by arcs of confocal quadrics and their generalizations, generalized billiards, where the motion occurs on a locally planar surface obtained by gluing several planar domains isometrically along their boundaries, which are arcs of confocal quadrics. We describe two new classes of integrable billiards bounded by arcs of confocal quadrics, namely, non-compact billiards and generalized billiards obtained by gluing planar billiards along non-convex parts of their boundaries. We completely classify non-compact billiards bounded by arcs of confocal quadrics and study their topology using the Fomenko invariants that describe the bifurcations of singular leaves of the additional integral. We study the topology of isoenergy surfaces for some non-convex generalized billiards. It turns out that they possess exotic Liouville foliations: the integral trajectories of the billiard that lie on some singular leaves admit no continuous extension. Such billiards appear to be leafwise equivalent to billiards bounded by arcs of confocal quadrics in the Minkowski metric.

  6. Ergodicity of the generalized lemon billiards

    Chen, Jingyu [Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801-2302 (United States); Mohr, Luke; Zhang, Hong-Kun, E-mail: hongkun@math.umass.edu; Zhang, Pengfei [Department of Mathematics and Statistics, UMass Amherst, Amherst, Massachusetts 01003 (United States)

    2013-12-15

    In this paper, we study a two-parameter family of convex billiard tables, by taking the intersection of two round disks (with different radii) in the plane. These tables give a generalization of the one-parameter family of lemon-shaped billiards. Initially, there is only one ergodic table among all lemon tables. In our generalized family, we observe numerically the prevalence of ergodicity among the some perturbations of that table. Moreover, numerical estimates of the mixing rate of the billiard dynamics on some ergodic tables are also provided.

  7. Infinite genus surfaces and irrational polygonal billiards

    Valdez, Ferrán

    2009-01-01

    We prove that the natural invariant surface associated with the billiard game on an irrational polygonal table is homeomorphic to the Loch Ness monster, that is, the only orientable infinite genus topological real surface with exactly one end.

  8. Geometry and billiards

    Tabachnikov, Serge

    2005-01-01

    Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...

  9. Discrete symmetries in the Weyl expansion for quantum billiards

    Pavloff, N.

    1994-01-01

    2 and 3 dimensional quantum billiards with discrete symmetries are considered. The boundary condition is either Dirichlet or Neumann. The first terms of the Weyl expansion are derived for the level density projected onto the irreducible representations of the symmetry group. The formulae require only the knowledge of the character table of the group and the geometrical properties (such as surface, perimeter etc.) of sub-parts of the billiard invariant under a group transformation. (author). 17 refs., 1 fig., 1 tab

  10. Integrable billiards and quadrics

    Dragovic, Vladimir I; Radnovic, Milena [Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrad (Serbia)

    2010-07-27

    Billiards inside quadrics are considered as integrable dynamical systems with a rich geometric structure. The two-way interaction between the dynamics of billiards and the geometry of pencils of quadrics in an arbitrary dimension is considered. Several well-known classical and modern genus-1 results are generalized to arbitrary dimension and genus, such as: the Poncelet theorem, the Darboux theorem, the Weyr theorem, and the Griffiths-Harris space theorem. A synthetic approach to higher-genera addition theorems is presented. Bibliography: 77 titles.

  11. Triaxial Ellipsoidal Quantum Billiards

    Waalkens, Holger; Wiersig, Jan; Dullin, Holger R.

    1999-01-01

    The classical mechanics, exact quantum mechanics and semiclassical quantum mechanics of the billiard in the triaxial ellipsoid are investigated. The system is separable in ellipsoidal coordinates. A smooth description of the motion is given in terms of a geodesic flow on a solid torus, which is a

  12. Super-Liouville — double Liouville correspondence

    Hadasz, Leszek; Jaskólski, Zbigniew

    2014-05-01

    The AGT motivated relation between the tensor product of the = 1 super-Liouville field theory with the imaginary free fermion (SL) and a certain projected tensor product of the real and the imaginary Liouville field theories (LL) is analyzed. Using conformal field theory techniques we give a complete proof of the equivalence in the NS sector. It is shown that the SL-LL correspondence is based on the equivalence of chiral objects including suitably chosen chiral structure constants of all the three Liouville theories involved.

  13. Super-Liouville — double Liouville correspondence

    Hadasz, Leszek; Jaskólski, Zbigniew

    2014-01-01

    The AGT motivated relation between the tensor product of the N=1 super-Liouville field theory with the imaginary free fermion (SL) and a certain projected tensor product of the real and the imaginary Liouville field theories (LL) is analyzed. Using conformal field theory techniques we give a complete proof of the equivalence in the NS sector. It is shown that the SL-LL correspondence is based on the equivalence of chiral objects including suitably chosen chiral structure constants of all the three Liouville theories involved.

  14. Super-Liouville — double Liouville correspondence

    Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagiellonian University,W. Reymonta 4, 30-059 Kraków (Poland); Jaskólski, Zbigniew [Institute of Theoretical Physics, University of Wrocław,pl. M. Borna 1, 95-204 Wrocław (Poland)

    2014-05-27

    The AGT motivated relation between the tensor product of the N=1 super-Liouville field theory with the imaginary free fermion (SL) and a certain projected tensor product of the real and the imaginary Liouville field theories (LL) is analyzed. Using conformal field theory techniques we give a complete proof of the equivalence in the NS sector. It is shown that the SL-LL correspondence is based on the equivalence of chiral objects including suitably chosen chiral structure constants of all the three Liouville theories involved.

  15. Geometric Liouville gravity

    La, H.

    1992-01-01

    A new geometric formulation of Liouville gravity based on the area preserving diffeo-morphism is given and a possible alternative to reinterpret Liouville gravity is suggested, namely, a scalar field coupled to two-dimensional gravity with a curvature constraint

  16. Coding chaotic billiards. Pt. 2

    Giannoni, M.J.; Ullmo, D.

    1993-01-01

    A method was proposed earlier to derive exact symbolic dynamics for polygonal billiards defined on a negative curvature surface, whose all vertices lie at infinity. This method is now extended to the case of compact billiards tiling the Poincare disk, using elementary tools such as the bounce mapping. An exact coding is derived also in this case. Furthermore, some results are obtained without using the tiling property. They allow to tackle the more complicated case of non-tiling billiards. (authors). 18 refs., 13 figs

  17. Liouvilles's imaginary shadow

    Schomerus, Volker; Suchanek, Paulina; Univ. of Wroclaw

    2012-10-01

    N=1 super Liouville field theory is one of the simplest non-rational conformal field theories. It possesses various important extensions and interesting applications, e.g. to the AGT relation with 4D gauge theory or the construction of the OSP(1 vertical stroke 2) WZW model. In both setups, the N=1 Liouville field is accompanied by an additional free fermion. Recently, Belavin et al. suggested a bosonization of the product theory in terms of two bosonic Liouville fields. While one of these Liouville fields is standard, the second turns out to be imaginary (or time-like). We extend the proposal to the R sector and perform extensive checks based on detailed comparison of 3-point functions involving several super-conformal primaries and descendants. On the basis of such strong evidence we sketch a number of interesting potential applications of this intriguing bozonization.

  18. Indication for quantum Darwinism in electron billiards

    Brunner, R.; Akis, R.; Meisels, R.; Kuchar, F.; Ferry, D. K.

    2010-02-01

    In this paper, we investigate the dynamics in electron billiards by using classical and quantum mechanical calculations. We report on the existence of pointer states in single-dot and double-dot electron billiards. Additionally, we show that the two types of pointer states have the propensity to create offspring, i.e. they can be observed in the individual modes propagating between the external reservoirs. This can be understood as an indication that quantum Darwinism is present in the electron billiards.

  19. Linear and nonlinear stability of periodic orbits in annular billiards

    Dettmann, Carl P.; Fain, Vitaly

    2017-04-01

    An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

  20. Quantum Monodromy in Prolate Ellipsoidal Billiards

    Waalkens, Holger; Dullin, Holger R.

    2002-01-01

    This is the third in a series of three papers on quantum billiards with elliptic and ellipsoidal boundaries. In the present paper we show that the integrable billiard inside a prolate ellipsoid has an isolated singular point in its bifurcation diagram and, therefore, exhibits classical and quantum

  1. Connections of the Liouville model and XXZ spin chain

    Faddeev, Ludvig D.; Tirkkonen, Olav

    1995-02-01

    The quantum theory of the Liouville model with imaginary field is considered using the Quantum Inverse Scattering Method. An integrable structure with non-trivial spectral-parameter dependence is developed for lattice Liouville theory by scaling the L-matrix of lattice sine-Gordon theory. This L-matrix yields Bethe ansatz equations for Liouville theory, by the methods of the algebraic Bethe ansatz. Using the string picture of excited Bethe states, the lattice Liouville Bethe equations are mapped to the corresponding spin- {1}/{2} XXZ chain equations. The well developed theory of finite-size corrections in spin chains is used to deduce the conformal properties of the lattice Liouville Bethe states. The unitary series of conformal field theories emerge for Liouville couplings of the form γ = πν/( ν + 1), corresponding to root of unity XXZ anisotropies. The Bethe states give the full spectrum of the corresponding unitary conformal field theory, with the primary states in the Kač table parameterized by a string length K, and the remnant of the chain length mod ( ν + 1).

  2. Connections of the Liouville model and XXZ spin chain

    Faddeev, L.D.; Tirkkonen, O.

    1995-01-01

    The quantum theory of the Liouville model with imaginary field is considered using the Quantum Inverse Scattering Method. An integrable structure with non-trivial spectral-parameter dependence is developed for lattice Liouville theory by scaling the L-matrix of lattice sine-Gordon theory. This L-matrix yields Bethe ansatz equations for Liouville theory, by the methods of the algebraic Bethe ansatz. Using the string picture of excited Bethe states, the lattice Liouville Bethe equations are mapped to the corresponding spin-1/2 XXZ chain equations. The well developed theory of finite-size corrections in spin chains is used to deduce the conformal properties of the lattice Liouville Bethe states. The unitary series of conformal field theories emerge for Liouville couplings of the form γ= πν/(ν+1), corresponding to root of unity XXZ anisotropies. The Bethe states give the full spectrum of the corresponding unitary conformal field theory, with the primary states in the Kac table parameterized by a string length K, and the remnant of the chain length mod (ν+1). (orig.)

  3. Brany Liouville inflation

    Ellis, John; Mavromatos, Nikolaos; Nanopoulos, Dimitri; Sakharov, Alexander

    2004-01-01

    We present a specific model for cosmological inflation driven by the Liouville field in a non-critical supersymmetric string framework, in which the departure from criticality is due to open strings stretched between two moving Type-II 5-branes. We use WMAP and other data on fluctuations in the cosmic microwave background to fix the parameters of the model, such as the relative separation and velocity of the 5-branes, respecting also the constraints imposed by data on light propagation from distant gamma-ray bursters. The model also suggests a small, relaxing component in the present vacuum energy that may accommodate the breaking of supersymmetry

  4. Sturm--Liouville eigenvalue problem

    Bailey, P.B.

    1977-01-01

    The viewpoint is taken that Sturn--Liouville problem is specified and the problem of computing one or more of the eigenvalues and possibly the corresponding eigenfunctions is presented for solution. The procedure follows the construction of a computer code, although such a code is not constructed, intended to solve Sturn--Liouville eigenvalue problems whether singular or nonsingular

  5. Mechanisms of chaos in billiards: dispersing, defocusing and nothing else

    Bunimovich, Leonid A.

    2018-02-01

    We explain and justify that the only mechanisms of chaotic dynamics for billiards are dispersing and defocusing. We also introduce boomerang billiards which dynamics demonstrate that two rather broadly accepted views about some features of nonlinear dynamics are actually wrong. Namely correlations in billiards having focusing components of the boundary can decay exponentially, and continuous time correlations for a billiard flow may decay faster than discrete time correlations for a billiard map.

  6. Coding chaotic billiards. Pt. 3

    Ullmo, D.; Giannoni, M.J.

    1993-01-01

    Non-tiling compact billiard defined on the pseudosphere is studied 'a la Morse coding'. As for most bounded systems, the coding is non exact. However, two sets of approximate grammar rules can be obtained, one specifying forbidden codes, and the other allowed ones. In-between some sequences remain in the 'unknown' zone, but their relative amount can be reduced to zero if one lets the length of the approximate grammar rules goes to infinity. The relationship between these approximate grammar rules and the 'pruning front' introduced by Cvitanovic et al. is discussed. (authors). 13 refs., 10 figs., 1 tab

  7. Algebraic non-integrability of magnetic billiards

    Bialy, Misha; Mironov, Andrey E

    2016-01-01

    We consider billiard ball motion in a convex domain of the Euclidean plane bounded by a piece-wise smooth curve under the action of a constant magnetic field. We show that if there exists a first integral polynomial in the velocities of the magnetic billiard flow, then every smooth piece γ of the boundary must be algebraic, and either is a circle or satisfies very strong restrictions. In particular, it follows that any non-circular magnetic Birkhoff billiard is not algebraically integrable for all but finitely many values of the magnitude of the magnetic field. Moreover, a magnetic billiard in ellipse is not algebraically integrable for all values of the magnitude of the magnetic field. We conjecture that the circle is the only integrable magnetic billiard, not only in the algebraic sense, but also for a broader meaning of integrability. We also introduce what we call outer magnetic billiards. As an application of our method, we prove analogous results on algebraically integrable outer magnetic billiards. (paper)

  8. Spectral statistics of 'cellular' billiards

    Gutkin, Boris

    2011-01-01

    For a bounded domain Ω 0 subset of R 2 whose boundary contains a number of flat pieces Γ i , i = 1, ..., l we consider a family of non-symmetric billiards Ω constructed by patching several copies of Ω 0 along Γ i s. It is demonstrated that the length spectrum of the periodic orbits in Ω is degenerate with the multiplicities determined by a matrix group G. We study the energy spectrum of the corresponding quantum billiard problem in Ω and show that it can be split into a number of uncorrelated subspectra corresponding to a set of irreducible representations α of G. Assuming that the classical dynamics in Ω 0 are chaotic, we derive a semiclassical trace formula for each spectral component and show that their energy level statistics are the same as in standard random matrix ensembles. Depending on whether α is real, pseudo-real or complex, the spectrum has either Gaussian orthogonal, Gaussian symplectic or Gaussian unitary types of statistics, respectively

  9. Behaviour of boundary functions for quantum billiards

    Baecker, A; Fuerstberger, S; Schubert, R; Steiner, F

    2002-01-01

    We study the behaviour of the normal derivative of eigenfunctions of the Helmholtz equation inside billiards with Dirichlet boundary condition. These boundary functions are of particular importance because they uniquely determine the eigenfunctions inside the billiard and also other physical quantities of interest. Therefore, they form a reduced representation of the quantum system, analogous to the Poincare section of the classical system. For the normal derivatives we introduce an equivalent to the standard Green function and derive an integral equation on the boundary. Based on this integral equation we compute the first two terms of the mean asymptotic behaviour of the boundary functions for large energies. The first term is universal and independent of the shape of the billiard. The second one is proportional to the curvature of the boundary. The asymptotic behaviour is compared with numerical results for the stadium billiard, different limacon billiards and the circle billiard, and good agreement is found. Furthermore, we derive an asymptotic completeness relation for the boundary functions

  10. Quantum billiards in multidimensional models with branes

    Ivashchuk, V.D.; Melnikov, V.N. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia, Institute of Gravitation and Cosmology, Moscow (Russian Federation)

    2014-03-15

    gravitational D-dimensional model with l scalar fields and several forms is considered. When a cosmological-type diagonal metric is chosen, an electromagnetic composite brane ansatz is adopted and certain restrictions on the branes are imposed; the conformally covariant Wheeler-DeWitt (WDW) equation for the model is studied. Under certain restrictions asymptotic solutions to WDW equation are found in the limit of the formation of the billiard walls which reduce the problem to the so-called quantum billiard on the (D+l-2)-dimensional Lobachevsky space. Two examples of quantum billiards are considered. The first one deals with 9-dimensional quantum billiard for D = 11 model with 330 four-forms which mimic space-like M2- and M5-branes of D = 11 supergravity. The second one deals with the 9-dimensional quantum billiard for D = 10 gravitational model with one scalar field, 210 four-forms and 120 three-forms which mimic space-like D2-, D4-, FS1- and NS5-branes in D = 10 IIA supergravity. It is shown that in both examples wave functions vanish in the limit of the formation of the billiard walls (i.e. we get a quantum resolution of the singularity for 11D model) but magnetic branes could not be neglected in calculations of quantum asymptotic solutions while they are irrelevant for classical oscillating behavior when all 120 electric branes are present. (orig.)

  11. Coding chaotic billiards: I-Non-Compact billiards on a negative curvature manifold

    Giannoni, M.J.; Ullmo, D.

    1989-03-01

    This paper presents a method for coding billiards. The main device is to use a proper surface of section, the bounce mapping, and foliate the reduced phase space into regions associated with a given code. The alphabet is merely the ensemble of the labels of the sides of the billiard. The procedure is applied here to non-compact polygonal billiard defined on a manifold of constant negative curvature, with all vertices at infinity. A simple grammar rule is necessary and sufficient to insure existence and uniqueness of the coding

  12. Rotation in a gravitational billiard

    Peraza-Mues, G. G.; Carvente, Osvaldo; Moukarzel, Cristian F.

    Gravitational billiards composed of a viscoelastic frictional disk bouncing on a vibrating wedge have been studied previously, but only from the point of view of their translational behavior. In this work, the average rotational velocity of the disk is studied under various circumstances. First, an experimental realization is briefly presented, which shows sustained rotation when the wedge is tilted. Next, this phenomenon is scrutinized in close detail using a precise numerical implementation of frictional forces. We show that the bouncing disk acquires a spontaneous rotational velocity whenever the wedge angle is not bisected by the direction of gravity. Our molecular dynamics (MD) results are well reproduced by event-driven (ED) simulations. When the wedge aperture angle θW>π/2, the average tangential velocity Rω¯ of the disk scales with the typical wedge vibration velocity vb, and is in general a nonmonotonic function of the overall tilt angle θT of the wedge. The present work focuses on wedges with θW=2π/3, which are relevant for the problem of spontaneous rotation in vibrated disk packings. This study makes part of the PhD Thesis of G. G. Peraza-Mues.

  13. Topological strings from Liouville gravity

    Ishibashi, N.; Li, M.

    1991-01-01

    We study constrained SU(2) WZW models, which realize a class of two-dimensional conformal field theories. We show that they give rise to topological gravity coupled to the topological minimal models when they are coupled to Liouville gravity. (orig.)

  14. Raising and lowering operators for quantum billiards

    AYUSH KUMAR MANDWAL

    2017-08-16

    Aug 16, 2017 ... Abstract. For planar integrable billiards, the eigenstates can be classified with respect to a quantity determined by the quantum numbers. Given the quantum numbers as m, n, the index which represents a class is c = m mod kn for a natural number, k. We show here that the entire tower of states can be ...

  15. Raising and lowering operators for quantum billiards

    For planar integrable billiards, the eigenstates can be classified with respect to a quantity determined by the quantum numbers. Given the quantum numbers as m , n , the index which represents a class is c = m mod k n for a natural number, k . We show here that the entire tower of states can be generated from an initially ...

  16. Spectral properties of billiards and quantum chaos

    Schmit, C [Institut de Physique Nucleaire, 91 - Orsay (France)

    1984-06-01

    The first 800 eigenvalues of the stadium billiard have been evaluated numerically. It is shown that the four spectra obtained (corresponding to the four types of symmetry of the wave function) exhibit the fluctuation properties of the Gaussian Orthogonal Ensemble of Random Matrices. This reinforces the belief that these fluctuation properties are characteristic of quantum chaotic systems.

  17. Liouville action in cone gauge

    Zamolodchikov, A.B.

    1989-01-01

    The effective action of the conformally invariant field theory in the curved background space is considered in the light cone gauge. The effective potential in the classical background stress is defined as the Legendre transform of the Liouville action. This potential is tightly connected with the sl(2) current algebra. The series of the covariant differential operators is constructed and the anomalies of their determinants are reduced to this effective potential. 7 refs

  18. Liouville gravity on bordered surfaces

    Jaskolski, Z.

    1991-11-01

    The functional quantization of the Liouville gravity on bordered surfaces in the conformal gauge is developed. It was shown that the geometrical interpretation of the Polyakov path integral as a sum over bordered surfaces uniquely determines the boundary conditions for the fields involved. The gravitational scaling dimensions of boundary and bulk operators and the critical exponents are derived. In particular, the boundary Hausdorff dimension is calculated. (author). 21 refs

  19. Semi-classical quantization of chaotic billiards

    Smilansky, U.

    1992-02-01

    The semi-classical quantization of chaotic billiards will be developed using scattering theory approach. This will be used to introduce and explain the inherent difficulties in the semi-classical quantization of chaos, and to show some of the modern tools which were developed recently to overcome these difficulties. To this end, we shall first obtain a semi-classical secular equation which is based on a finite number of classical periodic orbits. We shall use it to derive some spectral properties, and in particular to investigate the relationship between spectral statistics of quantum chaotic systems and the predictions of random-matrix theory. We shall finally discuss an important family of chaotic billiard, whose statistics does not follow any of the canonical ensembles, (GOE,GUE,...) but rather, corresponds to a new universality class. (author)

  20. Quantum level statistics of pseudointegrable billiards

    Cheon, T.; Cohen, T.D.

    1989-01-01

    We study the spectral statistics of systems of two-dimensional pseudointegrable billiards. These systems are classically nonergodic, but nonseparable. It is found that such systems possess quantum spectra which are closely simulated by the Gaussian orthogonal ensemble. We discuss the implications of these results on the conjectured relation between classical chaos and quantum level statistics. We emphasize the importance of the semiclassical nature of any such relation

  1. Gauge theory loop operators and Liouville theory

    Drukker, Nadav; Teschner, Joerg

    2009-10-01

    We propose a correspondence between loop operators in a family of four dimensional N=2 gauge theories on S 4 - including Wilson, 't Hooft and dyonic operators - and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these N=2 gauge theories and Liouville correlators found by Alday, Gaiotto and Tachikawa. We show that the computation of these Liouville correlators with the insertion of a Liouville loop operator reproduces Pestun's formula capturing the expectation value of a Wilson loop operator in the corresponding gauge theory. We prove that our definition of Liouville loop operators is invariant under modular transformations, which given our correspondence, implies the conjectured action of S-duality on the gauge theory loop operators. Our computations in Liouville theory make an explicit prediction for the exact expectation value of 't Hooft and dyonic loop operators in these N=2 gauge theories. The Liouville loop operators are also found to admit a simple geometric interpretation within quantum Teichmueller theory as the quantum operators representing the length of geodesics. We study the algebra of Liouville loop operators and show that it gives evidence for our proposal as well as providing definite predictions for the operator product expansion of loop operators in gauge theory. (orig.)

  2. Exact solution of super Liouville model

    Yang Zhanying; Zhao Liu; Zhen Yi

    2000-01-01

    Using Leznov-Saveliev algebraic analysis and Drinfeld-Sokolov construction, the authors obtained the explicit solutions to the super Liouville system in super covariant form and component form. The explicit solution in component form reduces naturally into the Egnchi-Hanson instanton solution of the usual Liouville equation if all the Grassmann odd components are set equal to zero

  3. Gauge theory loop operators and Liouville theory

    Drukker, Nadav [Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Gomis, Jaume; Okuda, Takuda [Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Teschner, Joerg [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2009-10-15

    We propose a correspondence between loop operators in a family of four dimensional N=2 gauge theories on S{sup 4} - including Wilson, 't Hooft and dyonic operators - and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these N=2 gauge theories and Liouville correlators found by Alday, Gaiotto and Tachikawa. We show that the computation of these Liouville correlators with the insertion of a Liouville loop operator reproduces Pestun's formula capturing the expectation value of a Wilson loop operator in the corresponding gauge theory. We prove that our definition of Liouville loop operators is invariant under modular transformations, which given our correspondence, implies the conjectured action of S-duality on the gauge theory loop operators. Our computations in Liouville theory make an explicit prediction for the exact expectation value of 't Hooft and dyonic loop operators in these N=2 gauge theories. The Liouville loop operators are also found to admit a simple geometric interpretation within quantum Teichmueller theory as the quantum operators representing the length of geodesics. We study the algebra of Liouville loop operators and show that it gives evidence for our proposal as well as providing definite predictions for the operator product expansion of loop operators in gauge theory. (orig.)

  4. Wave packet construction in three-dimensional quantum billiards

    We examine the dynamical evolution of wave packets in a cubical billiard where three quantum numbers (, , ) determine its energy spectrum and consequently its dynamical behaviour. We have constructed the wave packet in the cubical billiard and have observed its time evolution for various closed orbits.

  5. Remarks on interior transmission eigenvalues, Weyl formula and branching billiards

    Lakshtanov, E; Vainberg, B

    2012-01-01

    This paper contains the Weyl formula for the counting function of the interior transmission problem when the latter is parameter elliptic. Branching billiard trajectories are constructed, and the second term of the Weyl asymptotics is estimated from above under some conditions on the set of periodic billiard trajectories. (paper)

  6. Recognizing chaotic states in stadium billiard by calculating gyration radius

    M. Barezi

    2006-12-01

    Full Text Available   Nowadays study of chaotic quantum billiards because of their relation to Nano technology. In this paper distribution of zeros of wave function on the boundary of two circular and stadium billiards are investigated. By calculating gyration radius for these points chaotic and non-chaotic states are distinguished.

  7. H3+-WZNW correlators from Liouville theory

    Ribault, Sylvain; Teschner, Joerg

    2005-01-01

    We prove that arbitrary correlation functions of the H 3 + -WZNW model on a sphere have a simple expression in terms of Liouville theory correlation functions. This is based on the correspondence between the KZ and BPZ equations, and on relations between the structure constants of Liouville theory and the H 3 + -WZNW model. In the critical level limit, these results imply a direct link between eigenvectors of the Gaudin hamiltonians and the problem of uniformization of Riemann surfaces. We also present an expression for correlation functions of the SL(2)/U(1) gauged WZNW model in terms of correlation functions in Liouville theory

  8. Electron billiards: einselection and quantum Darwinism

    Brunner, R.; Meisels, R.; Kuchar, F.; Akis, R.; Ferry, D.K.

    2008-01-01

    Full text: The measurement of open quantum systems has been a main topic since the advent of quantum theory. It is a basic ingredient in quantum information processing. Here, the border where the two worlds of classical and quantum mechanics meet is of significant importance due to the problem of measurement. It has been shown by Zurek that in an open system the environment imposes so-called superselection rules leading to environment-induced superselection (einselection). This means that a set of preferred states (pointer states) survive the coupling with the environment. These pointer states are characterized by their robustness and their ability to create offspring. This ability to advertise information about themselves makes it possible for different observers to measure the same information. The natural promotion of certain information in a quantum system is known as quantum Darwinism. The 'fitness' in the Darwinian sense of the selected states is essentially a measure of their classicality. That is in order to measure a quantum system objectively a system has to be designed where the transition between the classical and quantum world is observable. In this respect we show by a combination of experiment and calculation that an array of electron billiards (open quantum dots) is very well suited. We demonstrate that einselection takes place in electron billiards and a set of pointer states arises. We illustrate that beside the 'regular' (single dot) pointer states a new type of einselected states arise when two or more quantum dots are coupled together and to the environment. This new type of states can not be represented by a linear combination of pointer states of the individual dots. Finally, we discuss the propensity of the new type of einselected states to make offspring in order to see if quantum Darwinism is in action in the array of electron billiards.(author)

  9. Advanced statistical properties of dispersing billiards

    Chernov, N

    2005-01-01

    A new approach to statistical properties of hyperbolic dynamical systems emerged recently; it was introduced by L.-S.~Young and modified by D.~Dolgopyat. It is based on coupling method borrowed from probability theory. We apply it here to one of the most physically interesting models -- Sinai billiards. It allows us to derive a series of new results, as well as make significant improvements in the existing results. First we establish sharp bounds on correlations (including multiple correlations). Then we use our correlation bounds to obtain the central limit theorem (CLT), the almost sure invariance principle (ASIP), the law of iterated logarithms, and integral tests.

  10. Liouvilles's imaginary shadow

    Schomerus, Volker [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Suchanek, Paulina [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Univ. of Wroclaw (Poland). Inst. for Theoretical Physics

    2012-10-15

    N=1 super Liouville field theory is one of the simplest non-rational conformal field theories. It possesses various important extensions and interesting applications, e.g. to the AGT relation with 4D gauge theory or the construction of the OSP(1 vertical stroke 2) WZW model. In both setups, the N=1 Liouville field is accompanied by an additional free fermion. Recently, Belavin et al. suggested a bosonization of the product theory in terms of two bosonic Liouville fields. While one of these Liouville fields is standard, the second turns out to be imaginary (or time-like). We extend the proposal to the R sector and perform extensive checks based on detailed comparison of 3-point functions involving several super-conformal primaries and descendants. On the basis of such strong evidence we sketch a number of interesting potential applications of this intriguing bozonization.

  11. Semiclassical limit of the FZZT Liouville theory

    Hadasz, Leszek; Jaskolski, Zbigniew

    2006-01-01

    The semiclassical limit of the FZZT Liouville theory on the upper half plane with bulk operators of arbitrary type and with elliptic boundary operators is analyzed. We prove the Polyakov conjecture for an appropriate classical Liouville action. This action is calculated in a number of cases: One bulk operator of arbitrary type, one bulk and one boundary, and two boundary elliptic operators. The results are in agreement with the classical limits of the corresponding quantum correlators

  12. Semiclassical limit of the FZZT Liouville theory

    Hadasz, Leszek; Jaskólski, Zbigniew

    2006-11-01

    The semiclassical limit of the FZZT Liouville theory on the upper half plane with bulk operators of arbitrary type and with elliptic boundary operators is analyzed. We prove the Polyakov conjecture for an appropriate classical Liouville action. This action is calculated in a number of cases: One bulk operator of arbitrary type, one bulk and one boundary, and two boundary elliptic operators. The results are in agreement with the classical limits of the corresponding quantum correlators.

  13. Semiclassical limit of the FZZT Liouville theory

    Hadasz, Leszek; Jaskolski, Zbigniew

    2006-01-01

    The semiclassical limit of the FZZT Liouville theory on the upper half plane with bulk operators of arbitrary type and with elliptic boundary operators is analyzed. We prove the Polyakov conjecture for an appropriate classical Liouville action. This action is calculated in a number of cases: one bulk operator of arbitrary type, one bulk and one boundary, and two boundary elliptic operators. The results are in agreement with the classical limits of the corresponding quantum correlators.

  14. Semiclassical limit of the FZZT Liouville theory

    Hadasz, Leszek [Physikalisches Institut, Rheinische Friedrich-Wilhelms-Universitaet, Nussallee 12, 53115 Bonn (Germany); M. Smoluchowski Institute of Physics, Jagiellonian University, W. Reymonta 4, 30-059 Cracow (Poland)]. E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew [Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna 9, 50-204 Wroclaw (Poland)]. E-mail: jask@ift.uni.wroc.pl

    2006-11-27

    The semiclassical limit of the FZZT Liouville theory on the upper half plane with bulk operators of arbitrary type and with elliptic boundary operators is analyzed. We prove the Polyakov conjecture for an appropriate classical Liouville action. This action is calculated in a number of cases: One bulk operator of arbitrary type, one bulk and one boundary, and two boundary elliptic operators. The results are in agreement with the classical limits of the corresponding quantum correlators.

  15. Liouville's theorem and phase-space cooling

    Mills, R.L.; Sessler, A.M.

    1993-01-01

    A discussion is presented of Liouville's theorem and its consequences for conservative dynamical systems. A formal proof of Liouville's theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur

  16. Spectral statistics in the quantized cardioid billiard

    Baecker, A.; Steiner, F.; Stifter, P.

    1994-11-01

    The spectral statistics in the strongly chaotic cardioid billiard are studied. The analysis is based on the first 11000 quantal energy levels for odd and even symmetry respectively. It is found that the level-spacing distribution is in good agreement with the GOE distribution of random-matrix theory. In case of the number variance and rigidity we observe agreement with the random-matrix model for short-range correlations only, whereas for long-range correlations both statistics saturate in agreement with semiclassical expectations. Furthermore the conjecture that for classically chaotic systems the normalized mode fluctuations have a universal Gaussian distribution with unit variance is tested and found to be in very good agreement for both symmetry classes. By means of the Gutzwiller trace formula the trace of the cosine-modulated heat kernel is studied. Since the billiard boundary is focusing there are conjugate points giving rise to zeros at the locations of the periodic orbits instead of exclusively Gaussian peaks. (orig.)

  17. Vertical motion and ''scarred'' eigenfunctions in the stadium billiard

    Christoffel, K.M.; Brumer, P.

    1985-01-01

    A subset of pseudoregular eigenfunctions of the classically chaotic stadium billiard is shown to participate strongly in vertically directed motion, supporting the conjectures of McDonald and of Heller regarding periodic orbits and pseudoregular eigenfunctions

  18. Dynamic modeling and simulation of a real world billiard

    Hartl, Alexandre E.; Miller, Bruce N.; Mazzoleni, Andre P.

    2011-01-01

    Gravitational billiards provide an experimentally accessible arena for testing formulations of nonlinear dynamics. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic billiard for arbitrary boundaries. Simulations of the model are applied to parabolic, wedge and hyperbolic billiards that are driven sinusoidally. Direct comparisons are made between the model's predictions and previously published experimental data. It is shown that the data can be successfully modeled with a simple set of parameters without an assumption of exotic energy dependence. -- Highlights: → We create a model of a gravitational billiard that includes rotation and dissipation. → Predictions of the model are compared with the experiments of Felt and Olafsen. → The simulations correctly predict the essential features of the experiments.

  19. Topology of the elliptical billiard with the Hooke's potential

    Radnović Milena

    2015-01-01

    Full Text Available Using Fomenko graphs, we present a topological description of the elliptical billiard with Hooke's potential. [Projekat Ministarstva nauke Republike Srbije, br. 174020: Geometry and Topology of Manifolds and Integrable Dynamical Systems

  20. Magnetic focusing in triangular electron billiards

    Bøggild, Peter; Kristensen, A.; Lindelof, Poul Erik

    1999-01-01

    The classical ballistic magnetotransport in triangular electron billiards fabricated in a high mobility GaAs heterostructure has been studied at 4.2 K. The sample geometry may be viewed as a double-slit structure with a skewed injection angle. We observe a striking cancellation of the magnetic...... focusing spectrum compared to the case of a perpendicular injection angle. From numerical and analytical analysis, we confirm that the quenching is a fundamental geometrical effect, and identify two mechanisms responsible for the anomaly. The focusing spectrum of the considered skewed geometry...... is remarkably sensitive to the angular distribution of injected electrons as well as the overall injection angle. [S0163-1829(99)06619-9]....

