WorldWideScience

Sample records for non-null lie quadratics

  1. Solvable quadratic Lie algebras

    Institute of Scientific and Technical Information of China (English)

    ZHU; Linsheng

    2006-01-01

    A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.

  2. Finite dimensional quadratic Lie superalgebras

    CERN Document Server

    Jarvis, Peter; Yates, Luke

    2010-01-01

    We consider a special class of Z_2-graded, polynomial algebras of degree 2, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. Based on the factorisation of the enveloping algebra, we derive the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate the method for one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.

  3. Structure of Solvable Quadratic Lie Algebras

    Institute of Scientific and Technical Information of China (English)

    ZHU Lin-sheng

    2005-01-01

    @@ Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics[10,12,13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the Kac-Moody algebras and the Extended Affine Lie algebras.

  4. Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method

    Science.gov (United States)

    Bizyaev, I. A.; Kozlov, V. V.

    2015-12-01

    We consider differential equations with quadratic right-hand sides that admit two quadratic first integrals, one of which is a positive-definite quadratic form. We indicate conditions of general nature under which a linear change of variables reduces this system to a certain 'canonical' form. Under these conditions, the system turns out to be divergenceless and can be reduced to a Hamiltonian form, but the corresponding linear Lie-Poisson bracket does not always satisfy the Jacobi identity. In the three-dimensional case, the equations can be reduced to the classical equations of the Euler top, and in four-dimensional space, the system turns out to be superintegrable and coincides with the Euler-Poincaré equations on some Lie algebra. In the five-dimensional case we find a reducing multiplier after multiplying by which the Poisson bracket satisfies the Jacobi identity. In the general case for n>5 we prove the absence of a reducing multiplier. As an example we consider a system of Lotka-Volterra type with quadratic right-hand sides that was studied by Kovalevskaya from the viewpoint of conditions of uniqueness of its solutions as functions of complex time. Bibliography: 38 titles.

  5. Non-null annular subaperture stitching interferometry for aspheric test

    Science.gov (United States)

    Zhang, Lei; Liu, Dong; Shi, Tu; Yang, Yongying; Chong, Shiyao; Miao, Liang; Huang, Wei; Shen, Yibing; Bai, Jian

    2015-10-01

    A non-null annular subaperture stitching interferometry (NASSI), combining the subaperture stitching idea and non-null test method, is proposed for steep aspheric testing. Compared with standard annular subaperture stitching interferometry (ASSI), a partial null lens (PNL) is employed as an alternative to the transmission sphere, to generate different aspherical wavefronts as the references. The coverage subaperture number would thus be reduced greatly for the better performance of aspherical wavefronts in matching the local slope of aspheric surfaces. Instead of various mathematical stitching algorithms, a simultaneous reverse optimizing reconstruction (SROR) method based on system modeling and ray tracing is proposed for full aperture figure error reconstruction. All the subaperture measurements are simulated simultaneously with a multi-configuration model in a ray-tracing program, including the interferometric system modeling and subaperture misalignments modeling. With the multi-configuration model, full aperture figure error would be extracted in form of Zernike polynomials from subapertures wavefront data by the SROR method. This method concurrently accomplishes subaperture retrace error and misalignment correction, requiring neither complex mathematical algorithms nor subaperture overlaps. A numerical simulation exhibits the comparison of the performance of the NASSI and standard ASSI, which demonstrates the high accuracy of the NASSI in testing steep aspheric. Experimental results of NASSI are shown to be in good agreement with that of Zygo® VerifireTM Asphere interferometer.

  6. Error analysis and system optimization of non-null aspheric testing system

    Science.gov (United States)

    Luo, Yongjie; Yang, Yongying; Liu, Dong; Tian, Chao; Zhuo, Yongmo

    2010-10-01

    A non-null aspheric testing system, which employs partial null lens (PNL for short) and reverse iterative optimization reconstruction (ROR for short) technique, is proposed in this paper. Based on system modeling in ray tracing software, the parameter of each optical element is optimized and this makes system modeling more precise. Systematic error of non-null aspheric testing system is analyzed and can be categorized into two types, the error due to surface parameters of PNL in the system modeling and the rest from non-null interferometer by the approach of error storage subtraction. Experimental results show that, after systematic error is removed from testing result of non-null aspheric testing system, the aspheric surface is precisely reconstructed by ROR technique and the consideration of systematic error greatly increase the test accuracy of non-null aspheric testing system.

  7. Proton acceleration in three-dimensional non-null magnetic reconnection

    Science.gov (United States)

    Akbari, Z.; Hosseinpour, M.; Mohammadi, M. A.

    2016-10-01

    In a three-dimensional non-null magnetic reconnection, the process of magnetic reconnection takes place in the absence of a null point where the magnetic field vanishes. By randomly injecting a population of 10 000 protons, the trajectory and energy distribution of accelerated protons are investigated in the presence of magnetic and electric fields of a particular model of non-null magnetic reconnection with the typical parameters for the solar corona. The results show that protons are accelerated along the magnetic field lines away from the non-null point only at azimuthal angles where the magnitude of the electric field is strongest and therefore particles obtain kinetic energies of the order of thousands of MeV and even higher. Moreover, the energy distribution of the population depends strongly on the amplitude of the electric and magnetic fields. Comparison shows that a non-null magnetic reconnection is more efficient in accelerating protons to very high GeV energies than a null-point reconnection.

  8. Moving non-null curves according to Bishop frame in Minkowski 3-space

    Science.gov (United States)

    Gürbüz, Nevin

    2015-04-01

    In this paper, we introduce three new transformations and establish connections between moving non-null curves and soliton equations according to Bishop frame in Minkowski 3-space. Later we find formulas for differentials of these three new transformations associated with the nonlinear heat system and repulsive type nonlinear Schrödinger equation.

  9. Generalized double extension and descriptions of qadratic Lie superalgebras

    CERN Document Server

    Bajo, I; Bordemann, M

    2007-01-01

    A Lie superalgebra endowed with a supersymmetric, even, non-degenerate, invariant bilinear form is called a quadratic Lie superalgebra. In this paper we give inductive descriptions of quadratic Lie superalgebras in terms of generalized double extensions.

  10. Scalar perturbations in a Friedmann-like metric with non-null Weyl tensor

    CERN Document Server

    Santos, Grasiele B; Salim, José M

    2013-01-01

    In a previous work some of the authors have solved the Einstein equations of General Relativity for a class of metrics with constant spatial curvature, where it was found a non vanishing Weyl tensor in the presence of an energy-momentum tensor with an anisotropic pressure component. Here, we perform the perturbative analysis of this model in order to study the gravitational stability under linear scalar perturbations. For this purpose, we take the Quasi-Maxwellian formalism of General Relativity as our framework, which offers a naturally covariant and gauge-invariant approach to deal with perturbations that are directly linked to observational quantities. We also consider a generalization of the causal thermodynamics to include the effect of the non-null Weyl tensor, which introduces a "viscosity" due solely to the gravitational tidal forces.

  11. Two special classes of space-times admitting a non-null valence two Killing spinor

    CERN Document Server

    Bergh, Norbert Van den

    2009-01-01

    Non-conformally flat space-times admitting a non-null Killing spinor of valence two are investigated in the Geroch-Held-Penrose formalism. Contrary to popular belief these space-times are not all explicitly known. It is shown that the standard construction hinges on the tacit assumption that certain integrability conditions hold, implying two algebraic relations, KS1 and KS2, for the spin coefficients and the components of the Ricci spinor. An exhaustive list of (conformal classes of) space-times, in which either KS1 or KS2 are violated, is presented. The resulting space-times are each other's Sachs transforms, in general admit no Killing vectors and are characterized by a single arbitrary function.

  12. Quadratic choreographies

    CERN Document Server

    Ryckelynck, Philippe

    2011-01-01

    This paper addresses the classical and discrete Euler-Lagrange equations for systems of $n$ particles interacting quadratically in $\\mathbb{R}^d$. By highlighting the role played by the center of mass of the particles, we solve the previous systems via the classical quadratic eigenvalue problem (QEP) and its discrete transcendental generalization. The roots of classical and discrete QEP being given, we state some conditional convergence results. Next, we focus especially on periodic and choreographic solutions and we provide some numerical experiments which confirm the convergence.

  13. DERIVATIONS AND EXTENSIONS OF LIE COLOR ALGEBRA

    Institute of Scientific and Technical Information of China (English)

    Zhang Qingcheng; Zhang Yongzheng

    2008-01-01

    In this article, the authors obtain some results concerning derivations of fi-nitely generated Lie color algebras and discuss the relation between skew derivation space SkDer(L) and central extension H2(L, F) on some Lie color algebras. Meanwhile, they generalize the notion of double extension to quadratic Lie color algebras, a sufficient con-dition for a quadratic Lie color algebra to be a double extension and further properties are given.

  14. Practical retrace error correction in non-null aspheric testing: A comparison

    Science.gov (United States)

    Shi, Tu; Liu, Dong; Zhou, Yuhao; Yan, Tianliang; Yang, Yongying; Zhang, Lei; Bai, Jian; Shen, Yibing; Miao, Liang; Huang, Wei

    2017-01-01

    In non-null aspheric testing, retrace error forms the primary error source, making it hard to recognize the desired figure error from the aliasing interferograms. Careful retrace error correction is a must bearing on the testing results. Performance of three commonly employed methods in practical, i.e. the GDI (geometrical deviation based on interferometry) method, the TRW (theoretical reference wavefront) method and the ROR (reverse optimization reconstruction) method, are compared with numerical simulations and experiments. Dynamic range of these methods are sought out and the application is recommended. It is proposed that with aspherical reference wavefront, dynamic range can be further enlarged. Results show that the dynamic range of the GDI method is small while that of the TRW method can be enlarged with aspherical reference wavefront, and the ROR method achieves the largest dynamic range with highest accuracy. It is recommended that the GDI and TRW methods be applied to apertures with small figure error and small asphericity, and the ROR method for commercial and research applications calling for high accuracy and large dynamic range.

  15. The Quadratic Graver Cone, Quadratic Integer Minimization, and Extensions

    CERN Document Server

    Lee, Jon; Romanchuk, Lyubov; Weismantel, Robert

    2010-01-01

    We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the system is given, and the quadratic function lies in a suitable {\\em dual Graver cone}, the problem can be solved in polynomial time. We discuss the relation between this cone and the cone of positive semidefinite matrices, and show that none contains the other. So we can minimize in polynomial time some non-convex and some (including all separable) convex quadrics. We conclude by extending our results to efficient integer minimization of multivariate polynomial functions of arbitrary degree lying in suitable cones.

  16. Effect of a non null pressure on the evolution of perturbations in the matter dominated epoch

    CERN Document Server

    Herrero, A

    2003-01-01

    We analyze the effect of pressure on the evolution of perturbations of an Einstein-de Sitter Universe in the matter dominated epoch assuming an ideal gas equation of state. For the sake of simplicity the temperature is considered uniform. The goal of the paper is to examine the validity of the linear approximation. With this purpose the evolution equations are developed including quadratic terms in the derivatives of the metric perturbations and using coordinate conditions that, in the linear case, reduce to the longitudinal gauge. We obtain the general solution, in the coordinate space, of the evolution equation for the scalar mode, and, in the case of spherical symmetry, we express this solution in terms of unidimensional integrals of the initial conditions: the initial values of the Newtonian potential and its first time derivative. We find that the contribution of the initial first time derivative, which has been systematically forgotten, allows to form inhomogeneities similar to a cluster of galaxies sta...

  17. Lie algebras

    CERN Document Server

    Jacobson, Nathan

    1979-01-01

    Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its

  18. Lie Superalgebras

    CERN Document Server

    Papi, Paolo; Advances in Lie Superalgebras

    2014-01-01

    The volume is the outcome of the conference "Lie superalgebras," which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held provided comprehensive insights into the newest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field and provides a complete account of the newest trends in research on Lie Superalgebras.

  19. The quadratic Fock functor

    CERN Document Server

    Accardi, Luigi

    2009-01-01

    We construct the quadratic analogue of the boson Fock functor. While in the first order case all contractions on the 1--particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. Within this semigroup we characterize the unitary and the isometric elements.

  20. Quadratic eigenvalue problems.

    Energy Technology Data Exchange (ETDEWEB)

    Walsh, Timothy Francis; Day, David Minot

    2007-04-01

    In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.

  1. Multistage quadratic stochastic programming

    Science.gov (United States)

    Lau, Karen K.; Womersley, Robert S.

    2001-04-01

    Quadratic stochastic programming (QSP) in which each subproblem is a convex piecewise quadratic program with stochastic data, is a natural extension of stochastic linear programming. This allows the use of quadratic or piecewise quadratic objective functions which are essential for controlling risk in financial and project planning. Two-stage QSP is a special case of extended linear-quadratic programming (ELQP). The recourse functions in QSP are piecewise quadratic convex and Lipschitz continuous. Moreover, they have Lipschitz gradients if each QP subproblem is strictly convex and differentiable. Using these properties, a generalized Newton algorithm exhibiting global and superlinear convergence has been proposed recently for the two stage case. We extend the generalized Newton algorithm to multistage QSP and show that it is globally and finitely convergent under suitable conditions. We present numerical results on randomly generated data and modified publicly available stochastic linear programming test sets. Efficiency schemes on different scenario tree structures are discussed. The large-scale deterministic equivalent of the multistage QSP is also generated and their accuracy compared.