  1. Unpredictable Property of a Kicked Billiard Ball

    Shen Ying; Dai Jun; Jiang Yumei; He Yue; He Daren

    2006-01-01

    A simultaneous change in the systemic property of a kicked billiard ball is observed from an entirely smooth and conservative state to a piecewise smooth and quasi-dissipative state when a single controlling parameter has been adjusted. The transition induces a sudden change of a typical conservative stochastic web into a transient web. The iterations on the transient web eventually escape to some elliptic islands. In the meantime, a fat fractal forbidden web, which appears also at the threshold, grows up and cuts away increasingly more parts from the original conservative stochastic web. We numerically show that the initial conditions that generated different attractors are mixed in a random manner and the pattern remains unchanged even when smaller and smaller scales are used for examination, indicating a riddle-like basin structure that practically rules out the possibility of predicting the attractors from a given initial condition

  2. Correlation decay in certain soft billiards

    Balint, P

    2003-01-01

    Motivated by the 2D finite horizon periodic Lorentz gas, soft planar billiard systems with axis-symmetric potentials are studied in this paper. Since Sinai's celebrated discovery that elastic collisions of a point particle with strictly convex scatterers give rise to hyperbolic, and consequently, nice ergodic behaviour, several authors (most notably Sinai, Kubo, Knauf) have found potentials with analogous properties. These investigations concluded in the work of V. Donnay and C. Liverani who obtained general conditions for a 2-D rotationally symmetric potential to provide ergodic dynamics. Our main aim here is to understand when these potentials lead to stronger stochastic properties, in particular to exponential decay of correlations and central limit theorem. In the main argument we work with systems in general for which the rotation function satisfies certain conditions. One of these conditions has already been used by Donnay and Liverani to obtain hyperbolicity and ergodicity. What we prove is that if, in...

  3. Deterministic diffusion in flower-shaped billiards.

    Harayama, Takahisa; Klages, Rainer; Gaspard, Pierre

    2002-08-01

    We propose a flower-shaped billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles in the shape of a flower, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form using different schemes, all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance in reproducing the precise parameter dependence of the diffusion coefficent.

  4. Cayley-type conditions for billiards within k quadrics in Rd

    Dragovic, Vladimir; Radnovic, Milena

    2004-01-01

    The notions of reflection from outside, reflection from inside and signature of a billiard trajectory within a quadric are introduced. Cayley-type conditions for periodical trajectories for the billiard in the region bounded by k quadrics in R d and for the billiard ordered game within k ellipsoids in R d are derived. In a limit, the condition describing periodic trajectories of billiard systems on a quadric in R d is obtained

  5. Touching random surfaces and Liouville gravity

    Klebanov, I.R.

    1995-01-01

    Large N matrix models modified by terms of the form g(TrΦ n ) 2 generate random surfaces which touch at isolated points. Matrix model results indicate that, as g is increased to a special value g t , the string susceptibility exponent suddenly jumps from its conventional value γ to γ/(γ-1). We study this effect in Liouville gravity and attribute it to a change of the interaction term from Oe α + φ for g t to Oe α - φ for g=g t (α + and α - are the two roots of the conformal invariance condition for the Liouville dressing of a matter operator O). Thus, the new critical behavior is explained by the unconventional branch of Liouville dressing in the action

  6. Liouville quantum gravity on complex tori

    David, François [Institut de Physique Théorique, CNRS, URA 2306, CEA, IPhT, Gif-sur-Yvette (France); Rhodes, Rémi [Université Paris-Est Marne la Vallée, LAMA, Champs sur Marne (France); Vargas, Vincent [ENS Paris, DMA, 45 rue d’Ulm, 75005 Paris (France)

    2016-02-15

    In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov [Phys. Lett. B 103, 207 (1981)]. Our approach follows the construction carried out by the authors together with Kupiainen in the case of the Riemann sphere [“Liouville quantum gravity on the Riemann sphere,” e-print arXiv:1410.7318]. The difference is here that the moduli space for complex tori is non-trivial. Modular properties of LQFT are thus investigated. This allows us to integrate the LQFT on complex tori over the moduli space, to compute the law of the random Liouville modulus, therefore recovering (and extending) formulae obtained by physicists, and make conjectures about the relationship with random planar maps of genus one, eventually weighted by a conformal field theory and conformally embedded onto the torus.

  7. Sturm-Liouville operators and applications

    Marchenko, Vladimir A

    2011-01-01

    The spectral theory of Sturm-Liouville operators is a classical domain of analysis, comprising a wide variety of problems. Besides the basic results on the structure of the spectrum and the eigenfunction expansion of regular and singular Sturm-Liouville problems, it is in this domain that one-dimensional quantum scattering theory, inverse spectral problems, and the surprising connections of the theory with nonlinear evolution equations first become related. The main goal of this book is to show what can be achieved with the aid of transformation operators in spectral theory as well as in their

  8. Classical Liouville action on the sphere with three hyperbolic singularities

    Hadasz, Leszek E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew E-mail: jask@ift.uniwroc.pl

    2004-08-30

    The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.

  9. Classical Liouville action on the sphere with three hyperbolic singularities

    Hadasz, Leszek; Jaskólski, Zbigniew

    2004-08-01

    The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.

  10. Classical Liouville action on the sphere with three hyperbolic singularities

    Hadasz, Leszek; Jaskolski, Zbigniew

    2004-01-01

    The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory

  11. Modular bootstrap in Liouville field theory

    Hadasz, Leszek; Jaskolski, Zbigniew; Suchanek, Paulina

    2010-01-01

    The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.

  12. Modular bootstrap in Liouville field theory

    Hadasz, Leszek, E-mail: hadasz@th.if.uj.edu.p [M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Krakow (Poland); Jaskolski, Zbigniew, E-mail: jask@ift.uni.wroc.p [Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna, 50-204 Wroclaw (Poland); Suchanek, Paulina, E-mail: paulina@ift.uni.wroc.p [Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna, 50-204 Wroclaw (Poland)

    2010-02-22

    The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.

  13. Modular bootstrap in Liouville field theory

    Hadasz, Leszek; Jaskólski, Zbigniew; Suchanek, Paulina

    2010-02-01

    The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.

  14. 'Footballs', conical singularities, and the Liouville equation

    Redi, Michele

    2005-01-01

    We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints

  15. Sturm-Liouville BVPs with Caratheodory nonlinearities

    Abdelhamid Benmezai

    2016-11-01

    Full Text Available In this article we study the existence and multiplicity of solutions for several classes of Sturm-Liouville boundary value problems having Caratheodory nonlinearities. Many results existing in the literature for such boundary value problems in the continuous framework will find in this work their extensions to the Caratheodory setting.

  16. Quasi-equilibria in reduced Liouville spaces.

    Halse, Meghan E; Dumez, Jean-Nicolas; Emsley, Lyndon

    2012-06-14

    The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.

  17. Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards.

    Yu, Pei; Li, Zi-Yuan; Xu, Hong-Ya; Huang, Liang; Dietz, Barbara; Grebogi, Celso; Lai, Ying-Cheng

    2016-12-01

    A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular-sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.

  18. Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards

    Yu, Pei; Li, Zi-Yuan; Xu, Hong-Ya; Huang, Liang; Dietz, Barbara; Grebogi, Celso; Lai, Ying-Cheng

    2016-12-01

    A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular-sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.

  19. Geometrical origin of chaoticity in the bouncing ball billiard

    Mátyás, L.; Barna, I.F.

    2011-01-01

    Highlights: ► We study the possible separation of neighouring trajectories in the bouncing ball billiard. ► In a certain interval of frequencies semianalitical evaluations are possible. ► One may find a lower bound for the maximal Lyapunov exponent in case of a resonance. - Abstract: We present a study of the chaotic behaviour of the bouncing ball billiard. The work is realised on the purpose of finding at least certain causes of separation of the neighbouring trajectories. Having in view the geometrical construction of the system, we report a clear origin of chaoticity of the bouncing ball billiard. By this we claim that in case when the floor is made of arc of circles – in a certain interval of frequencies – one can give semi-analytical estimates on chaotic behaviour.

  20. Coulomb-interacting billiards in circular cavities

    Solanpää, J; Räsänen, E; Nokelainen, J; Luukko, P J J

    2013-01-01

    We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. As such, the system resembles a prototype model for a semiconductor quantum dot. The interaction strength is varied from the noninteracting limit with zero potential energy up to the strongly interacting regime where the relative kinetic energy approaches zero. At weak interactions the bouncing maps show jumps between quasi-regular orbits. In the strong-interaction limit we find an analytic expression for the bouncing map. Its validity in the general case is assessed by comparison with our numerical data. To obtain a more quantitative view on the dynamics as the interaction strength is varied, we compute and analyze the escape rates of the system. Apart from very weak or strong interactions, the escape rates show consistently exponential behavior, thus suggesting strongly chaotic dynamics and a phase space without significant sticky regions within the considered time scales. (paper)

  1. Classical geometry from the quantum Liouville theory

    Hadasz, Leszek; Jaskólski, Zbigniew; Piaţek, Marcin

    2005-09-01

    Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.

  2. Classical geometry from the quantum Liouville theory

    Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Cracow (Poland)]. E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: jask@ift.uni.wroc.pl; Piatek, Marcin [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: piatek@ift.uni.wroc.pl

    2005-09-26

    Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.

  3. Classical geometry from the quantum Liouville theory

    Hadasz, Leszek; Jaskolski, Zbigniew; Piatek, Marcin

    2005-01-01

    Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere

  4. Unitarity relations in c=1 Liouville theory

    Lowe, D.A.

    1992-01-01

    In this paper, the authors consider the S-matrix of c = 1 Liouville theory with vanishing cosmological constant. The authors examine some of the constraints imposed by unitarity. These completely determine (N,2) amplitudes at tree level in terms of the (N,1) amplitudes when the plus tachyon momenta take generic values. A surprising feature of the matrix model results is the lack of particle creation branch cuts in the higher genus amplitudes. In fact, the authors show that the naive field theory limit of Liouville theory would predict such branch cuts. However, unitarity in the full string theory ensures that such cuts do not appear in genus one (N,1) amplitudes. The authors conclude with some comments about the genus one (N,2) amplitudes

  5. L-1 constraint in Liouville gravity

    Kitazawa, Y.

    1992-01-01

    In this paper, the authors study recursion relations among the amplitudes which involve discrete states in c = 1 Liouville gravity on the sphere. The authors find that the spin J = 1/2 discrete state gives rise to the L -1 type recursion relation. Multiple point correlation functions are determined recursively from fewer point functions by this recursion relation. The authors further point out that the analogs of J = 1/2 state exist in c -1 type recursion relation

  6. Chaotic correlations in barrier billiards with arbitrary barriers

    Osbaldestin, A H; Adamson, L N C

    2013-01-01

    We study autocorrelation functions in symmetric barrier billiards for golden mean trajectories with arbitrary barriers. Renormalization analysis reveals the presence of a chaotic invariant set and thus that, for a typical barrier, there are chaotic correlations. The chaotic renormalization set is the analogue of the so-called orchid that arises in a generalized Harper equation. (paper)

  7. Wave packet construction in three-dimensional quantum billiards ...

    E-mail: mannu_711@yahoo.co.in. MS received 14 ... The motivation to extend the study to a three-dimensional (3D) system is .... with a GWP centred around the central value of the principle quantum number n0 instead of a GWP ...... Cubical and parallelepiped billiards are the potential candidates for the creation of arti-.

  8. Constrained Quantum Mechanics: Chaos in Non-Planar Billiards

    Salazar, R.; Tellez, G.

    2012-01-01

    We illustrate some of the techniques to identify chaos signatures at the quantum level using as guiding examples some systems where a particle is constrained to move on a radial symmetric, but non-planar, surface. In particular, two systems are studied: the case of a cone with an arbitrary contour or "dunce hat billiard" and the rectangular…

  9. A Note on Upper Tail Behavior of Liouville Copulas

    Lei Hua

    2016-11-01

    Full Text Available The family of Liouville copulas is defined as the survival copulas of multivariate Liouville distributions, and it covers the Archimedean copulas constructed by Williamson’s d-transform. Liouville copulas provide a very wide range of dependence ranging from positive to negative dependence in the upper tails, and they can be useful in modeling tail risks. In this article, we study the upper tail behavior of Liouville copulas through their upper tail orders. Tail orders of a more general scale mixture model that covers Liouville distributions is first derived, and then tail order functions and tail order density functions of Liouville copulas are derived. Concrete examples are given after the main results.

  10. Noncritical String Liouville Theory and Geometric Bootstrap Hypothesis

    Hadasz, Leszek; Jaskólski, Zbigniew

    The applications of the existing Liouville theories for the description of the longitudinal dynamics of noncritical Nambu-Goto string are analyzed. We show that the recently developed DOZZ solution to the Liouville theory leads to the cut singularities in tree string amplitudes. We propose a new version of the Polyakov geometric approach to Liouville theory and formulate its basic consistency condition — the geometric bootstrap equation. Also in this approach the tree amplitudes develop cut singularities.

  11. Liouville theory with a central charge less than one

    Ribault, Sylvain [CEA Saclay, Institut de Physique Théorique,F-91191, Gif-sur-Yvette (France); Santachiara, Raoul [LPTMS, Université Paris Sud,15 rue Georges Clemenceau, Orsay (France)

    2015-08-21

    We determine the spectrum and correlation functions of Liouville theory with a central charge less than (or equal) one. This completes the definition of Liouville theory for all complex values of the central charge. The spectrum is always spacelike, and there is no consistent timelike Liouville theory. We also study the non-analytic conformal field theories that exist at rational values of the central charge. Our claims are supported by numerical checks of crossing symmetry. We provide Python code for computing Virasoro conformal blocks, and correlation functions in Liouville theory and (generalized) minimal models.

  12. Accidental bound states in the continuum in an open Sinai billiard

    Pilipchuk, A.S. [Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk (Russian Federation); Siberian Federal University, 660080 Krasnoyarsk (Russian Federation); Sadreev, A.F., E-mail: almas@tnp.krasn.ru [Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk (Russian Federation)

    2017-02-19

    The fundamental mechanism of the bound states in the continuum is the full destructive interference of two resonances when two eigenlevels of the closed system are crossing. There is, however, a wide class of quantum chaotic systems which display only avoided crossings of eigenlevels. As an example of such a system we consider the Sinai billiard coupled with two semi-infinite waveguides. We show that notwithstanding the absence of degeneracy bound states in the continuum occur due to accidental decoupling of the eigenstates of the billiard from the waveguides. - Highlights: • Bound states in the continuum in open chaotic billiards occur to accidental vanishing of coupling of eigenstate of billiard with waveguides.

  13. Symmetry-adapted Liouville space. Pt. 7

    Temme, F.P.

    1990-01-01

    In examining nuclear spin dynamics of NMR spin clusters in density operator/generalized torque formalisms over vertical strokekqv>> operator bases of Liouville space, it is necessary to consider the symmetry mappings and carrier spaces under a specialized group for such (k i = 1) nuclear spin clusters. The SU2 X S n group provides the essential mappings and the form of H carrier space, which allows one to: (a) draw comparisons with Hilbert space duality, and (b) outline the form of the Coleman-Kotani genealogical hierarchy under induced S n -symmetry. (orig.)

  14. On Multi-Point Liouville Field Theory

    Zarrinkamar, S.; Rajabi, A. A.; Hassanabadi, H.

    2013-01-01

    In many cases, the classical or semi-classical Liouville field theory appears in the form of Fuchsian or Riemann differential equations whose solutions cannot be simply found, or at least require a comprehensive knowledge on analytical techniques of differential equations of mathematical physics. Here, instead of other cumbersome methodologies such as treating with the Heun functions, we use the quasi-exact ansatz approach and thereby solve the so-called resulting two- and three-point differential equations in a very simple manner. We apply the approach to two recent papers in the field. (author)

  15. Dressing symmetry of the uniformization solution of Liouville equation

    Shen Jianmin.

    1994-10-01

    In this paper, the relations between monodromy group and dressing group for Liouville equation in uniformization theorem are discussed. The representation of monodromy transformation, acting on the chiral components of the solution of Liouville equation, is obtained. The non-trivial exchange algebra for monodromy transformation is calculated. (author). 14 refs

  16. Quantum and wave dynamical chaos in superconducting microwave billiards.

    Dietz, B; Richter, A

    2015-09-01

    Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose of the present article is to recapitulate some of the highlights achieved. We briefly review (i) results obtained with flat, cylindrical microwave resonators, so-called microwave billiards, concerning the universal fluctuation properties of the eigenvalues of classically chaotic systems with no, a threefold and a broken symmetry; (ii) summarize our findings concerning the wave-dynamical chaos in three-dimensional microwave cavities; (iii) present a new approach for the understanding of the phenomenon of dynamical tunneling which was developed on the basis of experiments that were performed recently with unprecedented precision, and finally, (iv) give an insight into an ongoing project, where we investigate universal properties of (artificial) graphene with superconducting microwave photonic crystals that are enclosed in a microwave resonator, i.e., so-called Dirac billiards.

  17. Bosonic Liouville string theory in conformal gauge

    Schnittger, J.

    1990-01-01

    The object of the present thesis are the so-called Liouville theories as possibilities for the consistent formulation of string theories beyond the critical dimension. First we discuss the general framework for the quantum theory and explain common properties and differences of different approaches. These considerations lead us to the main demand of the thesis, the formulation of a unified quantum theory for open and closed strings. Of central importance is thereby the construction of the field operator for the Weyl degree of freedom on a suitably defined Hilbert space, so that also in the quantum theory locality and Hermiticity of the Energy-Momentum tensor are respected. In the study of the allowed ground states of the Hilbert space an interesting particularity in comparison to the structure of usual conformal field theories comes across, the importance and consequences of which we intensively study. In the last section we enter the consistence of the theory on the 1-loop level and come then to the final consideration, where we indicate some still open questions of the Liouville theory. (orig.) [de

  18. Universality in level spacing fluctuations of a chaotic optical billiard

    Laprise, J.F.; Hosseinizadeh, A.; Lamy-Poirier, J. [Departement de Physique, Universite Laval, Quebec, Quebec G1V 0A6 (Canada); Zomorrodi, R. [Departement de Physique, Universite Laval, Quebec, Quebec G1V 0A6 (Canada)] [Centre de Recherche Universite Laval Robert Giffard, Quebec, Quebec G1J 2G3 (Canada); Kroeger, J. [Physics Department and Center for Physics of Materials, McGill University, Montreal, Quebec H3A 2T8 (Canada)] [Department of Physiology, McGill University, Montreal, Quebec H3G 1Y6 (Canada); Kroeger, H., E-mail: hkroger@phy.ulaval.c [Departement de Physique, Universite Laval, Quebec, Quebec G1V 0A6 (Canada)] [Functional Neurobiology, University of Utrecht, 3584 CH Utrecht (Netherlands)

    2010-04-19

    We study chaotic behavior of a classical optical stadium billiard model. We construct a matrix of time-of-travel along trajectories corresponding to a set of boundary points. We carry out a level spacing fluctuation analysis and compute the Dyson-Mehta spectral rigidity. The distribution of time-of-travel is approximately described by a Gaussian. The results for level spacing distribution and spectral rigidity show universal behavior.

  19. Quantum billiards with branes on product of Einstein spaces

    Ivashchuk, V.D. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia, Institute of Gravitation and Cosmology, Moscow (Russian Federation)

    2016-05-15

    We consider a gravitational model in dimension D with several forms, l scalar fields and a Λ-term. We study cosmological-type block-diagonal metrics defined on a product of an 1-dimensional interval and n oriented Einstein spaces. As an electromagnetic composite brane ansatz is adopted and certain restrictions on the branes are imposed the conformally covariant Wheeler-DeWitt (WDW) equation for the model is studied. Under certain restrictions, asymptotic solutions to the WDW equation are found in the limit of the formation of the billiard walls. These solutions reduce the problem to the so-called quantum billiard in (n + l -1)-dimensional hyperbolic space. Several examples of quantum billiards in the model with electric and magnetic branes, e.g. corresponding to hyperbolic Kac-Moody algebras, are considered. In the case n = 2 we find a set of basis asymptotic solutions to the WDW equation and derive asymptotic solutions for the metric in the classical case. (orig.)

  20. Quantum wave-packet revivals in circular billiards

    Robinett, R.W.; Heppelmann, S.

    2002-01-01

    We examine the long-term time dependence of Gaussian wave packets in a circular infinite well (billiard) system and find that there are approximate revivals. For the special case of purely m=0 states (central wave packets with no momentum) the revival time is T rev (m=0) =8μR 2 /(ℎ/2π)π, where μ is the mass of the particle, and the revivals are almost exact. For all other wave packets, we find that T rev (m≠0) =(π 2 /2)T rev (m=0) ≅5T rev (m=0) and the nature of the revivals becomes increasingly approximate as the average angular momentum or number of m≠0 states is increased. The dependence of the revival structure on the initial position, energy, and angular momentum of the wave packet and the connection to the energy spectrum is discussed in detail. The results are also compared to two other highly symmetrical two-dimensional infinite well geometries with exact revivals, namely, the square and equilateral triangle billiards. We also show explicitly how the classical periodicity for closed orbits in a circular billiard arises from the energy eigenvalue spectrum, using a WKB analysis

  1. Classical and quantum dynamics of driven elliptical billiards

    Lenz, Florian

    2009-12-09

    Subject of this thesis is the investigation of the classical dynamics of the driven elliptical billiard and the development of a numerical method allowing the propagation of arbitrary initial states in the quantum version of the system. In the classical case, we demonstrate that there is Fermi acceleration in the driven billiard. The corresponding transport process in momentum space shows a surprising crossover from sub- to normal diffusion. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. The four-dimensional phase space is analyzed in depth, especially how its composition changes in different velocity regimes. We show that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change of the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion. In the quantum case, a series of transformations tailored to the elliptical billiard is applied to circumvent the time-dependent Dirichlet boundary conditions. By means of an expansion ansatz, this eventually yields a large system of coupled ordinary differential equations, which can be solved by standard techniques. (orig.)

  2. Classical and quantum dynamics of driven elliptical billiards

    Lenz, Florian

    2009-01-01

    Subject of this thesis is the investigation of the classical dynamics of the driven elliptical billiard and the development of a numerical method allowing the propagation of arbitrary initial states in the quantum version of the system. In the classical case, we demonstrate that there is Fermi acceleration in the driven billiard. The corresponding transport process in momentum space shows a surprising crossover from sub- to normal diffusion. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. The four-dimensional phase space is analyzed in depth, especially how its composition changes in different velocity regimes. We show that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change of the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion. In the quantum case, a series of transformations tailored to the elliptical billiard is applied to circumvent the time-dependent Dirichlet boundary conditions. By means of an expansion ansatz, this eventually yields a large system of coupled ordinary differential equations, which can be solved by standard techniques. (orig.)

  3. The K-property of 4D billiards with nonorthogonal cylindric scatterers

    Simanyi, N.; Szasz, D.

    1994-01-01

    The K-property of cylindric billiards give on the 4-torus is established. These billiards are neither open-quotes orthogonal,close quotes where general necessary and sufficient conditions were obtained by D.Szasz, nor isomorphic to hard-ball systems, where the connecting path formula of N. Simanyi is a hand

  4. A difference-equation formalism for the nodal domains of separable billiards

    Manjunath, Naren; Samajdar, Rhine [Indian Institute of Science, Bangalore 560012 (India); Jain, Sudhir R., E-mail: srjain@barc.gov.in [Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085 (India)

    2016-09-15

    Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in Samajdar and Jain (2014). The exact solutions of these equations give the number of domains explicitly. For complete generality, we demonstrate this novel formulation for three additional separable systems and thus extend the statement to all integrable billiards.

  5. The Solution Construction of Heterotic Super-Liouville Model

    Yang, Zhan-Ying; Zhen, Yi

    2001-12-01

    We investigate the heterotic super-Liouville model on the base of the basic Lie super-algebra Osp(1|2).Using the super extension of Leznov-Saveliev analysis and Drinfeld-Sokolov linear system, we construct the explicit solution of the heterotic super-Liouville system in component form. We also show that the solutions are local and periodic by calculating the exchange relation of the solution. Finally starting from the action of heterotic super-Liouville model, we obtain the conserved current and conserved charge which possessed the BRST properties.

  6. Two- and three-point functions in Liouville theory

    Dorn, H.; Otto, H.J.

    1994-04-01

    Based on our generalization of the Goulian-Li continuation in the power of the 2D cosmological term we construct the two and three-point correlation functions for Liouville exponentials with generic real coefficients. As a strong argument in favour of the procedure we prove the Liouville equation of motion on the level of three-point functions. The analytical structure of the correlation functions as well as some of its consequences for string theory are discussed. This includes a conjecture on the mass shell condition for excitations of noncritical strings. We also make a comment concerning the correlation functions of the Liouville field itself. (orig.)

  7. An inverse Sturm–Liouville problem with a fractional derivative

    Jin, Bangti; Rundell, William

    2012-01-01

    In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical

  8. The exchange algebra for Liouville theory on punctured Riemann sphere

    Shen Jianmin; Sheng Zhengmao

    1991-11-01

    We consider in this paper the classical Liouville field theory on the Riemann sphere with n punctures. In terms of the uniformization theorem of Riemann surface, we show explicitly the classical exchange algebra (CEA) for the chiral components of the Liouville fields. We find that the matrice which dominate the CEA is related to the symmetry of the Lie group SL(n) in a nontrivial manner with n>3. (author). 10 refs

  9. Liouville theory and uniformization of four-punctured sphere

    Hadasz, Leszek; Jaskolski, Zbigniew

    2006-01-01

    Few years ago Zamolodchikov and Zamolodchikov proposed an expression for the 4-point classical Liouville action in terms of the 3-point actions and the classical conformal block. In this paper we develop a method of calculating the uniformizing map and the uniformizing group from the classical Liouville action on n-punctured sphere and discuss the consequences of Zamolodchikovs conjecture for an explicit construction of the uniformizing map and the uniformizing group for the sphere with four ...

  10. Defects and permutation branes in the Liouville field theory

    Sarkissian, Gor

    2009-01-01

    The defects and permutation branes for the Liouville field theory are considered. By exploiting cluster condition, equations satisfied by permutation branes and defects reflection amplitudes are obtained. It is shown that two types of solutions exist, discrete and continuous families.......The defects and permutation branes for the Liouville field theory are considered. By exploiting cluster condition, equations satisfied by permutation branes and defects reflection amplitudes are obtained. It is shown that two types of solutions exist, discrete and continuous families....

  11. A family of stadium-like billiards with parabolic boundaries under scaling analysis

    Livorati, Andre L P; Loskutov, Alexander; Leonel, Edson D

    2011-01-01

    Some chaotic properties of a family of stadium-like billiards with parabolic focusing components, which is described by a two-dimensional nonlinear area-preserving map, are studied. Critical values of billiard geometric parameters corresponding to a sudden change of the maximal Lyapunov exponent are found. It is shown that the maximal Lyapunov exponent obtained for chaotic orbits of this family is scaling invariant with respect to the control parameters describing the geometry of the billiard. We also show that this behavior is observed for a generic one-parameter family of mapping with the nonlinearity given by a tangent function.

  12. Liouville equation of relativistic charged fermion

    Wang Renchuan; Zhu Dongpei; Huang Zhuoran; Ko Che-ming

    1991-01-01

    As a form of density martrix, the Wigner function is the distribution in quantum phase space. It is a 2 X 2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4 x 4 matrix function. In this paper authors obtain a Wigner function for the relativistic fermion in the form of 2 x 2 matrix, and the Liouville equation satisfied by the Wigner function. this equivalent to the Dirac equation of changed fermion in QED. The equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). Authors prove that the 2 x 2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with above Wigner function

  13. Minimal Liouville gravity correlation numbers from Douglas string equation

    Belavin, Alexander; Dubrovin, Boris; Mukhametzhanov, Baur

    2014-01-01

    We continue the study of (q,p) Minimal Liouville Gravity with the help of Douglas string equation. We generalize the results of http://dx.doi.org/10.1016/0550-3213(91)90548-Chttp://dx.doi.org/10.1088/1751-8113/42/30/304004, where Lee-Yang series (2,2s+1) was studied, to (3,3s+p 0 ) Minimal Liouville Gravity, where p 0 =1,2. We demonstrate that there exist such coordinates τ m,n on the space of the perturbed Minimal Liouville Gravity theories, in which the partition function of the theory is determined by the Douglas string equation. The coordinates τ m,n are related in a non-linear fashion to the natural coupling constants λ m,n of the perturbations of Minimal Lioville Gravity by the physical operators O m,n . We find this relation from the requirement that the correlation numbers in Minimal Liouville Gravity must satisfy the conformal and fusion selection rules. After fixing this relation we compute three- and four-point correlation numbers when they are not zero. The results are in agreement with the direct calculations in Minimal Liouville Gravity available in the literature http://dx.doi.org/10.1103/PhysRevLett.66.2051http://dx.doi.org/10.1007/s11232-005-0003-3http://dx.doi.org/10.1007/s11232-006-0075-8

  14. Inequalities among eigenvalues of Sturm–Liouville problems

    Kong Q

    1999-01-01

    Full Text Available There are well-known inequalities among the eigenvalues of Sturm–Liouville problems with periodic, semi-periodic, Dirichlet and Neumann boundary conditions. In this paper, for an arbitrary coupled self-adjoint boundary condition, we identify two separated boundary conditions corresponding to the Dirichlet and Neumann conditions in the classical case, and establish analogous inequalities. It is also well-known that the lowest periodic eigenvalue is simple; here we prove a similar result for the general case. Moreover, we show that the algebraic and geometric multiplicities of the eigenvalues of self-adjoint regular Sturm–Liouville problems with coupled boundary conditions are the same. An important step in our approach is to obtain a representation of the fundamental solutions for sufficiently negative values of the spectral parameter. Our approach yields the existence and boundedness from below of the eigenvalues of arbitrary self-adjoint regular Sturm–Liouville problems without using operator theory.

  15. Dynamics and constraints of the Dissipative Liouville Cosmology

    Basilakos, Spyros; Mitsou, Vasiliki A; Plionis, Manolis

    2012-01-01

    In this article we investigate the properties of the FLRW flat cosmological models in which the cosmic expansion of the Universe is affected by a dilaton dark energy (Liouville scenario). In particular, we perform a detailed study of these models in the light of the latest cosmological data, which serves to illustrate the phenomenological viability of the new dark energy paradigm as a serious alternative to the traditional scalar field approaches. By performing a joint likelihood analysis of the recent supernovae type Ia data (SNIa), the differential ages of passively evolving galaxies, and the Baryonic Acoustic Oscillations (BAOs) traced by the Sloan Digital Sky Survey (SDSS), we put tight constraints on the main cosmological parameters. Furthermore, we study the linear matter fluctuation field of the above Liouville cosmological models. In this framework, we compare the observed growth rate of clustering measured from the optical galaxies with those predicted by the current Liouville models. Performing vari...

  16. A covariant canonical description of Liouville field theory

    Papadopoulos, G.; Spence, B.

    1993-03-01

    This paper presents a new parametrisation of the space of solutions of Liouville field theory on a cylinder. In this parametrisation, the solutions are well-defined and manifestly real functions over all space-time and all of parameter space. It is shown that the resulting covariant phase space of the Liouville theory is diffeomorphic to the Hamiltonian one, and to the space of initial data of the theory. The Poisson brackets are derived and shown to be those of the co-tangent bundle of the loop group of the real line. Using Hamiltonian reduction, it is shown that this covariant phase space formulation of Liouville theory may also be obtained from the covariant phase space formulation of the Wess-Zumino-Witten model. 19 refs

  17. Control of magnetotransport in quantum billiards theory, computation and applications

    Morfonios, Christian V

    2017-01-01

    In this book the coherent quantum transport of electrons through two-dimensional mesoscopic structures is explored in dependence of the interplay between the confining geometry and the impact of applied magnetic fields, aiming at conductance controllability. After a top-down, insightful presentation of the elements of mesoscopic devices and transport theory, a computational technique which treats multiterminal structures of arbitrary geometry and topology is developed. The method relies on the modular assembly of the electronic propagators of subsystems which are inter- or intra-connected providing large flexibility in system setups combined with high computational efficiency. Conductance control is first demonstrated for elongated quantum billiards and arrays thereof where a weak magnetic field tunes the current by phase modulation of interfering lead-coupled states geometrically separated from confined states. Soft-wall potentials are then employed for efficient and robust conductance switching by isolating...

  18. A boundary integral formalism for stochastic ray tracing in billiards

    Chappell, David J.; Tanner, Gregor

    2014-01-01

    Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics limit of linear wave equations. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty. This paper presents a boundary integral framework for propagating flows including uncertainties, which is shown to systematically interpolate between a deterministic and a completely random description of the trajectory propagation. A simple but efficient discretisation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain

  19. Suppressing Fermi acceleration in two-dimensional driven billiards.

    Leonel, Edson D; Bunimovich, Leonid A

    2010-07-01

    We consider a dissipative oval-like shaped billiard with a periodically moving boundary. The dissipation considered is proportional to a power of the velocity V of the particle. The three specific types of power laws used are: (i) F∝-V ; (ii) F∝-V(2) and (iii) F∝-V(δ) with 1unlimited energy gain for cases (ii) and (iii). The critical exponents obtained for the phase transition in the case (ii) are the same as those obtained for the dissipative bouncer model. Therefore near this phase transition, these two rather different models belong to the same class of universality. For all types of dissipation, the results obtained allow us to conclude that suppression of the unlimited energy growth is indeed observed.

  20. Classical diffusion, Anderson localization, and spectral statistics in billiard chains

    Dittrich, T.; Doron, E.; Smilansky, U.

    1993-03-01

    We study spectral properties of quasi one-dimensional extended systems that show deterministic diffusion on the classical level and Anderson localization in the quantal description. Using semiclassical arguments, we relate to universal aspects of the spectral fluctuations to features of the set of classical periodic orbits, expressed in terms of probability to perform periodic motion, that are likewise universal. This allows to derive an analytical expression for the spectral form factor which reflects the diffusive nature of the corresponding classical dynamics. It defines a novel spectral universality class which covers the transition between GOE statistics in the limit of a small ratio of the system size to the localization length, corresponding to the metallic regime of disordered systems, to Poissonian level fluctuations in the opposite limit. Our semiclassical predictions are illustrated and confirmed by a numerical investigation of aperiodic chains of chaotic billiards. (authors)

  1. H+3 WZNW model from Liouville field theory

    Hikida, Yasuaki; Schomerus, Volker

    2007-01-01

    There exists an intriguing relation between genus zero correlation functions in the H + 3 WZNW model and in Liouville field theory. We provide a path integral derivation of the correspondence and then use our new approach to generalize the relation to surfaces of arbitrary genus g. In particular we determine the correlation functions of N primary fields in the WZNW model explicitly through Liouville correlators with N+2g-2 additional insertions of certain degenerate fields. The paper concludes with a list of interesting further extensions and a few comments on the relation to the geometric Langlands program

  2. Similarities of discrete and continuous Sturm-Liouville problems

    Kazem Ghanbari

    2007-12-01

    Full Text Available In this paper we present a study on the analogous properties of discrete and continuous Sturm-Liouville problems arising in matrix analysis and differential equations, respectively. Green's functions in both cases have analogous expressions in terms of the spectral data. Most of the results associated to inverse problems in both cases are identical. In particular, in both cases Weyl's m-function determines the Sturm-Liouville operators uniquely. Moreover, the well known Rayleigh-Ritz Theorem in linear algebra can be proved by using the concept of Green's function in discrete case.

  3. Liouville theory and uniformization of four-punctured sphere

    Hadasz, Leszek; Jaskólski, Zbigniew

    2006-08-01

    A few years ago Zamolodchikov and Zamolodchikov proposed an expression for the four-point classical Liouville action in terms of the three-point actions and the classical conformal block [Nucl. Phys. B 477, 577 (1996)]. In this paper we develop a method of calculating the uniformizing map and the uniformizing group from the classical Liouville action on n-punctured sphere and discuss the consequences of Zamolodchikovs conjecture for an explicit construction of the uniformizing map and the uniformizing group for the sphere with four punctures.

  4. The local structure of a Liouville vector field

    Ciriza, E.

    1990-05-01

    In this work we investigate the local structure of a Liouville vector field ξ of a Kaehler manifold (P,Ω) which vanishes on an isotropic submanifold Q of P. Some of the eigenvalues of its linear part at the singular points are zero and the remaining ones are in resonance. We show that there is a C 1 -smooth linearizing conjugation between the Liouville vector field ξ and its linear part. To do this we construct Darboux coordinates adapted to the unstable foliation which is provided by the Centre Manifold Theorem. We then apply recent linearization results due to G. Sell. (author). 11 refs

  5. Theory of a higher-order Sturm-Liouville equation

    Kozlov, Vladimir

    1997-01-01

    This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.

  6. The Interaction of Physics, Mechanics and Mathematics in Joseph Liouville's Research

    Lützen, Jesper

    2013-01-01

    Som for mange af hans samtidige var fysik og mekanik en stor inspirationskilde for Liouville's matematiske forskning. Laplaces tilgang til fysik var oprindelsen til Liouvilles teori om differentiation af vilkårlig orden, Kelvins elektrostatiske forskning var oprindelsen til Liouvilles sætning om ...

  7. Quantization of bosonic closed strings and the Liouville model

    Paycha, S.

    1988-01-01

    The author shows that by means of a reasonable interpretation of the Lebesgue measure describing the partition function the quantization of closed bosonic strings described by compact surfaces of genus p>1 can be related to that of the Liouville model. (HSI)

  8. Discontinuous Sturm-Liouville Problems with Eigenvalue Dependent Boundary Condition

    Amirov, R. Kh., E-mail: emirov@cumhuriyet.edu.tr; Ozkan, A. S., E-mail: sozkan@cumhuriyet.edu.tr [Cumhuriyet University, Department of Mathematics Faculty of Art and Science (Turkey)

    2014-12-15

    In this study, an inverse problem for Sturm-Liouville differential operators with discontinuities is studied when an eigenparameter appears not only in the differential equation but it also appears in the boundary condition. Uniqueness theorems of inverse problems according to the Prüfer angle, the Weyl function and two different eigenvalues sets are proved.

  9. The many faces of the quantum Liouville exponentials

    Gervais, Jean-Loup; Schnittger, Jens

    1994-01-01

    First, it is proven that the three main operator approaches to the quantum Liouville exponentials—that is the one of Gervais-Neveu (more recently developed further by Gervais), Braaten-Curtright-Ghandour-Thorn, and Otto-Weigt—are equivalent since they are related by simple basis transformations in the Fock space of the free field depending upon the zero-mode only. Second, the GN-G expressions for quantum Liouville exponentials, where the U q( sl(2)) quantum-group structure is manifest, are shown to be given by q-binomial sums over powers of the chiral fields in the J = {1}/{2} representation. Third, the Liouville exponentials are expressed as operator tau functions, whose chiral expansion exhibits a q Gauss decomposition, which is the direct quantum analogue of the classical solution of Leznov and Saveliev. It involves q exponentials of quantum-group generators with group "parameters" equal to chiral components of the quantum metric. Fourth, we point out that the OPE of the J = {1}/{2} Liouville exponential provides the quantum version of the Hirota bilinear equation.

  10. Selfadjointness of the Liouville operator for infinite classical systems

    Marchioro, C [Camerino Univ. (Italy). Istituto di Matematica; Pellegrinotti, A [Rome Univ. (Italy). Istituto di Matematica; Pulvirenti, M [Ancona Univ. (Italy). Istituto di Matematica

    1978-02-01

    We study some properties of the time evolution of an infinite one dimensional hard core system with singular two body interaction. We show that the Liouville operator is essentially antiselfadjoint an the algebra of local observables. Some consequences of this result are also discussed.

  11. An efficient method for solving fractional Sturm-Liouville problems

    Al-Mdallal, Qasem M.

    2009-01-01

    The numerical approximation of the eigenvalues and the eigenfunctions of the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, is considered. The present results can be implemented on the numerical solution of the fractional diffusion-wave equation. The results show the simplicity and efficiency of the numerical method.

  12. Liouville's theorem and the method of the inverse problem

    Its, A.R.

    1985-01-01

    An approach to the investigation of the Zakharov-Shabat equations is developed. This approach is based on a classical theorem of Liouville and is the synthesis of ''finite-zone'' integration, the matrix Riemann problem method and the theory of isomonodromy deformations of differential equations. The effectiveness of the proposed scheme is demonstrated by developing ''dressing procedures'' for the Bullough-Dodd equation

  13. On the solution of the Liouville equation over a rectangle

    A. M. Arthurs

    1996-01-01

    Full Text Available Methods for integral equations are used to derive pointwise bounds for the solution of a boundary value problem for the nonlinear Liouville partial differential equation over a rectangle. Several test calculations are performed and the resulting solutions are more accurate than those obtained previously by other methods.

  14. Selfadjointness of the Liouville operator for infinite classical systems

    Marchioro, C.; Pellegrinotti, A.; Pulvirenti, M.

    1978-01-01

    We study some properties of the time evolution of an infinite one dimensional hard core system with singular two body interaction. We show that the Liouville operator is essentially antiselfadjoint an the algebra of local observables. Some consequences of this result are also discussed. (orig.) [de

  15. Weyl transforms associated with the Riemann-Liouville operator

    N. B. Hamadi

    2006-01-01

    Full Text Available For the Riemann-Liouville transform ℛα, α∈ℝ+, associated with singular partial differential operators, we define and study the Weyl transforms Wσ connected with ℛα, where σ is a symbol in Sm, m∈ℝ. We give criteria in terms of σ for boundedness and compactness of the transform Wσ.

  16. Liouville equation with boundary conditions derived from classical strings

    Marnelius, R.

    1983-01-01

    It is shown in terms of the classical string theory that a breaking of the Weyl invariance necessarily requires the Liouville equation for the variable phi=1n rho, where rho is the variable that appears in the conformal gauge gsub(α#betta#)=rhoetasub(α#betta#). Appropriate boundary conditions on phi for open and closed strings are then derived. (orig.)

  17. Weyl and Riemann-Liouville multifractional Ornstein-Uhlenbeck processes

    Lim, S C; Teo, L P

    2007-01-01

    This paper considers two new multifractional stochastic processes, namely the Weyl multifractional Ornstein-Uhlenbeck process and the Riemann-Liouville multifractional Ornstein-Uhlenbeck process. Basic properties of these processes such as locally self-similar property and Hausdorff dimension are studied. The relationship between the multifractional Ornstein-Uhlenbeck processes and the corresponding multifractional Brownian motions is established

  18. Heat kernel expansion for fermionic billiards in an external magnetic field

    Antoine, M.; Comtet, A.; Knecht, M.

    1989-05-01

    Using Seeley's heat kernel expansion, we compute the asymptotic density of states of the Dirac operator coupled to a magnetic field on a two dimensional manifold with boundary (fermionic billiard). Local boundary conditions compatible with vector current conservation depend on a free parameter α. It is shown that the perimeter correction identically vanishes for α = 0. In that case, the next order constant term is found to be proportional to the Euler characteristic of the manifold. These results are independent of the external magnetic field and of the shape of the billiard, provided the boundary is sufficiently smooth. For the flat circular billiard, the constant term is found to be - 1/12, in agreement with a numerical result by M.V. BERRY and R.J. MONDRAGON (1987)

  19. Uni-directional transport properties of a serpent billiard

    Horvat, Martin; Prosen, Tomaz

    2004-01-01

    We present a dynamical analysis of a classical billiard chain-a channel with parallel semi-circular walls, which can serve as a model for a bent optical fibre. An interesting feature of this model is the fact that the phase space separates into two disjoint invariant components corresponding to the left and right uni-directional motions. Dynamics is decomposed into the jump map, a Poincare map between the two ends of a basic cell, and the time function, travelling time across a basic cell of a point on a surface of section. The jump map has a mixed phase space where the relative sizes of the regular and chaotic components depend on the width of the channel. For a suitable value of this parameter, we can have almost fully chaotic phase space. We have studied numerically the Lyapunov exponents, time auto-correlation functions and diffusion of particles along the chain. As a result of the singularity of the time function, we obtain marginally normal diffusion after we subtract the average drift. The last result is also supported by some analytical arguments

  20. BILLIARDS: Baseline Instrumented Lithology Lander, Inspector and Asteroid Redirection Demonstration System

    Marcus, Matthew; Sloane, Joshua; Ortiz, Oliver; Barbee, Brent

    2015-01-01

    BILLIARDS Baseline Instrumented Lithology Lander, Inspector, and Asteroid Redirection Demonstration System Proposed demonstration mission for Billiard-Ball concept Select asteroid pair with natural close approach to minimize cost and complexity Primary Objectives Rendezvous with a small (10m), near Earth (alpha) asteroid Maneuver the alpha asteroid to a collision with a 100m (beta) asteroid Produce a detectable deflection or disruption of the beta asteroid Secondary objectives Contribute knowledge of asteroid composition and characteristics Contribute knowledge of small-body formation Opportunity for international collaboration

  1. H+3 WZNW model from Liouville field theory

    Hikida, Y.; Schomerus, V.

    2007-06-01

    There exists an intriguing relation between genus zero correlation functions in the H + 3 WZNW model and in Liouville field theory. This was found by Ribault and Teschner based in part on earlier ideas by Stoyanovsky. We provide a path integral derivation of the correspondence and then use our new approach to generalize the relation to surfaces of arbitrary genus g. In particular we determine the correlation functions of N primary fields in the WZNW model explicitly through Liouville correlators with N+2g-2 additional insertions of certain degenerate fields. The paper concludes with a list of interesting further extensions and a few comments on the relation to the geometric Langlands program. (orig.)

  2. Covariant currents in N=2 super-Liouville theory

    Gomis, J.; Suzuki, Hiroshi

    1993-01-01

    Based on a path-integral prescription for anomaly calculation, we analyze an effective theory of the two-dimensional N=2 supergravity, i.e. N=2 super-Liouville theory. We calculate the anomalies associated with the BRST supercurrent and the ghost-number supercurrent. From those expressions of anomalies, we construct covariant BRST and ghost-number supercurrents in the effective theory. We then show that the (super-)coordinate BRST current algebra forms a superfield extension of the topological conformal algebra for an arbitrary type of conformal matter or, in terms of the string theory, for an arbitrary number of space-time dimensions. This fact is in great contrast with N=0 and N=1 (super-)Liouville theory, where the topological algebra singles out a particular value of dimensions. Our observation suggests a topological nature of the two-dimensional N=2 supergravity as a quantum theory. (orig.)

  3. Extended Riemann-Liouville type fractional derivative operator with applications

    Agarwal P.

    2017-12-01

    Full Text Available The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.

  4. A hierarchy of Liouville integrable discrete Hamiltonian equations

    Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn

    2008-05-12

    Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.

  5. Adomian decomposition method for nonlinear Sturm-Liouville problems

    Sennur Somali

    2007-09-01

    Full Text Available In this paper the Adomian decomposition method is applied to the nonlinear Sturm-Liouville problem-y" + y(tp=λy(t, y(t > 0, t ∈ I = (0, 1, y(0 = y(1 = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.

  6. An inverse Sturm–Liouville problem with a fractional derivative

    Jin, Bangti

    2012-05-01

    In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical reconstructions of the potential with a Newton method from finite spectral data are presented. Surprisingly, it allows very satisfactory reconstructions for both smooth and discontinuous potentials, provided that the order . α∈. (1,. 2) of fractional derivative is sufficiently away from 2. © 2012 Elsevier Inc.

  7. Exploiting broad-area surface emitting lasers to manifest the path-length distributions of finite-potential quantum billiards.

    Yu, Y T; Tuan, P H; Chang, K C; Hsieh, Y H; Huang, K F; Chen, Y F

    2016-01-11

    Broad-area vertical-cavity surface-emitting lasers (VCSELs) with different cavity sizes are experimentally exploited to manifest the influence of the finite confinement strength on the path-length distribution of quantum billiards. The subthreshold emission spectra of VCSELs are measured to obtain the path-length distributions by using the Fourier transform. It is verified that the number of the resonant peaks in the path-length distribution decreases with decreasing the confinement strength. Theoretical analyses for finite-potential quantum billiards are numerically performed to confirm that the mesoscopic phenomena of quantum billiards with finite confinement strength can be analogously revealed by using broad-area VCSELs.

  8. Characteristics of level-spacing statistics in chaotic graphene billiards.

    Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso

    2011-03-01

    A fundamental result in nonrelativistic quantum nonlinear dynamics is that the spectral statistics of quantum systems that possess no geometric symmetry, but whose classical dynamics are chaotic, are described by those of the Gaussian orthogonal ensemble (GOE) or the Gaussian unitary ensemble (GUE), in the presence or absence of time-reversal symmetry, respectively. For massless spin-half particles such as neutrinos in relativistic quantum mechanics in a chaotic billiard, the seminal work of Berry and Mondragon established the GUE nature of the level-spacing statistics, due to the combination of the chirality of Dirac particles and the confinement, which breaks the time-reversal symmetry. A question is whether the GOE or the GUE statistics can be observed in experimentally accessible, relativistic quantum systems. We demonstrate, using graphene confinements in which the quasiparticle motions are governed by the Dirac equation in the low-energy regime, that the level-spacing statistics are persistently those of GOE random matrices. We present extensive numerical evidence obtained from the tight-binding approach and a physical explanation for the GOE statistics. We also find that the presence of a weak magnetic field switches the statistics to those of GUE. For a strong magnetic field, Landau levels become influential, causing the level-spacing distribution to deviate markedly from the random-matrix predictions. Issues addressed also include the effects of a number of realistic factors on level-spacing statistics such as next nearest-neighbor interactions, different lattice orientations, enhanced hopping energy for atoms on the boundary, and staggered potential due to graphene-substrate interactions.

  9. Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism

    Costa, Diogo Ricardo da; Dettmann, Carl P.; Oliveira, Juliano A. de; Leonel, Edson D.

    2015-01-01

    Some dynamical properties for an oval billiard with a scatterer in its interior are studied. The dynamics consists of a classical particle colliding between an inner circle and an external boundary given by an oval, elliptical, or circle shapes, exploring for the first time some natural generalizations. The billiard is indeed a generalization of the annular billiard, which is of strong interest for understanding marginally unstable periodic orbits and their role in the boundary between regular and chaotic regions in both classical and quantum (including experimental) systems. For the oval billiard, which has a mixed phase space, the presence of an obstacle is an interesting addition. We demonstrate, with details, how to obtain the equations of the mapping, and the changes in the phase space are discussed. We study the linear stability of some fixed points and show both analytically and numerically the occurrence of direct and inverse parabolic bifurcations. Lyapunov exponents and generalized bifurcation diagrams are obtained. Moreover, histograms of the number of successive iterations for orbits that stay in a cusp are studied. These histograms are shown to be scaling invariant when changing the radius of the scatterer, and they have a power law slope around −3. The results here can be generalized to other kinds of external boundaries

  10. Statistics of resonances for a class of billiards on the Poincare half-plane

    Howard, P J; Mota-Furtado, F; O'Mahony, P F; Uski, V

    2005-01-01

    The lower boundary of Artin's billiard on the Poincare half-plane is continuously deformed to generate a class of billiards with classical dynamics varying from fully integrable to completely chaotic. The quantum scattering problem in these open billiards is described and the statistics of both real and imaginary parts of the resonant momenta are investigated. The evolution of the resonance positions is followed as the boundary is varied which leads to large changes in their distribution. The transition to arithmetic chaos in Artin's billiard, which is responsible for the Poissonian level-spacing statistics of the bound states in the continuum (cusp forms) at the same time as the formation of a set of resonances all with width 1/4 and real parts determined by the zeros of Riemann's zeta function, is closely examined. Regimes are found which obey the universal predictions of random matrix theory (RMT) as well as exhibiting non-universal long-range correlations. The Brody parameter is used to describe the transitions between different regimes

  11. Shaping old age: Innovation partnerships, senior centres and billiards tables as active ageing technologies

    Lassen, Aske Juul

    2017-01-01

    During the past decade active ageing has been positioned as a solution to the problem of global ageing. While the scientific, economic and even moral arguments for pursuing a more active old age has been many, the integration of active ageing in everyday practices face challenges. This chapter ex...

  12. Stochastic transition of free motion in billiards with borders given by equipotential lines of the diamagnetic Kepler problem

    Abul-Magd, A.Y.; Mueller, K.

    1992-01-01

    We compare the transition from ordered to chaotic motion in a potential with that in a billiard, whose borders are defined by the maximal equipotential line of the potential system in the case of hydrogen in a uniform magnetic field. For the billiard we calculate the Poincare maps, the fraction of regular motion on the surface of section, and the stability properties of the shortest periodic orbits. In contrast to the H atom, the billiard shows a generic transition to chaos. While the shape of the orbits is determined by the boundary and is thus very similar, their properties of stability are different: The potential tends to stabilize the motion. The onset of instability in the billiard can be understood in terms of the curvature of the boundary; for the potential system the Gaussian curvature of the potential-energy surface is shown to be the relevant parameter

  13. Schramm-Loewner evolution and Liouville quantum gravity.

    Duplantier, Bertrand; Sheffield, Scott

    2011-09-23

    We show that when two boundary arcs of a Liouville quantum gravity random surface are conformally welded to each other (in a boundary length-preserving way) the resulting interface is a random curve called the Schramm-Loewner evolution. We also develop a theory of quantum fractal measures (consistent with the Knizhnik-Polyakov-Zamolochikov relation) and analyze their evolution under conformal welding maps related to Schramm-Loewner evolution. As an application, we construct quantum length and boundary intersection measures on the Schramm-Loewner evolution curve itself.

  14. Time-reversal symmetry breaking in quantum billiards

    Schaefer, Florian

    2009-01-26

    The present doctoral thesis describes experimentally measured properties of the resonance spectra of flat microwave billiards with partially broken timereversal invariance induced by an embedded magnetized ferrite. A vector network analyzer determines the complex scattering matrix elements. The data is interpreted in terms of the scattering formalism developed in nuclear physics. At low excitation frequencies the scattering matrix displays isolated resonances. At these the effect of the ferrite on isolated resonances (singlets) and pairs of nearly degenerate resonances (doublets) is investigated. The hallmark of time-reversal symmetry breaking is the violation of reciprocity, i.e. of the symmetry of the scattering matrix. One finds that reciprocity holds in singlets; it is violated in doublets. This is modeled by an effective Hamiltonian of the resonator. A comparison of the model to the data yields time-reversal symmetry breaking matrix elements in the order of the level spacing. Their dependence on the magnetization of the ferrite is understood in terms of its magnetic properties. At higher excitation frequencies the resonances overlap and the scattering matrix elements fluctuate irregularly (Ericson fluctuations). They are analyzed in terms of correlation functions. The data are compared to three models based on random matrix theory. The model by Verbaarschot, Weidenmueller and Zirnbauer describes time-reversal invariant scattering processes. The one by Fyodorov, Savin and Sommers achieves the same for systems with complete time-reversal symmetry breaking. An extended model has been developed that accounts for partial breaking of time-reversal invariance. This extended model is in general agreement with the data, while the applicability of the other two models is limited. The cross-correlation function between forward and backward reactions determines the time-reversal symmetry breaking matrix elements of the Hamiltonian to up to 0.3 mean level spacings. Finally

  15. Time-reversal symmetry breaking in quantum billiards

    Schaefer, Florian

    2009-01-01

    The present doctoral thesis describes experimentally measured properties of the resonance spectra of flat microwave billiards with partially broken timereversal invariance induced by an embedded magnetized ferrite. A vector network analyzer determines the complex scattering matrix elements. The data is interpreted in terms of the scattering formalism developed in nuclear physics. At low excitation frequencies the scattering matrix displays isolated resonances. At these the effect of the ferrite on isolated resonances (singlets) and pairs of nearly degenerate resonances (doublets) is investigated. The hallmark of time-reversal symmetry breaking is the violation of reciprocity, i.e. of the symmetry of the scattering matrix. One finds that reciprocity holds in singlets; it is violated in doublets. This is modeled by an effective Hamiltonian of the resonator. A comparison of the model to the data yields time-reversal symmetry breaking matrix elements in the order of the level spacing. Their dependence on the magnetization of the ferrite is understood in terms of its magnetic properties. At higher excitation frequencies the resonances overlap and the scattering matrix elements fluctuate irregularly (Ericson fluctuations). They are analyzed in terms of correlation functions. The data are compared to three models based on random matrix theory. The model by Verbaarschot, Weidenmueller and Zirnbauer describes time-reversal invariant scattering processes. The one by Fyodorov, Savin and Sommers achieves the same for systems with complete time-reversal symmetry breaking. An extended model has been developed that accounts for partial breaking of time-reversal invariance. This extended model is in general agreement with the data, while the applicability of the other two models is limited. The cross-correlation function between forward and backward reactions determines the time-reversal symmetry breaking matrix elements of the Hamiltonian to up to 0.3 mean level spacings. Finally

  16. Integrability of Liouville system on high genus Riemann surface: Pt. 1

    Chen Yixin; Gao Hongbo

    1992-01-01

    By using the theory of uniformization of Riemann-surfaces, we study properties of the Liouville equation and its general solution on a Riemann surface of genus g>1. After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices, we prove the classical integrability of Liouville system on high genus Riemann surface

  17. Classical and quantum Liouville theory on the Riemann sphere with n>3 punctures (III)

    Shen Jianmin; Sheng Zhengmao; Wang Zhonghua

    1992-02-01

    We study the Classical and Quantum Liouville theory on the Riemann sphere with n>3 punctures. We get the quantum exchange algebra relations between the chiral components in the Liouville theory from our assumption on the principle of quantization. (author). 5 refs

  18. Liouville and Painleve equations and Yang--Mills strings

    Saclioglu, C.K.

    1984-01-01

    Stringlike solutions of the self-dual Yang--Mills equations (dimensionally reduced to R 2 ) are sought. A multistring Ansatz results in the sinh--Gordon and Liouville equations. According to a general theorem, the solutions must be either real and singular and have infinite action, or complex and nonsingular, with zero action. In the Liouville case, explicit arbitrarily separated n-string solutions of both classes are given. The magnetic flux for these solutions is found to be the Chern class of a Kaehler manifold, and it consequently assumes quantized values 4πn/e. The axisymmetric version of the sinh--Gordon is solved by the third Painleve transcendent P 3 , using the results on P 3 by Wu et al. [Phys. Rev. B 13, 316 (1976)] and McCoy et al. [J. Math. Phys. 18, 10 (1977)]. The axisymmetric case can be cast into the Ernst equation framework for the generation of further solutions. In the Appendix, the Euclideanized Ernst equation is shown to give self-dual Gibbons--Hawking gravitational instantons

  19. WKB analysis of PT-symmetric Sturm–Liouville problems

    Bender, Carl M; Jones, Hugh F

    2012-01-01

    Most studies of PT-symmetric quantum-mechanical Hamiltonians have considered the Schrödinger eigenvalue problem on an infinite domain. This paper examines the consequences of imposing the boundary conditions on a finite domain. As is the case with regular Hermitian Sturm–Liouville problems, the eigenvalues of the PT-symmetric Sturm–Liouville problem grow like n 2 for large n. However, the novelty is that a PT eigenvalue problem on a finite domain typically exhibits a sequence of critical points at which pairs of eigenvalues cease to be real and become complex conjugates of one another. For the potentials considered here this sequence of critical points is associated with a turning point on the imaginary axis in the complex plane. WKB analysis is used to calculate the asymptotic behaviours of the real eigenvalues and the locations of the critical points. The method turns out to be surprisingly accurate even at low energies. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)

  20. Correlation functions in unitary minimal Liouville gravity and Frobenius manifolds

    Belavin, V. [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute,Leninsky prospect 53, 119991 Moscow (Russian Federation); Department of Quantum Physics, Institute for Information Transmission Problems,Bolshoy Karetny per. 19, 127994 Moscow (Russian Federation); Department of Theoretical Physics, National Research Nuclear University MEPhI,Kashirskoe shosse 31, 115409 Moscow (Russian Federation)

    2015-02-10

    We continue to study minimal Liouville gravity (MLG) using a dual approach based on the idea that the MLG partition function is related to the tau function of the A{sub q} integrable hierarchy via the resonance transformations, which are in turn fixed by conformal selection rules. One of the main problems in this approach is to choose the solution of the Douglas string equation that is relevant for MLG. The appropriate solution was recently found using connection with the Frobenius manifolds. We use this solution to investigate three- and four-point correlators in the unitary MLG models. We find an agreement with the results of the original approach in the region of the parameters where both methods are applicable. In addition, we find that only part of the selection rules can be satisfied using the resonance transformations. The physical meaning of the nonzero correlators, which before coupling to Liouville gravity are forbidden by the selection rules, and also the modification of the dual formulation that takes this effect into account remains to be found.

  1. Quantum and classical properties of some billiards on the hyperbolic plane

    Schmit, C.

    1991-01-01

    Some 'experimental' results are given on the quantal spectrum of some billiards on two-dimensional manifolds of constant negative curvature. It is shown that the use of the Selberg trace formula may bring some interesting new results on the properties of the classical motion. Some new (and quite unexpected) results are presented about the quantal spectrum of the octagon on the hyperbolic plane. (K.A.) 8 refs.; 17 figs.; 2 tabs

  2. Influence of stability islands in the recurrence of particles in a static oval billiard with holes

    Hansen, Matheus, E-mail: mathehansen@gmail.com [Instituto de Física da Universidade de São Paulo, Rua do Matão, Travessa R 187, Cidade Universitária, 05314-970 São Paulo, SP (Brazil); Egydio de Carvalho, R., E-mail: regydio@rc.unesp.br [Universidade Estadual Paulista – UNESP, Rio Claro, SP (Brazil); Leonel, Edson D., E-mail: edleonel@rc.unesp.br [Departamento de Física, UNESP – Univ Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900, Rio Claro, SP (Brazil); Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy)

    2016-10-23

    Statistical properties for the recurrence of particles in an oval billiard with a hole in the boundary are discussed. The hole is allowed to move in the boundary under two different types of motion: (i) counterclockwise periodic circulation with a fixed step length and; (ii) random movement around the boundary. After injecting an ensemble of particles through the hole we show that the surviving probability of the particles without recurring – without escaping – from the billiard is described by an exponential law and that the slope of the decay is proportional to the relative size of the hole. Since the phase space of the system exhibits islands of stability we show there are preferred regions of escaping in the polar angle, hence given a partial answer to an open problem: Where to place a hole in order to maximize or minimize a suitable defined measure of escaping. - Highlights: • Statistical properties in an oval billiard is studied. • Where to place a hole in order to maximize or minimize the escape. • We found a partial answer to an open problem of escape of particles.

  3. M-theory and E10: Billiards, Branes, and Imaginary Roots

    Brown, Jeffrey; Ganor, Ori J.; Helfgott, Craig

    2004-01-09

    Eleven dimensional supergravity compactified on $T^10$ admits classical solutions describing what is known as billiard cosmology - a dynamics expressible as an abstract (billiard) ball moving in the 10-dimensional root space of the infinite dimensional Lie algebra E10, occasionally bouncing off walls in that space. Unlike finite dimensional Lie algebras, E10 has negative and zero norm roots, in addition to the positive norm roots. The walls above are related to physical fluxes that, in turn, are related to positive norm roots (called real roots) of E10. We propose that zero and negative norm roots, called imaginary roots, are related to physical branes. Adding 'matter' to the billiard cosmology corresponds to adding potential terms associated to imaginary roots. The, as yet, mysterious relation between E10 and M-theory on $T^10$ can now be expanded as follows: real roots correspond to fluxes or instantons, and imaginary roots correspond to particles and branes (in the cases we checked). Interactions between fluxes and branes and between branes and branes are classified according to the inner product of the corresponding roots (again in the cases we checked). We conclude with a discussion of an effective Hamiltonian description that captures some features of M-theory on $T^10.$

  4. The Sturm-Liouville spectrum problem: quartic oscillator case

    Voros, Andre.

    1982-11-01

    The Sturm-Liouville eigenvalue problem given by the steady-state Schroedinger equation in quantum mechanics is considered on the real axis. There are, however, exact expressions available only for a harmonic oscillator (the Hermite equation); consequently, semi-classical asymptotic methods (in powers of the Planck's constant), which yield very good approximations, have been much studied analytically and as regards their relationships to geometrical optics. These methods relate the asymptotic form of the spectrum to the closed orbits of the Hamiltonian vector field of the function H(p,q) = p 2 + V(q) in the phase space R 2 . We seek to show that these supposedly approximate methods are in fact an exact way of solving the problem. The quartic oscillator, with V(q) = q 4 , is used as an example [fr

  5. Isomonodromic tau-functions from Liouville conformal blocks

    Iorgov, N.; Lisovyy, O.

    2014-01-01

    The goal of this note is to show that the Riemann-Hilbert problem to find multivalued analytic functions with SL(2,C)-valued monodromy on Riemann surfaces of genus zero with n punctures can be solved by taking suitable linear combinations of the conformal blocks of Liouville theory at c=1. This implies a similar representation for the isomonodromic tau-function. In the case n=4 we thereby get a proof of the relation between tau-functions and conformal blocks discovered in O. Gamayun, N. Iorgov, and O. Lisovyy (2012). We briefly discuss a possible application of our results to the study of relations between certain N=2 supersymmetric gauge theories and conformal field theory.

  6. A quantum group approach to cL > 1 Liouville gravity

    Suzuki, Takashi.

    1995-03-01

    A candidate of c L > 1 Liouville gravity is studied via infinite dimensional representations of U q sl(2, C) with q at a root of unity. We show that vertex operators in this Liouville theory are factorized into classical vertex operators and those which are constructed from finite dimensional representations of U q sl(2, C). Expressions of correlation functions and transition amplitudes are presented. We discuss about our results and find an intimate relation between our quantization of the Liouville theory and the geometric quantization of moduli space of Riemann surfaces. An interpretation of quantum space-time is also given within this formulation. (author)

  7. Spectral theory of Sturm-Liouville differential operators: proceedings of the 1984 workshop

    Kaper, H.G.; Zettl, A. (eds.)

    1984-12-01

    This report contains the proceedings of the workshop which was held at Argonne during the period May 14 through June 15, 1984. The report contains 22 articles, authored or co-authored by the participants in the workshop. Topics covered at the workshop included the asymptotics of eigenvalues and eigenfunctions; qualitative and quantitative aspects of Sturm-Liouville eigenvalue problems with discrete and continuous spectra; polar, indefinite, and nonselfadjoint Sturm-Liouville eigenvalue problems; and systems of differential equations of Sturm-Liouville type.

  8. Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems

    Johnny Henderson

    2016-01-01

    Full Text Available We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.

  9. Hardy inequality and properties of the quasilinear Sturm-Liouville problem

    Drábek, P.; Kufner, Alois

    2007-01-01

    Roč. 18, č. 1 (2007), s. 125-138 ISSN 1120-6330 Institutional research plan: CEZ:AV0Z10190503 Keywords : Hardy inequality * weighted spaces * Sturm-Liouville problem Subject RIV: BA - General Mathematics

  10. Minimal Liouville gravity on the torus via the Douglas string equation

    Spodyneiko, Lev

    2015-01-01

    In this paper we assume that the partition function in minimal Liouville gravity (MLG) obeys the Douglas string equation. This conjecture makes it possible to compute the torus correlation numbers in (3,p) MLG. We perform this calculation using also the resonance relations between the coupling constants in the KdV frame and in the Liouville frame. We obtain explicit expressions for the torus partition function and for the one- and two-point correlation numbers. (paper)

  11. Essay on Fractional Riemann-Liouville Integral Operator versus Mikusinski’s

    Ming Li

    2013-01-01

    Full Text Available This paper presents the representation of the fractional Riemann-Liouville integral by using the Mikusinski operators. The Mikusinski operators discussed in the paper may yet provide a new view to describe and study the fractional Riemann-Liouville integral operator. The present result may be useful for applying the Mikusinski operational calculus to the study of fractional calculus in mathematics and to the theory of filters of fractional order in engineering.

  12. Fractal analysis on a classical hard-wall billiard with openings using a two-dimensional set of initial conditions

    Ree, Suhan

    2003-01-01

    Fractal analysis is performed to measure the chaoticity of a classical hard-wall billiard with openings. We use the circular billiard with a straight cut with two openings, and a two-dimensional (2D) set of initial conditions that produce all possible trajectories of a particle injected from one opening. We numerically compute the fractal dimension of singular points of the function that maps an initial condition to the number of collisions with the wall before the exit, using the box-counting algorithm that uses uniformly distributed points inside the 2D set of initial conditions. Finally, the classical chaotic properties are observed while the parameters of the billiard are varied, and the results are compared with those with the one-dimensional set of initial conditions

  13. The hyperbola billiard: A model for the semiclassical quantization of chaotic systems

    Sieber, M.

    1991-04-01

    Classical and quantum mechanical properties of a chaotic billiard system are studied with special emphasis on a detailed numerical investigation of the periodic-orbit theory of Gutzwiller. This theory gives semiclassical approximations to the quantum mechanical energies of a classically chaotic system by means of a sum over all periodic orbits of the system. Parts of the derivation of the periodic-orbit theory are reviewed. The convergence properties of the periodic-orbit sum are discussed and smoothing techniques are introduced, which allow the determination of the energies by absolutely convergent sums. A code is introduced for the periodic orbits of the hyperbola billiard, a chaotic system which is bounded by the x-axis, the y-axis and the hyperbola y=1/x. An extremum principle for the periodic orbits is proved, which allows a very fast and accurate determination of the periodic orbits. The distributions of lengths and Lyapunov exponents of the orbits are studied. The quantum mechanical energies of the hyperbola billiard are determined by a boundary element method. A correction to the asymptotic approximation for the spectral staircase N(E), which counts the number of energy eigenvalues of the Schroedinger equation below a given energy E, is determined numerically. The properties of the periodic-orbit theory are investigated by an evaluation of the unsmoothed Gutzwiller trace formula and various versions of smoothed trace formulae. The advantage of different smoothing methods are discussed and compared. The effect of the semiclassical approximation is demonstrated by a smoothing, which leads to a truncation of the periodic-orbit sum. An alternative approximation for the energies in terms of a dynamical zeta function is investigated and shown to yield comparable results as the previous trace formulae. An approximation to this zeta function in analogy to the Riemann-Siegel formula for the Riemann zeta function is studied. (orig./HSI)

  14. Classical and quantum chaos in a circular billiard with a straight cut

    Ree, S.; Reichl, L.E.

    1999-01-01

    We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. Classically, this system can be integrable, nonintegrable with soft chaos, or nonintegrable with hard chaos as we vary the size of the cut. We plot Poincaracute e surfaces of section to study chaos. Quantum mechanically, we look at Husimi plots, and also use the quantum web, the technique primarily used in spin systems so far, to try to see differences in quantum manifestations of soft and hard chaos. copyright 1999 The American Physical Society

  15. On the decay of correlations in Sinai billiards with infinite horizon

    Dahlqvist, Per; Artuso, Roberto

    1996-02-01

    We compute the decay of the autocorrelation function of the observable | vx| in the Sinai billiard and of the observable vx in the associated Lorentz gas with an approximation due to Baladi, Eckmann and Ruelle. We consider the standard configuration where the disk is centered inside a unit square. The asymptotic decay is found to be C( t) ∼ c( R)/ t. An explicit expression is given for the prefactor c( R) as a function of the radius of the scatterer. For the small scatterer case we also present expressions for the preasymptotic regime. Our findings are supported by numerical computations.