  2. Twisted Hamiltonian Lie Algebras and Their Multiplicity-Free Representations

    Institute of Scientific and Technical Information of China (English)

    Ling CHEN

    2011-01-01

    We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras (or corresponding Hamiltonian operators) associated with Poisson algebras and a quasi-derivation found by Xu. These algebras can be viewed as certain twists of Xu's generalized Hamiltonian Lie algebras. The simplicity of these algebras is completely determined. Moreover, we construct a family of multiplicity-free representations of these Lie algebras and prove their irreducibility.

  3. Lie groups and Lie algebras for physicists

    CERN Document Server

    Das, Ashok

    2015-01-01

    The book is intended for graduate students of theoretical physics (with a background in quantum mechanics) as well as researchers interested in applications of Lie group theory and Lie algebras in physics. The emphasis is on the inter-relations of representation theories of Lie groups and the corresponding Lie algebras.

  4. Semidefinite programming for quadratically constrained quadratic programs

    Science.gov (United States)

    Olkin, Julia A.; Titterton, Paul J., Jr.

    1995-06-01

    We consider the linear least squares problem subject to multiple quadratic constraints, which is motivated by a practical application in controller design. We use the techniques of convex optimization, in particluar, interior-point methods for semi-definite programming. We reduce a quasi-convex potential function. Each iteration requires calculating a primal and dual search direction and minimizing along the plane defined by these search directions. The primal search direction requires solving a least squares problem whose matrix is composed of a block- Toeplitz portion plus other structured matrices. We make use of Kronecker products and FFTs to greatly reduce the calculation. In addition, the matrix updates and matrix inverses in the plane search are actually low-rank updates to structured matrices so we are able to further reduce the flops required. Consequently, we can design controllers for problems of considerable size.

  5. On Convex Quadratic Approximation

    NARCIS (Netherlands)

    den Hertog, D.; de Klerk, E.; Roos, J.

    2000-01-01

    In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

  6. On Convex Quadratic Approximation

    NARCIS (Netherlands)

    den Hertog, D.; de Klerk, E.; Roos, J.

    2000-01-01

    In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

  7. On Quadratic Differential Forms

    NARCIS (Netherlands)

    Willems, J.C.; Trentelman, H.L.

    1998-01-01

    This paper develops a theory around the notion of quadratic differential forms in the context of linear differential systems. In many applications, we need to not only understand the behavior of the system variables but also the behavior of certain functionals of these variables. The obvious cases w

  8. Aspects of Quadratic Gravity

    CERN Document Server

    Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio

    2016-01-01

    We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...

  9. Weak Lie symmetry and extended Lie algebra

    Energy Technology Data Exchange (ETDEWEB)

    Goenner, Hubert [Institute for Theoretical Physics, Friedrich-Hund-Platz 1, University of Goettingen, D-37077 Gottingen (Germany)

    2013-04-15

    The concept of weak Lie motion (weak Lie symmetry) is introduced. Applications given exhibit a reduction of the usual symmetry, e.g., in the case of the rotation group. In this context, a particular generalization of Lie algebras is found ('extended Lie algebras') which turns out to be an involutive distribution or a simple example for a tangent Lie algebroid. Riemannian and Lorentz metrics can be introduced on such an algebroid through an extended Cartan-Killing form. Transformation groups from non-relativistic mechanics and quantum mechanics lead to such tangent Lie algebroids and to Lorentz geometries constructed on them (1-dimensional gravitational fields).

  10. 3-LIE BIALGEBRAS

    Institute of Scientific and Technical Information of China (English)

    白瑞蒲; 程宇; 李佳倩; 孟伟

    2014-01-01

    3-Lie algebras have close relationships with many important fields in mathemat-ics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char-acteristic zero are provided.

  11. Hidden conic quadratic representation of some nonconvex quadratic optimization problems

    NARCIS (Netherlands)

    Ben-Tal, A.; den Hertog, D.

    2014-01-01

    The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated S-lemma

  12. Quaternion orders, quadratic forms, and Shimura curves

    CERN Document Server

    Alsina, Montserrat

    2004-01-01

    Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...

  13. Extended gcd of quadratic integers

    CERN Document Server

    Miled, Abdelwaheb

    2010-01-01

    Computation of the extended gcd of two quadratic integers. The ring of integers considered is principal but could be euclidean or not euclidean ring. This method rely on principal ideal ring and reduction of binary quadratic forms.

  14. On Characterization of Quadratic Splines

    DEFF Research Database (Denmark)

    Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong

    2005-01-01

    A quadratic spline is a differentiable piecewise quadratic function. Many problems in numerical analysis and optimization literature can be reformulated as unconstrained minimizations of quadratic splines. However, only special cases of quadratic splines are studied in the existing literature...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general......., and algorithms are developed on a case by case basis. There lacks an analytical representation of a general or even a convex quadratic spline. The current paper fills this gap by providing an analytical representation of a general quadratic spline. Furthermore, for convex quadratic spline, it is shown...

  15. Stochastic Lie group integrators

    CERN Document Server

    Malham, Simon J A

    2007-01-01

    We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold, we pull back the stochastic flow on the manifold to the Lie group via the action, and subsequently pull back the flow to the corresponding Lie algebra via the exponential map. We construct an approximation to the stochastic flow in the Lie algebra via closed operations and then push back to the Lie group and then to the manifold, thus ensuring our approximation lies in the manifold. We call such schemes stochastic Munthe-Kaas methods after their deterministic counterparts. We also present stochastic Lie group integration schemes based on Castell--Gaines methods. These involve using an underlying ordinary differential integrator to approximate the flow generated by a truncated stochastic exponential Lie series. They become stochastic Lie group integrator schemes if...

  16. A CLASS OF QUADRATIC HAMILTONIAN SYSTEMS UNDER QUADRATIC PERTURBATION

    Institute of Scientific and Technical Information of China (English)

    丰建文; 陈士华

    2001-01-01

    This paper deals with a class of quadratic Hamiltonian systems with quadratic perturbation. The authors prove that if the first order Melnikov function M1(h) = 0 and the second order Melnikov function M2(h) ≡ 0, then the origin of the Hamiltonian system with small perturbation is a center.

  17. Quadratic solitons as nonlocal solitons

    DEFF Research Database (Denmark)

    Nikolov, Nikola Ivanov; Neshev, D.; Bang, Ole

    2003-01-01

    We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for analytical...

  18. On Characterization of Quadratic Splines

    DEFF Research Database (Denmark)

    Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong

    2005-01-01

    that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...

  19. Lying with Maps

    OpenAIRE

    Monmonier, Mark

    2005-01-01

    Darrell Huff’s How to Lie with Statistics was the inspiration for How to Lie with Maps, in which the author showed that geometric distortion and graphic generalization of data are unavoidable elements of cartographic representation. New examples of how ill-conceived or deliberately contrived statistical maps can greatly distort geographic reality demonstrate that lying with maps is a special case of lying with statistics. Issues addressed include the effects of map scale on geometry and featu...

  20. Parenting by Lying

    Science.gov (United States)

    Heyman, Gail D.; Luu, Diem H.; Lee, Kang

    2009-01-01

    The present set of studies identifies the phenomenon of "parenting by lying", in which parents lie to their children as a means of influencing their emotional states and behaviour. In Study 1, undergraduates (n = 127) reported that their parents had lied to them while maintaining a concurrent emphasis on the importance of honesty. In Study 2 (n =…

  1. Effects of Low Incoming Turbulence on the Flow around a 5 : 1 Rectangular Cylinder at Non-Null-Attack Angle

    Directory of Open Access Journals (Sweden)

    M. Ricci

    2016-01-01

    Full Text Available The incompressible high Reynolds number flow around the rectangular cylinder with aspect ratio 5 : 1 has been extensively studied in the recent literature and became a standard benchmark in the field of bluff bodies aerodynamics. The majority of the proposed contributions focus on the simulation of the flow when a smooth inlet condition is adopted. Nevertheless, even when nominally smooth conditions are reproduced in wind tunnel tests, a low turbulence intensity is present together with environmental disturbances and model imperfections. Additionally, many turbulence models are known to be excessively dissipative in laminar-to-turbulent transition zones, generally leading to overestimation of the reattachment length. In this paper, Large Eddy Simulations are performed on a 5 : 1 rectangular cylinder at non-null-attack angle aiming at studying the sensitivity of such flow to a low level of incoming disturbances and compare the performance of standard Smagorinsky-Lilly and Kinetic Energy Transport turbulence models.

  2. Orbit structure of Hamiltonian systems arising from Lie transformation group actions

    Science.gov (United States)

    Garzia, M. R.; Loparo, K. A.; Martin, C. F.

    1983-01-01

    This paper associates the Riccati group and its group action on linear-quadratic optimal control problems to the action of a Lie transformation group on a set of Hamiltonian matrices. In this Lie theoretic setting results are presented concerning the associated orbit structure and the structure of the group itself. These results are of importance in understanding the solution structure of matrix Riccati differential equations, and thus also of importance in linear-quadratic optimal control.

  3. Orbit structure of Hamiltonian systems arising from Lie transformation group actions

    Science.gov (United States)

    Garzia, M. R.; Loparo, K. A.; Martin, C. F.

    This paper associates the Riccati group and its group action on linear-quadratic optimal control problems to the action of a Lie transformation group on a set of Hamiltonian matrices. In this Lie theoretic setting results are presented concerning the associated orbit structure and the structure of the group itself. These results are of importance in understanding the solution structure of matrix Riccati differential equations, and thus also of importance in linear-quadratic optimal control.

  4. SMOOTHING BY CONVEX QUADRATIC PROGRAMMING

    Institute of Scientific and Technical Information of China (English)

    Bing-sheng He; Yu-mei Wang

    2005-01-01

    In this paper, we study the relaxed smoothing problems with general closed convex constraints. It is pointed out that such problems can be converted to a convex quadratic minimization problem for which there are good programs in software libraries.

  5. Quantum quadratic operators and processes

    CERN Document Server

    Mukhamedov, Farrukh

    2015-01-01

    Covering both classical and quantum approaches, this unique and self-contained book presents the most recent developments in the theory of quadratic stochastic operators and their Markov and related processes. The asymptotic behavior of dynamical systems generated by classical and quantum quadratic operators is investigated and various properties of quantum quadratic operators are studied, providing an insight into the construction of quantum channels. This book is suitable as a textbook for an advanced undergraduate/graduate level course or summer school in quantum dynamical systems. It can also be used as a reference book by researchers looking for interesting  problems to work on, or useful techniques and discussions of particular problems. Since it includes the latest developments in the fields of quadratic dynamical systems, Markov processes and quantum stochastic processes, researchers at all levels are likely to find the book inspiring and useful.

  6. Quadratic Tangles in Planar Algebras

    CERN Document Server

    Jones, Vaughan F R

    2010-01-01

    In planar algebras, we show how to project certain simple "quadratic" tangles onto the linear space spanned by "linear" and "constant" tangles. We obtain some corollaries about the principal graphs and annular structure of subfactors.

  7. Additive Lie ($\\xi$-Lie) Derivations and Generalized Lie ($\\xi$-Lie) Derivations on Prime Algebras

    CERN Document Server

    Qi, Xiaofei

    2010-01-01

    The additive (generalized) $\\xi$-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumption, that an additive map $L$ is an additive (generalized) Lie derivation if and only if it is the sum of an additive (generalized) derivation and an additive map from the algebra into its center vanishing all commutators; is an additive (generalized) $\\xi$-Lie derivation with $\\xi\

  8. Lie symmetries of the shigesada-Kawasaki-Teramoto system

    Science.gov (United States)

    Cherniha, Roman; Davydovych, Vasyl'; Muzyka, Liliia

    2017-04-01

    The Shigesada-Kawasaki-Teramoto system, which consists of two reaction-diffusion equations with variable cross-diffusion and quadratic nonlinearities, is considered. The system is the most important case of the biologically motivated model proposed by Shigesada et al. (J. Theor. Biol.79(1979) 83-99). A complete description of Lie symmetries for this system is derived. It is proved that the Shigesada-Kawasaki-Teramoto system admits a wide range of different Lie symmetries depending on coefficient values. In particular, the Lie symmetry operators with highly unusual structure are unveiled and applied for finding exact solutions of the relevant nonlinear system with cross-diffusion.

  9. The ease of lying

    NARCIS (Netherlands)

    Verschuere, B.; Spruyt, A.; Meijer, E.H.; Otgaar, H.

    2011-01-01

    Brain imaging studies suggest that truth telling constitutes the default of the human brain and that lying involves intentional suppression of the predominant truth response. By manipulating the truth proportion in the Sheffield lie test, we investigated whether the dominance of the truth response i

  10. The ease of lying

    NARCIS (Netherlands)

    Verschuere, B.; Spruyt, A.; Meijer, E.H.; Otgaar, H.

    2011-01-01

    Brain imaging studies suggest that truth telling constitutes the default of the human brain and that lying involves intentional suppression of the predominant truth response. By manipulating the truth proportion in the Sheffield lie test, we investigated whether the dominance of the truth response

  11. Whoppers and White Lies.

    Science.gov (United States)

    Vermillion, Marti

    1985-01-01

    Lying is a symptom of a much broader problem. Primary motivations are need for acceptance, fear of punishment, and desire for attention. Children learn about honesty through observation, both directly and indirectly. Admitting mistakes, especially to children, is invaluable and can help break the lying syndrome. (MT)

  12. Medicine, lies and deceptions.

    Science.gov (United States)

    Benn, P

    2001-04-01

    This article offers a qualified defence of the view that there is a moral difference between telling lies to one's patients, and deceiving them without lying. However, I take issue with certain arguments offered by Jennifer Jackson in support of the same conclusion. In particular, I challenge her claim that to deny that there is such a moral difference makes sense only within a utilitarian framework, and I cast doubt on the aptness of some of her examples of non-lying deception. But I argue that lies have a greater tendency to damage trust than does non-lying deception, and suggest that since many doctors do believe there is a moral boundary between the two types of deception, encouraging them to violate that boundary may have adverse general effects on their moral sensibilities.