  16. BILLIARDS: A Demonstration Mission for Hundred-Meter Class Near Earth Asteroid Disruption

    Marcus, Matthew; Sloane, Joshua; Ortiz, Oliver; Barbee, Brent W.

    2015-01-01

    Currently, no planetary defense demonstration mission has ever been flown. While Nuclear Explosive Devices (NEDs) have significantly more energy than a kinetic impactor launched directly from Earth, they present safety and political complications, and therefore may only be used when absolutely necessary. The Baseline Instrumented Lithology Lander, Inspector, and Asteroid Redirection Demonstration System (BILLIARDS) is a demonstration mission for planetary defense, which is capable of delivering comparable energy to the lower range of NED capabilities in the form of a safer kinetic impactor. A small asteroid (disrupt the larger asteroid. To reduce the cost and complexity, an asteroid pair which has a natural close approach is selected.

  17. Coupling-Induced Bipartite Pointer States in Arrays of Electron Billiards: Quantum Darwinism in Action?

    Brunner, R.; Akis, R.; Ferry, D. K.; Kuchar, F.; Meisels, R.

    2008-07-01

    We discuss a quantum system coupled to the environment, composed of an open array of billiards (dots) in series. Beside pointer states occurring in individual dots, we observe sets of robust states which arise only in the array. We define these new states as bipartite pointer states, since they cannot be described in terms of simple linear combinations of robust single-dot states. The classical existence of bipartite pointer states is confirmed by comparing the quantum-mechanical and classical results. The ability of the robust states to create “offspring” indicates that quantum Darwinism is in action.

  18. Biilliards, rhythms, collectives - Billiards at a Danish activity center as a culturally specific form of active ageing

    Lassen, Aske Juul

    2014-01-01

    Through an ethnographic study of older men playing billiards at an activity centre and a document study of how the concept of activity has changed during the last 60 years, this article argues that active ageing policies overlook that activities are culturally significant forms of practise situated...

  19. Deformed type 0A matrix model and super-Liouville theory for fermionic black holes

    Ahn, Changrim; Kim, Chanju; Park, Jaemo; Suyama, Takao; Yamamoto, Masayoshi

    2006-01-01

    We consider a c-circumflex = 1 model in the fermionic black hole background. For this purpose we consider a model which contains both the N 1 and the N = 2 super-Liouville interactions. We propose that this model is dual to a recently proposed type 0A matrix quantum mechanics model with vortex deformations. We support our conjecture by showing that non-perturbative corrections to the free energy computed by both the matrix model and the super-Liouville theories agree exactly by treating the N = 2 interaction as a small perturbation. We also show that a two-point function on sphere calculated from the deformed type 0A matrix model is consistent with that of the N = 2 super-Liouville theory when the N = 1 interaction becomes small. This duality between the matrix model and super-Liouville theories leads to a conjecture for arbitrary n-point correlation functions of the N = 1 super-Liouville theory on the sphere

  20. Visualising Berry phase and diabolical points in a quantum exciton-polariton billiard.

    Estrecho, E; Gao, T; Brodbeck, S; Kamp, M; Schneider, C; Höfling, S; Truscott, A G; Ostrovskaya, E A

    2016-11-25

    Diabolical points (spectral degeneracies) can naturally occur in spectra of two-dimensional quantum systems and classical wave resonators due to simple symmetries. Geometric Berry phase is associated with these spectral degeneracies. Here, we demonstrate a diabolical point and the corresponding Berry phase in the spectrum of hybrid light-matter quasiparticles-exciton-polaritons in semiconductor microcavities. It is well known that sufficiently strong optical pumping can drive exciton-polaritons to quantum degeneracy, whereby they form a macroscopically populated quantum coherent state similar to a Bose-Einstein condensate. By pumping a microcavity with a spatially structured light beam, we create a two-dimensional quantum billiard for the exciton-polariton condensate and demonstrate a diabolical point in the spectrum of the billiard eigenstates. The fully reconfigurable geometry of the potential walls controlled by the optical pump enables a striking experimental visualization of the Berry phase associated with the diabolical point. The Berry phase is observed and measured by direct imaging of the macroscopic exciton-polariton probability densities.

  1. Quantum mechanical analysis of the equilateral triangle billiard: Periodic orbit theory and wave packet revivals

    Doncheski, M.A.; Robinett, R.W.

    2002-01-01

    Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semi-classical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by T rev =9μa 2 /4(h/2π) where a and μ are the length of one side and the mass of the point particle, respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral (60 deg. -60 deg. -60 deg. ) triangle, such as the half equilateral (30 deg. -60 deg. -90 deg.) triangle and other 'foldings', which have related energy spectra and revival structures

  2. Nonadiabatic dynamics in the semiclassical Liouville representation: Locality, transformation theory, and the energy budget

    Martens, Craig C., E-mail: cmartens@uci.edu

    2016-12-20

    In this paper, we revisit the semiclassical Liouville approach to describing molecular dynamics with electronic transitions using classical trajectories. Key features of the formalism are highlighted. The locality in phase space and presence of nonclassical terms in the generalized Liouville equations are emphasized and discussed in light of trajectory surface hopping methodology. The representation dependence of the coupled semiclassical Liouville equations in the diabatic and adiabatic bases are discussed and new results for the transformation theory of the Wigner functions representing the corresponding density matrix elements given. We show that the diagonal energies of the state populations are not conserved during electronic transitions, as energy is stored in the electronic coherence. We discuss the implications of this observation for the validity of imposing strict energy conservation in trajectory based methods for simulating nonadiabatic processes.

  3. A quantum group approach to c{sub L} > 1 Liouville gravity

    Suzuki, Takashi

    1995-03-01

    A candidate of c{sub L} > 1 Liouville gravity is studied via infinite dimensional representations of U{sub q}sl(2, C) with q at a root of unity. We show that vertex operators in this Liouville theory are factorized into classical vertex operators and those which are constructed from finite dimensional representations of U{sub q}sl(2, C). Expressions of correlation functions and transition amplitudes are presented. We discuss about our results and find an intimate relation between our quantization of the Liouville theory and the geometric quantization of moduli space of Riemann surfaces. An interpretation of quantum space-time is also given within this formulation. (author).

  4. Bargmann Symmetry Constraint for a Family of Liouville Integrable Differential-Difference Equations

    Xu Xixiang

    2012-01-01

    A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system. (general)

  5. BILLIARDS: A Demonstration Mission for Hundred-Meter Class Near-Earth Asteroid Disruption

    Marcus, Matthew; Sloane, Joshua; Ortiz, Oliver; Barbee, Brent William

    2015-01-01

    Collisions from near-Earth asteroids (NEAs) have the potential to cause widespread harm to life on Earth. The hypervelocity nature of these collisions means that a relatively small asteroid (about a quartermile in diameter) could cause a global disaster. Proposed strategies for deflecting or disrupting such a threatening asteroid include detonation of a nuclear explosive device (NED) in close proximity to the asteroid, as well as intercepting the asteroid with a hypervelocity kinetic impactor. NEDs allow for the delivery of large amounts of energy to a NEA for a given mass launched from the Earth, but have not yet been developed or tested for use in deep space. They also present safety and political complications, and therefore may only be used when absolutely necessary. Kinetic impactors require a relatively simple spacecraft compared to NEDs, but also deliver a much lower energy for a given launch mass. To date, no demonstration mission has been conducted for either case, and such a demonstration mission must be conducted prior to the need to utilize them during an actual scenario to ensure that an established, proven system is available for planetary defense when the need arises. One method that has been proposed to deliver a kinetic impactor with impact energy approaching that of an NED is the "billiard-ball" approach. This approach would involve capturing an asteroid approximately ten meters in diameter with a relatively small spacecraft (compared to the launch mass of an equivalent direct kinetic impactor), and redirecting it into the path of an Earth-threatening asteroid. This would cause an impact which would disrupt the Earth-threatening asteroid or deflect it from its Earth-crossing trajectory. The BILLIARDS Project seeks to perform a demonstration of this mission concept in order to establish a protocol that can be used in the event of an impending Earth/asteroid collision. In order to accomplish this objective, the mission must (1) rendezvous with a

  6. Liouville's equation and radiative acceleration in general relativity

    Keane, A.J.

    1999-01-01

    This thesis examines thoroughly the general motion of a material charged particle in the intense radiation field of a static spherically symmetric compact object with spherical emitting surface outside the Schwarzschild radius. Such a test particle will be pulled in by the gravitational attraction of the compact object and pushed out by the radiation pressure force, therefore the types of trajectory admitted will depend the gravitational field, the radiation field and the particle cross-section. The presence of a strong gravitational field demands a fully general relativistic treatment of the problem. This type of calculation is interesting not only as a formal problem in general relativity but also since it has important astrophysical implications, for example, application to astrophysical discs and jets. In chapter 1 we review the classical radiation force problem and outline the transition to a fully general relativistic scenario. We discuss the method for obtaining the radiation pressure force and calculating the particle trajectories. We review previous work in this area and outline the aims of the thesis. Then we consider some astrophysical applications and discuss how realistic our calculations are. In chapter 2 we give an introduction and overview of differential geometry as this is necessary for an accurate description of tensors on a curved manifold. Then we review the general theory of relativity and in particular obtain the Schwarzschild metric describing a static spherically symmetric vacuum spacetime. Chapter 3 deals with test particle motion through a curved spacetime. Liouville's equation describes the statistical distribution in phase space of a collection of test particles and is based upon a Hamiltonian formulation of the dynamical system - this material also relies heavily upon the concepts of differential geometry introduced in chapter 2. In particular we are interested in photon transport and find the general solutions for some symmetric

  7. Error of semiclassical eigenvalues in the semiclassical limit - an asymptotic analysis of the Sinai billiard

    Dahlqvist, Per

    1999-10-01

    We estimate the error in the semiclassical trace formula for the Sinai billiard under the assumption that the largest source of error is due to penumbra diffraction: namely, diffraction effects for trajectories passing within a distance Ricons/Journals/Common/cdot" ALT="cdot" ALIGN="TOP"/>O((kR)-2/3) to the disc and trajectories being scattered in very forward directions. Here k is the momentum and R the radius of the scatterer. The semiclassical error is estimated by perturbing the Berry-Keating formula. The analysis necessitates an asymptotic analysis of very long periodic orbits. This is obtained within an approximation originally due to Baladi, Eckmann and Ruelle. We find that the average error, for sufficiently large values of kR, will exceed the mean level spacing.

  8. The quantum spectral analysis of the two-dimensional annular billiard system

    Yan-Hui, Zhang; Ji-Quan, Zhang; Xue-You, Xu; Sheng-Lu, Lin

    2009-01-01

    Based on the extended closed-orbit theory together with spectral analysis, this paper studies the correspondence between quantum mechanics and the classical counterpart in a two-dimensional annular billiard. The results demonstrate that the Fourier-transformed quantum spectra are in very good accordance with the lengths of the classical ballistic trajectories, whereas spectral strength is intimately associated with the shapes of possible open orbits connecting arbitrary two points in the annular cavity. This approach facilitates an intuitive understanding of basic quantum features such as quantum interference, locations of the wavefunctions, and allows quantitative calculations in the range of high energies, where full quantum calculations may become impractical in general. This treatment provides a thread to explore the properties of microjunction transport and even quantum chaos under the much more general system. (general)

  9. Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard.

    Livorati, André L P; Caldas, Iberê L; Leonel, Edson D

    2012-06-01

    The behavior of the average energy for an ensemble of non-interacting particles is studied using scaling arguments in a dissipative time-dependent stadium-like billiard. The dynamics of the system is described by a four dimensional nonlinear mapping. The dissipation is introduced via inelastic collisions between the particles and the moving boundary. For different combinations of initial velocities and damping coefficients, the long time dynamics of the particles leads them to reach different states of final energy and to visit different attractors, which change as the dissipation is varied. The decay of the average energy of the particles, which is observed for a large range of restitution coefficients and different initial velocities, is described using scaling arguments. Since this system exhibits unlimited energy growth in the absence of dissipation, our results for the dissipative case give support to the principle that Fermi acceleration seems not to be a robust phenomenon.

  10. Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I

    Teschner, J.

    2010-05-01

    It was in particular recently argued that the gauge theory in the presence of a certain one-parameter deformation can at low energies effectively be described in terms the quantization of an algebraically integrable system, which is canonically associated to this theory. It seems, however, that the deeper reasons for this relationship between a two- and a fourdimensional theory remain to be understood. A clue in this direction may be seen in the fact that the instanton partition functions which represent the building blocks of the partition functions are obtained by specializing a two-parameter family Z(a,ε 1 ,ε 2 ;q) of instanton partition functions. These functions were identified with the conformal blocks of Liouville theory. This indicates that the relationship between certain gauge theories and Liouville theory involves in particular a two-parametric deformation of the algebraically integrable model associated to the gauge theories on R 4 which ultimately produces Liouville theory as a result. One of my intentions in this paper is to clarify in which sense this point of view is correct. Another piece of motivation comes from relations between fourdimensional gauge theories and the geometric Langlands correspondence. The author feels that the mentioned relations between gauge theory and conformal field theory offer new clues in this regard. It is therefore my second main aim to clarify the relations between the quantization of the Hitchin system, the geometric Langlands correspondence and the Liouville conformal field theory. (orig.)

  11. The Sturm-Liouville inverse spectral problem with boundary conditions depending on the spectral parameter

    Cornelis van der Mee

    2005-01-01

    Full Text Available We present the complete version including proofs of the results announced in [van der Mee C., Pivovarchik V.: A Sturm-Liouville spectral problem with boundary conditions depending on the spectral parameter. Funct. Anal. Appl. 36 (2002, 315–317 [Funkts. Anal. Prilozh. 36 (2002, 74–77 (Russian

  12. Accurate high-lying eigenvalues of Schroedinger and Sturm-Liouville problems

    Vanden Berghe, G.; Van Daele, M.; De Meyer, H.

    1994-01-01

    A modified difference and a Numerov-like scheme have been introduced in a shooting algorithm for the determination of the (higher-lying) eigenvalues of Schroedinger equations and Sturm-Liouville problems. Some numerical experiments are introduced. Time measurements have been performed. The proposed algorithms are compared with other previously introduced shooting schemes. The structure of the eigenvalue error is discussed. ((orig.))

  13. Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I

    Teschner, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie

    2010-05-15

    It was in particular recently argued that the gauge theory in the presence of a certain one-parameter deformation can at low energies effectively be described in terms the quantization of an algebraically integrable system, which is canonically associated to this theory. It seems, however, that the deeper reasons for this relationship between a two- and a fourdimensional theory remain to be understood. A clue in this direction may be seen in the fact that the instanton partition functions which represent the building blocks of the partition functions are obtained by specializing a two-parameter family Z(a,{epsilon}{sub 1},{epsilon}{sub 2};q) of instanton partition functions. These functions were identified with the conformal blocks of Liouville theory. This indicates that the relationship between certain gauge theories and Liouville theory involves in particular a two-parametric deformation of the algebraically integrable model associated to the gauge theories on R{sup 4} which ultimately produces Liouville theory as a result. One of my intentions in this paper is to clarify in which sense this point of view is correct. Another piece of motivation comes from relations between fourdimensional gauge theories and the geometric Langlands correspondence. The author feels that the mentioned relations between gauge theory and conformal field theory offer new clues in this regard. It is therefore my second main aim to clarify the relations between the quantization of the Hitchin system, the geometric Langlands correspondence and the Liouville conformal field theory. (orig.)

  14. Half-linear Sturm-Liouville problem with weights: asymptotic behavior of eigenfunctions

    Drábek, P.; Kufner, Alois; Kuliev, K.

    2014-01-01

    Roč. 284, č. 1 (2014), s. 148-154 ISSN 0081-5438 Institutional support: RVO:67985840 Keywords : Sturm-Liouville problem * spectral problems * Hardy inequality Subject RIV: BA - General Mathematics Impact factor: 0.302, year: 2014 http://link.springer.com/article/10.1134%2FS008154381401009X

  15. A novel scheme for Liouville's equation with a discontinuous Hamiltonian and applications to geometrical optics

    Lith, van B.S.; Thije Boonkkamp, ten J.H.M.; IJzerman, W.L.; Tukker, T.W.

    2015-01-01

    We compute numerical solutions of Liouville's equation with a discontinuous Hamiltonian. We assume that the underlying Hamiltonian system has a well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell's law or

  16. Modeling of open quantum dots and wave billiards using imaginary potentials for the source and the sink

    Berggren, Karl-Fredrik; Yakimenko, Irina I; Hakanen, Jani

    2010-01-01

    A heuristic model for particle states and current flow in open ballistic two-dimensional (2D) quantum dots/wave billiards is proposed. The model makes use of complex potentials first introduced in phenomenological nuclear inelastic scattering theory (the optical model). Here we assume that external input and output leads connecting the system to the source and the drain regions may be represented by complex potentials. In this way, a current may be set up between the two 'pseudo-leads'. Probability densities and current flows for an open quantum dot are analyzed here numerically and the results are compared with the microwave measurements used to emulate the system. The model is of conceptual as well as practical interest. In addition to quantum billiards, it may be used as a tool per se to analyze transport in classical wave analogues, such as microwave resonators, acoustic resonators, effects of leakage on such systems, etc.

  17. Spotting expertise in the eyes: billiards knowledge as revealed by gaze shifts in a dynamic visual prediction task.

    Crespi, Sofia; Robino, Carlo; Silva, Ottavia; de'Sperati, Claudio

    2012-10-31

    In sports, as in other activities and knowledge domains, expertise is a highly valuable asset. We assessed whether expertise in billiards is associated with specific patterns of eye movements in a visual prediction task. Professional players and novices were presented a number of simplified billiard shots on a computer screen, previously filmed in a real set, with the last part of the ball trajectory occluded. They had to predict whether or not the ball would have hit the central skittle. Experts performed better than novices, in terms of both accuracy and response time. By analyzing eye movements, we found that during occlusion, experts rarely extrapolated with the gaze the occluded part of the ball trajectory-a behavior that was widely diffused in novices-even when the unseen path was long and with two bounces interposed. Rather, they looked selectively at specific diagnostic points on the cushions along the ball's visible trajectory, in accordance with a formal metrical system used by professional players to calculate the shot coordinates. Thus, the eye movements of expert observers contained a clear signature of billiard expertise and documented empirically a strategy upgrade in visual problem solving from dynamic, analog simulation in imagery to more efficient rule-based, conceptual knowledge.

  18. H{sup +}{sub 3} WZNW model from Liouville field theory

    Hikida, Y.; Schomerus, V.

    2007-06-15

    There exists an intriguing relation between genus zero correlation functions in the H{sup +}{sub 3} WZNW model and in Liouville field theory. This was found by Ribault and Teschner based in part on earlier ideas by Stoyanovsky. We provide a path integral derivation of the correspondence and then use our new approach to generalize the relation to surfaces of arbitrary genus g. In particular we determine the correlation functions of N primary fields in the WZNW model explicitly through Liouville correlators with N+2g-2 additional insertions of certain degenerate fields. The paper concludes with a list of interesting further extensions and a few comments on the relation to the geometric Langlands program. (orig.)

  19. A Lax integrable hierarchy, bi-Hamiltonian structure and finite-dimensional Liouville integrable involutive systems

    Xia Tiecheng; Chen Xiaohong; Chen Dengyuan

    2004-01-01

    An eigenvalue problem and the associated new Lax integrable hierarchy of nonlinear evolution equations are presented in this paper. As two reductions, the generalized nonlinear Schroedinger equations and the generalized mKdV equations are obtained. Zero curvature representation and bi-Hamiltonian structure are established for the whole hierarchy based on a pair of Hamiltonian operators (Lenard's operators), and it is shown that the hierarchy of nonlinear evolution equations is integrable in Liouville's sense. Thus the hierarchy of nonlinear evolution equations has infinitely many commuting symmetries and conservation laws. Moreover the eigenvalue problem is nonlinearized as a finite-dimensional completely integrable system under the Bargmann constraint between the potentials and the eigenvalue functions. Finally finite-dimensional Liouville integrable system are found, and the involutive solutions of the hierarchy of equations are given. In particular, the involutive solutions are developed for the system of generalized nonlinear Schroedinger equations

  20. Sectors of solutions and minimal energies in classical Liouville theories for strings

    Johansson, L.; Kihlberg, A.; Marnelius, R.

    1984-01-01

    All classical solutions of the Liouville theory for strings having finite stable minimum energies are calculated explicitly together with their minimal energies. Our treatment automatically includes the set of natural solitonlike singularities described by Jorjadze, Pogrebkov, and Polivanov. Since the number of such singularities is preserved in time, a sector of solutions is not only characterized by its boundary conditions but also by its number of singularities. Thus, e.g., the Liouville theory with periodic boundary conditions has three different sectors of solutions with stable minimal energies containing zero, one, and two singularities. (Solutions with more singularities have no stable minimum energy.) It is argued that singular solutions do not make the string singular and therefore may be included in the string quantization

  1. Higher equations of motion in N=2 superconformal Liouville field theory

    Ahn, Changrim; Stanishkov, Marian; Stoilov, Michail

    2011-01-01

    We present an infinite set of higher equations of motion in N=2 supersymmetric Liouville field theory. They are in one to one correspondence with the degenerate representations and are enumerated in addition to the U(1) charge ω by the positive integers m or (m,n) respectively. We check that in the classical limit these equations hold as relations among the classical fields.

  2. Green's functions and trace formulas for generalized Sturm-Liouville problems related by Darboux transformations

    Schulze-Halberg, Axel

    2010-01-01

    We study Green's functions of the generalized Sturm-Liouville problems that are related to each other by Darboux -equivalently, supersymmetrical - transformations. We establish an explicit relation between the corresponding Green's functions and derive a simple formula for their trace. The class of equations considered here includes the conventional Schroedinger equation and generalizations, such as for position-dependent mass and with linearly energy-dependent potential, as well as the stationary Fokker-Planck equation.

  3. Memoria sobre el papel de Liouville en la historia de las funciones elípticas

    Leonardo Solanilla Chavarro

    2014-06-01

    Full Text Available Este artículo recoge las principales conclusiones de una investigación sobre las contribuciones de J. Liouville a la teoría contemporánea de las funciones elípticas. Cubre la mayor parte de los resultados de una colaboración entre el grupo SUMMA del Departamento de Ciencias Básicas de la Universidad de Medellín y el grupo Mat del Departamento de Matemáticas y Estadística de la Universidad del Tolima. El proyecto ha sido financiado parcialmente por la Vicerrectoría de Investigaciones de la Universidad de Medellín y la Facultad de Ciencias de la Universidad del Tolima. Comienza con una descripción de la circunstancia histórica de Liouville, luego de la emergencia del concepto moderno de función elíptica en los trabajos de Abel y Jacobi. Después se discuten ciertos pormenores de las Leçons impartidas por el célebre matemático francés en el año de 1847. Ellos cubren el teorema que hemos llamado de Liouville-Borchardt, las proposiciones fundamentales sobre el número de ceros de las funciones meromorfas doblemente periódicas y los resultados sobre la relación entre los ceros y los polos. Al final, se esbozan importantes conclusiones sobre el legado de Liouville a la teoría de las funciones elípticas de hoy.

  4. Comments on fusion matrix in N=1 super Liouville field theory

    Hasmik Poghosyan

    2016-08-01

    Full Text Available We study several aspects of the N=1 super Liouville theory. We show that certain elements of the fusion matrix in the Neveu–Schwarz sector are related to the structure constants according to the same rules which we observe in rational conformal field theory. We collect some evidences that these relations should hold also in the Ramond sector. Using them the Cardy–Lewellen equation for defects is studied, and defects are constructed.

  5. The Euler anomaly and scale factors in Liouville/Toda CFTs

    Balasubramanian, Aswin [Theory Group, Department of Physics, University of Texas at Austin,2515 Speedway Stop C1608, Austin, TX 78712-1197 (United States)

    2014-04-22

    The role played by the Euler anomaly in the dictionary relating sphere partition functions of four dimensional theories of class S and two dimensional non rational CFTs is clarified. On the two dimensional side, this involves a careful treatment of scale factors in Liouville/Toda correlators. Using ideas from tinkertoy constructions for Gaiotto duality, a framework is proposed for evaluating these scale factors. The representation theory of Weyl groups plays a critical role in this framework.

  6. Analysis of the Forward-Backward Trajectory Solution for the Mixed Quantum-Classical Liouville Equation

    Hsieh, Chang-Yu; Kapral, Raymond

    2013-01-01

    Mixed quantum-classical methods provide powerful algorithms for the simulation of quantum processes in large and complex systems. The forward-backward trajectory solution of the mixed quantum-classical Liouville equation in the mapping basis [J. Chem. Phys. 137, 22A507 (2012)] is one such scheme. It simulates the dynamics via the propagation of forward and backward trajectories of quantum coherent state variables, and the propagation of bath trajectories on a mean-field potential determined j...

  7. A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation

    Abdon Atangana

    2014-01-01

    Full Text Available The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as function of time and space. The function u accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method.

  8. Online learning of a Dirichlet process mixture of Beta-Liouville distributions via variational inference.

    Fan, Wentao; Bouguila, Nizar

    2013-11-01

    A large class of problems can be formulated in terms of the clustering process. Mixture models are an increasingly important tool in statistical pattern recognition and for analyzing and clustering complex data. Two challenging aspects that should be addressed when considering mixture models are how to choose between a set of plausible models and how to estimate the model's parameters. In this paper, we address both problems simultaneously within a unified online nonparametric Bayesian framework that we develop to learn a Dirichlet process mixture of Beta-Liouville distributions (i.e., an infinite Beta-Liouville mixture model). The proposed infinite model is used for the online modeling and clustering of proportional data for which the Beta-Liouville mixture has been shown to be effective. We propose a principled approach for approximating the intractable model's posterior distribution by a tractable one-which we develop-such that all the involved mixture's parameters can be estimated simultaneously and effectively in a closed form. This is done through variational inference that enjoys important advantages, such as handling of unobserved attributes and preventing under or overfitting; we explain that in detail. The effectiveness of the proposed work is evaluated on three challenging real applications, namely facial expression recognition, behavior modeling and recognition, and dynamic textures clustering.

  9. On some spectral properties of billiards and nuclei. Similarities and differences

    Richter, A.

    2005-01-01

    Generic and non-generic features of billiards and nuclei which show up in certain spectral properties are discussed by way of selected examples. First, the short and long range correlations of levels belonging to the magnetic dipole Scissors Mode in heavy deformed nuclei at an excitation energy of about 3 MeV prove that this mode is indeed caused by an ordered or regular collective motion. Second, the fine structure distribution of the so called electric Pygmy Dipole Resonance around 6 to 7 MeV excitation energy seems to indicate a situation where the spectral properties are governed by mixed dynamics, i.e. by regular and chaotic features. However, in nuclei quantitative conclusions are always severely hampered by missing levels due to limited experimental resolution and detector efficiency. Third, it is shown that this situation can be largely overcome by studying spectral properties in superconducting microwave billards considered as nuclear analogs. As an example resonance strength distributions in billards of mixed and fully chaotic dynamics are considered. Finally it is demonstrated how symmetry breaking effects in nuclei - e.g. isospin symmetry breaking - can be studied through those resonance strength distributions by modelling the nuclear problem with coupled billards. (orig.)

  10. On some spectral properties of billiards and nuclei. Similarities and differences

    Richter, A.

    2005-07-01

    Generic and non-generic features of billiards and nuclei which show up in certain spectral properties are discussed by way of selected examples. First, the short and long range correlations of levels belonging to the magnetic dipole Scissors Mode in heavy deformed nuclei at an excitation energy of about 3 MeV prove that this mode is indeed caused by an ordered or regular collective motion. Second, the fine structure distribution of the so called electric Pygmy Dipole Resonance around 6 to 7 MeV excitation energy seems to indicate a situation where the spectral properties are governed by mixed dynamics, i.e. by regular and chaotic features. However, in nuclei quantitative conclusions are always severely hampered by missing levels due to limited experimental resolution and detector efficiency. Third, it is shown that this situation can be largely overcome by studying spectral properties in superconducting microwave billards considered as nuclear analogs. As an example resonance strength distributions in billards of mixed and fully chaotic dynamics are considered. Finally it is demonstrated how symmetry breaking effects in nuclei - e.g. isospin symmetry breaking - can be studied through those resonance strength distributions by modelling the nuclear problem with coupled billards. (orig.)

  11. Scanning table

    1960-01-01

    Before the invention of wire chambers, particles tracks were analysed on scanning tables like this one. Today, the process is electronic and much faster. Bubble chamber film - currently available - (links can be found below) was used for this analysis of the particle tracks.

  12. Quantum kinetic field theory in curved spacetime: Covariant Wigner function and Liouville-Vlasov equations

    Calzetta, E.; Habib, S.; Hu, B.L.

    1988-01-01

    We consider quantum fields in an external potential and show how, by using the Fourier transform on propagators, one can obtain the mass-shell constraint conditions and the Liouville-Vlasov equation for the Wigner distribution function. We then consider the Hadamard function G 1 (x 1 ,x 2 ) of a real, free, scalar field in curved space. We postulate a form for the Fourier transform F/sup (//sup Q//sup )/(X,k) of the propagator with respect to the difference variable x = x 1 -x 2 on a Riemann normal coordinate centered at Q. We show that F/sup (//sup Q//sup )/ is the result of applying a certain Q-dependent operator on a covariant Wigner function F. We derive from the wave equations for G 1 a covariant equation for the distribution function and show its consistency. We seek solutions to the set of Liouville-Vlasov equations for the vacuum and nonvacuum cases up to the third adiabatic order. Finally we apply this method to calculate the Hadamard function in the Einstein universe. We show that the covariant Wigner function can incorporate certain relevant global properties of the background spacetime. Covariant Wigner functions and Liouville-Vlasov equations are also derived for free fermions in curved spacetime. The method presented here can serve as a basis for constructing quantum kinetic theories in curved spacetime or for near-uniform systems under quasiequilibrium conditions. It can also be useful to the development of a transport theory of quantum fields for the investigation of grand unification and post-Planckian quantum processes in the early Universe

  13. A bifurcation result for Sturm-Liouville problems with a set-valued term

    Georg Hetzer

    1998-11-01

    Full Text Available It is established in this note that $-(ku''+g(cdot,uin mu F(cdot,u$, $u'(0=0=u'(1$, has a multiple bifurcation point at $ (0, 0}$ in the sense that infinitely many continua meet at $(0,0$. $F$ is a ``set-valued representation'' of a function with jump discontinuities along the line segment $[0,1]imes{0}$. The proof relies on a Sturm-Liouville version of Rabinowitz's bifurcation theorem and an approximation procedure.

  14. Duality and the Knizhnik-Polyakov-Zamolodchikov relation in Liouville quantum gravity.

    Duplantier, Bertrand; Sheffield, Scott

    2009-04-17

    We present a (mathematically rigorous) probabilistic and geometrical proof of the Knizhnik-Polyakov-Zamolodchikov relation between scaling exponents in a Euclidean planar domain D and in Liouville quantum gravity. It uses the properly regularized quantum area measure dmicro_{gamma}=epsilon;{gamma;{2}/2}e;{gammah_{epsilon}(z)}dz, where dz is the Lebesgue measure on D, gamma is a real parameter, 02 is shown to be related to the quantum measure dmu_{gamma;{'}}, gamma;{'}<2, by the fundamental duality gammagamma;{'}=4.

  15. Remarks on the Liouville type results for the compressible Navier–Stokes equations in RN

    Chae, Dongho

    2012-01-01

    In this paper, we prove Liouville type result for the stationary solutions to the compressible Navier–Stokes equations (NS) and the compressible Navier–Stokes–Poisson (NSP) equations and in R N , N ≥ 2. Assuming suitable integrability and the uniform boundedness conditions for the solutions we are led to the conclusion that v = 0. In the case of (NS) we deduce that the similar integrability conditions imply v = 0 and ρ = constant on R N . This shows that if we impose the the non-vacuum boundary condition at spatial infinity for (NS), v → 0 and ρ → ρ ∞ > 0, then v = 0, ρ = ρ ∞ are the solutions

  16. Cauchy problem for a parabolic equation with Bessel operator and Riemann–Liouville partial derivative

    Fatima G. Khushtova

    2016-03-01

    Full Text Available In this paper Cauchy problem for a parabolic equation with Bessel operator and with Riemann–Liouville partial derivative is considered. The representation of the solution is obtained in terms of integral transform with Wright function in the kernel. It is shown that when this equation becomes the fractional diffusion equation, obtained solution becomes the solution of Cauchy problem for the corresponding equation. The uniqueness of the solution in the class of functions that satisfy the analogue of Tikhonov condition is proved.

  17. Symmetric duality for left and right Riemann–Liouville and Caputo fractional differences

    Thabet Abdeljawad

    2017-07-01

    Full Text Available A discrete version of the symmetric duality of Caputo–Torres, to relate left and right Riemann–Liouville and Caputo fractional differences, is considered. As a corollary, we provide an evidence to the fact that in case of right fractional differences, one has to mix between nabla and delta operators. As an application, we derive right fractional summation by parts formulas and left fractional difference Euler–Lagrange equations for discrete fractional variational problems whose Lagrangians depend on right fractional differences.

  18. Structure constants in the N=1 super-Liouville field theory

    Poghossian, R.H.

    1997-01-01

    The symmetry algebra of N=1 super-Liouville field theory in two dimensions is the infinite-dimensional N=1 superconformal algebra, which allows one to prove that correlation functions containing degenerated fields obey some partial linear differential equations. In the special case of four-point function, including a primary field degenerated at the first level, these differential equations can be solved via hypergeometric functions. Taking into account mutual locality properties of fields and investigating s- and t-channel singularities we obtain some functional relations for three-point correlation functions. Solving this functional equations we obtain three-point functions in both Neveu-Schwarz and Ramond sectors. (orig.)

  19. Spectral inversion of an indefinite Sturm-Liouville problem due to Richardson

    Shanley, Paul E

    2009-01-01

    We study an indefinite Sturm-Liouville problem due to Richardson whose complicated eigenvalue dependence on a parameter has been a puzzle for decades. In atomic physics a process exists that inverts the usual Schroedinger situation of an energy eigenvalue depending on a coupling parameter into the so-called Sturmian problem where the coupling parameter becomes the eigenvalue which then depends on the energy. We observe that the Richardson equation is of the Sturmian type. This means that the Richardson and its related Schroedinger eigenvalue functions are inverses of each other and that the Richardson spectrum is therefore no longer a puzzle

  20. On the singular Sturm-Liouville problems that have the same spectrum

    Gulsen, Tuba [Department of Mathematics, Firat University, 23119, Elazig (Turkey); Ulusoy, Ismail [Department of Mathematics, Adiyaman University, 02040,Adiyaman (Turkey)

    2016-06-08

    The problem of efficaciously constucting the potential q (x) and the numbers h and H was solved in [1]. Trubowitz [2] investigated the isospectrality problem which have the same spectrum with other same type of problems. Then Jodeit and Levitan [3] considered this problem with a different approach, based on transmutation operators and integral equation. In this work, we discussed this problem for singular Sturm-Liouville operator and obtained some important formulas for the number H, the potential q (x) and the norming constants α{sub n}.

  1. A Liouville Problem for the Stationary Fractional Navier-Stokes-Poisson System

    Wang, Y.; Xiao, J.

    2017-06-01

    This paper deals with a Liouville problem for the stationary fractional Navier-Stokes-Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier-Stokes systems in R^{N≥2} . An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre's technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245-1260, 2007).

  2. Distance measurement and wave dispersion in a Liouville-string approach to quantum gravity

    Amelino-Camelia, G; Mavromatos, Nikolaos E; Nanopoulos, Dimitri V

    1997-01-01

    Within a Liouville approach to non-critical string theory, we discuss space-time foam effects on the propagation of low-energy particles. We find an induced frequency-dependent dispersion in the propagation of a wave packet, and observe that this would affect the outcome of measurements involving low-energy particles as probes. In particular, the maximum possible order of magnitude of the space-time foam effects would give rise to an error in the measurement of distance comparable to that independently obtained in some recent heuristic quantum-gravity analyses. We also briefly compare these error estimates with the precision of astrophysical measurements.

  3. Effect of trapping on transport coherence III: Dissipation in the stochastic Liouville equation approach

    Barvik, I [International Centre for Theoretical Physics, Trieste (Italy); Polasek, M [Charles Univ., Prague (Czech Republic). Inst. of Physics; Herman, P [Pedagogical Univ., Hradec Kralove (Czech Republic)

    1995-08-01

    We used the formal stochastic Liouville equations within Haken-Strobl-Reineker parametrization for the description of the influence of the bath on the memory functions entering the GME for a dimer and a linear trimer with a trap (here modeled as a sink). The often used inclusion of the noncoherent regime in the MF by an exponentially damped prefactor (after Kenkre`s prescription) does not hold for finite systems. The analytical form of the MF is changed more pronouncely and the influence of the sink in the center of the trimer runs parallel with the influence of the bath in destroying the coherence. (author). 60 refs.

  4. Path integral Liouville dynamics: Applications to infrared spectra of OH, water, ammonia, and methane

    Liu, Jian; Zhang, Zhijun

    2016-01-01

    Path integral Liouville dynamics (PILD) is applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane). The dipole-derivative autocorrelation function is employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems

  5. A Liouville integrable hierarchy, symmetry constraint, new finite-dimensional integrable systems, involutive solution and expanding integrable models

    Sun Yepeng; Chen Dengyuan

    2006-01-01

    A new spectral problem and the associated integrable hierarchy of nonlinear evolution equations are presented in this paper. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamiltonian structure. An explicit symmetry constraint is proposed for the Lax pairs and the adjoint Lax pairs of the hierarchy. Moreover, the corresponding Lax pairs and adjoint Lax pairs are nonlinearized into a hierarchy of commutative, new finite-dimensional completely integrable Hamiltonian systems in the Liouville sense. Further, an involutive representation of solution of each equation in the hierarchy is given. Finally, expanding integrable models of the hierarchy are constructed by using a new Loop algebra

  6. Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae

    Bleher, P.M.; Kosygin, D.V.; Sinai, Y.G.

    1995-01-01

    We consider the Weyl asymptotic formula [{E n ≤R 2 }=Area Q.R 2 /(4π)+n(R), for eigenvalues of the Laplace-Beltrami operator on a two-dimensional torus Q with a Liouville metric which is in a sense the most general case of an integrable metric. We prove that if the surface Q is non-degenerate then the remainder term n(R) has the form n(R)=R 1/2 θ(R), where θ(R) is an almost periodic function of the Besicovitch class B 1 , and the Fourier amplitudes and the Fourier frequencies of θ(R) can be expressed via lengths of closed geodesics on Q and other simple geometric characteristics of these geodesics. We prove then that if the surface Q is generic then the limit distribution of θ(R) has a density p(t), which is an entire function of t possessing an asymptotics on a real line, logp(t)∝-C ± t 4 as t→±∞. An explicit expression for the Fourier transform of p(t) via Fourier amplitudes of θ(R) is also given. We obtain the analogue of the Guillemin-Duistermaat trace formula for the Liouville surfaces and discuss its accuracy. (orig.)

  7. Brief comments on Jackiw-Teitelboim gravity coupled to Liouville theory

    Giribet, Gaston E

    2003-06-07

    The Jackiw-Teitelboim gravity with non-vanishing cosmological constant coupled to Liouville theory is considered as a non-critical string on d dimensional flat spacetime. In terms of this interpretation of the model as a consistent string theory, it is discussed as to how the presence of a cosmological constant leads one to consider additional constraints on the parameters of the theory, even though the conformal anomaly is independent of the cosmological constant. The constraints agree with the necessary conditions required to ensure that the tachyon field turns out to be a primary prelogarithmic operator within the context of the worldsheet conformal field theory. Thus, the linearized tachyon field equation allows one to impose the diagonal condition for the interaction term. We analyse the neutralization of the Liouville mode induced by the coupling to the Jackiw-Teitelboim Lagrangian. The standard free field prescription leads one to obtain explicit expressions for three-point functions for the case of vanishing cosmological constant in terms of a product of Shapiro-Virasoro integrals; this fact is a consequence of the mentioned neutralization effect.

  8. A simple finite element method for boundary value problems with a Riemann–Liouville derivative

    Jin, Bangti; Lazarov, Raytcho; Lu, Xiliang; Zhou, Zhi

    2016-01-01

    © 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

  9. A simple finite element method for boundary value problems with a Riemann–Liouville derivative

    Jin, Bangti

    2016-02-01

    © 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

  10. Comparison between the Variational Iteration Method and the Homotopy Perturbation Method for the Sturm-Liouville Differential Equation

    R. Darzi

    2010-01-01

    Full Text Available We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.

  11. Comparison between the Variational Iteration Method and the Homotopy Perturbation Method for the Sturm-Liouville Differential Equation

    Darzi R; Neamaty A

    2010-01-01

    We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.

  12. Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary conditions

    Guliyev, Namig J.

    2008-01-01

    International audience; Inverse problems of recovering the coefficients of Sturm–Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: 1) from the sequences of eigenvalues and norming constants; 2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.

  13. Some mathematical aspects of the Sturm-Liouville expansion with special reference to the nucleon-nucleus potential

    Bang, J.M.; Gareev, F.A.

    1977-01-01

    Different convergence properties of the Sturm-Liouville expansion are investigated with particular attention to the case of states which satisfy Schroedinger-like equations with a fixed energy and different depths of a potential, particulary of the Woods-Saxon used in nuclear physics

  14. Existence and Solution-representation of IVP for LFDE with Generalized Riemann-Liouville fractional derivatives and $n$ terms

    Kim, Myong-Ha; Ri, Guk-Chol; O, Hyong-Chol

    2013-01-01

    This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.

  15. Bulk-boundary correlators in the hermitian matrix model and minimal Liouville gravity

    Bourgine, Jean-Emile; Ishiki, Goro; Rim, Chaiho

    2012-01-01

    We construct the one matrix model (MM) correlators corresponding to the general bulk-boundary correlation numbers of the minimal Liouville gravity (LG) on the disc. To find agreement between both discrete and continuous approach, we investigate the resonance transformation mixing boundary and bulk couplings. It leads to consider two sectors, depending on whether the matter part of the LG correlator is vanishing due to the fusion rules. In the vanishing case, we determine the explicit transformation of the boundary couplings at the first order in bulk couplings. In the non-vanishing case, no bulk-boundary resonance is involved and only the first order of pure boundary resonances have to be considered. Those are encoded in the matrix polynomials determined in our previous paper. We checked the agreement for the bulk-boundary correlators of MM and LG in several non-trivial cases. In this process, we developed an alternative method to derive the boundary resonance encoding polynomials.

  16. A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems

    Muhammed I. Syam

    2017-11-01

    Full Text Available This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional $2\\alpha $-order Sturm-Liouville problem where $\\frac{1}{2}< \\alpha \\leq 1$. In this paper, we implement the reproducing kernel method RKM to approximate the eigenvalues. To find the eigenvalues, we force the approximate solution produced by the RKM satisfy the boundary condition at $x=1$. The fractional derivative is described in the Caputo sense. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the eigenfunctions of the proposed problem. Uniformly convergence of the approximate eigenfunctions produced by the RKM to the exact eigenfunctions is proven.

  17. Riemann-Hilbert treatment of Liouville theory on the torus: the general case

    Menotti, Pietro

    2011-01-01

    We extend the previous treatment of Liouville theory on the torus to the general case in which the distribution of charges is not necessarily symmetric. This requires the concept of Fuchsian differential equation on Riemann surfaces. We show through a group theoretic argument that the Heun parameter and a weight constant are sufficient to satisfy all monodromy conditions. We then apply the technique of differential equations on a Riemann surface to the two-point function on the torus in which one source is arbitrary and the other small. As a byproduct, we give in terms of quadratures the exact Green function on the square and on the rhombus with opening angle 2π/6 in the background of the field generated by an arbitrary charge.

  18. Riemann-Liouville integrals of fractional order and extended KP hierarchy

    Kamata, Masaru; Nakamula, Atsushi

    2002-01-01

    An attempt to formulate the extensions of the KP hierarchy by introducing fractional-order pseudo-differential operators is given. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/Nth-order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding the new extensions of the KP hierarchy, a brief introduction to the Riemann-Liouville integral is provided to yield a candidate for the fractional-order pseudo-differential operators

  19. A trick loop algebra and a corresponding Liouville integrable hierarchy of evolution equations

    Zhang Yufeng; Xu Xixiang

    2004-01-01

    A subalgebra of loop algebra A-bar 2 is first constructed, which has its own special feature. It follows that a new Liouville integrable hierarchy of evolution equations is obtained, possessing a tri-Hamiltonian structure, which is proved by us in this paper. Especially, three symplectic operators are constructed directly from recurrence relations. The conjugate operator of a recurrence operator is a hereditary symmetry. As reduction cases of the hierarchy presented in this paper, the celebrated MKdV equation and heat-conduction equation are engendered, respectively. Therefore, we call the hierarchy a generalized MKdV-H system. At last, a high-dimension loop algebra G-bar is constructed by making use of a proper scalar transformation. As a result, a type expanding integrable model of the MKdV-H system is given

  20. The Liouville equation for flavour evolution of neutrinos and neutrino wave packets

    Hansen, Rasmus Sloth Lundkvist; Smirnov, Alexei Yu., E-mail: rasmus@mpi-hd.mpg.de, E-mail: smirnov@mpi-hd.mpg.de [Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg (Germany)

    2016-12-01

    We consider several aspects related to the form, derivation and applications of the Liouville equation (LE) for flavour evolution of neutrinos. To take into account the quantum nature of neutrinos we derive the evolution equation for the matrix of densities using wave packets instead of Wigner functions. The obtained equation differs from the standard LE by an additional term which is proportional to the difference of group velocities. We show that this term describes loss of the propagation coherence in the system. In absence of momentum changing collisions, the LE can be reduced to a single derivative equation over a trajectory coordinate. Additional time and spatial dependence may stem from initial (production) conditions. The transition from single neutrino evolution to the evolution of a neutrino gas is considered.

  1. An anisotropic standing wave braneworld and associated Sturm-Liouville problem

    Gogberashvili, Merab; Herrera-Aguilar, Alfredo; Malagón-Morejón, Dagoberto

    2012-01-01

    We present a consistent derivation of the recently proposed 5D anisotropic standing wave braneworld generated by gravity coupled to a phantom-like scalar field. We explicitly solve the corresponding junction conditions, a fact that enables us to give a physical interpretation to the anisotropic energy-momentum tensor components of the brane. So matter on the brane represents an oscillating fluid which emits anisotropic waves into the bulk. We also analyze the Sturm-Liouville problem associated with the correct localization condition of the transverse to the brane metric and scalar fields. It is shown that this condition restricts the physically meaningful space of solutions for the localization of the fluctuations of the model. (paper)

  2. D-branes in N=2 Liouville theory and its mirror

    Israel, Dan; Pakman, Ari; Troost, Jan

    2005-01-01

    We study D-branes in the mirror pair N=2 Liouville/supersymmetric SL(2,R)/U(1) coset superconformal field theories. We build D0-, D1- and D2-branes, on the basis of the boundary state construction for the H 3 + conformal field theory. We also construct D0-branes in an orbifold that rotates the angular direction of the cigar. We show how the poles of correlators associated to localized states and bulk interactions naturally decouple in the one-point functions of localized and extended branes. We stress the role played in the analysis of D-brane spectra by primaries in SL(2,R)/U(1) which are descendents of the parent theory

  3. Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories, I

    Gaiotto, D. [Institute for Advanced Study (IAS), Princeton, NJ (United States); Teschner, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2012-03-15

    Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on S{sup 4}. (orig.)

  4. A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian

    Quaas, Alexander; Xia, Aliang

    2016-08-01

    We establish a Liouville type theorem for the fractional Lane-Emden system: {(-Δ)αu=vqin  RN,(-Δ)αv=upin  RN, where α \\in (0,1) , N>2α and p, q are positive real numbers and in an appropriate new range. To prove our result we will use the local realization of fractional Laplacian, which can be constructed as a Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre (2007 Commun. PDE 32 1245-60). Our proof is based on a monotonicity argument for suitable transformed functions and the method of moving planes in a half infinite cylinder ({IR}× S+N , where S+N is the half unit sphere in {{{R}}N+1} ) based on maximum principles which are obtained by barrier functions and a coupling argument using a fractional Sobolev trace inequality.

  5. Kinetics of subdiffusion-assisted reactions: non-Markovian stochastic Liouville equation approach

    Shushin, A I

    2005-01-01

    Anomalous specific features of the kinetics of subdiffusion-assisted bimolecular reactions (time-dependence, dependence on parameters of systems, etc) are analysed in detail with the use of the non-Markovian stochastic Liouville equation (SLE), which has been recently derived within the continuous-time random-walk (CTRW) approach. In the CTRW approach, subdiffusive motion of particles is modelled by jumps whose onset probability distribution function is of a long-tailed form. The non-Markovian SLE allows for rigorous describing of some peculiarities of these reactions; for example, very slow long-time behaviour of the kinetics, non-analytical dependence of the reaction rate on the reactivity of particles, strong manifestation of fluctuation kinetics showing itself in very slowly decreasing behaviour of the kinetics at very long times, etc

  6. Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories, I

    Gaiotto, D.; Teschner, J.

    2012-03-01

    Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on S 4 . (orig.)

  7. On the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_1^\\alpha ({T^N})

    Ahmedov, Anvarjon; Materneh, Ehab; Zainuddin, Hishamuddin

    2017-09-01

    The relevance of waves in quantum mechanics naturally implies that the decomposition of arbitrary wave packets in terms of monochromatic waves plays an important role in applications of the theory. When eigenfunction expansions does not converge, then the expansions of the functions with certain smoothness should be considered. Such functions gained prominence primarily through their application in quantum mechanics. In this work we study the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_p^α ({T^N}), related to the self-adjoint extension of the Laplace operator in torus TN . The sufficient conditions for summability is obtained using the modified Poisson formula. Isomorphism properties of the elliptic differential operators is applied in order to obtain estimation for the Fourier series of the functions from the classes of Liouville L_p^α .

  8. Expansions with respect to squares, symplectic and Poisson structures associated with the Sturm-Liouville problem. II

    Arkad'ev, V.A.; Pogrebkov, A.K.; Polivanov, M.K.

    1988-01-01

    The concept of tangent vector is made more precise to meet the specific nature of the Sturm-Liouville problem, and on this basis a Poisson bracket that is modified compared with the Gardner form by special boundary terms is derived from the Zakharov-Faddeev symplectic form. This bracket is nondegenerate, and in it the variables of the discrete and continuous spectra are separated

  9. Calculating the Price for Derivative Financial Assets of Bessel Processes Using the Sturm-Liouville Theory

    Burtnyak Ivan V.

    2017-06-01

    Full Text Available In the paper we apply the spectral theory to find the price for derivatives of financial assets assuming that the processes described are Markov processes and such that can be considered in the Hilbert space L^2 using the Sturm-Liouville theory. Bessel diffusion processes are used in studying Asian options. We consider the financial flows generated by the Bessel diffusions by expressing them in terms of the system of Bessel functions of the first kind, provided that they take into account the linear combination of the flow and its spatial derivative. Such expression enables calculating the size of the market portfolio and provides a measure of the amount of internal volatility in the market at any given moment, allows investigating the dynamics of the equity market. The expansion of the Green function in terms of the system of Bessel functions is expressed by an analytic formula that is convenient in calculating the volume of financial flows. All assumptions are natural, result in analytic formulas that are consistent with the empirical data and, when applied in practice, adequately reflect the processes in equity markets.

  10. Analysis of geometric phase effects in the quantum-classical Liouville formalism.

    Ryabinkin, Ilya G; Hsieh, Chang-Yu; Kapral, Raymond; Izmaylov, Artur F

    2014-02-28

    We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.

  11. Physics-based models for measurement correlations: application to an inverse Sturm–Liouville problem

    Bal, Guillaume; Ren Kui

    2009-01-01

    In many inverse problems, the measurement operator, which maps objects of interest to available measurements, is a smoothing (regularizing) operator. Its inverse is therefore unbounded and as a consequence, only the low-frequency component of the object of interest is accessible from inevitably noisy measurements. In many inverse problems however, the neglected high-frequency component may significantly affect the measured data. Using simple scaling arguments, we characterize the influence of the high-frequency component. We then consider situations where the correlation function of such an influence may be estimated by asymptotic expansions, for instance as a random corrector in homogenization theory. This allows us to consistently eliminate the high-frequency component and derive a closed form, more accurate, inverse problem for the low-frequency component of the object of interest. We present the asymptotic expression of the correlation matrix of the eigenvalues in a Sturm–Liouville problem with unknown potential. We propose an iterative algorithm for the reconstruction of the potential from knowledge of the eigenvalues and show that using the approximate correlation matrix significantly improves the reconstructions

  12. Analysis of geometric phase effects in the quantum-classical Liouville formalism

    Ryabinkin, Ilya G.; Izmaylov, Artur F. [Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4 (Canada); Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 (Canada); Hsieh, Chang-Yu; Kapral, Raymond [Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 (Canada)

    2014-02-28

    We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.

  13. Synchronization of chaotic systems involving fractional operators of Liouville-Caputo type with variable-order

    Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.; Valtierra-Rodríguez, M.

    2017-12-01

    In this paper, we propose a state-observer-based approach to synchronize variable-order fractional (VOF) chaotic systems. In particular, this work is focused on complete synchronization with a so-called unidirectional master-slave topology. The master is described by a dynamical system in state-space representation whereas the slave is described by a state observer. The slave is composed of a master copy and a correction term which in turn is constituted of an estimation error and an appropriate gain that assures the synchronization. The differential equations of the VOF chaotic system are described by the Liouville-Caputo and Atangana-Baleanu-Caputo derivatives. Numerical simulations involving the synchronization of Rössler oscillators, Chua's systems and multi-scrolls are studied. The simulations show that different chaotic behaviors can be obtained if different smooths functions defined in the interval (0 , 1 ] are used as the variable order of the fractional derivatives. Furthermore, simulations show that the VOF chaotic systems can be synchronized.

  14. Geometric properties of static Einstein-Maxwell dilaton horizons with a Liouville potential

    Abdolrahimi, Shohreh; Shoom, Andrey A.

    2011-01-01

    We study nondegenerate and degenerate (extremal) Killing horizons of arbitrary geometry and topology within the Einstein-Maxwell-dilaton model with a Liouville potential (the EMdL model) in d-dimensional (d≥4) static space-times. Using Israel's description of a static space-time, we construct the EMdL equations and the space-time curvature invariants: the Ricci scalar, the square of the Ricci tensor, and the Kretschmann scalar. Assuming that space-time metric functions and the model fields are real analytic functions in the vicinity of a space-time horizon, we study the behavior of the space-time metric and the fields near the horizon and derive relations between the space-time curvature invariants calculated on the horizon and geometric invariants of the horizon surface. The derived relations generalize similar relations known for horizons of static four- and five-dimensional vacuum and four-dimensional electrovacuum space-times. Our analysis shows that all the extremal horizon surfaces are Einstein spaces. We present the necessary conditions for the existence of static extremal horizons within the EMdL model.

  15. NNDSS - Table III. Tuberculosis

    U.S. Department of Health & Human Services — NNDSS - Table III. Tuberculosis - 2018.This Table includes total number of cases reported in the United States, by region and by states, in accordance with the...

  16. Pension Insurance Data Tables

    Pension Benefit Guaranty Corporation — Find out about retirement trends in PBGC's data tables. The tables include statistics on the people and pensions that PBGC protects, including how many Americans are...

  17. NNDSS - Table IV. Tuberculosis

    U.S. Department of Health & Human Services — NNDSS - Table IV. Tuberculosis - 2016.This Table includes total number of cases reported in the United States, by region and by states, in accordance with the...

  18. NNDSS - Table IV. Tuberculosis

    U.S. Department of Health & Human Services — NNDSS - Table IV. Tuberculosis - 2014.This Table includes total number of cases reported in the United States, by region and by states, in accordance with the...

  19. NNDSS - Table II. Vibriosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Vibriosis - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding year), and selected...

  20. NNDSS - Table III. Tuberculosis

    U.S. Department of Health & Human Services — NNDSS - Table III. Tuberculosis - 2017.This Table includes total number of cases reported in the United States, by region and by states, in accordance with the...

  1. NNDSS - Table IV. Tuberculosis

    U.S. Department of Health & Human Services — NNDSS - Table IV. Tuberculosis - 2015.This Table includes total number of cases reported in the United States, by region and by states, in accordance with the...

  2. NNDSS - Table II. Vibriosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Vibriosis - 2018. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding year), and selected...

  3. Tabled Execution in Scheme

    Willcock, J J; Lumsdaine, A; Quinlan, D J

    2008-08-19

    Tabled execution is a generalization of memorization developed by the logic programming community. It not only saves results from tabled predicates, but also stores the set of currently active calls to them; tabled execution can thus provide meaningful semantics for programs that seemingly contain infinite recursions with the same arguments. In logic programming, tabled execution is used for many purposes, both for improving the efficiency of programs, and making tasks simpler and more direct to express than with normal logic programs. However, tabled execution is only infrequently applied in mainstream functional languages such as Scheme. We demonstrate an elegant implementation of tabled execution in Scheme, using a mix of continuation-passing style and mutable data. We also show the use of tabled execution in Scheme for a problem in formal language and automata theory, demonstrating that tabled execution can be a valuable tool for Scheme users.

  4. AcuTable

    Dibbern, Simon; Rasmussen, Kasper Vestergaard; Ortiz-Arroyo, Daniel

    2017-01-01

    In this paper we describe AcuTable, a new tangible user interface. AcuTable is a shapeable surface that employs capacitive touch sensors. The goal of AcuTable was to enable the exploration of the capabilities of such haptic interface and its applications. We describe its design and implementation...

  5. Table Tennis Club

    Table Tennis Club

    2013-01-01

    Apparently table tennis plays an important role in physics, not so much because physicists are interested in the theory of table tennis ball scattering, but probably because it provides useful breaks from their deep intellectual occupation. It seems that many of the greatest physicists took table tennis very seriously. For instance, Heisenberg could not even bear to lose a game of table tennis, Otto Frisch played a lot of table tennis, and had a table set up in his library, and Niels Bohr apparently beat everybody at table tennis. Therefore, as the CERN Table Tennis Club advertises on a poster for the next CERN Table Tennis Tournament: “if you want to be a great physicist, perhaps you should play table tennis”. Outdoor table at restaurant n° 1 For this reason, and also as part of the campaign launched by the CERN medical service “Move! & Eat better”, to encourage everyone at CERN to take regular exercise, the CERN Table Tennis Club, with the supp...

  6. Periodic Table of Students.

    Johnson, Mike

    1998-01-01

    Presents an exercise in which an eighth-grade science teacher decorated the classroom with a periodic table of students. Student photographs were arranged according to similarities into vertical columns. Students were each assigned an atomic number according to their placement in the table. The table is then used to teach students about…

  7. The unbounded solution of a periodic mixed Sturm–Liouville problem in an infinite strip for the Laplacian

    M.G. Elsheikh

    2013-10-01

    Full Text Available The unbounded solution, at the points where the boundary conditions change, for a mixed Sturm–Liouville problem of the Dirichlet–Neumann type can be obtained using the method of the integral equation formulation. Since this formulation is usually reduced to an infinite algebraic system in which the unknowns are the Fourier coefficients of the unknown unbounded entity, a study of ℓp-solutions imposes itself concerning the influence of the truncation on such systems. This study is achieved and the well-known theorem on the ℓ2-solutions of the infinite algebraic systems is generalized.

  8. Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

    Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

    2018-06-01

    In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

  9. Mortality table construction

    Sutawanir

    2015-12-01

    Mortality tables play important role in actuarial studies such as life annuities, premium determination, premium reserve, valuation pension plan, pension funding. Some known mortality tables are CSO mortality table, Indonesian Mortality Table, Bowers mortality table, Japan Mortality table. For actuary applications some tables are constructed with different environment such as single decrement, double decrement, and multiple decrement. There exist two approaches in mortality table construction : mathematics approach and statistical approach. Distribution model and estimation theory are the statistical concepts that are used in mortality table construction. This article aims to discuss the statistical approach in mortality table construction. The distributional assumptions are uniform death distribution (UDD) and constant force (exponential). Moment estimation and maximum likelihood are used to estimate the mortality parameter. Moment estimation methods are easier to manipulate compared to maximum likelihood estimation (mle). However, the complete mortality data are not used in moment estimation method. Maximum likelihood exploited all available information in mortality estimation. Some mle equations are complicated and solved using numerical methods. The article focus on single decrement estimation using moment and maximum likelihood estimation. Some extension to double decrement will introduced. Simple dataset will be used to illustrated the mortality estimation, and mortality table.

  10. CERN Table Tennis Club

    CERN Table Tennis Club

    2014-01-01

    CERN Table Tennis Club Announcing CERN 60th Anniversary Table Tennis Tournament to take place at CERN, from July 1 to July 15, 2014   The CERN Table Tennis Club, reborn in 2008, is encouraging people at CERN to take more regular exercise. This is why the Club, thanks to the strong support of the CERN Staff Association, installed last season a first outdoor table on the terrace of restaurant # 1, and will install another one this season on the terrace of Restaurant # 2. Table tennis provides both physical exercise and friendly social interactions. The CERN Table Tennis club is happy to use the unique opportunity of the 60th CERN anniversary to promote table tennis at CERN, as it is a game that everybody can easily play, regardless of level. Table tennis is particularly well suited for CERN, as many great physicists play table tennis, as you might already know: “Heisenberg could not even bear to lose a game of table tennis”; “Otto Frisch played a lot of table tennis;...

  11. Wave packet autocorrelation functions for quantum hard-disk and hard-sphere billiards in the high-energy, diffraction regime.

    Goussev, Arseni; Dorfman, J R

    2006-07-01

    We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision expansions we provide a first-principle analytical calculation of the time-dependent autocorrelation function for the wave packet in the high-energy diffraction regime, in which the particle's de Broglie wavelength, while being small compared to the size of the scatterers, is large enough to prevent the formation of geometric shadow over distances of the order of the particle's free flight path. The hard-disk or hard-sphere scattering system must be sufficiently dilute in order for this high-energy diffraction regime to be achievable. Apart from the overall exponential decay, the autocorrelation function exhibits a generally complicated sequence of relatively strong peaks corresponding to partial revivals of the wave packet. Both the exponential decay (or escape) rate and the revival peak structure are predominantly determined by the underlying classical dynamics. A relation between the escape rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the counterpart classical system, previously known for hard-disk billiards, is strengthened by generalization to three spatial dimensions. The results of the quantum mechanical calculation of the time-dependent autocorrelation function agree with predictions of the semiclassical periodic orbit theory.

  12. Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type

    Gorbachev, D V; Ivanov, V I

    2015-01-01

    Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles

  13. TABLE TENNIS CLUB

    TABLE TENNIS CLUB

    2010-01-01

    2010 CERN Table Tennis Tournament The CERN Table Tennis Club organizes its traditional CERN Table Tennis Tournament, at the Meyrin club, 2 rue de livron, in Meyrin, Saturday August 21st, in the afternoon. The tournament is open to all CERN staff, users, visitors and families, including of course summer students. See below for details. In order to register, simply send an E-mail to Jean-Pierre Revol (jean-pierre.revol@cern.ch). You can also download the registration form from the Club Web page (http://www.cern.ch/tabletennis), and send it via internal mail. Photo taken on August 22, 2009 showing some of the participants in the 2nd CERN Table Tennis tournament. INFORMATION ON CERN TABLE TENNIS CLUB CERN used to have a tradition of table tennis activities at CERN. For some reason, at the beginning of the 1980’s, the CERN Table Tennis club merged with the Meyrin Table Tennis club, a member of the Association Genevoise de Tennis de Table (AGTT). Therefore, if you want to practice table tennis, you...

  14. Sinh-Gordon, cosh-Gordon, and Liouville equations for strings and multistrings in constant curvature spacetimes

    Larsen, A.L.; Sanchez, N.

    1996-01-01

    We find that the fundamental quadratic form of classical string propagation in (2+1)-dimensional constant curvature spacetimes solves the sinh-Gordon equation, the cosh-Gordon equation, or the Liouville equation. We show that in both de Sitter and anti endash de Sitter spacetimes (as well as in the 2+1 black hole anti endash de Sitter spacetime), all three equations must be included to cover the generic string dynamics. The generic properties of the string dynamics are directly extracted from the properties of these three equations and their associated potentials (irrespective of any solution). These results complete and generalize earlier discussions on this topic (until now, only the sinh-Gordon sector in de Sitter spacetime was known). We also construct new classes of multistring solutions, in terms of elliptic functions, to all three equations in both de Sitter and anti endash de Sitter spacetimes. Our results can be straightforwardly generalized to constant curvature spacetimes of arbitrary dimension, by replacing the sinh-Gordon equation, the cosh-Gordon equation, and the Liouville equation by their higher dimensional generalizations. copyright 1996 The American Physical Society

  15. Standard Reference Tables -

    Department of Transportation — The Standard Reference Tables (SRT) provide consistent reference data for the various applications that support Flight Standards Service (AFS) business processes and...

  16. Projected interaction picture of field operators and memory superoperators. A master equation for the single-particle Green's function in a Liouville space

    Grinberg, H.

    1983-11-01

    The projection operator method of Zwanzig and Feshbach is used to construct the time-dependent field operators in the interaction picture. The formula developed to describe the time dependence involves time-ordered cosine and sine projected evolution (memory) superoperators, from which a master equation for the interaction-picture single-particle Green's function in a Liouville space is derived. (author)

  17. Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

    Manukure, Solomon

    2018-04-01

    We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

  18. Existence of 2m-1 Positive Solutions for Sturm-Liouville Boundary Value Problems with Linear Functional Boundary Conditions on the Half-Line

    Yanmei Sun

    2012-01-01

    Full Text Available By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.

  19. The Living Periodic Table

    Nahlik, Mary Schrodt

    2005-01-01

    To help make the abstract world of chemistry more concrete eighth-grade students, the author has them create a living periodic table that can be displayed in the classroom or hallway. This display includes information about the elements arranged in the traditional periodic table format, but also includes visual real-world representations of the…

  20. The G′G-expansion method using modified Riemann–Liouville derivative for some space-time fractional differential equations

    Ahmet Bekir

    2014-09-01

    Full Text Available In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear nonfractional ordinary differential equations. Then G′G-expansion method is applied to obtain exact solutions of the space-time fractional Burgers equation, the space-time fractional KdV-Burgers equation and the space-time fractional coupled Burgers’ equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation.

  1. arXiv Bose enhancement, the Liouville effective action and the high multiplicity tail in p-A collisions

    Kovner, Alex

    In the framework of dense-dilute CGC approach we study fluctuations in the multiplicity of produced particles in p-A collisions. We show that the leading effect that drives the fluctuations is the Bose enhancement of gluons in the proton wave function. We explicitly calculate the moment generating function that resums the effects of Bose enhancement. We show that it can be understood in terms of the Liouville effective action for the composite field which is identified with the fluctuating density, or saturation momentum of the proton. The resulting probability distribution turns out to be very close to the gamma-distribution. We also calculate the first correction to this distribution which is due to pairwise Hanbury Brown-Twiss correlations of produced gluons.

  2. Elementary Statistics Tables

    Neave, Henry R

    2012-01-01

    This book, designed for students taking a basic introductory course in statistical analysis, is far more than just a book of tables. Each table is accompanied by a careful but concise explanation and useful worked examples. Requiring little mathematical background, Elementary Statistics Tables is thus not just a reference book but a positive and user-friendly teaching and learning aid. The new edition contains a new and comprehensive "teach-yourself" section on a simple but powerful approach, now well-known in parts of industry but less so in academia, to analysing and interpreting process dat

  3. Empirical yield tables for Michigan.

    Jerold T. Hahn; Joan M. Stelman

    1984-01-01

    Describes the tables derived from the 1980 Forest Survey of Michigan and presents ways the tables can be used. These tables are broken down according to Michigan's four Forest Survey Units, 14 forest types, and 5 site-index classes.

  4. Empirical yield tables for Wisconsin.

    Jerold T. Hahn; Joan M. Stelman

    1989-01-01

    Describes the tables derived from the 1983 Forest Survey of Wisconsin and presents ways the tables can be used. These tables are broken down according to Wisconsin`s five Forest Survey Units and 14 forest types.

  5. Permit.LOA table

    National Oceanic and Atmospheric Administration, Department of Commerce — This table includes the effective dates by vessel and permit number for each issued letter of authorization (LOA) by the Permit Office (APSD)

  6. VMS forms Output Tables

    National Oceanic and Atmospheric Administration, Department of Commerce — These output tables contain parsed and format validated data from the various VMS forms that are sent from any given vessel, while at sea, from the VMS devices on...

  7. The Periodic Table CD.

    Banks, Alton J.; Holmes, Jon L.

    1995-01-01

    Describes the characteristics of the digitized version of The Periodic Table Videodisc. Provides details about the organization of information and access to the data via Macintosh and Windows computers. (DDR)

  8. Setting the Periodic Table.

    Saturnelli, Annette

    1985-01-01

    Examines problems resulting from different forms of the periodic table, indicating that New York State schools use a form reflecting the International Union of Pure and Applied Chemistry's 1984 recommendations. Other formats used and reasons for standardization are discussed. (DH)

  9. Body Mass Index Table

    ... Families ( We Can! ) Health Professional Resources Body Mass Index Table 1 for BMI greater than 35, go ... Health Information Email Alerts Jobs and Careers Site Index About NHLBI National Institute of Health Department of ...

  10. Decision table languages and systems

    Metzner, John R

    1977-01-01

    ACM Monograph Series: Decision Table Languages and Systems focuses on linguistic examination of decision tables and survey of the features of existing decision table languages and systems. The book first offers information on semiotics, programming language features, and generalization. Discussions focus on semantic broadening, outer language enrichments, generalization of syntax, limitations, implementation improvements, syntactic and semantic features, decision table syntax, semantics of decision table languages, and decision table programming languages. The text then elaborates on design im

  11. Empirical yield tables for Minnesota.

    Jerold T. Hahn; Gerhard K. Raile

    1982-01-01

    Describes the tables derived from the 1977 Forest Survey of Minnesota and presents examples of how the tables can be used. These tables are broken down according to Minnesota's four Forest Survey Units, 14 forest types, and 5 site index classes. Presents 210 of the 350 possible tables that contained sufficient data to justify publication.