  13. Evasive Lying in Strategic Communication

    OpenAIRE

    Khalmetski, Kiryl; Rockenbach, Bettina; Werner, Peter

    2017-01-01

    In a sender-receiver game we investigate if sanctions for lying induce more truth-telling. Senders may not only choose between truth-telling and (explicit) lying, but may also engage in evasive lying by credibly pretending not to know. Sanctions promote truth-telling if senders cannot engage in evasive lying. If evasive lying is possible, explicit lying is largely substituted by evasive lying, in line with the notion that evasive lying is perceived as sufficiently less psychologically costly.

  14. Students' understanding of quadratic equations

    Science.gov (United States)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-05-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.

  15. Successive quadratic programming multiuser detector

    Institute of Scientific and Technical Information of China (English)

    Mu Xuewen; Zhang Yaling; Liu Sanyang

    2007-01-01

    Based on the semidefinite programming relaxation of the CDMA maximum likelihood multiuser detection problem,a detection strategy by the successive quadratic programming algorithm is presented. Coupled with the randomized cut generation scheme, the suboptimal solution of the multiuser detection problem in obtained. Compared to the interior point methods previously reported based on semidefinite programming, simulations demonstrate that the successive quadratic programming algorithm often yields the similar BER performances of the multiuser detection problem. But the average CPU time of this approach is significantly reduced.

  16. Integer Quadratic Quasi-polyhedra

    Science.gov (United States)

    Letchford, Adam N.

    This paper introduces two fundamental families of 'quasi-polyhedra' - polyhedra with a countably infinite number of facets - that arise in the context of integer quadratic programming. It is shown that any integer quadratic program can be reduced to the minimisation of a linear function over a quasi-polyhedron in the first family. Some fundamental properties of the quasi-polyhedra are derived, along with connections to some other well-studied convex sets. Several classes of facet-inducing inequalities are also derived. Finally, extensions to the mixed-integer case are briefly examined.

  17. On lying and deceiving.

    Science.gov (United States)

    Bakhurst, D

    1992-06-01

    This article challenges Jennifer Jackson's recent defence of doctors' rights to deceive patients. Jackson maintains there is a general moral difference between lying and intentional deception: while doctors have a prima facie duty not to lie, there is no such obligation to avoid deception. This paper argues 1) that an examination of cases shows that lying and deception are often morally equivalent, and 2) that Jackson's position is premised on a species of moral functionalism that misconstrues the nature of moral obligation. Against Jackson, it is argued that both lying and intentional deception are wrong where they infringe a patient's right to autonomy or his/her right to be treated with dignity. These rights represent 'deontological constraints' on action, defining what we must not do whatever the functional value of the consequences. Medical ethics must recognise such constraints if it is to contribute to the moral integrity of medical practice.

  18. Lie algebras and applications

    CERN Document Server

    Iachello, Francesco

    2015-01-01

    This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators...

  19. Additive Lie (ζ-Lie) Derivations and Generalized Lie (ζ-Lie)Derivations on Prime Algebras

    Institute of Scientific and Technical Information of China (English)

    Xiao Fei QI; Jin Chuan HOU

    2013-01-01

    The additive (generalized) ζ-Lie derivations on prime algebras are characterized.It is shown,under some suitable assumptions,that an additive map L is an additive generalized Lie derivation if and only if it is the sum of an additive generalized derivation and an additive map from the algebra into its center vanishing all commutators; is an additive (generalized) ζ-Lie derivation with ζ ≠ 1 if and only if it is an additive (generalized) derivation satisfying L(ζA) =ζL(A) for all A.These results are then used to characterize additive (generalized) ζ-Lie derivations on several operator algebras such as Banach space standard operator algebras and von Neumman algebras.

  20. Lying, honor, and contradiction

    National Research Council Canada - National Science Library

    Michael Gilsenan

    2016-01-01

    .... +Superscript 1 -Superscript With a particular concentration on the manifold practices of what will be called "lying," I shall try to show the way in which individuals in a Lebanese village negotiate...

  1. Impurity solitons with quadratic nonlinearities

    DEFF Research Database (Denmark)

    Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis

    1998-01-01

    We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton p...

  2. Unramified extensions of quadratic fields

    Institute of Scientific and Technical Information of China (English)

    Wei Li; Dong Yang; Xianke Zhang

    2008-01-01

    Let K be a global quadratic field, then every unramified abelian extension of K is proved to be absolutely Galois when K is a number field or under some natural conditions when K is a function field. The absolute Galois group is also determined explicitly.

  3. Quadratic prediction of factor scores

    NARCIS (Netherlands)

    Wansbeek, T

    1999-01-01

    Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic

  4. Quadratic Variation by Markov Chains

    DEFF Research Database (Denmark)

    Hansen, Peter Reinhard; Horel, Guillaume

    We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...

  5. Quantum electroweak symmetry breaking through loop quadratic contributions

    Directory of Open Access Journals (Sweden)

    Dong Bai

    2015-06-01

    Full Text Available Based on two postulations that (i the Higgs boson has a large bare mass mH≫mh≃125 GeV at the characteristic energy scale Mc which defines the Standard Model (SM in the ultraviolet region, and (ii quadratic contributions of Feynman loop diagrams in quantum field theories are physically meaningful, we show that the SM electroweak symmetry breaking is induced by the quadratic contributions from loop effects. As the quadratic running of Higgs mass parameter leads to an additive renormalization, which distinguishes from the logarithmic running with a multiplicative renormalization, the symmetry breaking occurs once the sliding energy scale μ moves from Mc down to a transition scale μ=ΛEW at which the additive renormalized Higgs mass parameter mH2(Mc/μ gets to change the sign. With the input of current experimental data, this symmetry breaking energy scale is found to be ΛEW≃760 GeV, which provides another basic energy scale for the SM besides Mc. Studying such a symmetry breaking mechanism could play an important role in understanding both the hierarchy problem and naturalness problem. It also provides a possible way to explore the experimental implications of the quadratic contributions as ΛEW lies within the probing reach of the LHC and the future Great Collider.

  6. Consensus-ADMM for General Quadratically Constrained Quadratic Programming

    Science.gov (United States)

    Huang, Kejun; Sidiropoulos, Nicholas D.

    2016-10-01

    Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special cases are NP-hard as well. This paper proposes a new algorithm for general QCQP. The problem is first reformulated in consensus optimization form, to which the alternating direction method of multipliers (ADMM) can be applied. The reformulation is done in such a way that each of the sub-problems is a QCQP with only one constraint (QCQP-1), which is efficiently solvable irrespective of (non-)convexity. The core components are carefully designed to make the overall algorithm more scalable, including efficient methods for solving QCQP-1, memory efficient implementation, parallel/distributed implementation, and smart initialization. The proposed algorithm is then tested in two applications: multicast beamforming and phase retrieval. The results indicate superior performance over prior state-of-the-art methods.

  7. Lying in neuropsychology.

    Science.gov (United States)

    Seron, X

    2014-10-01

    The issue of lying occurs in neuropsychology especially when examinations are conducted in a forensic context. When a subject intentionally either presents non-existent deficits or exaggerates their severity to obtain financial or material compensation, this behaviour is termed malingering. Malingering is discussed in the general framework of lying in psychology, and the different procedures used by neuropsychologists to evidence a lack of collaboration at examination are briefly presented and discussed. When a lack of collaboration is observed, specific emphasis is placed on the difficulty in unambiguously establishing that this results from the patient's voluntary decision.

  8. Quadratic and 2-Crossed Modules of Algebras

    Institute of Scientific and Technical Information of China (English)

    Z. Arvasi; E. Ulualan

    2007-01-01

    In this work, we define the quadratic modules for commutative algebras and give relations among 2-crossed modules, crossed squares, quadratic modules and simplicial commutative algebras with Moore complex of length 2.

  9. Team Decision Problems with Convex Quadratic Constraints

    OpenAIRE

    Gattami, Ather

    2015-01-01

    In this paper, we consider linear quadratic team problems with an arbitrary number of quadratic constraints in both stochastic and deterministic settings. The team consists of players with different measurements about the state of nature. The objective of the team is to minimize a quadratic cost subject to additional finite number of quadratic constraints. We first consider the problem of countably infinite number of players in the team for a bounded state of nature with a Gaussian distributi...

  10. A polyhedral approach to quadratic assignment problem

    OpenAIRE

    Köksaldı, Ahmet Sertaç Murat

    1994-01-01

    Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 1994. Thesis (Master's) -- Bilkent University, 1994. Includes bibliographical references. In this thesis, Quadratic Assignment Problem is considered. Since Quadratic Assignment Problem is JVP-bard, no polynomial time exact solution method exists. Proving optimality of solutions to Quadratic Assignment Problems has been limited to instances of small dimension. In...

  11. Orthogonality preserving infinite dimensional quadratic stochastic operators

    Energy Technology Data Exchange (ETDEWEB)

    Akın, Hasan [Department of Mathematics, Faculty of Education, Zirve University, Gaziantep, 27260 (Turkey); Mukhamedov, Farrukh [Department of Computational & Theoretical Sciences Faculty of Science, International Islamic University Malaysia P.O. Box, 141, 25710, Kuantan Pahang (Malaysia)

    2015-09-18

    In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

  12. Extending the Scope of Robust Quadratic Optimization

    NARCIS (Netherlands)

    Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand

    2017-01-01

    In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in ge

  13. Quantum bouncer with quadratic dissipation

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez, G. [NanoScience Technology Center, University of Central Florida, Orlando, FL 32826 (United States)]. e-mail: ggonzalez@physics.ucf.edu

    2008-07-01

    The energy loss due to a quadratic velocity-dependent force on a quantum particle bouncing off a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new, effective, phenomenological Hamiltonian which corresponds to the actual energy of the system and obtain the correction to the eigenvalues of the energy in first-order quantum perturbation theory for the case of weak dissipation. (Author)

  14. Quantum bouncer with quadratic dissipation

    Science.gov (United States)

    González, G.

    2008-02-01

    The energy loss due to a quadratic velocity dependent force on a quantum particle bouncing on a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new effective phenomenological Hamiltonian which corresponds to the actual energy of the system and obtained the correction to the eigenvalues of the energy in first order quantum perturbation theory for the case of weak dissipation.

  15. Global Optimization of a Class of Nonconvex Quadratically Constrained Quadratic Programming Problems

    Institute of Scientific and Technical Information of China (English)

    Yong XIA

    2011-01-01

    In this paper we study a class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems.We show that each problem is polynomially solved.Strong duality holds if a redundant constraint is introduced.As an application,a new lower bound is proposed for the quadratic assignment problem.

  16. Solvable Lie algebras with naturally graded nilradicals and their invariants

    Energy Technology Data Exchange (ETDEWEB)

    Ancochea, J M; Campoamor-Stursberg, R; Vergnolle, L Garcia [Departamento GeometrIa y TopologIa, Fac. CC. Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias 3, E-28040 Madrid (Spain)

    2006-02-10

    The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analysed, and their generalized Casimir invariants are calculated. It is shown that rank one solvable algebras have a contact form, which implies the existence of an associated dynamical system. Moreover, due to the structure of the quadratic Casimir operator of the nilradical, these algebras contain a maximal non-abelian quasi-classical Lie algebra of dimension 2n - 1, indicating that gauge theories (with ghosts) are possible on these subalgebras.

  17. On the Logic of Lying

    NARCIS (Netherlands)

    H. van Ditmarsch (Hans); D.J.N. van Eijck (Jan); F.A.G. Sietsma (Floor); Y. Wang (Yanjing); D.J.N. van Eijck (Jan); R. Verbrugge

    2011-01-01

    htmlabstractWe look at lying as an act of communication, where (i) the proposition that is communicated is not true, (ii) the utterer of the lie knows (or believes) that what she communicates is not true, and (iii) the utterer of the lie intends the lie to be taken as truth. Rather than dwell on

  18. Lie algebraic noncommutative gravity

    Science.gov (United States)

    Banerjee, Rabin; Mukherjee, Pradip; Samanta, Saurav

    2007-06-01

    We exploit the Seiberg-Witten map technique to formulate the theory of gravity defined on a Lie algebraic noncommutative space-time. Detailed expressions of the Seiberg-Witten maps for the gauge parameters, gauge potentials, and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first order correction, exactly as happens for a canonical (i.e. constant) noncommutativity.

  19. Introduction to quantum Lie algebras

    CERN Document Server

    Delius, G W

    1996-01-01

    Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras \\uqg. The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. In this paper the recent general results about quantum Lie algebras are introduced with the help of the explicit example of (sl_2)_h.

  20. Lie groups, lie algebras, and representations an elementary introduction

    CERN Document Server

    Hall, Brian

    2015-01-01

    This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compac...

  1. Quadratic time dependent Hamiltonians and separation of variables

    Science.gov (United States)

    Anzaldo-Meneses, A.

    2017-06-01

    Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.

  2. Asymptotic Normality of Quadratic Estimators.

    Science.gov (United States)

    Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad

    2016-12-01

    We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.

  3. quadratic spline finite element method

    Directory of Open Access Journals (Sweden)

    A. R. Bahadir

    2002-01-01

    Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.