  12. On the completeness of systems of eigenfunctions of the Sturm-Liouville operator with a potential depending on the spectral parameter and a nonlinear problem

    Zhidkov, P.E.

    1996-01-01

    First, the eigenvalue problem on the segment [0,1] for the Sturm-Liouville operator with a potential depending on the spectral parameter with the zero Dirichlet boundary conditions is considered. For this problem, under some hypotheses on the potential, it is proved that the necessary and sufficient condition for an arbitrary system of eigenfunctions, possessing a unique function with n roots in the interval (0,1) for an arbitrary non-negative integer number n, being complete in the space L 2 (0,1) is the linear independence of the functions from this system in the space L 2 (0,1). Then, this result is applied to the investigation of an eigenvalue problem for a nonlinear operator on the Sturm-Liouville type. For this problem, the completeness of the system of its eigenfunctions in the space L 2 (0,1) is proved. (author). 12 refs

  13. X-ray table

    Craig, J.R.; Otto, G.W.

    1980-01-01

    An X-ray radiographic or fluoroscopic table is described which includes a film holder with a frame attached to a cable running over end pulleys for positioning the holder longitudinally as desired under the table top. The holder has a front opening to receive a cassette-supporting tray which can be slid out on tracks to change the cassette. A reed switch on the frame is opened by a permanent magnet on the tray only when the tray is half-way out. When the switch is closed, an electromagnet locks the pulley and the holder in place. The holder is thus automatically locked in place not only during exposure (tray in) but when the tray is out for changing the cassette. To re-position the holder, the operator pulls the tray half-out and, using the tray itself, pushes the holder along the table, the holder being counterbalanced by a weight. (author)

  14. Table Tennis Club

    Table Tennis Club

    2012-01-01

    The CERN Table Tennis club and the Meyrin CTT are organizing two Table Tennis workshops from 2 to 6 July and from 20 to 24 August 2012 inclusive in Meyrin. A professional would be with your children from 14.00 pm to 18.00 pm: an instructor J + S category A. Training courses with specific themes, individual courses would be given depending on the level of the child’s game, “discoveries –table tennis games” courses and games with the robot. Other activities (stretching, relaxation). Afternoons (from 18 to 20 children): 40 CHF per workshop and per child. Evenings (from 18 to 20 adults): 60 CHF per workshop and per adult. For further information, please contact Mr. Monteil : Mobile: (+33) 06 61 31 70 47 E-mail: wilfried.monteil@free.fr.

  15. Periodic table of elements

    Fluck, E.; Heumann, K.G.

    1985-01-01

    Following a recommendation by the International Union for Pure and Applied Chemistry (IUPAC), the groups of the periodic table shall be numbered from 1 to 18, instead of I to VIII as before. The recommendations has been approved of by the Committee on Nomenclature of the American Chemical Society. The new system abandons the distinction between main groups (a) and auxiliary groups (b), which in the past frequently has been the reason for misunderstandings between European and American chemists, due to different handling. The publishing house VCH Verlagsgesellschaft recently produced a new periodic table that shows the old and the new numbering system together at a glance, so that chemists will have time to get familiar with the new system. In addition the new periodic table represents an extensive data compilation arranged by elements. The front page lists the chemical properties of elements, the back page their physical properties. (orig./EF) [de

  16. Climate change : transportation table

    Ogilvie, K.

    1999-01-01

    The Kyoto Protocol sets greenhouse gas (GHG) reduction targets for the post-2000 period. If ratified, Canada will be committed to reduce emissions of GHGs by 6 per cent below 1990 levels during the period 2008-2012. A recommended national strategy is to establish 'issue tables' that will advise the Ministers of Energy and Environment on preferred options to reach the Kyoto target and to identify early actions that can be taken. The 'Transportation Table' which is the focus of this paper, is one of the 15 sectoral tables. The Transportation Table will identify by July 1999, specific measures to mitigate GHG emissions from Canada's transportation sector. Currently, GHG emissions from the transportation sector are predicted to be 27 per cent above 1990 levels by 2010. Fuel taxes, emissions trading, and research into improved vehicle technologies and automotive fuels are some of the recommended options which can help reduce emissions trading from the transportation sector. Studies are underway to deal with emissions from transport in two sub-groups, freight and passenger. 1 fig

  17. Statistical tables 2003

    2003-01-01

    The energy statistical table is a selection of statistical data for energies and countries from 1997 to 2002. It concerns the petroleum, the natural gas, the coal, the electric power, the production, the external market, the consumption per sector, the energy accounting 2002 and graphs on the long-dated forecasting. (A.L.B.)

  18. A Modern Periodic Table.

    Herrenden-Harker, B. D.

    1997-01-01

    Presents a modern Periodic Table based on the electron distribution in the outermost shell and the order of filling of the sublevels within the shells. Enables a student to read off directly the electronic configuration of the element and the order in which filling occurs. (JRH)

  19. Conversion tables. Appendix I

    McKerrell, H.

    1975-01-01

    Tables are presented for the conversion of standard (5568 year half-life) C-14 dates to calendar years. The major part of the data converts C-14 dates to tree-ring years: additional data are given, based on the Egyptian historical curve. (U.K.)

  20. Extending the D’alembert solution to space–time Modified Riemann–Liouville fractional wave equations

    Godinho, Cresus F.L.; Weberszpil, J.; Helayël-Neto, J.A.

    2012-01-01

    In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC. The non-differentiable nature of the microscopic dynamics may be connected with time scales. Based on the Modified Riemann–Liouville definition of fractional derivatives, we have worked out explicit solutions to a fractional wave equation with suitable initial conditions to carefully understand the time evolution of classical fields with a fractional dynamics. First, by considering space–time partial fractional derivatives of the same order in time and space, a generalized fractional D’alembertian is introduced and by means of a transformation of variables to light-cone coordinates, an explicit analytical solution is obtained. To address the situation of different orders in the time and space derivatives, we adopt different approaches, as it will become clear throughout this paper. Aspects connected to Lorentz symmetry are analyzed in both approaches.

  1. Liouville master equation for multielectron dynamics: Neutralization of highly charged ions near a LiF surface

    Wirtz, Ludger; Reinhold, Carlos O.; Lemell, Christoph; Burgdoerfer, Joachim

    2003-01-01

    We present a simulation of the neutralization of highly charged ions in front of a lithium fluoride surface including the close-collision regime above the surface. The present approach employs a Monte Carlo solution of the Liouville master equation for the joint probability density of the ionic motion and the electronic population of the projectile and the target surface. It includes single as well as double particle-hole (de)excitation processes and incorporates electron correlation effects through the conditional dynamics of population strings. The input in terms of elementary one- and two-electron transfer rates is determined from classical trajectory Monte Carlo calculations as well as quantum-mechanical Auger calculations. For slow projectiles and normal incidence, the ionic motion depends sensitively on the interplay between image acceleration towards the surface and repulsion by an ensemble of positive hole charges in the surface ('trampoline effect'). For Ne 10+ we find that image acceleration is dominant and no collective backscattering high above the surface takes place. For grazing incidence, our simulation delineates the pathways to complete neutralization. In accordance with recent experimental observations, most ions are reflected as neutral or even as singly charged negative particles, irrespective of the charge state of the incoming ions

  2. Tomographic examination table

    Redington, R.W.; Henkes, J.L.

    1979-01-01

    Equipment is described for positioning and supporting patients during tomographic mammography using X-rays. The equipment consists of a table and fabric slings which permit the examination of a downward, pendant breast of a prone patient by allowing the breast to pass through a aperture in the table into a fluid filled container. The fluid has an X-ray absorption coefficient similar to that of soft human tissue allowing high density resolution radiography and permitting accurate detection of breast tumours. The shape of the equipment and the positioning of the patient allow the detector and X-ray source to rotate 360 0 about a vertical axis through the breast. This permits the use of relatively simple image reconstruction algorithms and a divergent X-ray geometry. (UK)

  3. Seashore marine table quiz

    Institute, Marine

    2013-01-01

    Develop an increasing awareness of plants and animals that live in local marine environments including the seashore, seas and oceans of Ireland. After learning all about the seashore and other marine related lessons, this quiz can be used to evaluate the student’s knowledge of the marine related living things and natural environments. The table quiz can be used as a guide, highlighting facts about the marine environment and some of the animals that live there.

  4. Table Tennis Club

    Table Tennis Club

    2012-01-01

    2012 CERN Table Tennis Tournament As the campaign launched by the CERN medical service “Move! & Eat better” is designed in particular to encourage people at CERN to take more regular exercise, the CERN Table Tennis Club, with its traditional CERN Table Tennis Tournament is providing an excellent opportunity to practice moving. The tournament will take place at the Meyrin CTT, 2 rue de Livron, Saturday August 25, 2012, in the afternoon (starting at 13:30). It is open to all CERN staff, users, visitors and families, including of course summer students, who are strongly encouraged to participate. In order to register, simply send an E-mail to Jean-Pierre Revol (jean-pierre.revol@cern.ch). You may also find useful information on the Club Web page http://www.cern.ch/tabletennis CERN 2011 champion Savitha Flaecher, between the finalist Bertrand Mouches on her left, the winner of the consolation draw on her right (Sudarshan Paramesvaran), and far left, Denis Moriaud (semi-finalist a...

  5. SRTC - Gap Analysis Table

    M.L. Johnson

    2005-01-01

    The purpose of this document is to review the existing SRTC design against the ''Nuclear Safety Design Bases for License Application'' (NSDB) [Ref. 10] requirements and to identify codes and standards and supplemental requirements to meet these requirements. If these codes and standards and supplemental requirements can not fully meet these safety requirements then a ''gap'' is identified. These gaps will be identified here and addressed using the ''Site Rail Transfer Cart (SRTC) Design Development Plan'' [Ref. 14]. The codes and standards, supplemental requirements, and design development requirements are provided in the SRTC and associated rails gap analysis table in Appendix A. Because SRTCs are credited with performing functions important to safety (ITS) in the NSDB [Ref. 10], design basis requirements are applicable to ensure equipment is available and performs required safety functions when needed. The gap analysis table is used to identify design objectives and provide a means to satisfy safety requirements. To ensure that the SRTC and rail design perform required safety Functions and meet performance criteria, this portion of the gap analysis table supplies codes and standards sections and the supplemental requirements and identifies design development requirements, if needed

  6. Global Reference Tables Services Architecture

    Social Security Administration — This database stores the reference and transactional data used to provide a data-driven service access method to certain Global Reference Table (GRT) service tables.

  7. Aggregation Algorithms in Heterogeneous Tables

    Titus Felix FURTUNA

    2006-01-01

    Full Text Available The heterogeneous tables are most used in the problem of aggregation. A solution for this problem is to standardize these tables of figures. In this paper, we proposed some methods of aggregation based on the hierarchical algorithms.

  8. Operator product expansion in Liouville field theory and Seiberg-type transitions in log-correlated random energy models

    Cao, Xiangyu; Le Doussal, Pierre; Rosso, Alberto; Santachiara, Raoul

    2018-04-01

    We study transitions in log-correlated random energy models (logREMs) that are related to the violation of a Seiberg bound in Liouville field theory (LFT): the binding transition and the termination point transition (a.k.a., pre-freezing). By means of LFT-logREM mapping, replica symmetry breaking and traveling-wave equation techniques, we unify both transitions in a two-parameter diagram, which describes the free-energy large deviations of logREMs with a deterministic background log potential, or equivalently, the joint moments of the free energy and Gibbs measure in logREMs without background potential. Under the LFT-logREM mapping, the transitions correspond to the competition of discrete and continuous terms in a four-point correlation function. Our results provide a statistical interpretation of a peculiar nonlocality of the operator product expansion in LFT. The results are rederived by a traveling-wave equation calculation, which shows that the features of LFT responsible for the transitions are reproduced in a simple model of diffusion with absorption. We examine also the problem by a replica symmetry breaking analysis. It complements the previous methods and reveals a rich large deviation structure of the free energy of logREMs with a deterministic background log potential. Many results are verified in the integrable circular logREM, by a replica-Coulomb gas integral approach. The related problem of common length (overlap) distribution is also considered. We provide a traveling-wave equation derivation of the LFT predictions announced in a precedent work.

  9. On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators

    Krejčiřík, David; Siegl, Petr; Železný, Jakub

    2014-01-01

    Roč. 8, č. 1 (2014), s. 255-281 ISSN 1661-8254 R&D Projects: GA MŠk LC06002; GA MŠk LC527; GA ČR GAP203/11/0701 Grant - others:GA ČR(CZ) GD202/08/H072 Institutional support: RVO:61389005 Keywords : Sturm-Liouville operators * non-symmetric Robin boundary conditions * similarity to normal or self-adjoint operators * discrete spectral operator * complex symmetric operator * PT-symmetry * metric operator * C operator * Hilbert- Schmidt operators Subject RIV: BE - Theoretical Physics Impact factor: 0.545, year: 2014

  10. Radionuclide table. Pt. 1

    Legrand, Jean; Perolat, J.-P.; Lagoutine, Frederic; Le Gallic, Yves.

    The evaluation of the following 29 radionuclides is presented: 22 Na, 24 Na, sup(24m)Na, 51 Cr, 54 Mn, 57 Co, 58 Co, sup(58m)Co, 60 Co, sup(60m)Co, 75 Se, 103 Ru, sup(103m)Rh, sup(110m)Ag- 110 Ag, 109 Cd, 125 Sb, sup(125mTe), 125 I, 133 Xe, sup(133m)Xe, 131 Cs, 134 Cs, sup(134m)Cs, 139 Ce, 144 Ce- 144 Pr, 144 Pr, 169 Er, 186 Re, 203 Hg. The introduction contains a brief description of radioactive processes and the evaluation rules followed. The best values and associated uncertainties are given for each radionuclide for the major parameters of the decay scheme and the radiation intensities emitted, together with a decay table. Gamma, X-rays and sometimes conversion electron spectra are also provided [fr

  11. Gutzwiller's octagon and the triangular billiard T*(2,3,8) as models for the quantization of chaotic systems by Selberg's trace formula

    Ninnemann, H.

    1994-12-01

    Two strongly chaotic systems are investigated with respect to quantization rules based on Selberg's trace formula. One of them results from the action of a particular strictly hyperbolic Fuchsian group on the Poincare disk, leading to a compact Riemann surface of genus g=2. This Fuchsian group is denoted as Gutzwiller's group. The other one is a billiard inside a hyperbolic triangle, which is generated by the operation of a reflection group denoted as T * (2,3,8). Since both groups belong to the class of arithmetical groups, their elements can be characterized explicitly as 2x2 matrices containing entries, which are algebraic numbers subject to a particular set of restrictions. In the case of Gutzwiller's group this property can be used to determine the geodesic length spectrum of the associated dynamical system completely up to some cutoff length. For the triangular billiar T * (2,3,8) the geodesic length spectrum is calculated by building group elements as products of a suitable set of generators and separating a unique representative for each conjugacy class. The presence of reflections in T * (2,3,8) introduces additional classes of group elements besides the hyperbolic ones, which correspond to periodic orbits of the dynamical system. Due to different choices of boundary conditions along the edges of the fundamental domain of T * (2,3,8), several quantum mechanical systems are associated to one classical system. It has been observed, that these quantum mechanical systems can be divided into two classes according to the behavior of their spectral statistics. This peculiarity is examined from the point of view of classical quantities entering quantization rules. It can be traced back to a subtle influence of the boundary conditions, which introduces contributions from non-periodic orbits for one of the two classes. (orig.)

  12. SLIPM - a MAPLE package for numerical solution of Sturm-Liouville partial problems based on a continuous analog of Newton's method. II. Program realization

    Puzynin, I.V.; Puzynina, T.P.; Tkhak, V.Ch.

    2010-01-01

    SLIPM (Sturm-LIouville Problem in MAPLE) is a program complex written in the language of the computer algebras system MAPLE. It consists of the main program SLIPM.mw and of some procedures. It is intended for a numerical solution with the help of the continuous analog of Newton's method (CANM) of Sturm-Liouville partial problems, i.e. for calculating some eigenvalue of linear second-order differential operator and a corresponding eigenfunction satisfying homogeneous boundary conditions of the general type. SLIPM is the development of the program complexes SLIP1 and SLIPH4 written in the Fortran language. It is added by two new ways of calculating the initial value of iterative parameter τ 0 , by a procedure for calculating a higher precision solution (eigenvalue and corresponding eigenfunction) with the help of Richardson's extrapolation method, by graphical visualization procedures of intermediate and final results of the iterative process and by saving of the results on a disk file. The descriptions of the procedures purposes and their parameters are given

  13. Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

    Owolabi, Kolade M.

    2018-03-01

    In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

  14. Symbol Tables and Branch Tables: Linking Applications Together

    Handler, Louis M.

    2011-01-01

    This document explores the computer techniques used to execute software whose parts are compiled and linked separately. The computer techniques include using a branch table or indirect address table to connect the parts. Methods of storing the information in data structures are discussed as well as differences between C and C++.

  15. Volume tables for red alder.

    Floyd A. Johnson; R. M. Kallander; Paul G. Lauterbach

    1949-01-01

    The increasing importance of red alder as a commercial species in the Pacific Northwest has prompted the three agencies listed above to pool their tree measurement data for the construction of standard regional red alder volume tables. The tables included here were based on trees from a variety of sites and form classes. Approximately one quarter of the total number of...

  16. MCNPX Model/Table Comparison

    Hendricks, J.S.

    2003-01-01

    MCNPX is a Monte Carlo N-Particle radiation transport code extending the capabilities of MCNP4C. As with MCNP, MCNPX uses nuclear data tables to transport neutrons, photons, and electrons. Unlike MCNP, MCNPX also uses (1) nuclear data tables to transport protons; (2) physics models to transport 30 additional particle types (deuterons, tritons, alphas, pions, muons, etc.); and (3) physics models to transport neutrons and protons when no tabular data are available or when the data are above the energy range (20 to 150 MeV) where the data tables end. MCNPX can mix and match data tables and physics models throughout a problem. For example, MCNPX can model neutron transport in a bismuth germinate (BGO) particle detector by using data tables for bismuth and oxygen and using physics models for germanium. Also, MCNPX can model neutron transport in UO 2 , making the best use of physics models and data tables: below 20 MeV, data tables are used; above 150 MeV, physics models are used; between 20 and 150 MeV, data tables are used for oxygen and models are used for uranium. The mix-and-match capability became available with MCNPX2.5.b (November 2002). For the first time, we present here comparisons that calculate radiation transport in materials with various combinations of data charts and model physics. The physics models are poor at low energies (<150 MeV); thus, data tables should be used when available. Our comparisons demonstrate the importance of the mix-and-match capability and indicate how well physics models work in the absence of data tables

  17. MCNPX Model/Table Comparison

    Hendricks, J S

    2003-01-01

    MCNPX is a Monte Carlo N-Particle radiation transport code extending the capabilities of MCNP4C. As with MCNP, MCNPX uses nuclear data tables to transport neutrons, photons, and electrons. Unlike MCNP, MCNPX also uses (1) nuclear data tables to transport protons; (2) physics models to transport 30 additional particle types (deuterons, tritons, alphas, pions, muons, etc.); and (3) physics models to transport neutrons and protons when no tabular data are available or when the data are above the energy range (20 to 150 MeV) where the data tables end. MCNPX can mix and match data tables and physics models throughout a problem. For example, MCNPX can model neutron transport in a bismuth germinate (BGO) particle detector by using data tables for bismuth and oxygen and using physics models for germanium. Also, MCNPX can model neutron transport in UO sub 2 , making the best use of physics models and data tables: below 20 MeV, data tables are used; above 150 MeV, physics models are used; between 20 and 150 MeV, data t...

  18. Elekta Precise Table characteristics of IGRT remote table positioning

    Riis, Hans L.; Zimmermann, Sune J.

    2009-01-01

    Cone beam CT is a powerful tool to ensure an optimum patient positioning in radiotherapy. When cone beam CT scan of a patient is acquired, scan data of the patient are compared and evaluated against a reference image set and patient position offset is calculated. Via the linac control system, the patient is moved to correct for position offset and treatment starts. This procedure requires a reliable system for movement of patient. In this work we present a new method to characterize the reproducibility, linearity and accuracy in table positioning. The method applies to all treatment tables used in radiotherapy. Material and methods. The table characteristics are investigated on our two recent Elekta Synergy Platforms equipped with Precise Table installed in a shallow pit concrete cavity. Remote positioning of the table uses the auto set-up (ASU) feature in the linac control system software Desktop Pro R6.1. The ASU is used clinically to correct for patient positioning offset calculated via cone beam CT (XVI)-software. High precision steel rulers and a USB-microscope has been used to detect the relative table position in vertical, lateral and longitudinal direction. The effect of patient is simulated by applying external load on the iBEAM table top. For each table position an image is exposed of the ruler and display values of actual table position in the linac control system is read out. The table is moved in full range in lateral direction (50 cm) and longitudinal direction (100 cm) while in vertical direction a limited range is used (40 cm). Results and discussion. Our results show a linear relation between linac control system read out and measured position. Effects of imperfect calibration are seen. A reproducibility within a standard deviation of 0.22 mm in lateral and longitudinal directions while within 0.43 mm in vertical direction has been observed. The usage of XVI requires knowledge of the characteristics of remote table positioning. It is our opinion

  19. The Periodic Table in Croatia

    Raos, N.

    2011-12-01

    Full Text Available The Croatian (Yugoslav Academy of Sciences and Arts was the first academy to elect D. I. Mendeleev as its honorary member (1882, whereas the periodic table of the elements has been taught regularly at the Zagreb University since 1888. The early interest of Croatian chemists in the periodic table should be attributed primarily to their pan-Slavic attitude, particularly as proof that Slavic people were able to produce "their own Newtons" (M. V. Lomonosov and D. I. Mendeleev. Such enthusiastic views, however, did not help in analyzing the contribution of Mendeleev and other scientists to the discovery and development of the periodic table of the elements.

  20. Automation of BESSY scanning tables

    Hanton, J.; Kesteman, J.

    1981-01-01

    A micro processor M6800 is used for the automation of scanning and premeasuring BESSY tables. The tasks achieved by the micro processor are: 1. control of spooling of the four asynchronous film winding devices and switching on and off the 4 projections lamps, 2. pre-processing of the data coming from a bi-polar coordinates measuring device, 3. bi-directional interchange of informations between the operator, the BESSY table and the DEC PDP 11/34 mini computer controling the scanning operations, 4. control of the magnification on the table by swapping the projection lenses of appropriate focal lengths and the associated light boxes (under development). In connection with point 4, study is being made for the use of BESSY tables for accurate measurements (+/-5 microns), by encoding the displacements of the projections lenses. (orig.)

  1. The Table Mountain Field Site

    Federal Laboratory Consortium — The Table Mountain Field Site, located north of Boulder, Colorado, is designated as an area where the magnitude of strong, external signals is restricted (by State...

  2. The redoubtable ecological periodic table

    Ecological periodic tables are repositories of reliable information on quantitative, predictably recurring (periodic) habitat–community patterns and their uncertainty, scaling and transferability. Their reliability derives from their grounding in sound ecological principle...

  3. Table 1: Biofuels simulation scenarios

    U.S. Environmental Protection Agency — A spreadsheet containing information used to generate Table 1. Agricultural Market sector results presented in the spreadsheet were generated elsewhere (non-EPA) and...

  4. NNDSS - Table I. infrequently reported notifiable diseases

    U.S. Department of Health & Human Services — NNDSS - Table I. infrequently reported notifiable diseases - 2016. In this Table, provisional* cases of selected† infrequently reported notifiable diseases...

  5. Mathematical tables tables of in g [z] for complex argument

    Abramov, A A

    1960-01-01

    Mathematical Tables of In ? (z) for Complex Argument is a compilation of tables of In ? (z), z = x + iy, calculated for steps in x and y of 0.01 and with an accuracy of one unit in the last (the sixth) decimal place. Interpolation is used to calculate In ? (z) for intermediate values and is carried out separately for the real and imaginary parts of In ? (z). Six places are retained in interpolation.This book first explains how the values of In ? (z) are calculated using the asymptotic formula in a wide lattice with step h = 0.16, and how the tables and the nomograph are used. The values in the

  6. Characteristics of Tables for Disseminating Biobehavioral Results.

    Schneider, Barbara St Pierre; Nagelhout, Ed; Feng, Du

    2018-01-01

    To report the complexity and richness of study variables within biological nursing research, authors often use tables; however, the ease with which consumers understand, synthesize, evaluate, and build upon findings depends partly upon table design. To assess and compare table characteristics within research and review articles published in Biological Research for Nursing and Nursing Research. A total of 10 elements in tables from 48 biobehavioral or biological research or review articles were analyzed. To test six hypotheses, a two-level hierarchical linear model was used for each of the continuous table elements, and a two-level hierarchical generalized linear model was used for each of the categorical table elements. Additionally, the inclusion of probability values in statistical tables was examined. The mean number of tables per article was 3. Tables in research articles were more likely to contain quantitative content, while tables in review articles were more likely to contain both quantitative and qualitative content. Tables in research articles had a greater number of rows, columns, and column-heading levels than tables in review articles. More than one half of statistical tables in research articles had a separate probability column or had probability values within the table, whereas approximately one fourth had probability notes. Authors and journal editorial staff may be generating tables that better depict biobehavioral content than those identified in specific style guidelines. However, authors and journal editorial staff may want to consider table design in terms of audience, including alternative visual displays.

  7. 30 CFR 250.1401 - Index table.

    2010-07-01

    ... 30 Mineral Resources 2 2010-07-01 2010-07-01 false Index table. 250.1401 Section 250.1401 Mineral... OPERATIONS IN THE OUTER CONTINENTAL SHELF Outer Continental Shelf (OCS) Civil Penalties § 250.1401 Index table. The following table is an index of the sections in this subpart: § 250.1401Table Definitions...

  8. The Alfonsine tables of Toledo

    Chabás, José

    2003-01-01

    The Alfonsine Tables of Toledo is for historians working in the fields of astronomy, science, the Middle Ages, Spanish and other Romance languages. It is also of interest to scholars interested in the history of Castile, in Castilian-French relations in the Middle Ages and in the history of patronage. It explores the Castilian canons of the Alfonsine Tables and offers a study of their context, language, astronomical content, and diffusion. The Alfonsine Tables of Toledo is unique in that it: includes an edition of a crucial text in history of science; provides an explanation of astronomy as it was practiced in the Middle Ages; presents abundant material on early scientific language in Castilian; presents new material on the diffusion of Alfonsine astronomy in Europe; describes the role of royal patronage of science in a medieval context.

  9. Statistical probability tables CALENDF program

    Ribon, P.

    1989-01-01

    The purpose of the probability tables is: - to obtain dense data representation - to calculate integrals by quadratures. They are mainly used in the USA for calculations by Monte Carlo and in the USSR and Europe for self-shielding calculations by the sub-group method. The moment probability tables, in addition to providing a more substantial mathematical basis and calculation methods, are adapted for condensation and mixture calculations, which are the crucial operations for reactor physics specialists. However, their extension is limited by the statistical hypothesis they imply. Efforts are being made to remove this obstacle, at the cost, it must be said, of greater complexity

  10. Breakdown concepts for contingency tables

    Kuhnt, S.

    2010-01-01

    Loglinear Poisson models are commonly used to analyse contingency tables. So far, robustness of parameter estimators as well as outlier detection have rarely been treated in this context. We start with finite-sample breakdown points. We yield that the breakdown point of mean value estimators

  11. Superconductivity and the Periodic Table

    Chapnik, I.M.

    1985-01-01

    In view of the inability of the present theory of superconductivity to make reliable predictions for the magnitude of Tsub(c) it seems useful to search for empirical relationships between the composition of the compound and the Tsub(c) value. Table I gives a list of the available Tsub(c) data for transition metals (TM) having from 3 to 9 outer electrons and Tsub(c) data for non-transition elements (NTE) of groups IIB, IIIB and IVB, including data for amorphous (Am) structures and structures (marked by triangles) obtained at high pressures. The analogous metals have therefore the same structure. In Tables II to IV the Tsub(c) data are presented for analogous compounds of NTE from IB - VIB group. Conclusions are presented. (author)

  12. NNDSS - Table I. infrequently reported notifiable diseases

    U.S. Department of Health & Human Services — NNDSS - Table I. infrequently reported notifiable diseases - 2017. In this Table, provisional cases of selected infrequently reported notifiable diseases (<1,000...

  13. NNDSS - Table I. infrequently reported notifiable diseases

    U.S. Department of Health & Human Services — NNDSS - Table I. infrequently reported notifiable diseases - 2014.In this Table, provisional cases of selected infrequently reported notifiable diseases (<1,000...

  14. NNDSS - Table I. infrequently reported notifiable diseases

    U.S. Department of Health & Human Services — NNDSS - Table I. infrequently reported notifiable diseases - 2015. In this Table, provisional cases of selected infrequently reported notifiable diseases (<1,000...

  15. NNDSS - Table I. infrequently reported notifiable diseases

    U.S. Department of Health & Human Services — NNDSS - Table I. infrequently reported notifiable diseases - 2018. In this Table, provisional cases of selected infrequently reported notifiable diseases (<1,000...

  16. Toddlers at the Table: Avoiding Power Struggles

    ... Search English Español Toddlers at the Table: Avoiding Power Struggles KidsHealth / For Parents / Toddlers at the Table: ... common concerns into opportunities to teach healthy eating habits. Most Toddlers Are Picky Eaters Many toddlers express ...

  17. NNDSS - Table II. Babesiosis to Campylobacteriosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Babesiosis to Campylobacteriosis - 2018. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the...

  18. NNDSS - Table II. Cryptosporidiosis to Dengue

    U.S. Department of Health & Human Services — NNDSS - Table II. Cryptosporidiosis to Dengue - 2015.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding...

  19. NNDSS - Table II. Cryptosporidiosis to Dengue

    U.S. Department of Health & Human Services — NNDSS - Table II. Cryptosporidiosis to Dengue - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the preceding...

  20. NNDSS - Table II. Shiga toxin to Shigellosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Shiga toxin to Shigellosis - 2015. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding...

  1. NNDSS - Table II. West Nile virus disease

    U.S. Department of Health & Human Services — NNDSS - Table II. West Nile virus disease - 2015.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding year),...

  2. Handbook of thermodynamic tables and charts

    Raznjevic, K.

    1976-01-01

    A compilation of thermodynamic and thermophysical tables and charts is presented. Numerical values are cited in both technical and SI units. Solid, liquid, vapor, and gaseous forms of organic and inorganic materials are included. 12 figures, 137 tables

  3. Global Reference Tables for Management Information Systems

    Social Security Administration — This database is a collection of reference tables that store common information used throughout SSA. These tables standardize code structures and code usage of SSA...

  4. NNDSS - Table II. Mumps to Rabies, animal

    U.S. Department of Health & Human Services — NNDSS - Table II. Mumps to Rabies, animal - 2014.In this Table, all conditions with a 5-year average annual national total of more than or equals 1,000 cases but...

  5. NNDSS - Table II. Mumps to Rabies, animal

    U.S. Department of Health & Human Services — NNDSS - Table II. Mumps to Rabies, animal - 2015.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding year),...

  6. NNDSS - Table II. Mumps to Rabies, animal

    U.S. Department of Health & Human Services — NNDSS - Table II. Mumps to Rabies, animal - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the preceding...

  7. NNDSS - Table II. Legionellosis to Malaria

    U.S. Department of Health & Human Services — NNDSS - Table II. Legionellosis to Malaria - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding...

  8. NNDSS - Table II. Hepatitis (viral, acute) C

    U.S. Department of Health & Human Services — NNDSS - Table II. Hepatitis (viral, acute) C - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding...

  9. NNDSS - Table II. Babesiosis to Campylobacteriosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Babesiosis to Campylobacteriosis - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the...

  10. NNDSS - Table II. West Nile virus disease

    U.S. Department of Health & Human Services — NNDSS - Table II. West Nile virus disease - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding year),...

  11. NNDSS - Table II. Giardiasis to Haemophilus influenza

    U.S. Department of Health & Human Services — NNDSS - Table II. Giardiasis to Haemophilus influenza - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the...

  12. NNDSS - Table II. Meningococcal to Pertussis

    U.S. Department of Health & Human Services — NNDSS - Table II. Meningococcal to Pertussis - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding...

  13. NNDSS - Table II. Ehrlichiosis and Anaplasmosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Ehrlichiosis and Anaplasmosis - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding...

  14. NNDSS - Table II. Cryptosporidiosis to Dengue

    U.S. Department of Health & Human Services — NNDSS - Table II. Cryptosporidiosis to Dengue - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding...

  15. NNDSS - Table II. Tetanus to Varicella

    U.S. Department of Health & Human Services — NNDSS - Table II. Tetanus to Varicella - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding year),...

  16. NNDSS - Table II. Chlamydia to Coccidioidomycosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Chlamydia to Coccidioidomycosis - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the...

  17. NNDSS - Table II. Salmonellosis to Shigellosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Salmonellosis to Shigellosis - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding...

  18. NNDSS - Table II. West Nile to Zika

    U.S. Department of Health & Human Services — NNDSS - Table II. West Nile to Zika - 2018. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding year), and...

  19. NNDSS - Table II. Babesiosis to Coccidioidomycosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Babesiosis to Coccidioidomycosis - 2014.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the...

  20. Global Reference Tables for Production Systems

    Social Security Administration — This database is a collection of reference tables that store common information used throughout SSA. These tables standardized code structures and code usage of SSA...

  1. NNDSS - Table II. Giardiasis to Haemophilus influenza

    U.S. Department of Health & Human Services — NNDSS - Table II. Giardiasis to Haemophilus influenza - 2014. In this Table, all conditions with a 5-year average annual national total of more than or equals 1,000...

  2. NNDSS - Table II. Giardiasis to Haemophilus influenza

    U.S. Department of Health & Human Services — NNDSS - Table II. Giardiasis to Haemophilus influenza - 2018. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the...

  3. NNDSS - Table II. Giardiasis to Haemophilus influenza

    U.S. Department of Health & Human Services — NNDSS - Table II. Giardiasis to Haemophilus influenza - 2015.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the...

  4. NNDSS - Table II. Giardiasis to Haemophilus influenza

    U.S. Department of Health & Human Services — NNDSS - Table II. Giardiasis to Haemophilus influenza - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the...

  5. NNDSS - Table II. Hepatitis (viral, acute)

    U.S. Department of Health & Human Services — NNDSS - Table II. Hepatitis (viral, acute) - 2015.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding year),...

  6. NNDSS - Table II. Hepatitis (viral, acute)

    U.S. Department of Health & Human Services — NNDSS - Table II. Hepatitis (viral, acute) - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the preceding...

  7. NNDSS - Table II. Hepatitis (viral, acute)

    U.S. Department of Health & Human Services — NNDSS - Table II. Hepatitis (viral, acute) - 2014.In this Table, all conditions with a 5-year average annual national total of more than or equals 1,000 cases but...

  8. NNDSS - Table II. Meningococcal disease to Pertussis

    U.S. Department of Health & Human Services — NNDSS - Table II. Meningococcal disease to Pertussis - 2018. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the...

  9. NNDSS - Table II. Chlamydia to Coccidioidomycosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Chlamydia to Coccidioidomycosis - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the...

  10. NNDSS - Table II. Tetanus to Varicella

    U.S. Department of Health & Human Services — NNDSS - Table II. Tetanus to Varicella - 2018. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding year),...

  11. NNDSS - Table II. Invasive Pneumococcal to Legionellosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Invasive Pneumococcal to Legionellosis - 2014.In this Table, all conditions with a 5-year average annual national total of more than or equals...

  12. Stream Tables and Watershed Geomorphology Education.

    Lillquist, Karl D.; Kinner, Patricia W.

    2002-01-01

    Reviews copious stream tables and provides a watershed approach to stream table exercises. Results suggest that this approach to learning the concepts of fluvial geomorphology is effective. (Contains 39 references.) (DDR)

  13. NNDSS - Table II. Legionellosis to Malaria

    U.S. Department of Health & Human Services — NNDSS - Table II. Legionellosis to Malaria - 2018. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding...

  14. NNDSS - Table II. Lyme disease to Meningococcal

    U.S. Department of Health & Human Services — NNDSS - Table II. Lyme disease to Meningococcal - 2015.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding...

  15. NNDSS - Table II. Lyme disease to Meningococcal

    U.S. Department of Health & Human Services — NNDSS - Table II. Lyme disease to Meningococcal - 2014In this Table, all conditions with a 5-year average annual national total of more than or equals 1,000 cases...

  16. NNDSS - Table II. Lyme disease to Meningococcal

    U.S. Department of Health & Human Services — NNDSS - Table II. Lyme disease to Meningococcal - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the...

  17. NNDSS - Table II. Salmonellosis to Shigellosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Salmonellosis to Shigellosis - 2014.In this Table, all conditions with a 5-year average annual national total of more than or equals 1,000 cases...

  18. NNDSS - Table II. West Nile virus disease

    U.S. Department of Health & Human Services — NNDSS - Table II. West Nile virus disease - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the preceding...

  19. NNDSS - Table II. Rubella to Salmonellosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Rubella to Salmonellosis - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the preceding...

  20. NNDSS - Table II. Ehrlichiosis/Anaplasmosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Ehrlichiosis/Anaplasmosis - 2015.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding...

  1. NNDSS - Table II. Tetanus to Vibriosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Tetanus to Vibriosis - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the preceding year),...

  2. NNDSS - Table II. Shiga toxin to Shigellosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Shiga toxin to Shigellosis - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the preceding...

  3. NNDSS - Table II. Babesiosis to Campylobacteriosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Babesiosis to Campylobacteriosis - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the...

  4. NNDSS - Table II. Babesiosis to Campylobacteriosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Babesiosis to Campylobacteriosis - 2015.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the...

  5. NNDSS - Table II. Rubella to Salmonellosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Rubella to Salmonellosis - 2015.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding year),...

  6. NNDSS - Table II. Tetanus to Vibriosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Tetanus to Vibriosis - 2015.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding year), and...

  7. NNDSS - Table II. Chlamydia to Coccidioidomycosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Chlamydia to Coccidioidomycosis - 2015.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the preceding...

  8. NNDSS - Table II. Ehrlichiosis/Anaplasmosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Ehrlichiosis/Anaplasmosis - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the preceding...

  9. NNDSS - Table II. Invasive Pneumococcal to Legionellosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Invasive Pneumococcal to Legionellosis - 2015.In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the...

  10. NNDSS - Table II. Invasive Pneumococcal to Legionellosis

    U.S. Department of Health & Human Services — NNDSS - Table II. Invasive Pneumococcal to Legionellosis - 2016. In this Table, provisional* cases of selected† notifiable diseases (≥1,000 cases reported during the...

  11. On Importance of Rows for Decision Tables

    AbouEisha, Hassan M.; Azad, Mohammad; Moshkov, Mikhail

    2017-01-01

    In this paper, we propose a method for the evaluation of importance of rows for decision tables. It is based on indirect information about changes in the set of reducts after removing the considered row from the table. We also discuss results of computer experiments with decision tables from UCI Machine Learning Repository.

  12. 21 CFR 890.3750 - Mechanical table.

    2010-04-01

    ... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Mechanical table. 890.3750 Section 890.3750 Food... DEVICES PHYSICAL MEDICINE DEVICES Physical Medicine Prosthetic Devices § 890.3750 Mechanical table. (a) Identification. A mechanical table is a device intended for medical purposes that has a flat surface that can be...

  13. On Importance of Rows for Decision Tables

    AbouEisha, Hassan M.

    2017-06-21

    In this paper, we propose a method for the evaluation of importance of rows for decision tables. It is based on indirect information about changes in the set of reducts after removing the considered row from the table. We also discuss results of computer experiments with decision tables from UCI Machine Learning Repository.

  14. The Different Periodic Tables of Dmitrii Mendeleev

    Laing, Michael

    2008-01-01

    Between 1869 and 1905 the Russian chemist Dmitrii Mendeleev published several tables with different arrangements of the chemical elements. Four of these are compared with periodic tables by Russian scientists from 1934 and 1969. The difficulties caused by the lanthanoid elements are clearly seen in the table of 1905, which satisfactorily includes…

  15. Cohort Working Life Tables for Older Canadians

    Frank T. Denton

    2010-12-01

    those based on the period tables, for both men and women, and that is reflected in increased retirement expectancies. For example, a male aged 50 in 1976 could have expected to live three years longer and to have almost four more years in retirement, based on the male cohort table under medium assumptions, as compared with the corresponding period table.

  16. Guide to mathematical tables supplement no 1

    Burunova, N M; Fedorova, R M

    1960-01-01

    A Guide to Mathematical Tables is a supplement to the Guide to Mathematical Tables published by the U.S.S.R. Academy of Sciences in 1956. The tables contain information on subjects such as powers, rational and algebraic functions, and trigonometric functions, as well as logarithms and polynomials and Legendre functions. An index listing all functions included in both the Guide and the Supplement is included.Comprised of 15 chapters, this supplement first describes mathematical tables in the following order: the accuracy of the table (that is, the number of decimal places or significant

  17. Table-top job analysis

    1994-12-01

    The purpose of this Handbook is to establish general training program guidelines for training personnel in developing training for operation, maintenance, and technical support personnel at Department of Energy (DOE) nuclear facilities. TTJA is not the only method of job analysis; however, when conducted properly TTJA can be cost effective, efficient, and self-validating, and represents an effective method of defining job requirements. The table-top job analysis is suggested in the DOE Training Accreditation Program manuals as an acceptable alternative to traditional methods of analyzing job requirements. DOE 5480-20A strongly endorses and recommends it as the preferred method for analyzing jobs for positions addressed by the Order.

  18. A table-top LHC

    Barbara Warmbein

    2011-01-01

    Many years ago, when ATLAS was no more than a huge empty underground cavern and Russian artillery shell casings were being melted down to become part of the CMS calorimetry system, science photographer Peter Ginter started documenting the LHC’s progress. He was there when special convoys of equipment crossed the Jura at night, when cranes were lowering down detector slices and magnet coils were being wound in workshops. Some 18 years of LHC history have been documented by Ginter, and the result has just come out as a massive coffee table book full of double-page spreads of Ginter’s impressive images.   The new coffee table book, LHC: the Large Hadron Collider. Published by the Austrian publisher Edition Lammerhuber in cooperation with CERN and UNESCO Publishing, LHC: the Large Hadron Collider is an unusual piece in the company’s portfolio. As the publisher’s first science book, LHC: the Large Hadron Collider weighs close to five kilos and comes in a s...

  19. Health effects assessment summary tables

    1999-01-01

    The document is an excellent pointer system to identify current literature or changes in assessment criteria for many chemicals of interest to Superfund. It was prepared for Superfund use by the Environmental Criteria and Assessment Office (ECAO-Cin) in EPA's Office of Health and Environmental Assessment. Chemicals considered are those for which Health Effects Assessment Documents, Health and Environmental Effects Profiles, Health Assessment Documents or Air Quality Criteria Documents have been prepared by ECAO. Radionuclides considered are those believed to be most common at Superfund sites. Tables summarize reference doses (RfDs) for toxicity from subchronic and chronic inhalation, oral exposure, slope factors and unit risk values for carcinogenicity based on lifetime inhalation and oral exposure, and radionuclide carcinogenicity

  20. Setting Places at the Table

    James R. Briscoe

    2016-12-01

    Full Text Available A recent survey by the National Endowment for the Arts found that only 2% of Americans listen to “Classical” music with regularity, and fewer practice or play art or historic music even once in a year. The rotating kaleidoscope of new technologies, repertories, interpretation, and cultural values can become not an ultimate bewilderment, a nail in the coffin of art and historic music, but a powerful tool for revitalizing how it engages persons of all age groups and how it can broaden its understanding. The table of musical places we set can respond to the narrative we carefully conceive for any condition at hand, for the student or scholar or layperson we address, for an intentional kaleidoscope of presentations. Such an attitude might let the other 98% discover art and historic music and see their lives mirrored and bettered.

  1. The periodic table in Flatland

    Kibler, M.

    1995-01-01

    The D-dimensional Coulomb system serves as a starting point for generating generalized atomic shells. These shells are ordered according to a generalized Madelung rule in D dimensions. This rule together with an Aufbau Prinzip is applied to produce a D-dimensional periodic table. A model is developed to rationalize the ordering of the shells predicted by the generalized Madelung rule. This model is based on the introduction of an Hamiltonian, invariant under the q-deformed algebra U q (so(D)), that breaks down the SO (D + 1) dynamical symmetry of the hydrogen atom in D dimensions. The D = 2 case (Flatland) is investigated with some details. It is shown that the neutral atoms and the (moderately) positive ions correspond to the values q = 0.8 and q = 1, respectively, of the deformation parameter q. (authors). 55 refs

  2. An ECR table plasma generator

    Racz, R.; Palinkas, J.; Bin, S.

    2012-01-01

    A compact ECR plasma device was built in our lab using the 'spare parts' of the ATOMKI ECR ion source. We call it 'ECR Table Plasma Generator'. It consists of a relatively big plasma chamber (ID=10 cm, L=40 cm) in a thin NdFeB hexapole magnet with independent vacuum and gas dosing systems. For microwave coupling two low power TWTAs (Travelling Wave tube amplifier) can be applied individually or simultaneously, operating in the 6-18 GHz range. There is no axial magnetic trap and there is no extraction. The technical details of the plasma generator and preliminary plasma photo study results are shown. This paper is followed by the associated poster. (authors)

  3. A periodic table for cancer.

    Epstein, Richard J

    2015-01-01

    Cancers exhibit differences in metastatic behavior and drug sensitivity that correlate with certain tumor-specific variables such as differentiation grade, growth rate/extent and molecular regulatory aberrations. In practice, patient management is based on the past results of clinical trials adjusted for these biomarkers. Here, it is proposed that treatment strategies could be fine-tuned upfront simply by quantifying tumorigenic spatial (cell growth) and temporal (genetic stability) control losses, as predicted by genetic defects of cell-cycle-regulatory gatekeeper and genome-stabilizing caretaker tumor suppressor genes, respectively. These differential quantifications of tumor dysfunction may in turn be used to create a tumor-specific 'periodic table' that guides rational formulation of survival-enhancing anticancer treatment strategies.

  4. Environmental regulatory update table, March 1989

    Houlberg, L.; Langston, M.E.; Nikbakht, A.; Salk, M.S.

    1989-04-01

    The Environmental Regulatory Update Table provides information on regulatory initiatives of interest to DOE operations and contractor staff with environmental management responsibilities. The table is updated each month with information from the Federal Register and other sources, including direct contact with regulatory agencies. Each table entry provides a chronological record of the rulemaking process for that initiative with an abstract and a projection of further action

  5. Environmental Regulatory Update Table, April 1989

    Houlberg, L.; Langston, M.E.; Nikbakht, A.; Salk, M.S.

    1989-05-01

    The Environmental Regulatory Update Table provides information on regulatory initiatives of interest to DOE operations and contractor staff with environmental management responsibilities. The table is updated each month with information from the Federal Register and other sources, including direct contact with regulatory agencies. Each table entry provides a chronological record of the rulemaking process for that initiative with an abstract and a projection of further action

  6. Environmental Regulatory Update Table, August 1991

    Houlberg, L.M., Hawkins, G.T.; Salk, M.S.

    1991-09-01

    This Environmental Regulatory Update Table (August 1991) provides information on regulatory initiatives of interest to DOE operations and contractor staff with environmental management responsibilities. The table is updated each month with information from the Federal Register and other sources, including direct contact with regulatory agencies. Each table entry provides a chronological record of the rulemaking process for that initiative with an abstract and a projection of further action.

  7. Environmental Regulatory Update Table, December 1989

    Houlbert, L.M.; Langston, M.E.; Nikbakht, A.; Salk, M.S.

    1990-01-01

    The Environmental Regulatory Update Table provides information on regulatory initiatives of interest to DOE operations and contractor staff with environmental management responsibilities. The table is updated each month with information from the Federal Register and other sources, including direct contact with regulatory agencies. Each table entry provides a chronological record of the rulemaking process for that initiative with an abstract and a projection of further action

  8. Thermodynamic tables to accompany Modern engineering thermodynamics

    Balmer, Robert T

    2011-01-01

    This booklet is provided at no extra charge with new copies of Balmer's Modern Engineering Thermodynamics. It contains two appendices. Appendix C contains 40 thermodynamic tables, and Appendix D consists of 6 thermodynamic charts. These charts and tables are provided in a separate booklet to give instructors the flexibility of allowing students to bring the tables into exams. The booklet may be purchased separately if needed.

  9. Environmental Regulatory Update Table, December 1991

    Houlberg, L.M.; Hawkins, G.T.; Salk, M.S.

    1992-01-01

    The Environmental Regulatory Update Table provides information on regulatory initiatives of interest to DOE operations and contractor staff with environmental management responsibilities. The table is updated each month with information from the Federal Register and other sources, including direct contact with regulatory agencies. Each table entry provides a chronological record of the rulemaking process for that initiative with an abstract and a projection of further action.

  10. A table top exercise and workshop

    Lakey, J.R.A.

    1992-01-01

    Table top exercises are widely applied in training for emergency preparedness and have long been a feature of Courses on Planning for Nuclear Emergencies. Experience of a large number of table top exercises is used to provide a classification of the types of exercise indicating the application and the disadvantages. The use of workshops is considered to be complementary rather than an alternative to teaching methods available from table top exercises. (author)

  11. Environmental Regulatory Update Table, August 1990

    Houlberg, L.M.; Nikbakht, A.; Salk, M.S.

    1990-09-01

    The Environmental Regulatory Update Table provides information on regulatory initiatives of interest to DOE operations and contractor staff with environmental management responsibilities. The table is updated each month with information from the Federal Register and other sources, including direct contact with regulatory agencies. Each table entry provides a chronological record of the rulemaking process for that initiative with an abstract and a projection of further action

  12. Environmental Regulatory Update Table, October 1991

    Houlberg, L.M.; Hawkins, G.T.; Salk, M.S.

    1991-11-01

    The Environmental Regulatory Update Table provides information on regulatory initiatives of interest to DOE operations and contractor staff with environmental management responsibilities. The table is updated each month with information from the Federal Register and other sources, including direct contact with regulatory agencies. Each table entry provides a chronological record of the rulemaking process for that initiative with an abstract and a projection of further action.

  13. Environmental Regulatory Update Table, November 1991

    Houlberg, L.M.; Hawkins, G.T.; Salk, M.S.

    1991-12-01

    The Environmental Regulatory Update Table provides information on regulatory initiatives of interest to DOE operations and contractor staff with environmental management responsibilities. The table is updated each month with information from the Federal Register and other sources, including direct contact with regulatory agencies. Each table entry provides a chronological record of the rulemaking process for that initiative with an abstract and a projection of further action.

  14. Environmental Regulatory Update Table, September 1991

    Houlberg, L.M.; Hawkins, G.T.; Salk, M.S.

    1991-10-01

    The Environmental Regulatory Update Table provides information on regulatory initiatives of interest to DOE operations and contractor staff with environmental management responsibilities. The table is updated each month with information from the Federal Register and other sources, including direct contact with regulatory agencies. Each table entry provides a chronological record of the rulemaking process for that initiative with an abstract and a projection of further action.

  15. Environmental regulatory update table, July 1991

    Houlberg, L.M.; Hawkins, G.T.; Salk, M.S.

    1991-08-01

    This Environmental Regulatory Update Table (July 1991) provides information on regulatory initiatives of interest to DOE operations and contractor staff with environmental management responsibilities. The table is updated each month with information from the Federal Register and other sources, including direct contact with regulatory agencies. Each table entry provides a chronological record of the rulemaking process for that initiative with an abstract and a projection of further action.

  16. Table of specific activities of selected isotopes

    Shipley, G.

    The bulk of this publication consists of a table of the half-lives, decay modes, and specific activities of isotopes selected for their particular interest to the Environmental Health and Safety Department, LBL. The specific activities were calculated with a PDP 9/15 computer. Also included in the report is a table of stable isotopes, the Th and U decay chains, a chart of the nuclides for elements 101 through 106, the heavy element region of the periodic table, and a specific activity monograph. 5 figures, 2 tables

  17. Scenario-based table top simulations

    Broberg, Ole; Edwards, Kasper; Nielsen, J.

    2012-01-01

    This study developed and tested a scenario-based table top simulation method in a user-driven innovation setting. A team of researchers worked together with a user group of five medical staff members from the existing clinic. Table top simulations of a new clinic were carried out in a simple model...

  18. 21 CFR 892.1980 - Radiologic table.

    2010-04-01

    ... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Radiologic table. 892.1980 Section 892.1980 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES RADIOLOGY DEVICES Diagnostic Devices § 892.1980 Radiologic table. (a) Identification. A radiologic...

  19. Nuttall Oak Volume and Weight Tables

    Bryce E. Schlaegel; Regan B. Willson

    1983-01-01

    Volume and weight tables were constructed from a 62-tree sample of Nuttall oak (Quercus nuttallii Palmer) taken in the Mississippi Delta. The tables present volume, green weight, and dry weight of bole wood, bole wood plus bark, and total tree above a one-foot stump as predicted from the nonlinear model Y = 0Db

  20. CREATING INPUT TABLES FROM WAPDEG FOR RIP

    K.G. Mon

    1998-01-01

    The purpose of this calculation is to create tables for input into RIP ver. 5.18 (Integrated Probabilistic Simulator for Environmental Systems) from WAPDEG ver. 3.06 (Waste Package Degradation) output. This calculation details the creation of the RIP input tables for TSPA-VA REV.00

  1. Solar Cell Efficiency Tables (Version 51)

    Levi, Dean H [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Green, Martin A. [University of New South Wales; Hishikawa, Yoshihiro [National Institute of Advanced Industrial Science and Technology (AIST); Dunlop, Ewan D. [European Commission-Joint Research Centre; Hohl-Ebinger, Jochen [Fraunhofer Institute for Solar Energy Systems; Ho-Baillie, Anita W. Y. [University of New South Wales

    2017-12-14

    Consolidated tables showing an extensive listing of the highest independently confirmed efficiencies for solar cells and modules are presented. Guidelines for inclusion of results into these tables are outlined and new entries since July 2017 are reviewed, together with progress over the last 25 years. Appendices are included documenting area definitions and also listing recognised test centres.

  2. Online Periodic Table: A Cautionary Note

    Izci, Kemal; Barrow, Lloyd H.; Thornhill, Erica

    2013-01-01

    The purpose of this study was (a) to evaluate ten online periodic table sources for their accuracy and (b) to compare the types of information and links provided to users. Limited studies have been reported on online periodic table (Diener and Moore 2011; Slocum and Moore in "J Chem Educ" 86(10):1167, 2009). Chemistry students'…

  3. Relating Functional Groups to the Periodic Table

    Struyf, Jef

    2009-01-01

    An introduction to organic chemistry functional groups and their ionic variants is presented. Functional groups are ordered by the position of their specific (hetero) atom in the periodic table. Lewis structures are compared with their corresponding condensed formulas. (Contains 5 tables.)

  4. Des tables pascales aux tables astronomiques et retour.

    Max Lejbowicz

    2006-05-01

    Full Text Available L’article étudie la naissance et le développement du calendrier ecclésiastique chrétien, i. e. le comput, depuis les premiers témoignages de la célébration annuelle de la résurrection de Jésus jusqu’aux traductions des tables astronomiques arabes au xiie siècle. Il privilégie les procédures qui aboutissent à la détermination des dates pascales et à leur mise en forme tabulaire. Les analyses sont conduites à partir d’un double point de vue. L’un est scientifique. Il s’appuie sur les données astronomiques retenues par Ptolémée et sur l’apport de la tradition mathématique grecque au calcul par approximations. Les cycles soli-lunaires sont posés à partir des fractions continues et le cycle soli-hebdomadaire à partir du plus petit commun multiple. Le second point de vue est social : l’unification du comput participe à celle de la chrétienté comprise comme une configuration politico-religieuse. Deux conclusions s’imposent. Quelle que soit l’importance que la civilisation médiévale a attribuée au comput, il reste que : 1 / les Pâques sont porteuses de significations irréductibles aux techniques chronométriques qui inscrivent cette fête dans le déroulement de l’année ; 2 / ces techniques ont toutefois marqué profondément les curiosités intellectuelles des Latins et les ont préparé à accueillir avec ferveur les zīj et la numération de position.The article studies the birth and development of the Christian ecclesiastical calendar, i.e. the computus, from the first witnesses to the yearly celebration of the resurrection of Jesus to the translations of arabic astronomical tables in the 12th century. It focuses on the procedures which resulted in determinig the dates of Easter and their being put into tabular form. These analyses were undertaken from two perspectives. One was scientific, relying on the astronomical data preserved by Ptolemy and on the contribution of the Greek mathematical

  5. INTRODUCTION Outline of Round Tables Outline of Round Tables

    Abarzhi, Snezhana I.; Sreenivasan, Katepalli R.

    2010-12-01

    The Second International Conference and Advanced School 'Turbulent Mixing and Beyond', TMB-2009, was held at the Abdus Salam International Centre for Theoretical Physics, (ICTP), Trieste, Italy on 27 July-7 August 2009. TMB-2009 united over 180 participants ranging from students to members of the National Academies of Sciences and Engineering, and including researchers at experienced and early stages of their carriers from leading scientific institutions in academia, national laboratories, corporations and industry worldwide. Responding to the community's inquiry and reaffirming the practices established at TMB-2007, two Round Tables were organized for the participants of TMB-2009 on 30 July 2009 and 6 August 2009 in the Oppenheimer Room at the Centre. The goals of the Round Tables were to encourage the information exchange among the members of the interdisciplinary and international TMB community, promote discussions regarding the state-of-the-art in TMB-related scientific areas, identify directions for frontier research, and articulate recommendations for future developments. This article is a summary of the collective work of the Round Table participants (listed alphabetically below by their last names), whose contributions form its substance and, as such, are greatly appreciated. Abarzhi, Snezhana I (University of Chicago, USA) Andrews, Malcolm (Los Alamos National Laboratory, USA) Belotserkovskii, Oleg (Institute for Computer Aided Design of the Russian Academy of Sciences, Russia) Bershadskii, Alexander (ICAR, Israel) Brandenburg, Axel (Nordita, Denmark) Chumakov, Sergei (Stanford University, USA) Desai, Tara (University of Milano-Bicocca, Italy) Galperin, Boris (University of South Florida, USA) Gauthier, Serge (Commissariat à l'Energie Atomique, France) Gekelman, Walter (University of California at Los Angeles, USA) Gibson, Carl (University of California at San Diego, USA) Goddard III, William A (California Institute of Technology, USA) Grinstein, Fernando

  6. A Classification Table for Achondrites

    Chennaoui-Aoudjehane, H.; Larouci, N.; Jambon, A.; Mittlefehldt, D. W.

    2014-01-01

    Classifying chondrites is relatively easy and the criteria are well documented. It is based on mineral compositions, textural characteristics and more recently, magnetic susceptibility. It can be more difficult to classify achondrites, especially those that are very similar to terrestrial igneous rocks, because mineralogical, textural and compositional properties can be quite variable. Achondrites contain essentially olivine, pyroxenes, plagioclases, oxides, sulphides and accessory minerals. Their origin is attributed to differentiated parents bodies: large asteroids (Vesta); planets (Mars); a satellite (the Moon); and numerous asteroids of unknown size. In most cases, achondrites are not eye witnessed falls and some do not have fusion crust. Because of the mineralogical and magnetic susceptibility similarity with terrestrial igneous rocks for some achondrites, it can be difficult for classifiers to confirm their extra-terrestrial origin. We -as classifiers of meteorites- are confronted with this problem with every suspected achondrite we receive for identification. We are developing a "grid" of classification to provide an easier approach for initial classification. We use simple but reproducible criteria based on mineralogical, petrological and geochemical studies. We presented the classes: acapulcoites, lodranites, winonaites and Martian meteorites (shergottite, chassignites, nakhlites). In this work we are completing the classification table by including the groups: angrites, aubrites, brachinites, ureilites, HED (howardites, eucrites, and diogenites), lunar meteorites, pallasites and mesosiderites. Iron meteorites are not presented in this abstract.

  7. Radiation on the dining table

    Rossi, Laura; Watson, Dana; Escandarani, Soledad; Miranda, Andrea; Troncoso, Alcides

    2009-01-01

    Zero tolerance to bacterial contamination means considering the acceptance of 'radiation on the table'. The process of food irradiation has been extensively studied, nevertheless its use remains a matter of some controversy. Despite unanimous agreement within the medical community of the safety of this procedure, occasional concerns arise from the consumers. A common consumer misconception is that irradiation may turn the food 'radioactive'. A significant number of scientific studies on the topic were analyzed. We found no scientific study demonstrating that consumption of irradiated food might pose a risk to consumers. All studies conclude that food irradiation at the appropriate dose required to reduce contamination is safe and does not affect its nutritional value. In order to emphasize the issue we discuss the potential benefit vs harm of irradiation of food contaminated with E. coli 0157: H7. The association of this bacteria with severe disease and death has been clearly established in contrast with the lack of a demonstrated risk due to meat irradiation. We conclude that the risks of food irradiation remains 'unknown' simply because, after four decades of research, none has been identified. In contrast to the risks of acquiring a food transmitted bacterial disease, the risk of irradiation is negligible

  8. Isomers chart; Table des isomeres

    Dupont-Gautier, P; Chantelot, S; Moisson, N [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1967-07-01

    The nuclear isomers are nuclides offering the same mass number and the same atomic number, but different energy levels. In the following chart the zero energy ground states are omitted and the metastable isomers, i.e. of non-zero energy, known and of measurable lifetime, are listed. The lower limit of this lifetime was set here to 0.1 x 10{sup -6} s. The various isomers were classified in increasing lifetimes. (authors) [French] Les isomeres nucleaires sont des nucleides presentant le meme nombre de masse et le meme numero atomique, mais des niveaux energetiques differents. Dans la table suivante, on a neglige les etats fondamentaux d'energie nulle et on a recense les isomeres metastables, c'est-a-dire d'energie non nulle, connus et de periode mesurable. La limite inferieure de cette periode a ete fixee ici a 0,1 x 10{sup -6} s. Les differents isomeres ont ete classes par periodes croissantes. (auteurs)

  9. Isomers chart; Table des isomeres

    Dupont-Gautier, P.; Chantelot, S.; Moisson, N. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1967-07-01

    The nuclear isomers are nuclides offering the same mass number and the same atomic number, but different energy levels. In the following chart the zero energy ground states are omitted and the metastable isomers, i.e. of non-zero energy, known and of measurable lifetime, are listed. The lower limit of this lifetime was set here to 0.1 x 10{sup -6} s. The various isomers were classified in increasing lifetimes. (authors) [French] Les isomeres nucleaires sont des nucleides presentant le meme nombre de masse et le meme numero atomique, mais des niveaux energetiques differents. Dans la table suivante, on a neglige les etats fondamentaux d'energie nulle et on a recense les isomeres metastables, c'est-a-dire d'energie non nulle, connus et de periode mesurable. La limite inferieure de cette periode a ete fixee ici a 0,1 x 10{sup -6} s. Les differents isomeres ont ete classes par periodes croissantes. (auteurs)

  10. Thermodynamic properties of mineral compounds (tables); Proprietes thermodynamiques des composes mineraux (tables)

    Perrot, P. [Lille-1 Univ., Lab. de Metallurgie Physique, UMR CNRS 8517, 59 - Villeneuve-d' Ascq (France)

    2005-10-01

    This article presents, in the form of tables, the thermodynamic data necessary for the calculation of equilibrium constants of reactions between mineral compounds (Rb, Re, Ru, S, Sb, Sc, Se, Si, Sm, Sn, Sr, Ta, Tb, Tc, Te, Th, Ti, Tl, Tm, U, V, W, Xe, Y, Yb, Zn, and Zr compounds). Table 1 presents the data recommended by Codata; table 2 gives the minimum informations allowing the calculation of an equilibrium constant in first approximation; table 3 allows to take into consideration the thermal capacities. Finally, table 4 gathers the data relative to species in aqueous solution. (J.S.)

  11. Some Reflections on the Periodic Table and Its Use.

    Fernelius, W. Conard

    1986-01-01

    Discusses early periodic tables; effect on the periodic table of atomic numbers; the periodic table in relation to electron distribution in the atoms of elements; terms and concepts related to the table; and the modern basis of the periodic table. Additional comments about these and other topics are included. (JN)

  12. Authenticated hash tables

    Triandopoulos, Nikolaos; Papamanthou, Charalampos; Tamassia, Roberto

    2008-01-01

    Hash tables are fundamental data structures that optimally answer membership queries. Suppose a client stores n elements in a hash table that is outsourced at a remote server so that the client can save space or achieve load balancing. Authenticating the hash table functionality, i.e., verifying...... to a scheme that achieves different trade-offs---namely, constant update time and O(nε/logκε n) query time for fixed ε > 0 and κ > 0. An experimental evaluation of our solution shows very good scalability....

  13. The 2005 CHF look-up table

    Groeneveld, D.C.; Vasic, A.Z.; Leung, L.K.H.; Durmayaz, A.; Shan, J.Q.; Yang, J.; Cheng, S.C.

    2005-01-01

    Full text of publication follows: CHF Look-up tables have been used widely for the prediction of the Critical Heat Flux (CHF) The CHF look-up table is basically a normalized data bank. The first CHF look-up table was constructed by Doroshchuk et al. (1975), using a limited database of 5 000 data points. This table, and all subsequent tables, contain normalized CHF values for a vertical 8 mm water-cooled tube for various pressures, mass fluxes and qualities. The CHF table development work has since been in progress at various institutions (e.g. CENG-Grenoble, University of Ottawa (UO), Ottawa, IPPE, Obninsk, and AECL, Chalk River) using an ever increasing data base. The 1995 CHF look-up table employs a data base containing about 30 000 CHF points and provides CHF values for an 8 mm ID, water-cooled tube, for 19 pressures, 20 mass fluxes, and 23 qualities. covering the full range of conditions of practical interest. The 2005 CHF LUT is an update to the 1995 LUT and addresses several concerns raised in the literature. The major improvements made are: - enhancement of the quality of the data base of the CHF look-up table (identify outliers, improve screening procedures); - increase in the data base by adding recently obtained data; - employment of greater subdivision of the look-up table by using smaller intervals in the independent parameters (pressure, mass flux and quality) at conditions where the variation in CHF is significant; - improvement of the smoothness of the CHF look-up table. This was done by the use of logarithmic functions for CHF, using optimum Spline functions etc. A discussion of the impact of these changes on the prediction accuracy and table smoothness is presented. It will be shown that the 2005 CHF look-up table is characterized by a significant improvement in accuracy and smoothness. [1] D. Groeneveld is the corresponding author. He is an Adjunct Professor at the University of Ottawa. (authors)

  14. General-purpose radiographic and fluoroscopic table

    Ishizaki, Noritaka

    1982-01-01

    A new series of diagnostic tables, Model DT-KEL, was developed for general-purpose radiographic and fluoroscopic systems. Through several investigations, the table was so constructed that the basic techniques be general radiography and GI examination, and other techniques be optionally added. The diagnostic tables involve the full series of the type for various purposes and are systematized with the surrounding equipment. A retractable mechanism of grids was adopted first for general use. The fine grids with a density of 57 lines per cm, which was adopted in KEL-2, reduced the X-ray doses by 16 percent. (author)

  15. Medicaid Analytic eXtract (MAX) Rx Table Listing

    U.S. Department of Health & Human Services — The Statistical Compendium table listing (below) enables users to choose to view Medicaid prescription drug tables for 1999 - 2009, and to select the tables for the...

  16. New Generation of Los Alamos Opacity Tables

    Colgan, James; Kilcrease, D. P.; Magee, N. H.; Sherrill, M. E.; Abdallah, J.; Hakel, P.; Fontes, C. J.; Guzik, J. A.; Mussack, K. A.

    2016-05-01

    We present a new generation of Los Alamos OPLIB opacity tables that have been computed using the ATOMIC code. Our tables have been calculated for all 30 elements from hydrogen through zinc and are publicly available through our website. In this poster we discuss the details of the calculations that underpin the new opacity tables. We also show several recent applications of the use of our opacity tables to solar modeling and other astrophysical applications. In particular, we demonstrate that use of the new opacities improves the agreement between solar models and helioseismology, but does not fully resolve the long-standing `solar abundance' problem. The Los Alamos National Laboratory is operated by Los Alamos National Security, LLC for the National Nuclear Security Administration of the U.S. Department of Energy under Contract No. DE-AC5206NA25396.

  17. RESTAURANT RESERVATION MANAGEMENT CONSIDERING TABLE COMBINATION

    Qing Miao

    Full Text Available ABSTRACT This paper presents a case study of table reservation practice for restaurant business within Walt Disney World. A unique feature here is to consider table combination to capture revenue potentials from different party sizes and at different time periods. For example, a party of large size can be served by combining two or more small tables. A mixed integer programming (MIP model is developed to make the reservation recommendation. We propose a rolling horizon reservation policy such that the value of a particular table is periodically evaluated and updated. This is a typical revenue management method in the airlines and other industries, the essence of which is to compare the future expected revenue with a currently offered price. Using historical data, numerical test shows a significant revenue improvement potential from our proposed model.

  18. The astronomical tables of Giovanni Bianchini

    Chabas, Jose

    2009-01-01

    This book describes and analyses, for the first time, the astronomical tables of Giovanni Bianchini of Ferrara (d. after 1469), explains their context, inserts them into an astronomical tradition that began in Toledo, and addresses their diffusion.

  19. Installation Torque Tables for Noncritical Applications

    Rivera-Rosario, Hazel T.; Powell, Joseph S.

    2017-01-01

    The objective of this project is to define torque values for bolts and screws when loading is not a concern. Fasteners require a certain torque to fulfill its function and prevent failure. NASA Glenn Research Center did not have a set of fastener torque tables for non-critical applications without loads, usually referring to hand-tight or wrench-tight torqueing. The project is based on two formulas, torque and pullout load. Torque values are calculated giving way to preliminary data tables. Testing is done to various bolts and metal plates, torqueing them until the point of failure. Around 640 torque tables were developed for UNC, UNF, and M fasteners. Different lengths of thread engagement were analyzed for the 5 most common materials used at GRC. The tables were put together in an Excel spreadsheet and then formatted into a Word document. The plan is to later convert this to an official technical publication or memorandum.