  4. Optimal control linear quadratic methods

    CERN Document Server

    Anderson, Brian D O

    2007-01-01

    This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the

  5. Factorization method of quadratic template

    Science.gov (United States)

    Kotyrba, Martin

    2017-07-01

    Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.

  6. Quadratic reactivity fuel cycle model

    Energy Technology Data Exchange (ETDEWEB)

    Lewins, J.D.

    1985-11-01

    For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau/sup 2/ as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau/sup 2/ in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper.

  7. Lie algebraic Noncommutative Gravity

    CERN Document Server

    Banerjee, R; Samanta, S; Banerjee, Rabin; Mukherjee, Pradip; Samanta, Saurav

    2007-01-01

    The minimal (unimodular) formulation of noncommutative general relativity, based on gauging the Poincare group, is extended to a general Lie algebra valued noncommutative structure. We exploit the Seiberg -- Witten map technique to formulate the theory as a perturbative Lagrangian theory. Detailed expressions of the Seiberg -- Witten maps for the gauge parameters, gauge potentials and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first order correction, exactly as happens for a canonical (i.e. constant) noncommutativity.

  8. Lied Transplant Center

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1996-02-01

    The Department of Energy has prepared an Environmental Assessment (DOE/EA-1143) evaluating the construction, equipping and operation of the proposed Lied Transplant Center at the University of Nebraska Medical Center in Omaha, Nebraska. Based on the analysis in the EA, the DOE has determined that the proposed action does not constitute a major federal action significantly affecting the quality of the human environment within the meaning of the National Environmental Policy Act of 1969 (NEPA). Therefore, the preparation of an Environmental Statement in not required.

  9. Police lie detection accuracy: the effect of lie scenario.

    Science.gov (United States)

    O'Sullivan, Maureen; Frank, Mark G; Hurley, Carolyn M; Tiwana, Jaspreet

    2009-12-01

    Although most people are not better than chance in detecting deception, some groups of police professionals have demonstrated significant lie detection accuracy. One reason for this difference may be that the types of lies police are asked to judge in scientific experiments often do not represent the types of lies they see in their profession. Across 23 studies, involving 31 different police groups in eight countries, police officers tested with lie detection scenarios using high stakes lies (i.e., the lie was personally involving and/or resulted in substantial rewards or punishments for the liar) were significantly more accurate than law enforcement officials tested with low stakes lies. Face validity and construct validity of various lie scenarios are differentiated.

  10. A sequential quadratically constrained quadratic programming method with an augmented Lagrangian line search function

    Science.gov (United States)

    Tang, Chun-Ming; Jian, Jin-Bao

    2008-10-01

    Based on an augmented Lagrangian line search function, a sequential quadratically constrained quadratic programming method is proposed for solving nonlinearly constrained optimization problems. Compared to quadratic programming solved in the traditional SQP methods, a convex quadratically constrained quadratic programming is solved here to obtain a search direction, and the Maratos effect does not occur without any other corrections. The "active set" strategy used in this subproblem can avoid recalculating the unnecessary gradients and (approximate) Hessian matrices of the constraints. Under certain assumptions, the proposed method is proved to be globally, superlinearly, and quadratically convergent. As an extension, general problems with inequality and equality constraints as well as nonmonotone line search are also considered.

  11. [Diagnostic imaging of lying].

    Science.gov (United States)

    Lass, Piotr; Sławek, Jarosław; Sitek, Emilia; Szurowska, Edyta; Zimmermann, Agnieszka

    2013-01-01

    Functional diagnostic imaging has been applied in neuropsychology for more than two decades. Nowadays, the functional magnetic resonance (fMRI) seems to be the most important technique. Brain imaging in lying has been performed and discussed since 2001. There are postulates to use fMRI for forensic purposes, as well as commercially, e.g. testing the loyalty of employees, especially because of the limitations of traditional polygraph in some cases. In USA fMRI is performed in truthfulness/lying assessment by at least two commercial companies. Those applications are a matter of heated debate of practitioners, lawyers and specialists of ethics. The opponents of fMRI use for forensic purposes indicate the lack of common agreement on it and the lack of wide recognition and insufficient standardisation. Therefore it cannot serve as a forensic proof, yet. However, considering the development of MRI and a high failure rate of traditional polygraphy, forensic applications of MRI seem to be highly probable in future.

  12. On Algebraic Approach in Quadratic Systems

    Directory of Open Access Journals (Sweden)

    Matej Mencinger

    2011-01-01

    Full Text Available When considering friction or resistance, many physical processes are mathematically simulated by quadratic systems of ODEs or discrete quadratic dynamical systems. Probably the most important problem when such systems are applied in engineering is the stability of critical points and (nonchaotic dynamics. In this paper we consider homogeneous quadratic systems via the so-called Markus approach. We use the one-to-one correspondence between homogeneous quadratic dynamical systems and algebra which was originally introduced by Markus in (1960. We resume some connections between the dynamics of the quadratic systems and (algebraic properties of the corresponding algebras. We consider some general connections and the influence of power-associativity in the corresponding quadratic system.

  13. Telling Lies: The Irrepressible Truth?

    Science.gov (United States)

    Williams, Emma J.; Bott, Lewis A.; Patrick, John; Lewis, Michael B.

    2013-01-01

    Telling a lie takes longer than telling the truth but precisely why remains uncertain. We investigated two processes suggested to increase response times, namely the decision to lie and the construction of a lie response. In Experiments 1 and 2, participants were directed or chose whether to lie or tell the truth. A colored square was presented and participants had to name either the true color of the square or lie about it by claiming it was a different color. In both experiments we found that there was a greater difference between lying and telling the truth when participants were directed to lie compared to when they chose to lie. In Experiments 3 and 4, we compared response times when participants had only one possible lie option to a choice of two or three possible options. There was a greater lying latency effect when questions involved more than one possible lie response. Experiment 5 examined response choice mechanisms through the manipulation of lie plausibility. Overall, results demonstrate several distinct mechanisms that contribute to additional processing requirements when individuals tell a lie. PMID:23573277

  14. An Algorithm for Solving Quadratic Programming Problems

    Directory of Open Access Journals (Sweden)

    V. Moraru

    1997-08-01

    Full Text Available Herein is investigated the method of solution of quadratic programming problems. The algorithm is based on the effective selection of constraints. Quadratic programming with constraints-equalities are solved with the help of an algorithm, so that matrix inversion is avoided, because of the more convenient organization of the Calculus. Optimal solution is determined in a finite number of iterations. It is discussed the extension of the algorithm over solving quadratic non-convex programming problems.

  15. Group discussion improves lie detection

    National Research Council Canada - National Science Library

    Nadav Klein; Nicholas Epley

    2015-01-01

    ... identify when a person is lying. These experiments demonstrate that the group advantage in lie detection comes through the process of group discussion, and is not a product of aggregating individual opinions...

  16. The Random Quadratic Assignment Problem

    Science.gov (United States)

    Paul, Gerald; Shao, Jia; Stanley, H. Eugene

    2011-11-01

    The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P. Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for C min and C max , the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for C min and C max and their dependence on P only through its mean and standard deviation, independent of the details of P.

  17. Lying because we care: Compassion increases prosocial lying.

    Science.gov (United States)

    Lupoli, Matthew J; Jampol, Lily; Oveis, Christopher

    2017-07-01

    Prosocial lies, or lies intended to benefit others, are ubiquitous behaviors that have important social and economic consequences. Though emotions play a central role in many forms of prosocial behavior, no work has investigated how emotions influence behavior when one has the opportunity to tell a prosocial lie-a situation that presents a conflict between two prosocial ethics: lying to prevent harm to another, and honesty, which might also provide benefits to the target of the lie. Here, we examine whether the emotion of compassion influences prosocial lying, and find that compassion causally increases and positively predicts prosocial lying. In Studies 1 and 2, participants evaluated a poorly written essay and provided feedback to the essay writer. Experimentally induced compassion felt toward the essay writer (Study 1) and individual differences in trait compassion (Study 2) were positively associated with inflated feedback to the essay writer. In both of these studies, the relationship between compassion and prosocial lying was partially mediated by an enhanced importance placed on preventing emotional harm. In Study 3, we found moderation such that experimentally induced compassion increased lies that resulted in financial gains for a charity, but not lies that produced financial gains for the self. This research illuminates the emotional underpinnings of the common yet morally complex behavior of prosocial lying, and builds on work highlighting the potentially harmful effects of compassion-an emotion typically seen as socially beneficial. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  18. On the Logic of Lying

    NARCIS (Netherlands)

    H. van Ditmarsch (Hans); D.J.N. van Eijck (Jan); F.A.G. Sietsma (Floor)

    2012-01-01

    textabstractWe model lying as a communicative act changing the beliefs of the agents in a multi-agent system. With Augustine, we see lying as an utterance believed to be false by the speaker and uttered with the intent to deceive the addressee. The deceit is successful if the lie is believed

  19. Lying relies on the truth

    NARCIS (Netherlands)

    Debey, E.; De Houwer, J.; Verschuere, B.

    2014-01-01

    Cognitive models of deception focus on the conflict-inducing nature of the truth activation during lying. Here we tested the counterintuitive hypothesis that the truth can also serve a functional role in the act of lying. More specifically, we examined whether the construction of a lie can involve a

  20. Lying relies on the truth

    NARCIS (Netherlands)

    Debey, E.; De Houwer, J.; Verschuere, B.

    2014-01-01

    Cognitive models of deception focus on the conflict-inducing nature of the truth activation during lying. Here we tested the counterintuitive hypothesis that the truth can also serve a functional role in the act of lying. More specifically, we examined whether the construction of a lie can involve a

  1. Pre-Lie Deformation Theory

    NARCIS (Netherlands)

    Dotsenko, V.; Shadrin, S.; Vallette, B.

    2016-01-01

    In this paper, we develop the deformation theory controlled by pre-Lie algebras; the main tool is a new integration theory for preLie algebras. The main field of application lies in homotopy algebra structures over a Koszul operad; in this case, we provide a homotopical description of the associated

  2. Quantization on nilpotent Lie groups

    CERN Document Server

    Fischer, Veronique

    2016-01-01

    This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.

  3. Binary Quadratic Forms: A Historical View

    Science.gov (United States)

    Khosravani, Azar N.; Beintema, Mark B.

    2006-01-01

    We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

  4. Quadratic Boost A-Source Impedance Network

    DEFF Research Database (Denmark)

    Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii

    2016-01-01

    A novel quadratic boost type A-source impedance network is proposed in this paper for realizing converters that demand a very high voltage gain. To achieve that, the proposed network uses an auto-transformer, whose obtained gain is quadratically dependent on the duty ratio and is presently not ma...

  5. Quadratic Boost A-Source Impedance Network

    DEFF Research Database (Denmark)

    Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii

    2016-01-01

    A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance ...

  6. Factorising a Quadratic Expression with Geometric Insights

    Science.gov (United States)

    Joarder, Anwar H.

    2015-01-01

    An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…

  7. An example in linear quadratic optimal control

    NARCIS (Netherlands)

    Weiss, George; Zwart, Heiko J.

    1998-01-01

    We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme

  8. An example in linear quadratic optimal control

    NARCIS (Netherlands)

    Weiss, George; Zwart, Heiko J.

    1998-01-01

    We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme sim

  9. Lie Subalgebras in a Certain Operator Lie Algebra with Involution

    Institute of Scientific and Technical Information of China (English)

    Shan Li SUN; Xue Feng MA

    2011-01-01

    We show in a certain Lie'-algebra,the connections between the Lie subalgebra G+:=G+G*+[G,G*],generated by a Lie subalgebra G,and the properties of G.This allows us to investigate some useful information about the structure of such two Lie subalgebras.Some results on the relations between the two Lie subalgebras are obtained.As an application,we get the following conclusion:Let A (∪) B(X)be a space of self-adjoint operators and L:=A ⊕ iA the corresponding complex Lie*-algebra.G+=G+G*+[G,G*]and G are two LM-decomposable Lie subalgebras of,L with the decomposition G+=R(G+)+S,G=RG+SG,and RG (∪) R(C+).Then G+ is ideally finite iff RG+:=RG+RG*+[RG,RG*]is a quasisolvable Lie subalgebra,SG+:=SG+SG*+[SG,SG*]is an ideally finite semisimple Lie subalgebra,and [RG,SG]=[RG*,SG]={0}.

  10. Quadratic Hedging of Basis Risk

    Directory of Open Access Journals (Sweden)

    Hardy Hulley

    2015-02-01

    Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.

  11. On Quadratic Variation of Martingales

    Indian Academy of Sciences (India)

    Rajeeva L Karandikar; B V Rao

    2014-08-01

    We give a construction of an explicit mapping $$\\Psi: D([0,∞),\\mathbb{R})→ D([0,∞),\\mathbb{R}),$$ where $D([0,∞), \\mathbb{R})$ denotes the class of real valued r.c.l.l. functions on $[0,∞)$ such that for a locally square integrable martingale $(M_t)$ with r.c.l.l. paths, $$\\Psi(M.())=A.()$$ gives the quadratic variation process (written usually as $[M,M]_t$) of $(M_t)$. We also show that this process $(A_t)$ is the unique increasing process $(B_t)$ such that $M_t^2-B_t$ is a local martingale, $B_0=0$ and $$\\mathbb{P}(( B)_t=[( M)_t]^2, 0 < ∞)=1.$$ Apart from elementary properties of martingales, the only result used is the Doob’s maximal inequality. This result can be the starting point of the development of the stochastic integral with respect to r.c.l.l. martingales.