  20. Improving GRADE evidence tables part 2

    Langendam, Miranda; Carrasco-Labra, Alonso; Santesso, Nancy

    2016-01-01

    OBJECTIVES: The Grading of Recommendations Assessment, Development, and Evaluation (GRADE) working group has developed GRADE evidence profiles (EP) and summary of findings (SoF) tables to present evidence summaries in systematic reviews, clinical guidelines, and health technology assessments. Exp...

  1. Boat And Shore Oracle Data Tables

    National Oceanic and Atmospheric Administration, Department of Commerce — Oracle Tables To Provide Boat and Shore Data which contains the object of this system is to provide an inventory of vessels that answer two fundamental questions:...

  2. Ecological periodic tables: In principle and practice

    The chemical periodic table, the Linnaean system of classification and the Hertzsprung-Russell diagram are iconic information organizing structure in chemistry, biology and astronomy, respectively, because they are simple, exceptionally useful and they foster the expansion of sci...

  3. Toward an Organic Chemist's Periodic Table.

    Hall, H. K., Jr.

    1980-01-01

    An analogy between electron transfer reactions of the elements and those of organic molecules is offered. Examples of organic electron transfer reactions are presented. The rationale of constructing an organic chemists' periodic table is also discussed. (HM)

  4. Theodore William Richards and the Periodic Table

    Conant, James B.

    1970-01-01

    Discusses the contribution of Theodore Richards to the accurate determination of atomic weights of copper and other elements; his major contribution was to the building of the definitive periodic table of the elements. (BR)

  5. Cohort Working Life Tables for Older Canadians

    Spencer, Byron G.

    2010-01-01

    Full Text Available AbstractWe construct cohort working life tables for Canadian men and women aged 50and older and, for comparison, corresponding period tables. The tables arederived using annual single-age time series of participation rates for 1976-2006from the master files of the Statistics Canada Labour Force Survey. The cohortcalculations are based on stochastic projections of mortality coupled withalternative assumptions about future participation rates. Separate tables areprovided for the years 1976, 1991, and 2006, thus spanning a period ofsubstantial gains in life expectancy and strong upward trends in femaleparticipation. Life expectancies based on the cohort tables are greater thanthose based on the period tables, for both men and women, and that is reflectedin increased retirement expectancies. For example, a male aged 50 in 1976could have expected to live three years longer and to have almost four moreyears in retirement, based on the male cohort table under medium assumptions,as compared with the corresponding period table.RésuméNous avons établis des tables de vie active par génération pour les Canadiens etCanadiennes âgés de 50 ans ou plus ainsi que des tables du momentcorrespondantes pour servir de comparaison. Les tables sont dérivées à l'aidede séries chronologiques annuelles d'un seul âge pour le taux d'activité pour lesannées 1976 à 2006 provenant des fichiers maîtres de l'Enquête sur lapopulation active de Statistique Canada. Les calculs par génération sont baséessur des projections stochastiques de mortalité et sur des suppositions quant àde futurs taux d'activité possibles. Des tables séparées ont été établies pour lesannées 1976, 1991 et 2006 ; ce qui représente une période qui a vu des gainssubstantiels en ce qui concerne l'espérance de vie et une forte hausse d'activitéchez les femmes. Les espérance de vie basées sur les tables par génération sontplus élevées que celles basées sur les tables du

  6. Shaking table testing of mechanical components

    Jurukovski, D.; Taskov, Lj.; Mamucevski, D.; Petrovski, D.

    1995-01-01

    Presented is the experience of the Institute of Earthquake Engineering and Engineering Seismology, Skopje, Republic of Macedonia in seismic qualification of mechanical components by shaking table testing. Technical data and characteristics for the three shaking tables available at the Institute are given. Also, for characteristic mechanical components tested at the Institute laboratories, basic data such as producer, testing investor, description of the component, testing regulation, testing equipment and final user of the results. (author)

  7. Experiences with Interactive Multi-touch Tables

    Fikkert, Wim; Hakvoort, Michiel; van der Vet, Paul; Nijholt, Anton

    Interactive multi-touch tables can be a powerful means of communication for collaborative work as well as an engaging environment for competition. Through enticing gameplay we have evaluated user experience on competitive gameplay, collaborative work and musical expression. In addition, we report on our extensive experiences with two types of interactive multi-touch tables and we introduce a software framework that abstracts from their technical differences.

  8. Aplikasi Pembelajaran Table Manners Berbasis Multimedia

    Yosanny, Agustinna; Pradipta, Albert; Viles, Dody; Pensen, Pensen

    2011-01-01

    Table manners adalah aturan-aturan pokok yang berlaku di meja makan. Aturan ini biasanya diterapkan padajamuan makan resmi. Penelitian ini bertujuan untuk merancang dan mengembangkan suatu aplikasipembelajaran tentang table manners untuk memudahkan dalam mempelajari aturan-aturan yang perlu diketahuidalam jamuan makan resmi, meliputi etika sebelum dan saat proses menyantap makanan, serta penggunaanalat-alat makan. Metode penelitian yang digunakan adalah metode Interactive Multimedia System De...

  9. IUPAC Periodic Table of the Isotopes

    Holden, N.E.; Coplen, T.B.; Böhlke, J.K.; Wieser, M.E.; Singleton, G.; Walczyk, T.; Yoneda, S.; Mahaffy, P.G.; Tarbox, L.V.

    2011-01-01

    For almost 150 years, the Periodic Table of the Elements has served as a guide to the world of elements by highlighting similarities and differences in atomic structure and chemical properties. To introduce students, teachers, and society to the existence and importance of isotopes of the chemical elements, an IUPAC Periodic Table of the Isotopes (IPTI) has been prepared and can be found as a supplement to this issue.

  10. Listing of Available ACE Data Tables

    Conlin, Jeremy Lloyd [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2017-01-31

    This document is divided into multiple sections. Section 2 lists some of the more frequently used ENDF/B reaction types that can be used with the FM input card. The remaining sections (described below) contain tables showing the available ACE data tables for various types of data. These ACE data libraries are distributed by the Radiation Safety Information Computational Center (RSICC) with MCNP6.

  11. Nuclear data library table (Version November 1998)

    Baard, J.H.

    1998-11-01

    This report presents the edition of the Nuclear Data Library Table, valid from 1998-11-01. This library contains data for conversion of activity values to fluence rate and fluence values. The revised table is a modified version of the older library coded 1990-12-12. The older library has been extended with 23 reaction; the special 'background' reaction has been deleted. A table has been incorporated in this report which indicates the changes in this revised library data in comparison to previously used data. The data has been incorporated in this report which indicates the changes in this revised library data in comparison to previously used data. The data are presented as obtained as output from the program SAPNDLT. A table with half-lives of product nuclides is presented; in Appendix 2 these values have been calculated using the decay constants from this library. Surveys of thermal and fast cross sections are given for the various reactions in Appendix 3 and 4 respectively. Also a table with activities per mg mass for a fluence rate of 10 1 8 m -2 .s -1 is presented in Appendix 3 and 4 respectively. Also a table with activities per mg mass for a fluence rate of 10 1 8 m -1 is presented in Appendix 5 for various irradiation intervals. Appendix 6 gives for the various reactions the Kerma rate value. 8 refs

  12. Monitor tables for electron beams in radiotherapy

    Christ, G.; Dohm, O.S.

    2007-01-01

    The application of electron beams in radiotherapy is still based on tables of monitor units, although 3-D treatment planning systems for electron beams are available. This have several reasons: The need for 3-D treatment planning is not recognized; there is no confidence in the calculation algorithm; Monte-Carlo algorithms are too time-consuming; and the effort necessary to measure basic beam data for 3-D planning is considered disproportionate. However, the increasing clinical need for higher dosimetric precision and for more conformal electron beams leads to the requirement for more sophisticated tables of monitor units. The present paper summarizes and discusses the main aspects concerning the preparation of tables of monitor units for electron beams. The measurement equipment and procedures for measuring basic beam data needed for tables of monitor units for electron beams are described for a standard radiation therapy linac. The design of tables of monitor units for standard electron applicators is presented; this design can be extended for individual electron inserts, to variable applicator surface distances, to oblique beam incidence, and the use of bolus material. Typical data of an Elekta linac are presented in various tables. (orig.)

  13. TableMaker: An Excel Macro for Publication-Quality Tables

    Marek Hlavac

    2016-04-01

    Full Text Available This article introduces TableMaker, a Microsoft Excel macro that produces publicationquality tables and includes them as new sheets in workbooks. The macro provides an intuitive graphical user interface that allows for the full customization of all table features. It also allows users to save and load table templates, and thus allows layouts to be both reproducible and transferable. It is distributed in a single computer file. As such, the macro is easy to share, as well as accessible to even beginning and casual users of Excel. Since it allows for the quick creation of reproducible and fully customizable tables, TableMaker can be very useful to academics, policy-makers and businesses by making the presentation and formatting of results faster and more efficient.

  14. 40 CFR Table 7 to Subpart Vvvvvv... - Partially Soluble HAP

    2010-07-01

    ... 40 Protection of Environment 14 2010-07-01 2010-07-01 false Partially Soluble HAP 7 Table 7 to... Pt. 63, Subpt. VVVVVV, Table 7 Table 7 to Subpart VVVVVV of Part 63—Partially Soluble HAP As required... partially soluble HAP listed in the following table. Partially soluble HAP name CAS No. 1. 1,1,1...

  15. Radiation guard for x-ray table

    Collica, C.; Epifano, L.; Farella, R.

    1976-01-01

    A radiation guard suitable for use in conjunction with a diagnostic table and penetrable by the hands of an operator to facilitate moving or examining a patient positioned on a table. In accordance with the invention there is provided a supportive frame mountable at about an edge of the table so as to extend vertically from about the edge, the frame comprising at least a pair of spaced bars. A plurality of strips of flexible radiation shielding material are mounted across the bars in closely spaced relationship, the strips being mounted sufficiently close together to prevent substantial radiation leakage through the frame. The hands of an operator can be inserted between the adjacent strips to manually reposition or examine a patient while protecting most of the operator's body from substantial radiation. 9 claims, 4 drawing figures

  16. The Periodic Round Table (by Gary Katz)

    Rodgers, Reviewed By Glen E.

    2000-02-01

    Unwrapping and lifting the Periodic Round Table out of its colorful box is an exciting experience for a professional chemist or a chemistry student. Touted as a "new way of looking at the elements", it is certainly thatat least at first blush. The "table" consists of four sets of two finely finished hardwood discs each with the following elemental symbols and their corresponding atomic numbers pleasingly and symmetrically wood-burned into their faces. The four sets of two discs are 1 1/2, 3, 4 1/2, and 6 in. in diameter, each disc is 3/4 in. thick, and therefore the entire "round table" stands 6 in. high and is 6 in. in diameter at its base. The eight beautifully polished discs (represented below) are held together by center dowels that allow each to be rotated separately.

  17. Tests for homogeneity for multiple 2 x 2 contingency tables

    Carr, D.B.

    1986-01-01

    Frequently data are described by 2 x 2 contingency tables. For example, each 2 x 2 table arises from two dichotomous classifications such as control/treated and respond/did not respond. Multiple 2 x 2 tables result from stratifying the observational units on the basis of other characteristics. For example, stratifying by sex produces separate 2 x 2 tables for males and females. From each table a measure of difference between the response rates for the control and the treated groups is computed. The researcher usually wants to know if the response-rate difference is zero for each table. If the tables are homogeneous, the researcher can generalize from a statement concerning an average to a statement concerning each table. If tables are not homogeneous, homogeneous subsets of the tables should be described separately. This paper presents tests for homogeneity and illustrates their use. 11 refs., 6 tabs

  18. A contingency table approach to nonparametric testing

    Rayner, JCW

    2000-01-01

    Most texts on nonparametric techniques concentrate on location and linear-linear (correlation) tests, with less emphasis on dispersion effects and linear-quadratic tests. Tests for higher moment effects are virtually ignored. Using a fresh approach, A Contingency Table Approach to Nonparametric Testing unifies and extends the popular, standard tests by linking them to tests based on models for data that can be presented in contingency tables.This approach unifies popular nonparametric statistical inference and makes the traditional, most commonly performed nonparametric analyses much more comp

  19. Tables of nuclear level density parameters

    Chatterjee, A.; Ghosh, S.K.; Majumdar, H.

    1976-03-01

    The Renormalized Gas Model (RGM) has been used to calculate single particle level density parameters for more than 2000 nucleides over the range 9<=Z<=126 (15<=A<=338). Three separate tables present the elements on or near the valley of beta stability, neutron-rich fission fragment nucleides, and transitional nuclei, actinides and light-mass super heavy elements. Each table identifies the nucleus in terms of Z and N and presents the RGM deformation energy of binding, the total RGM structural energy correction over the free gas Fermi surface, and the level density parameter

  20. Thermodynamic tables for nuclear waste isolation

    Phillips, S.L.; Hale, F.V.; Silvester, L.F.; Siegel, M.D.

    1988-05-01

    Tables of consistent thermodynamic property values for nuclear waste isolation are given. The tables include critically assessed values for Gibbs energy of formation, enthalpy of formation, entropy and heat capacity for minerals; solids; aqueous ions; ion pairs and complex ions of selected actinide and fission decay products at 25 degree C and zero ionic strength. These intrinsic data are used to calculate equilibrium constants and standard potentials which are compared with typical experimental measurements and other work. Recommendations for additional research are given. 13 figs., 23 tabs

  1. Mathematics of Periodic Tables for Benzenoid Hydrocarbons.

    Dias, Jerry Ray

    2007-01-01

    The upper and lower bounds for invariants of polyhex systems based on the Harary and Harborth inequalities are studied. It is shown that these invariants are uniquely correlated by the Periodic Table for Benzenoid Hydrocarbons. A modified periodic table for total resonant sextet (TRS) benzenoids based on the invariants of Ds and r(empty) is presented; Ds is the number of disconnections among the empty rings for fused TRS benzenoid hydrocarbons. This work represents a contribution toward deciphering the topological information content of benzenoid formulas.

  2. Submatrices of character tables and basic sets

    Bessenrodt, Christine; Olsson, Jørn Børling

    2012-01-01

    In this investigation of character tables of nite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy lasses. For the symmetric groups we nd unexpected properties of characters on restricted sets of conjugacy classes, like beautiful...... combinatorial determinant formulae for submatrices of the character table and Cartan matrices with respect to basic sets; we observe that similar phenomena occur for the transition matrices between power sum symmetric functions to bounded partitions and the k-Schur functions dened by Lapointe and Morse...

  3. The UCSC Table Browser data retrieval tool

    Karolchik, Donna; Hinrichs, Angela S.; Furey, Terrence S.; Roskin, Krishna M.; Sugnet, Charles W.; Haussler, David; Kent, W. James

    2004-01-01

    The University of California Santa Cruz (UCSC) Table Browser (http://genome.ucsc.edu/cgi-bin/hgText) provides text-based access to a large collection of genome assemblies and annotation data stored in the Genome Browser Database. A flexible alternative to the graphical-based Genome Browser, this tool offers an enhanced level of query support that includes restrictions based on field values, free-form SQL queries and combined queries on multiple tables. Output can be filtered to restrict the f...

  4. Multi-Touch Tables and Collaborative Learning

    Higgins, Steve; Mercier, Emma; Burd, Liz; Joyce-Gibbons, Andrew

    2012-01-01

    The development of multi-touch tables, an emerging technology for classroom learning, offers valuable opportunities to explore how its features can be designed to support effective collaboration in schools. In this study, small groups of 10- to 11-year-old children undertook a history task where they had to connect various pieces of information…

  5. Monthly tables of measurements. October 2000

    2000-10-01

    This report of the O.P.R.I. (Office of Protection against Ionizing Radiations) exposes the principal results concerning the routine monitoring of environmental radioactivity in France: atmospheric dusts, rainwater, surface water, underground water, sewage water, drinking water, food chain (milk, vegetables, fishes), sea water around nuclear sites and other sites. The activities of various radioisotopes are presented in tables. (N.C.)

  6. Round table discussion during session 2

    Mays, C.

    2004-01-01

    The round table discussions of the second session of the FSC Belgium Workshop addressed the following questions: - Do local stakeholders have, internally or externally, all the expertise they need in order to address the issues raised by radioactive waste management projects? - Do institutional stakeholders have all the expertise they need to take local impacts into account? - What kinds of expert input are sought and attained by the different stakeholders? - Were any formal methods used to aid local partnerships perform technology assessments? Or other types of assessment? - How to maintain the knowledge and expertise achieved by the stakeholders? Discussion took place after the plenary presentations, at tables grouping Belgian stakeholders and FSC delegates. As in Session I, most of the round table discussion focussed specifically on the experience of the local partnerships. Many insights were shared about the nature and role of expertise in complex decision making. They are summarised below, on the basis of the feedback provided to the plenary by each round table. Some of these insights can be generalised to other contexts. All in all, a profile emerged of the local partnerships as a unique and effective tool to deal with knowledge issues in managing risk. (author)

  7. Modal Characterization of a Piezoelectric Shaker Table

    2015-06-01

    actuated shaker tables are often used for high frequency fatigue testing. Since natural frequencies can appear in the operating range of these...course of this thesis effort. I would also like to thank Dr. Tommy George and all of the helpful people in the Turbine Engine Fatigue Facility at the...4 Figure 2. Perovskite Crystal Structure of PZT Ceramics ................................................... 5 Figure 3

  8. Experiences with Interactive Multi-touch Tables

    Fikkert, F.W.; Hakvoort, M.; Hakvoort, M.C.; van der Vet, P.E.; Nijholt, Antinus; Nijholt, A.; Reidsma, D.; Reidsma, Dennis; Hondorp, G.H.W.

    2009-01-01

    Interactive multi-touch tables can be a powerful means of communication for collaborative work as well as an engaging environment for competition. Through enticing gameplay we have evaluated user experience on competitive gameplay, collaborative work and musical expression. In addition, we report on

  9. Table-top diffuse optical imaging

    Sturgeon, K.A.; Bakker, L.P.

    2006-01-01

    This report describes the work done during a six months internshipat Philips Research for a Masters in Electronic and Electrical Engineering. An existing table-top tomography system for measuring lightin phantom breasts was restored. Updated software control and image reconstruction software was

  10. The periodic table: icon and inspiration.

    Poliakoff, Martyn; Tang, Samantha

    2015-03-13

    To start this discussion meeting on the new chemistry of the elements held on 12 May 2014, Martyn Poliakoff, Foreign Secretary of the Royal Society, was invited to give the opening remarks. As a chemist and a presenter of the popular online video channel 'The periodic table of videos', Martyn communicates his personal and professional interest in the elements to the public, who in turn use these videos both as an educational resource and for entertainment purposes. Ever since Mendeleev's first ideas for the periodic table were published in 1869, the table has continued to grow as new elements have been discovered, and it serves as both icon and inspiration; its form is now so well established that it is recognized the world over as a symbol for science. This paper highlights but a few of the varied forms that the table can take, such as an infographic, which can convey the shortage of certain elements with great impact. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

  11. 3D virtual table in anatomy education

    Dahl, Mads Ronald; Simonsen, Eivind Ortind

    The ‘Anatomage’ is a 3D virtual human anatomy table, with touchscreen functionality, where it is possible to upload CT-scans and digital. Learning the human anatomy terminology requires time, a very good memory, anatomy atlas, books and lectures. Learning the 3 dimensional structure, connections...

  12. Ecological periodic tables for estuarine habitats

    Southwood (1977; J Anim Ecol 46: 337-365) compared the situation in ecology to that in chemistry before the development of the periodic table when each fact, for example, the solubility or reactivity of a chemical element, had to be discovered independently and remembered in isol...

  13. Trunnion Collar Removal Machine - Gap Analysis Table

    Johnson, M.

    2005-01-01

    The purpose of this document is to review the existing the trunnion collar removal machine against the ''Nuclear Safety Design Bases for License Application'' (NSDB) [Ref. 10] requirements and to identify codes and standards and supplemental requirements to meet these requirements. If these codes and standards can not fully meet these requirements then a ''gap'' is identified. These gaps will be identified here and addressed using the ''Trunnion Collar Removal Machine Design Development Plan'' [Ref. 15]. The codes and standards, supplemental requirements, and design development requirements for the trunnion collar removal machine are provided in the gap analysis table (Appendix A, Table 1). Because the trunnion collar removal machine is credited with performing functions important to safety (ITS) in the NSDB [Ref. 10], design basis requirements are applicable to ensure equipment is available and performs required safety functions when needed. The gap analysis table is used to identify design objectives and provide a means to satisfy safety requirements. To ensure that the trunnion collar removal machine performs required safety functions and meets performance criteria, this portion of the gap analysis tables supplies codes and standards sections and the supplemental requirements and identifies design development requirements, if needed

  14. From the Mendeleev periodic table to particle physics and back to the periodic table

    Kibler, Maurice R.

    2006-11-01

    We briefly describe in this paper the passage from Mendeleev's chemistry (1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and particle physics (from 1953 to 2006). We show how the consideration of symmetries, largely used in physics since the end of the 1920's, gave rise to a new format of the periodic table in the 1970's. More specifically, this paper is concerned with the application of the group SO(4,2)xSU(2) to the periodic table of chemical elements. It is shown how the Madelung rule of the atomic shell model can be used for setting up a periodic table that can be further rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative results are obtained from this nonstandard table. (author)

  15. From the Mendeleev periodic table to particle physics and back to the periodic table

    Kibler, Maurice R. [Universite de Lyon, Institut de Physique Nucleaire, Universite Lyon 1 and CNRS/IN2P3, 43 Bd du 11 Novembre 1918, F-69622 Villeurbanne Cedex (France)

    2006-11-15

    We briefly describe in this paper the passage from Mendeleev's chemistry (1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and particle physics (from 1953 to 2006). We show how the consideration of symmetries, largely used in physics since the end of the 1920's, gave rise to a new format of the periodic table in the 1970's. More specifically, this paper is concerned with the application of the group SO(4,2)xSU(2) to the periodic table of chemical elements. It is shown how the Madelung rule of the atomic shell model can be used for setting up a periodic table that can be further rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative results are obtained from this nonstandard table. (author)

  16. Half-life distribution table of radioactive nuclei; Table de distribution des periodes des noyaux radioactifs

    Gugenberger, P [Commissariat a l' Energie Atomique, Saclay(France). Centre d' Etudes Nucleaires

    1954-07-01

    This table allows to identify an element if its period is known. Data for this table were taken from the half-life values adopted by Hollander, PERLMAN and SEABORG (Rev. mod. Phys., 1953, 22 number 2). Moreover for each nucleus, the mass number, the charge number and the type of decay are given in the table. (author) [French] Cette table permet l'identification d'un element dont la periode est connue. Elle a ete etablie en utilisant les valeurs des periodes donnees par HOLLANDER, PERLMAN et SEABORG dans Rev. mod. Phys., 1953, 25 numero 2. On y trouve en outre, pour chaque nuclide, les caracteristiques suivantes: Z, A, modes de desintegration. (auteur)

  17. Half-life distribution table of radioactive nuclei; Table de distribution des periodes des noyaux radioactifs

    Gugenberger, P. [Commissariat a l' Energie Atomique, Saclay(France). Centre d' Etudes Nucleaires

    1954-07-01

    This table allows to identify an element if its period is known. Data for this table were taken from the half-life values adopted by Hollander, PERLMAN and SEABORG (Rev. mod. Phys., 1953, 22 number 2). Moreover for each nucleus, the mass number, the charge number and the type of decay are given in the table. (author) [French] Cette table permet l'identification d'un element dont la periode est connue. Elle a ete etablie en utilisant les valeurs des periodes donnees par HOLLANDER, PERLMAN et SEABORG dans Rev. mod. Phys., 1953, 25 numero 2. On y trouve en outre, pour chaque nuclide, les caracteristiques suivantes: Z, A, modes de desintegration. (auteur)

  18. Scanning table BIP 101 for bubble chamber pictures

    Calmels, C.

    1966-09-01

    BIP 101 is a new scanning table for bubble chamber pictures, especially aimed at the full scale projection of the CERN 2 m hydrogen chamber. The table itself is divided in two half tables, each of them receiving, successively or simultaneously, the projections of 2 of the 4 films. Projectors with film transport are located in the central space between both half tables. Their light is reflected on 2 mirrors fixed at the ceiling. Thus the 4 sides of the table are freely accessible to the scanners. It will be possible to equip later the table with digitizers, allowing pre-measurements of the events for HPD device, or even measurements. (author) [fr

  19. Experiences with the Mobile Interactive Learning Table: a custom table for education

    Wilson, Gregory

    2011-01-01

    Multi-touch technology on tabletop displays lets children interact with digital objects in collaborative and competitive ways. Multi-touch tables are not a part of classroom instruction because of high cost and lack of meaningful applications. This thesis explores possible solutions to building hardware and software that support the engagement of children. Outlined is a demonstration of our Mobile Interactive Learning Table (MILT), a custom hardware system that can be built for a cost well...

  20. The Table of Chords and Greek Trigonometry

    Stefano Buscherini

    2010-12-01

    Full Text Available Trigonometry was born due to the need of ancient astronomy to calculate and to predict the movement of the heavenly bodies. However it is hard to know who the founder of this mathematical branch was: it is likely that its origins date back to Hipparchus of Nicaea who compiled the first table of chords, which are the forerunners of the modern trigonometric function “sine”. Nevertheless the most ancient existing work on trigonometry is the Almagest of Ptolemy in which the author describes the mathematical steps that are necessary for the compilation of the table of chords. These steps are based on more ancient theories and for this reason one gets the impression that they could be the result of a preparatory study. This article is not only a brief survey of Greek trigonometry but it also analyzes the Greek numeration system, the sexagesimal fractions and the arithmetical operations which were used in the calculation of the chords.

  1. Radiative otacity tables for 40 stellar mixtures

    Cox, A.N.; Tabor, J.E.

    1976-01-01

    Using improved methods, radiative opacities for 40 mixtures of elements are given for use in calculations of stellar structure, stellar evolution, and stellar pulsation. The major improvements over previous Los Alamos data are increased iron abundance in the composition, better allowance for the continuum depression for bound electrons, and corrections in some bound-electron energy levels. These opacities have already been widely used, and represent a relatively homogeneous set of data for stellar structures. Further improvements to include more bound-bound (line) transitions by a smearing technique and to include molecular absorptions are becoming available, and in a few years these tables, as well as all previous tables, will be outdated. At high densities the conduction of energy will dominate radiation flow, and this effect must be added separately

  2. Scalable Packet Classification with Hash Tables

    Wang, Pi-Chung

    In the last decade, the technique of packet classification has been widely deployed in various network devices, including routers, firewalls and network intrusion detection systems. In this work, we improve the performance of packet classification by using multiple hash tables. The existing hash-based algorithms have superior scalability with respect to the required space; however, their search performance may not be comparable to other algorithms. To improve the search performance, we propose a tuple reordering algorithm to minimize the number of accessed hash tables with the aid of bitmaps. We also use pre-computation to ensure the accuracy of our search procedure. Performance evaluation based on both real and synthetic filter databases shows that our scheme is effective and scalable and the pre-computation cost is moderate.

  3. AVLIS documentation overview and tables of contents

    1984-01-01

    Three documents constitute the executive summary series in Data Package III: this document (Documentation Overview and Tables of Contents (E001)) plus the AVLIS Production Plant Executive Summary (E010) and the AVLIS Production Plant Overall Design Report (E020). They provide progressively greater detail on the key information and conclusions contained within the data package. The Executive Summary and Overall Design Report present summaries of each Data Package III document. They are intended to provide a global overview of AVLIS Production Plant deployment including program planning, project management, schedules, engineering design, production, operations, capital cost, and operating cost. The purpose of Overview and Tables of Contents is threefold: to briefly review AVLIS goals for Data Package III documentation, to present an overview of the contents of the data package, and to provide a useful guide to information contained in the numerous documents comprising the package

  4. Tables of double beta decay data

    Tretyak, V.I.

    1995-01-01

    A compilation of experimental data on double beta decay is presented. The tables contain the most stringent known experimental limits or positive results of 2β transitions of 69 natural nuclides to ground and excited states of daughter nuclei for different channels (2β - ; 2β + ; εβ + ; 2ε) and modes (0ν; 2ν; 0νM) of decay. (authors). 189 refs., 9 figs., 3 tabs

  5. Tables of double beta decay data

    Tretyak, V.I. [AN Ukrainskoj SSR, Kiev (Ukraine)]|[Strasbourg-1 Univ., 67 (France). Centre de Recherches Nucleaires; Zdesenko, Y.G. [AN Ukrainskoj SSR, Kiev (Ukraine)

    1995-12-31

    A compilation of experimental data on double beta decay is presented. The tables contain the most stringent known experimental limits or positive results of 2{beta} transitions of 69 natural nuclides to ground and excited states of daughter nuclei for different channels (2{beta}{sup -}; 2{beta}{sup +}; {epsilon}{beta}{sup +}; 2{epsilon}) and modes (0{nu}; 2{nu}; 0{nu}M) of decay. (authors). 189 refs., 9 figs., 3 tabs.

  6. Uncertainty and the de Finetti tables

    Baratgin , Jean; Over , David; Politzer , Guy

    2013-01-01

    International audience; The new paradigm in the psychology of reasoning adopts a Bayesian, or prob-abilistic, model for studying human reasoning. Contrary to the traditional binary approach based on truth functional logic, with its binary values of truth and falsity, a third value that represents uncertainty can be introduced in the new paradigm. A variety of three-valued truth table systems are available in the formal literature, including one proposed by de Finetti. We examine the descripti...

  7. The attenuation of the periodic table

    Cook, N.D.

    1990-01-01

    Unique among models of nuclear structure, the face-centered-cubic (FCC) lattice model predicts the attenuation of the periodic table at Z < 110 and the impossibility of superheavy nuclei. The total binding energies of superheavy nuclei in the FCC model (109 < Z < 127) were calculated on the basis of parameters obtained from a least-squares best-fit for 914 nuclei (Z < 99). No indication of increased stability is found for any of the transuranic elements

  8. Tables of thermodynamic properties of sodium

    Fink, J.K.

    1982-06-01

    The thermodynamic properties of saturated sodium, superheated sodium, and subcooled sodium are tabulated as a function of temperature. The temperature ranges are 380 to 2508 K for saturated sodium, 500 to 2500 K for subcooled sodium, and 400 to 1600 K for superheated sodium. Tabulated thermodynamic properties are enthalpy, heat capacity, pressure, entropy, density, instantaneous thermal expansion coefficient, compressibility, and thermal pressure coefficient. Tables are given in SI units and cgs units

  9. A novel HTS magnetic levitation dining table

    Lu, Yiyun; Huang, Huiying

    2018-05-01

    High temperature superconducting (HTS) bulk can levitate above or suspend below a permanent magnet stably. Many magnificent potential applications of HTS bulk are proposed by researchers. Until now, few reports have been found for real applications of HTS bulk. A complete set of small-scale HTS magnetic levitation table is proposed in the paper. The HTS magnetic levitation table includes an annular HTS magnetic levitation system which is composed of an annular HTS bulk array and an annular permanent magnet guideway (PMG). The annular PMG and the annular cryogenics vessel which used to maintain low temperature environment of the HTS bulk array are designed. 62 YBCO bulks are used to locate at the bottom of the annular vessel. A 3D-model finite element numerical method is used to design the HTS bulk magnetic levitation system. Equivalent magnetic levitation and guidance forces calculation rules are proposed aimed at the annular HTS magnetic levitation system stability. Based on the proposed method, levitation and guidance forces curves of the one YBCO bulk magnetic above PMG could be obtained. This method also can use to assist PMG design to check whether the designed PMG could reach the basic demand of the HTS magnetic levitation table.

  10. Mini table de radionucléides

    2015-01-01

    Cette table est un outil pratique et quotidien pour tous les travailleurs opérant au contact de radionucléides. Elle concerne tous les secteurs scientifiques et techniques, comme la médecine, la recherche ou l'industrie. La Mini Table de radionucléides a été conçue comme un instrument permettant de repérer et valider rapidement les principales caractéristiques des radionucléides les plus utilisés (environ 300) que l'on rencontre en milieu médical, industriel, nucléaire, gestion des déchets, etc. Présentée en format de poche, elle permet pour chaque radionucléide d'indiquer ses caractéristiques fondamentales : La période radioactive ; Le ou les principaux modes de désintégration ; Les principales émissions en termes d'énergie et d'intensité. Pour des caractéristiques complètes, l'ouvrage renvoie aux Tables de Données de référence. Au sein du CEA, le Laboratoire National Henri Becquerel (LNHB) est mandaté par le Laboratoire National de Métrologie et d'Essais (LNE) comme laboratoir...

  11. Karna Particle Size Dataset for Tables and Figures

    U.S. Environmental Protection Agency — This dataset contains 1) table of bulk Pb-XAS LCF results, 2) table of bulk As-XAS LCF results, 3) figure data of particle size distribution, and 4) figure data for...

  12. NNDSS - Table II. Cryptosporidiosis to Dengue virus infection

    U.S. Department of Health & Human Services — NNDSS - Table II. Cryptosporidiosis to Dengue virus infection - 2018. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during...

  13. NNDSS - Table II. Cryptosporidiosis to Dengue Hemorrhagic Fever

    U.S. Department of Health & Human Services — NNDSS - Table II. Cryptosporidiosis to Dengue Hemorrhagic Fever - 2014.In this Table, all conditions with a 5-year average annual national total of more than or...

  14. NNDSS - Table II. Varicella to West Nile virus disease

    U.S. Department of Health & Human Services — NNDSS - Table II. Varicella to West Nile virus disease - 2014.In this Table, all conditions with a 5-year average annual national total of more than or equals 1,000...

  15. Literature review tables for Karna et al. 2017

    U.S. Environmental Protection Agency — N/A. Users will need to access the manuscript to see non-EPA data presented in tables and figures. This dataset is not publicly accessible because: The tables in the...

  16. Tropical forest biomass estimation from truncated stand tables.

    A. J. R. Gillespie; S. Brown; A. E. Lugo

    1992-01-01

    Total aboveground forest biomass may be estimated through a variety of techniques based on commercial inventory stand and stock tables. Stand and stock tables from tropical countries commonly omit trees bellow a certain commercial limit.

  17. NNDSS - Table II. Rabies, animal to Rubella, congenital syndrome

    U.S. Department of Health & Human Services — NNDSS - Table II. Rabies, animal to Rubella, congenital syndrome - 2018. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported...

  18. NNDSS - Table II. Rabies, animal to Rubella, congenital syndrome

    U.S. Department of Health & Human Services — NNDSS - Table II. Rabies, animal to Rubella, congenital syndrome - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported...

  19. NNDSS - Table II. Carbapenemase-producing carbapenem-resistant Enterobacteriaceae

    U.S. Department of Health & Human Services — NNDSS - Table II. Carbapenemase-producing carbapenem-resistant Enterobacteriaceae - 2018. In this Table, provisional cases of selected notifiable diseases (≥1,000...

  20. NNDSS - Table II. Hepatitis (viral, acute) A & B

    U.S. Department of Health & Human Services — NNDSS - Table II. Hepatitis (viral, acute) A & B - 2017. In this Table, provisional cases of selected notifiable diseases (≥1,000 cases reported during the...