  12. THE ACQM THEORETICAL CALCULATION OF LOW—LYING EXCITED STATES FOR HeH

    Institute of Scientific and Technical Information of China (English)

    Q.Q.GOU; Z.Y.Huang; 等

    1990-01-01

    The Low-lying excited states of HeH have been calculated by arrangement channel quantum mechanics(ACQM),The calculated potential curves,equilibrium geometry,Rc.dissociation energy Dc.harmonic vibration frequency ω0 and quadratic force coustant F2 are comparable with Ci calculations.

  13. Lie groups and automorphic forms

    CERN Document Server

    Ji, Lizhen; Xu, H W; Yau, Shing-Tung

    2006-01-01

    Lie groups are fundamental objects in mathematics. They occur naturally in differential geometry, algebraic geometry, representation theory, number theory, and other areas. Closely related are arithmetic subgroups, locally symmetric spaces and the spectral theory of automorphic forms. This book consists of five chapters which give comprehensive introductions to Lie groups, Lie algebras, arithmetic groups and reduction theories, cohomology of arithmetic groups, and the Petersson and Kuznetsov trace formulas.

  14. Bosonization and Lie Group Structure

    CERN Document Server

    Ha, Yuan K

    2015-01-01

    We introduce a concise quantum operator formula for bosonization in which the Lie group structure appears in a natural way. The connection between fermions and bosons is found to be exactly the connection between Lie group elements and the group parameters. Bosonization is an extraordinary way of expressing the equation of motion of a complex fermion field in terms of a real scalar boson in two dimensions. All the properties of the fermion field theory are known to be preserved under this remarkable transformation with substantial simplification and elucidation of the original theory, much like Lie groups can be studied by their Lie algebras.

  15. Lying relies on the truth.

    Science.gov (United States)

    Debey, Evelyne; De Houwer, Jan; Verschuere, Bruno

    2014-09-01

    Cognitive models of deception focus on the conflict-inducing nature of the truth activation during lying. Here we tested the counterintuitive hypothesis that the truth can also serve a functional role in the act of lying. More specifically, we examined whether the construction of a lie can involve a two-step process, where the first step entails activating the truth, based upon which a lie response can be formulated in a second step. To investigate this hypothesis, we tried to capture the covert truth activation in a reaction-time based deception paradigm. Together with each question, we presented either the truth or lie response as distractors. If lying depends on the covert activation of the truth, deceptive responses would thus be facilitated by truth distractors relative to lie distractors. Our results indeed revealed such a "covert congruency" effect, both in errors and reaction times (Experiment 1). Moreover, stimulating participants to use the distractor information by increasing the proportion of truth distractor trials enlarged the "covert congruency" effects, and as such confirmed that the effects operate at a covert response level (Experiment 2). Our findings lend support to the idea that lying relies on a first step of truth telling, and call for a shift in theoretical thinking that highlights both the functional and interfering properties of the truth activation in the lying process. Copyright © 2014 Elsevier B.V. All rights reserved.

  16. Differential geometry on Lie groups

    OpenAIRE

    2013-01-01

    Resumo: Neste trabalho estudamos os aspectos geométricos dos grupos de Lie do ponto de vista da geometria Riemanniana, geometria Hermitiana e geometria Kähler, através das estruturas geométricas invariantes associadas. Exploramos resultados relacionados às curvaturas da variedade Riemanniana subjacente a um grupo de Lie através do estudo de sua álgebra de Lie correspondente. No contexto da geometria Hermitiana e geometria Kähler, para um caso concreto de grupo de Lie complexo, investigaram su...

  17. Affective Priming Caused by Lying

    Directory of Open Access Journals (Sweden)

    Megumi Sato

    2011-10-01

    Full Text Available Typically, arousal increases when telling a lie, as indicated in psychophysiological studies about lie detection. But the emotional valence induced by lying is unknown, though intuition indicates that it may be negative. Indeed, the Electrodermal Activity (EDA, used in such studies, only shows arousal changes during an emotional response. In this study, we examined the emotional valence induced by lying using two tasks. First, in the deceptive task, participants answered “no” to every question regarding the nature of displayed playing cards. Therefore, they told a lie about specific cards. During the task, their EDA was recorded. Secondly, in the figure estimation task, they assessed pictures by “like” or “dislike” after looking at playing cards visibly or subliminally as prime stimuli. We expected them to tend to estimate figures by “dislike” when cards relevant to deception were previously shown. This would mean that an affective priming effect due to telling a lie happened. Actually, this effect was found only when prime stimuli were displayed visibly. This result suggests that lying per se induces negative emotions even without motivation or punishment due to lying. Furthermore, we found that such effect was more blatant in participants whose EDA changes were salient while lying.

  18. The Pure Virtual Braid Group Is Quadratic

    CERN Document Server

    Lee, Peter

    2011-01-01

    If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra gr_I K need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a criterion which is equivalent to gr_I K being quadratic. We apply this criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic.

  19. Specialization of Quadratic and Symmetric Bilinear Forms

    CERN Document Server

    Knebusch, Manfred

    2010-01-01

    The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed for fields of characteristic different from 2, are explored here without this restriction. In addition to chapters on specialization theory, generic splitting t

  20. Quadratic stabilization of switched nonlinear systems

    Institute of Scientific and Technical Information of China (English)

    DONG YaLi; FAN JiaoJiao; MEI ShengWei

    2009-01-01

    In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems.

  1. Theatres of the lie: 'crazy' deception and lying as drama.

    Science.gov (United States)

    Dongen, Els van

    2002-08-01

    In this article, the author argues that lying is drama, theatre, which brings about transition, reflection, reversal and involvement of the participants in the drama. By means of ethnographic data of a psychiatric ward, the author shows that lying of mental patients is not pathological, but a ritual of affliction. By using Turner's theory about rituals and performance and Goffman's theory about presentation of the self it will be showed that lying serves the redefinition of reciprocity and solidarity. With the help of Bakhtin's work on Rabelais, the author discusses the nature of the drama of the lie. It is concluded that a perspective on lying as theatre may be of use outside psychiatric wards and will occur in imbalanced power relationships.

  2. Explicit Soliton and Periodic Solutions to Three-Wave System with Quadratic and Cubic Nonlinearities

    Institute of Scientific and Technical Information of China (English)

    LIN Ji; ZHAO Li-Na; LI Hua-Mei

    2011-01-01

    Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency (FF) and a single second harmonic (SH) one by competing x(2)(quadratic) and x(3) (cubic) nonlinearities and birefringence.This system shares some of the nice properties of soliton system.On the phase-locked condition, we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.

  3. Symmetries of the One-Dimensional Fokker-Planck-Kolmogorov Equation with a Nonlocal Quadratic Nonlinearity

    Science.gov (United States)

    Levchenko, E. A.; Trifonov, A. Yu.; Shapovalov, A. V.

    2017-06-01

    The one-dimensional Fokker-Planck-Kolmogorov equation with a special type of nonlocal quadratic nonlinearity is represented as a consistent system of differential equations, including a dynamical system describing the evolution of the moments of the unknown function. Lie symmetries are found for the consistent system using methods of classical group analysis. An example of an invariant-group solution obtained with an additional integral constraint imposed on the system is considered.

  4. Deciding isomorphism of Lie algebras

    NARCIS (Netherlands)

    Graaf, W.A. de

    2001-01-01

    When doing calculations with Lie algebras one of the main problems is to decide whether two given Lie algebras are isomorphic. A partial solution to this problem is obtained by calculating structural invariants. There is also a direct method available which involves the computation of Grobner bases.

  5. The low lying glueball spectrum

    Energy Technology Data Exchange (ETDEWEB)

    Adam Szczepaniak; Eric Swanson

    2003-12-18

    The complete low-lying positive charge conjugation glueball spectrum is obtained from QCD. The formalism relies on the construction of an efficient quasiparticle gluon basis for Hamiltonian QCD in Coulomb gauge. The resulting rapidly convergent Fock space expansion is exploited to derive quenched low-lying glueball masses with no free parameters which are in remarkable agreement with lattice gauge theory.

  6. Lie Symmetries of Ishimori Equation

    Institute of Scientific and Technical Information of China (English)

    SONG Xu-Xia

    2013-01-01

    The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.

  7. Lying despite telling the truth.

    Science.gov (United States)

    Wiegmann, Alex; Samland, Jana; Waldmann, Michael R

    2016-05-01

    According to the standard definition of lying an utterance counts as a lie if the agent believes the statement to be false. Thus, according to this view it is possible that a lie states something that happens to be true. This subjective view on lying has recently been challenged by Turri and Turri (2015) who presented empirical evidence suggesting that people only consider statements as lies that are objectively false (objective view). We argue that the presented evidence is in fact consistent with the standard subjective view if conversational pragmatics is taken into account. Three experiments are presented that directly test and support the subjective view. An additional experiment backs up our pragmatic hypothesis by using the uncontroversial case of making a promise.

  8. Group discussion improves lie detection.

    Science.gov (United States)

    Klein, Nadav; Epley, Nicholas

    2015-06-16

    Groups of individuals can sometimes make more accurate judgments than the average individual could make alone. We tested whether this group advantage extends to lie detection, an exceptionally challenging judgment with accuracy rates rarely exceeding chance. In four experiments, we find that groups are consistently more accurate than individuals in distinguishing truths from lies, an effect that comes primarily from an increased ability to correctly identify when a person is lying. These experiments demonstrate that the group advantage in lie detection comes through the process of group discussion, and is not a product of aggregating individual opinions (a "wisdom-of-crowds" effect) or of altering response biases (such as reducing the "truth bias"). Interventions to improve lie detection typically focus on improving individual judgment, a costly and generally ineffective endeavor. Our findings suggest a cheap and simple synergistic approach of enabling group discussion before rendering a judgment.

  9. Compression limits in cascaded quadratic soliton compression

    DEFF Research Database (Denmark)

    Bache, Morten; Bang, Ole; Krolikowski, Wieslaw;

    2008-01-01

    Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency.......Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency....

  10. Radiotherapy treatment planning linear-quadratic radiobiology

    CERN Document Server

    Chapman, J Donald

    2015-01-01

    Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil

  11. Quadratic stabilization for uncertain stochastic systems

    Institute of Scientific and Technical Information of China (English)

    Jun'e FENG; Weihai ZHANG

    2005-01-01

    This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems,where the uncertain matrix is norm bounded,and the external disturbance is a stochastic process.Two kinds of controllers are designed,which include state feedback case and output feedback case.The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities.The detailed design methods are presented.Numerical examples show the effectiveness of our results.

  12. Cascaded quadratic soliton compression at 800 nm

    DEFF Research Database (Denmark)

    Bache, Morten; Bang, Ole; Moses, Jeffrey;

    2007-01-01

    We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion.......We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....

  13. A NEW INEXACT SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM

    Institute of Scientific and Technical Information of China (English)

    倪勤

    2002-01-01

    This paper represents an inexact sequential quadratic programming (SQP ) algorithm which can solve nonlinear programming (NLP ) problems. An inexact solution of the quadratic programming subproblem is determined by a projection and contraction method such that only matrix-vector product is required. Some truncated criteria are chosen such that the algorithm is suitable to large scale NLP problem. The global convergence of the algorithm is proved.

  14. The explicit dependence of quadrat variance on the ratio of clump size to quadrat size.

    Science.gov (United States)

    Ferrandino, Francis J

    2005-05-01

    ABSTRACT In the past decade, it has become common practice to pool mapped binary epidemic data into quadrats. The resultant "quadrat counts" can then be analyzed by fitting them to a probability distribution (i.e., betabinomial). Often a binary form of Taylor's power law is used to relate the quadrat variance to the quadrat mean. The fact that there is an intrinsic dependence of such analyses on quadrat size and shape is well known. However, a clear-cut exposition of the direct connection between the spatial properties of the two-dimensional pattern of infected plants in terms of the geometry of the quadrat and the results of quadrat-based analyses is lacking. This problem was examined both empirically and analytically. The empirical approach is based on a set of stochastically generated "mock epidemics" using a Neyman-Scott cluster process. The resultant spatial point-patterns of infected plants have a fixed number of disease foci characterized by a known length scale (monodisperse) and saturated to a known disease level. When quadrat samples of these epidemics are fit to a beta-binomial distribution, the resulting measures of aggregation are totally independent of disease incidence and most strongly dependent on the ratio of the length scale of the quadrat to the length scale of spatial aggregation and to a lesser degree on disease saturation within individual foci. For the analytical approach, the mathematical form for the variation in the sum of random variates is coupled to the geometry of a quadrat through an assumed exponential autocorrelation function. The net result is an explicit equation expressing the intraquadrat correlation, quadrat variance, and the index of dispersion in terms of the ratio of the quadrat length scale to the correlative length scale.

  15. Detecting true lies: police officers' ability to detect suspects' lies.

    Science.gov (United States)

    Mann, Samantha; Vrij, Aldert; Bull, Ray

    2004-02-01

    Ninety-nine police officers, not identified in previous research as belonging to groups that are superior in lie detection, attempted to detect truths and lies told by suspects during their videotaped police interviews. Accuracy rates were higher than those typically found in deception research and reached levels similar to those obtained by specialized lie detectors in previous research. Accuracy was positively correlated with perceived experience in interviewing suspects and with mentioning cues to detecting deceit that relate to a suspect's story. Accuracy was negatively correlated with popular stereotypical cues such as gaze aversion and fidgeting. As in previous research, accuracy and confidence were not significantly correlated, but the level of confidence was dependent on whether officers judged actual truths or actual lies and on the method by which confidence was measured.

  16. Lying aversion and prosocial behaviour

    CERN Document Server

    Biziou-van-Pol, Laura; Novaro, Arianna; Liberman, Andrés Occhipinti; Capraro, Valerio

    2015-01-01

    The focus of this paper is the moral conflict between lying aversion and prosociality. What does telling a white lie signal about a person's prosocial tendencies? How does believing a possibly untruthful message signal about a listener's prosocial tendencies? To answer these questions, we conducted a 2x3 experiment. In the first stage we measured altruistic tendencies using a Dictator Game and cooperative tendencies using a Prisoner's dilemma. In the second stage, we used a sender-receiver game to measure aversion to telling a Pareto white lie (i.e., a lie that helps both the liar and the listener), aversion to telling an altruistic white lie (i.e., a lie that helps the listener at the expense of the liar), and skepticism towards believing a possibly untruthful message. We found three major results: (i) both altruism and cooperation are positively correlated with aversion to telling a Pareto white lie; (ii) neither altruism nor cooperation are significantly correlated with aversion to telling an altruistic wh...

  17. Lies, Calculations and Constructions: Beyond How to Lie with Statistics

    OpenAIRE

    Best, Joel

    2005-01-01

    Darrell Huff’s How to Lie with Statistics remains the best-known, nontechnical call for critical thinking about statistics. However, drawing a distinction between statistics and lying ignores the process by which statistics are socially constructed. For instance, bad statistics often are disseminated by sincere, albeit innumerate advocates (e.g., inflated estimates for the number of anorexia deaths) or through research findings selectively highlighted to attract media coverage (e.g., a recent...

  18. Last Multipliers on Lie Algebroids

    Indian Academy of Sciences (India)

    Mircea Crasmareanu; Cristina-Elena Hreţcanu

    2009-06-01

    In this paper we extend the theory of last multipliers as solutions of the Liouville’s transport equation to Lie algebroids with their top exterior power as trivial line bundle (previously developed for vector fields and multivectors). We define the notion of exact section and the Liouville equation on Lie algebroids. The aim of the present work is to develop the theory of this extension from the tangent bundle algebroid to a general Lie algebroid (e.g. the set of sections with a prescribed last multiplier is still a Gerstenhaber subalgebra). We present some characterizations of this extension in terms of Witten and Marsden differentials.

  19. The applications of a higher-dimensional Lie algebra and its decomposed subalgebras.

    Science.gov (United States)

    Yu, Zhang; Zhang, Yufeng

    2009-01-15

    With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6 x 6 matrix Lie algebra smu(6) is constructed. It follows a type of new loop algebra is presented. By using a (2 + 1)-dimensional partial-differential equation hierarchy we obtain the integrable coupling of the (2 + 1)-dimensional KN integrable hierarchy, then its corresponding Hamiltonian structure is worked out by employing the quadratic-form identity. Furthermore, a higher-dimensional Lie algebra denoted by E, is given by decomposing the Lie algebra smu(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras smu(6) and E is used to directly construct integrable couplings.

  20. Gravitating fluids with Lie symmetries

    CERN Document Server

    Msomi, A M; Maharaj, S D

    2010-01-01

    We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means of Lie point symmetries. The method utilised reduces the partial differential equation to an ordinary differential equation according to the Lie symmetry admitted. We show that a class of solutions found previously can be characterised by a particular Lie generator. Several new families of solutions are found explicitly. In particular we find the relevant ordinary differential equation for all one-dimensional optimal subgroups; in several cases the ordinary differential equation can be solved in general. We are in a position to characterise particular solutions with a linear barotropic equation of state.

  1. Historical Techniques of Lie Detection

    Directory of Open Access Journals (Sweden)

    Martina Vicianova

    2015-08-01

    Full Text Available Since time immemorial, lying has been a part of everyday life. For this reason, it has become a subject of interest in several disciplines, including psychology. The purpose of this article is to provide a general overview of the literature and thinking to date about the evolution of lie detection techniques. The first part explores ancient methods recorded circa 1000 B.C. (e.g., God’s judgment in Europe. The second part describes technical methods based on sciences such as phrenology, polygraph and graphology. This is followed by an outline of more modern-day approaches such as FACS (Facial Action Coding System, functional MRI, and Brain Fingerprinting. Finally, after the familiarization with the historical development of techniques for lie detection, we discuss the scope for new initiatives not only in the area of designing new methods, but also for the research into lie detection itself, such as its motives and regulatory issues related to deception.

  2. Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

    DEFF Research Database (Denmark)

    Mak, Vicky; Thomadsen, Tommy

    2006-01-01

    This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...

  3. Linear-quadratic control and quadratic differential forms for multidimensional behaviors

    NARCIS (Netherlands)

    Napp, D.; Trentelman, H.L.

    2011-01-01

    This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look

  4. A Mixed-Binary Convex Quadratic Reformulation for Box-Constrained Nonconvex Quadratic Integer Program

    OpenAIRE

    Xia, Yong; Han, Ying-Wei

    2014-01-01

    In this paper, we propose a mixed-binary convex quadratic programming reformulation for the box-constrained nonconvex quadratic integer program and then implement IBM ILOG CPLEX 12.6 to solve the new model. Computational results demonstrate that our approach clearly outperform the very recent state-of-the-art solvers.

  5. Binary classification posed as a quadratically constrained quadratic programming and solved using particle swarm optimization

    Indian Academy of Sciences (India)

    DEEPAK KUMAR; A G RAMAKRISHNAN

    2016-03-01

    Particle swarm optimization (PSO) is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The central idea is to use PSO to move in the direction towards optimal solution rather than searching the entire feasibleregion. Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or classification boundary for a data set. Our results on the Iris, Pima, Wine, Thyroid, Balance, Bupa, Haberman, and TAE datasets show that the proposed method works better than a neural network and the performance is close to that of a support vector machine

  6. Fast approximate quadratic programming for graph matching.

    Directory of Open Access Journals (Sweden)

    Joshua T Vogelstein

    Full Text Available Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs, we find that it efficiently achieves performance.

  7. Fast approximate quadratic programming for graph matching.

    Science.gov (United States)

    Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.

  8. Quadratic Interpolation Algorithm for Minimizing Tabulated Function

    Directory of Open Access Journals (Sweden)

    E. A. Youness

    2008-01-01

    Full Text Available Problem statement: The problem of finding the minimum value of objective function, when we know only some values of it, is needed in more practical fields. Quadratic interpolation algorithms are the famous tools deal with this kind of these problems. These algorithms interested with the polynomial space in which the objective function is approximated. Approach: In this study we approximated the objective function by a one dimensional quadratic polynomial. This approach saved the time and the effort to get the best point at which the objective is minimized. Results: The quadratic polynomial in each one of the steps of the proposed algorithm, accelerate the convergent to the best value of the objective function without taking into account all points of the interpolation set. Conclusion: Any n-dimensional problem of finding a minimal value of a function, given by some values, can be converted to one dimensional problem easier in deal.

  9. Quadratic gravity: from weak to strong

    CERN Document Server

    Holdom, Bob

    2016-01-01

    More than three decades ago quadratic gravity was found to present a perturbative, renormalizable and asymptotically free theory of quantum gravity. Unfortunately the theory appeared to have problems with a spin-2 ghost. In this essay we revisit quadratic gravity in a different light by considering the case that the asymptotically free interaction flows to a strongly interacting regime. This occurs when the coefficient of the Einstein-Hilbert term is smaller than the scale $\\Lambda_{\\mathrm{QG}}$ where the quadratic couplings grow strong. Here QCD provides some useful insights. By pushing the analogy with QCD, we conjecture that the nonperturbative effects can remove the naive spin-2 ghost and lead to the emergence of general relativity in the IR.

  10. The Wiener maximum quadratic assignment problem

    CERN Document Server

    Cela, Eranda; Woeginger, Gerhard J

    2011-01-01

    We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the Wiener maximum quadratic assignment problem, is NP-hard in the ordinary sense and solvable in pseudo-polynomial time. Our approach also yields a polynomial time solution for the following problem from chemical graph theory: Find a tree that maximizes the Wiener index among all trees with a prescribed degree sequence. This settles an open problem from the literature.

  11. A CART extention using Quadratic Decision Borders

    DEFF Research Database (Denmark)

    Hartelius, Karsten

    1999-01-01

    In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature......-space into subsets which are successively more class-homogeneous. Guided by the fact that class-distributions in feature-space are very often hyper-elliptical shaped, we give an extension to the original CART which also uses quadratic shaped decision borders which can be modelled by a mean-vector and a dispersion...

  12. A CART extension using Quadratic Decision Borders

    DEFF Research Database (Denmark)

    Hartelius, Karsten

    1999-01-01

    In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature......-space into subsets which are successively more class-homogeneous. Guided by the fact that class-distributions in feature-space are very often hyper-elliptical shaped, we give an extension to the original CART which also uses quadratic shaped decision borders which can be modelled by a mean-vector and a dispersion...

  13. PSQP: Puzzle Solving by Quadratic Programming.

    Science.gov (United States)

    Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

    2017-02-01

    In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

  14. Quintessence with quadratic coupling to dark matter

    CERN Document Server

    Boehmer, Christian G; Chan, Nyein; Lazkoz, Ruth; Maartens, Roy

    2009-01-01

    We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.

  15. Guises and disguises of quadratic divergences

    Energy Technology Data Exchange (ETDEWEB)

    Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)

    2014-12-15

    In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

  16. Indirect quantum tomography of quadratic Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

    2011-01-15

    A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

  17. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2004-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...

  18. Lambda-lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, O.; Schultz, U.P.

    2004-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...

  19. On orthogonality preserving quadratic stochastic operators

    Energy Technology Data Exchange (ETDEWEB)

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)

    2015-05-15

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

  20. Discrete fractional Radon transforms and quadratic forms

    CERN Document Server

    Pierce, Lillian B

    2010-01-01

    We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove sharp results for this class of discrete operators in all dimensions, providing necessary and sufficient conditions for them to extend to bounded operators from $\\ell^p$ to $\\ell^q$. The method involves an intricate spectral decomposition according to major and minor arcs, motivated by ideas from the circle method of Hardy and Littlewood. Techniques from harmonic analysis, in particular Fourier transform methods and oscillatory integrals, as well as the number theoretic structure of quadratic forms, exponential sums, and theta functions, play key roles in the proof.

  1. Lie bialgebras of generalized Witt type

    Institute of Scientific and Technical Information of China (English)

    SONG; Guang'ai; SU; Yucai

    2006-01-01

    In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W (x) W) is trivial.

  2. An evaluation on Real Semisimple Lie Algebras

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    @@ The theory of Lie groups and Lie algebras stem from that of continuous groups founded by Sophus Lie at the end of 19th century. From the beginning, the theory of Lie groups and Lie algebras has displayed great value in both theoretical researches and applications.

  3. Cohomology of Heisenberg Lie superalgebras

    Science.gov (United States)

    Bai, Wei; Liu, Wende

    2017-02-01

    Suppose the ground field to be algebraically closed and of characteristic different from 2 and 3. All Heisenberg Lie superalgebras consist of two super-versions of the Heisenberg Lie algebras, 𝔥2m,n and 𝔟𝔞n with m a non-negative integer and n a positive integer. The space of a "classical" Heisenberg Lie superalgebra 𝔥2m,n is the direct sum of a superspace with a non-degenerate anti-supersymmetric even bilinear form and a one-dimensional space of values of this form constituting the even center. The other super-analog of the Heisenberg Lie algebra, 𝔟𝔞n, is constructed by means of a non-degenerate anti-supersymmetric odd bilinear form with values in the one-dimensional odd center. In this paper, we study the cohomology of 𝔥2m,n and 𝔟𝔞n with coefficients in the trivial module by using the Hochschild-Serre spectral sequences relative to a suitable ideal. In the characteristic zero case, for any Heisenberg Lie superalgebra, we determine completely the Betti numbers and associative superalgebra structures for their cohomology. In the characteristic p > 3 case, we determine the associative superalgebra structure for the divided power cohomology of 𝔟𝔞n and we also make an attempt to determine the divided power cohomology of 𝔥2m,n by computing it in a low-dimensional case.

  4. Truth therapy/lie therapy.

    Science.gov (United States)

    Langs, R

    In this paper an attempt is made to conceptualize a basic dimension of various psychotherapeutic treatment modalities, especially psychoanalysis and psychoanalytically oriented psychotherapy. The central variable under consideration is the extent to which each endeavors to approach the truth within both patient and therapist as it exists dynamically in terms of their spiraling unconscious communicative interaction. That treatment modality which takes into account every possible dimension of such truths is termed truth therapy. Treatment modalities that make no attempt to arrive at these truths or that deliberately or inadvertently falsify their nature are termed lie or barrier therapies. Extensive consideration is given to truth therapy and the truth system on which it is based. The basis for the need for lie therapies is explored, and lie systems, which may arise from either patient or therapist, or both, are identified. A classification of common types of lie patients and lie therapists (and their main techniques) is offered. The implications of this delineation for our understanding of the dynamic therapies are discussed, and a number of new clinical issues arising from this perspective are addressed.

  5. On Split Lie Triple Systems

    Indian Academy of Sciences (India)

    Antonio J Calderón Martín

    2009-04-01

    We begin the study of arbitrary split Lie triple systems by focussing on those with a coherent 0-root space. We show that any such triple systems with a symmetric root system is of the form $T=\\mathcal{U}+\\sum_j I_j$ with $\\mathcal{U}$ a subspace of the 0-root space $T_0$ and any $I_j$ a well described ideal of , satisfying $[I_j,T,I_k]=0$ if $j≠ k$. Under certain conditions, it is shown that is the direct sum of the family of its minimal ideals, each one being a simple split Lie triple system, and the simplicity of is characterized. The key tool in this job is the notion of connection of roots in the framework of split Lie triple systems.

  6. Loop Virasoro Lie conformal algebra

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Henan, E-mail: wuhenanby@163.com; Chen, Qiufan; Yue, Xiaoqing [Department of Mathematics, Tongji University, Shanghai 200092 (China)

    2014-01-15

    The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.

  7. Test-assignment: a quadratic coloring problem

    NARCIS (Netherlands)

    Duives, Jelle; Lodi, Andrea; Malaguti, Enrico

    2013-01-01

    We consider the problem of assigning the test variants of a written exam to the desks of a classroom in such a way that desks that are close-by receive different variants. The problem is a generalization of the Vertex Coloring and we model it as a binary quadratic problem. Exact solution methods bas

  8. Experimental results on quadratic assignment problem

    Directory of Open Access Journals (Sweden)

    N.P. Nikolov

    1999-08-01

    Full Text Available The paper presents experimental results on quadratic assignment problem. The "scanning area" method formulated for radioelectronic equipment design is applied. For all more complex tests ours results are better or coincident with the ones known in literature. Conclusion concerning the effectiveness of method are given.

  9. Quadratic Forms%二次型

    Institute of Scientific and Technical Information of China (English)

    谭亚茹

    2016-01-01

    The quadratic Higher Algebra is an important part of this paper, the definition of quadratic forms, introduces the second type of representation, and then describes how to use the allocation method, elementary transformation, orthogonal transformation method, etc. II second type into the standard form, and the second type of normal form, finally introduced posi-tive definite quadratic form and method for determining positive definite quadratic form.%二次型是高等代数的重要组成部分,本文从二次型的定义出发,介绍了二次型的表示方法,然后介绍了如何用配方法、初等变换法、正交变换法等将二次型化为标准形,以及二次型的规范形,最后介绍了正定二次型和判定正定二次型的方法。

  10. On Quadratic Programming with a Ratio Objective

    CERN Document Server

    Bhaskara, Aditya; Manokaran, Rajsekar; Vijayaraghavan, Aravindan

    2011-01-01

    Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \\sum_ij a_ij x_i x_j. QP captures many known combinatorial optimization problems and SDP techniques have given optimal approximation algorithms for many of these problems. We extend this body of work by initiating the study of Quadratic Programming problems where the variables take values in the domain {-1,0,1}. The specific problem we study is: QP-Ratio: max_{-1,0,1}^n (x^T A x) / (x^T x). This objective function is a natural relative of several well studied problems. Yet, it is a good testbed for both algorithms and complexity because the techniques used for quadratic problems for the {-1,1} and {0,1} domains do not seem to carry over to the {-1,0,1} domain. We give approximation algorithms and evidence for the hardness of approximating the QP-Ratio problem. We consider an SDP relaxation obtained by adding constraints to the natural SDP relaxation for this problem and obtain an O(n^{2/7}) algorithm for...

  11. Distortion control of conjugacies between quadratic polynomials

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    We use a new type of distortion control of univalent functions to give an alternative proof of Douady-Hubbard’s ray-landing theorem for quadratic Misiurewicz polynomials. The univalent maps arise from Thurston’s iterated algorithm on perturbation of such polynomials.

  12. Target manifold formation using a quadratic SDF

    Science.gov (United States)

    Hester, Charles F.; Risko, Kelly K. D.

    2013-05-01

    Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.

  13. The GCD property and irreduciable quadratic polynomials

    Directory of Open Access Journals (Sweden)

    Saroj Malik

    1986-01-01

    Full Text Available The proof of the following theorem is presented: If D is, respectively, a Krull domain, a Dedekind domain, or a Prüfer domain, then D is correspondingly a UFD, a PID, or a Bezout domain if and only if every irreducible quadratic polynomial in D[X] is a prime element.

  14. Modulational instability in periodic quadratic nonlinear materials

    DEFF Research Database (Denmark)

    Corney, Joel Frederick; Bang, Ole

    2001-01-01

    We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never complete...

  15. Integration of the Quadratic Function and Generalization

    Science.gov (United States)

    Mitsuma, Kunio

    2011-01-01

    We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

  16. Solitons in quadratic nonlinear photonic crystals

    DEFF Research Database (Denmark)

    Corney, Joel Frederick; Bang, Ole

    2001-01-01

    We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families...

  17. Range-based estimation of quadratic variation

    DEFF Research Database (Denmark)

    Christensen, Kim; Podolskij, Mark

    In this paper, we propose using realized range-based estimation to draw inference about the quadratic variation of jump-diffusion processes. We also construct a new test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the test...

  18. Range-based estimation of quadratic variation

    DEFF Research Database (Denmark)

    Christensen, Kim; Podolskij, Mark

    This paper proposes using realized range-based estimators to draw inference about the quadratic variation of jump-diffusion processes. We also construct a range-based test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient...

  19. Isomorphism of Intransitive Linear Lie Equations

    Directory of Open Access Journals (Sweden)

    Jose Miguel Martins Veloso

    2009-11-01

    Full Text Available We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the intransitive Lie algebra we recover the linear Lie equation, unless of formal isomorphism. The intransitive Lie algebra gives the structure functions introduced by É. Cartan.

  20. Integrability of Quadratic Non-autonomous Quantum Linear Systems

    Science.gov (United States)

    Lopez, Raquel

    The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schrodinger equation for the simple harmonic oscillator in one dimension is

  1. Cartan Connections and Lie Algebroids

    Directory of Open Access Journals (Sweden)

    Michael Crampin

    2009-06-01

    Full Text Available This paper is a study of the relationship between two constructions associated with Cartan geometries, both of which involve Lie algebroids: the Cartan algebroid, due to [Blaom A.D., Trans. Amer. Math. Soc. 358 (2006, 3651–3671], and tractor calculus [Cap A., Gover A.R., Trans. Amer. Math. Soc. 354 (2001, 1511–1548].

  2. Cartan Connections and Lie Algebroids

    CERN Document Server

    Crampin, Michael

    2009-01-01

    This paper is a study of the relationship between two constructions associated with Cartan geometries, both of which involve Lie algebroids: the Cartan algebroid, due to [Blaom A.D., Trans. Amer. Math. Soc. 358 (2006), 3651-3671], and tractor calculus [Cap A., Gover A.R., Trans. Amer. Math. Soc. 354 (2001), 1511-1548].

  3. String Topology for Lie Groups

    DEFF Research Database (Denmark)

    A. Hepworth, Richard

    2010-01-01

    In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a direct description of this Batalin-Vilkovisky algebra in the case that the manifold is a compact Lie group G. Our answer ...

  4. Quadratically constrained quadratic programs on acyclic graphs with application to power flow

    CERN Document Server

    Bose, Subhonmesh; Low, Steven H; Chandy, K Mani

    2012-01-01

    This paper proves that non-convex quadratically constrained quadratic programs have an exact semidefinite relaxation when their underlying graph is acyclic, provided the constraint set satisfies a certain technical condition. When the condition is not satisfied, we propose a heuristic to obtain a feasible point starting from a solution of the relaxed problem. These methods are then demonstrated to provide exact solutions to a richer class of optimal power flow problems than previously solved.

  5. Non-coboundary Poisson-Lie structures on the book group

    CERN Document Server

    Ballesteros, Angel; Musso, Fabio

    2011-01-01

    All possible Poisson-Lie (PL) structures on the 3D real Lie group generated by a dilation and two commuting translations are obtained. Its classification is fully performed by relating these PL groups with the corresponding Lie bialgebra structures on the corresponding "book" Lie algebra. By construction, all these Poisson structures are quadratic Poisson-Hopf algebras for which the group multiplication is a Poisson map. In contrast to the case of simple Lie groups, it turns out that most of the PL structures on the book group are non-coboundary ones. Moreover, from the viewpoint of Poisson dynamics, the most interesting PL book structures are just some of these non-coboundaries, which are explicitly analysed. In particular, we show that the two different q-deformed Poisson versions of the sl(2,R) algebra appear as two distinguished cases in this classification, as well as the quadratic Poisson structure that underlies the integrability of a large class of 3D Lotka-Volterra equations. Finally, the quantizatio...

  6. Lie Group Classification of a Generalized Lane-Emden Type System in Two Dimensions

    Directory of Open Access Journals (Sweden)

    Motlatsi Molati

    2012-01-01

    Full Text Available The aim of this work is to perform a complete Lie symmetry classification of a generalized Lane-Emden type system in two dimensions which models many physical phenomena in biological and physical sciences. The classical approach of group classification is employed for classification. We show that several cases arise in classifying the arbitrary parameters, the forms of which include amongst others the power law nonlinearity, and exponential and quadratic forms.

  7. Geometric Approaches to Quadratic Equations from Other Times and Places.

    Science.gov (United States)

    Allaire, Patricia R.; Bradley, Robert E.

    2001-01-01

    Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

  8. Semiclassical states on Lie algebras

    Energy Technology Data Exchange (ETDEWEB)

    Tsobanjan, Artur, E-mail: artur.tsobanjan@gmail.com [King’s College, 133 North River Street, Kingston, Pennsylvania 18702 (United States)

    2015-03-15

    The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.

  9. On quadratic residue codes and hyperelliptic curves

    Directory of Open Access Journals (Sweden)

    David Joyner

    2008-01-01

    Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''

  10. Higgsed Stueckelberg vector and Higgs quadratic divergence

    Directory of Open Access Journals (Sweden)

    Durmuş Ali Demir

    2015-01-01

    Full Text Available Here we show that, a hidden vector field whose gauge invariance is ensured by a Stueckelberg scalar and whose mass is spontaneously generated by the Standard Model Higgs field contributes to quadratic divergences in the Higgs boson mass squared, and even leads to its cancellation at one-loop when Higgs coupling to gauge field is fine-tuned. In contrast to mechanisms based on hidden scalars where a complete cancellation cannot be achieved, stabilization here is complete in that the hidden vector and the accompanying Stueckelberg scalar are both free from quadratic divergences at one-loop. This stability, deriving from hidden exact gauge invariance, can have important implications for modeling dark phenomena like dark matter, dark energy, dark photon and neutrino masses. The hidden fields can be produced at the LHC.

  11. Linear quadratic output tracking and disturbance rejection

    Science.gov (United States)

    Karimi-Ghartemani, Masoud; Khajehoddin, S. Ali; Jain, Praveen; Bakhshai, Alireza

    2011-08-01

    This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilisability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard linear quadratic regulation problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed.

  12. Estimating quadratic variation using realized variance

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole Eiler; Shephard, N.

    2002-01-01

    This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process is a semimar......This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process...... have to impose some weak regularity assumptions. We illustrate the use of the limit theory on some exchange rate data and some stock data. We show that even with large values of M the RV is sometimes a quite noisy estimator of integrated variance. Copyright © 2002 John Wiley & Sons, Ltd....

  13. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2002-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  14. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2004-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  15. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2003-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  16. Lambda-lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, O.; Schultz, U.P.

    2004-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  17. Symmetry via Lie algebra cohomology

    CERN Document Server

    Eastwood, Michael

    2010-01-01

    The Killing operator on a Riemannian manifold is a linear differential operator on vector fields whose kernel provides the infinitesimal Riemannian symmetries. The Killing operator is best understood in terms of its prolongation, which entails some simple tensor identities. These simple identities can be viewed as arising from the identification of certain Lie algebra cohomologies. The point is that this case provides a model for more complicated operators similarly concerned with symmetry.

  18. A Finite Continuation Algorithm for Bound Constrained Quadratic Programming

    DEFF Research Database (Denmark)

    Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.

    1999-01-01

    The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...

  19. Elementary Components of the Quadratic Assignment Problem

    CERN Document Server

    Chicano, Francisco; Alba, Enrique

    2011-01-01

    The Quadratic Assignment Problem (QAP) is a well-known NP-hard combinatorial optimization problem that is at the core of many real-world optimization problems. We prove that QAP can be written as the sum of three elementary landscapes when the swap neighborhood is used. We present a closed formula for each of the three elementary components and we compute bounds for the autocorrelation coefficient.

  20. Cubic Lienard Equations with Quadratic Damping (Ⅱ)

    Institute of Scientific and Technical Information of China (English)

    Yu-quan Wang; Zhu-jun Jing

    2002-01-01

    Applying Hopf bifurcation theory and qualitative theory, we show that the general cubic Lienard equations with quadratic damping have at most three limit cycles. This implies that the guess in which the system has at most two limit cycles is false. We give the sufficient conditions for the system has at most three limit cycles or two limit cycles. We present two examples with three limit cycles or two limit cycles by using numerical simulation.

  1. Characterization of a Quadratic Function in Rn

    Science.gov (United States)

    Xu, Conway

    2010-01-01

    It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.

  2. Can Lies Be Detected Unconsciously?

    Directory of Open Access Journals (Sweden)

    David eShanks

    2015-08-01

    Full Text Available People are typically poor at telling apart truthful and deceptive statements. Based on the Unconscious Thought Theory, it has been suggested that poor lie detection arises from the intrinsic limitations of conscious thinking and can be improved by facilitating the contribution of unconscious thought. In support of this hypothesis, Reinhard, Greifeneder, and Scharmach (2013 observed improved lie detection among participants engaging in unconscious thought. The present study aimed to replicate this unconscious thought advantage using a similar experimental procedure but with an important improvement in a key control condition. Specifically, participants judged the truthfulness of 8 video recordings in three thinking modes: immediately after watching them or after a period of unconscious or conscious deliberation. Results from two experiments (combined N = 226 failed to reveal a significant difference in lie detection accuracy between the thinking modes, even after efforts were made to facilitate the occurrence of an unconscious thought advantage in Experiment 2. The results imply that the unconscious thought advantage in deception detection is not a robust phenomenon.

  3. Quadratic forms representing all odd positive integers

    CERN Document Server

    Rouse, Jeremy

    2011-01-01

    We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove that an arbitrary, positive-definite quadratic form represents all positive odds if and only if it represents the odd numbers from 1 up to 451. This result is analogous to Bhargava and Hanke's celebrated 290-theorem. In addition, we prove that these three remaining ternaries represent all positive odd integers, assuming the generalized Riemann hypothesis. This result is made possible by a new analytic method for bounding the cusp constants of integer-valued quaternary quadratic forms $Q$ with fundamental discriminant. This method is based on the analytic properties of Rankin-Selberg $L$-functions, and we use it to prove...

  4. Optimal Approximation of Quadratic Interval Functions

    Science.gov (United States)

    Koshelev, Misha; Taillibert, Patrick

    1997-01-01

    Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.

  5. Particle-like structure of Lie algebras

    Science.gov (United States)

    Vinogradov, A. M.

    2017-07-01

    If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i's, we say that 𝔤 is simply assembled from the 𝔤i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i's, one obtains a Lie algebra assembled in two steps from 𝔤i's, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions: which Lie algebras can be assembled from a given family of Lie algebras, and from which Lie algebras can a given Lie algebra be assembled. We develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of Lie algebras. The main result of our theory is that any finite-dimensional Lie algebra over an algebraically closed field of characteristic zero or over R can be assembled in a finite number of steps from two elementary constituents, which we call dyons and triadons. Up to an abelian summand, a dyon is a Lie algebra structure isomorphic to the non-abelian 2-dimensional Lie algebra, while a triadon is isomorphic to the 3-dimensional Heisenberg Lie algebra. As an example, we describe constructions of classical Lie algebras from triadons.

  6. Statistical properties of high-lying chaotic eigenstates

    CERN Document Server

    Li, B; Li, Baowen; Robnik, Marko

    1995-01-01

    We study the statistical properties of the high-lying chaotic eigenstates (200,000 and above) which are deep in the semiclassical regime. The system we are analyzing is the billiard system inside the region defined by the quadratic (complex) conformal map of the unit disk as introduced by Robnik (1983). We are using Heller's method of plane wave decomposition of the numerical eigenfunctions, and perform extensive statistical analysis with the following conclusions: (1) The local average probability density is in excellent agreement with the microcanonical assumption and all statistical properties are also in excellent agreement with the Gaussian random model; \\qquad (2) The autocorrelation function is found to be strongly direction dependent and only after averaging over all directions agrees well with Berry's (1977) prediction; \\qquad (3) Although the scars of unstable classical periodic orbits (in such ergodic regime) are expected to exist, so far we have not found any (around 200,000th state) but a scar-li...

  7. Lichnerowicz modes and black hole families in Ricci quadratic gravity

    Science.gov (United States)

    Lü, Hong; Perkins, A.; Pope, C. N.; Stelle, K. S.

    2017-08-01

    A new branch of black hole solutions occurs along with the standard Schwarzschild branch in n -dimensional extensions of general relativity including terms quadratic in the Ricci tensor. The standard and new branches cross at a point determined by a static negative-eigenvalue eigenfunction of the Lichnerowicz operator, analogous to the Gross-Perry-Yaffe eigenfunction for the Schwarzschild solution in standard n =4 dimensional general relativity. This static eigenfunction has two roles: both as a perturbation away from Schwarzschild along the new black-hole branch and also as a threshold unstable mode lying at the edge of a domain of Gregory-Laflamme-type instability of the Schwarzschild solution for small-radius black holes. A thermodynamic analogy with the Gubser and Mitra conjecture on the relation between quantum thermodynamic and classical dynamical instabilities leads to a suggestion that there may be a switch of stability properties between the old and new black-hole branches for small black holes with radii below the branch crossing point.

  8. Projection of curves on B-spline surfaces using quadratic reparameterization

    KAUST Repository

    Yang, Yijun

    2010-09-01

    Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a hyperbola approximation method based on the quadratic reparameterization of Bézier surfaces, which generates reasonable low degree curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the projected curve and the original curve is controlled under the user-specified distance tolerance. The projected curve is T-G 1 continuous, where T is the user-specified angle tolerance. Examples are given to show the performance of our algorithm. © 2010 Elsevier Inc. All rights reserved.

  9. A sequential quadratic programming algorithm using an incomplete solution of the subproblem

    Energy Technology Data Exchange (ETDEWEB)

    Murray, W. [Stanford Univ., CA (United States). Systems Optimization Lab.; Prieto, F.J. [Universidad `Carlos III` de Madrid (Spain). Dept. de Estadistica y Econometria

    1993-05-01

    We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is not assumed that the iterates lie on a compact set.

  10. Filiform Lie algebras of order 3

    Science.gov (United States)

    Navarro, R. M.

    2014-04-01

    The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, "Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes," Bull. Soc. Math. France 98, 81-116 (1970)]. Also we give the dimension, using an adaptation of the {sl}(2,{C})-module Method, and a basis of such infinitesimal deformations in some generic cases.

  11. Transformation groups and Lie algebras

    CERN Document Server

    Ibragimov, Nail H

    2013-01-01

    This book is based on the extensive experience of teaching for mathematics, physics and engineering students in Russia, USA, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics. The methods of local Lie groups discussed in the book provide universal and effective method for solving nonlinear differential equations analytically. Introduction to approximate transformation groups also contained in the book helps to develop skills in constructing approximate solutions for differential equations with a small parameter.

  12. Constrained neural approaches to quadratic assignment problems.

    Science.gov (United States)

    Ishii, S; Sato, M

    1998-08-01

    In this paper, we discuss analog neural approaches to the quadratic assignment problem (QAP). These approaches employ a hard constraints scheme to restrict the domain space, and are able to obtain much improved solutions over conventional neural approaches. Since only a few strong heuristics for QAP have been known to date, our approaches are good alternatives, capable of obtaining fairly good solutions in a short period of time. Some of them can also be applied to large-scale problems, say of size N>/=300.

  13. Automatic differentiation for reduced sequential quadratic programming

    Institute of Scientific and Technical Information of China (English)

    Liao Liangcai; Li Jin; Tan Yuejin

    2007-01-01

    In order to slove the large-scale nonlinear programming (NLP) problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming (rSQP) and automatic differentiation (AD) is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.

  14. Bianchi I solutions of effective quadratic gravity

    CERN Document Server

    Müller, Daniel

    2012-01-01

    It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model $E^3$ for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity. This work is a generalization for non diagonal spatial metrics of a previous result obtained by one of us and a collaborator for Bianchi $I$ spaces.

  15. Linear Stability Analysis of Dynamical Quadratic Gravity

    CERN Document Server

    Ayzenberg, Dimitry; Yunes, Nicolas

    2013-01-01

    We perform a linear stability analysis of dynamical, quadratic gravity in the high-frequency, geometric optics approximation. This analysis is based on a study of gravitational and scalar modes propagating on spherically-symmetric and axially-symmetric, vacuum solutions of the theory. We find dispersion relations that do no lead to exponential growth of the propagating modes, suggesting the theory is linearly stable on these backgrounds. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry, just as in dynamical Chern-Simons gravity.

  16. Range-based estimation of quadratic variation

    DEFF Research Database (Denmark)

    Christensen, Kim; Podolskij, Mark

    In this paper, we propose using realized range-based estimation to draw inference about the quadratic variation of jump-diffusion processes. We also construct a new test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the te...... is well-sized and more powerful than a return-based t-statistic for sampling frequencies normally used in empirical work. Applied to equity data, we find that the intensity of the jump process is not as high as previously reported....

  17. Range-based estimation of quadratic variation

    DEFF Research Database (Denmark)

    Christensen, Kim; Podolskij, Mark

    This paper proposes using realized range-based estimators to draw inference about the quadratic variation of jump-diffusion processes. We also construct a range-based test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the ......, the test is well-sized and more powerful than a return-based t-statistic for sampling frequencies normally used in empirical work. Applied to equity data, we show that the intensity of the jump process is not as high as previously reported....

  18. Quadratic forms for Feynman-Kac semigroups

    Energy Technology Data Exchange (ETDEWEB)

    Hibey, Joseph L. [Department of Electrical Engineering, University of Colorado at Denver, Campus Box 110, Denver, CO 80217 (United States)]. E-mail: joseph.hibey@cudenver.edu; Charalambous, Charalambos D. [Electrical and Computer Engineering Department, University of Cyprus, 75 Kallipoleos Avenue, Nicosia (Cyprus)]. E-mail: chadcha@ucy.ac.cy

    2006-05-15

    Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions.

  19. Facets for the Cardinality Constrained Quadratic Knapsack Problem and the Quadratic Selective Travelling Salesman Problem

    DEFF Research Database (Denmark)

    Mak, Vicky; Thomadsen, Tommy

    2004-01-01

    A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...

  20. Infinite-dimensional Hamiltonian Lie superalgebras

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements.We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.

  1. SOME RESULTS OF MODULAR LIE SUPERALGEBRAS

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups.Moreover, they announce and prove some results of modular complete Lie superalgebras.

  2. Emergence of Lying in Very Young Children

    Science.gov (United States)

    Evans, Angela D.; Lee, Kang

    2013-01-01

    Lying is a pervasive human behavior. Evidence to date suggests that from the age of 42 months onward, children become increasingly capable of telling lies in various social situations. However, there is limited experimental evidence regarding whether very young children will tell lies spontaneously. The present study investigated the emergence of…

  3. A Kind of Braided-Lie Structures

    Institute of Scientific and Technical Information of China (English)

    2003-01-01

    @@ We introduce a family of braidedLie algebras.They are Lie algebras in the unifying YetterDrinfeldLong module categoryJJMQQ where J and Q are Hopf algebras.We study their structure and the braidedLie structure of an algebra A in JJM QQ.

  4. Probability on real Lie algebras

    CERN Document Server

    Franz, Uwe

    2016-01-01

    This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.

  5. Quadratic independence of coordinate functions of certain homogeneous spaces and action of compact quantum groups

    Indian Academy of Sciences (India)

    Debashish Goswami

    2015-02-01

    Let be one of the classical compact, simple, centre-less, connected Lie groups of rank with a maximal torus , the Lie algebra $\\mathcal{G}$ and let $\\{E_{i},F_{i},H_{i},i=1,\\ldots,n\\}$ be tha standard set of generators corresponding to a basis of the root system. Consider the adjoint-orbit space $M=\\{\\text{Ad}_{g}(H_{1}), g\\in G\\}$, identified with the homogeneous space / where $L=\\{g\\in G : \\text{Ad}_{g}(H_{1})=H_{1}\\}$. We prove that the coordinate functions $f_{i}(g):=_{i}(\\text{Ad}_{g}(H_{1}))$, $i=1,\\ldots,n$, where $\\{_{1},\\ldots,_{n}\\}$ is basis of $\\mathcal{G}'$ are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on $C(M)$ such that the action leaves invariant the linear span of the above coordinate functions. As a corollary, it is also shown that any compact quantum group having a faithful action on the noncommutative manifold obtained by Rieffel deformation of satisfying a similar `linearity' condition must be a Rieffel-Wang type deformation of some compact group.

  6. On a general class of quadratic hopping sequences

    Institute of Scientific and Technical Information of China (English)

    JIA HuaDing; YUAN Ding; PENG DaiYuan; GUO Ling

    2008-01-01

    Based upon quadratic polynomials over the finite field, a new class of frequency hopping sequences with large family size suitable for applications in time/frequency hopping CDMA systems, multi-user radar and sonar systems is proposed and investigated. It is shown that the new time/frequency hopping sequences have at most one hit in their autocorrelation functions and at most two hits in their crosscorrelation functions except for a special case, and their family size is much larger than the conventional quadratic hopping sequences. The percentage of full collisions for the new quadratic hopping sequences is discussed. In addition, the average number of hits for the new quadratic hopping sequences, quadratic congruence sequences, extended quadratic congruence sequences and the general linear hopping sequences are also derived.

  7. Quadratic residues and non-residues selected topics

    CERN Document Server

    Wright, Steve

    2016-01-01

    This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.

  8. On Quadratic BSDEs with Final Condition in L2

    OpenAIRE

    Yang, Hanlin

    2015-01-01

    This thesis consists of three parts. In the first part, we study $\\mathbb{L}^p$ solutions of a large class of BSDEs. Existence, comparison theorem, uniqueness and a stability result are proved. In the second part, we establish the solvability of quadratic semimartingale BSDEs. In contrast to current literature, we use Lipschitz-quadratic regularization and obtain the existence and uniqueness results with minimal assumptions. The third part is a brief summary of quadratic semimartingales and t...

  9. Quadratic forms and Clifford algebras on derived stacks

    OpenAIRE

    Vezzosi, Gabriele

    2013-01-01

    In this paper we present an approach to quadratic structures in derived algebraic geometry. We define derived n-shifted quadratic complexes, over derived affine stacks and over general derived stacks, and give several examples of those. We define the associated notion of derived Clifford algebra, in all these contexts, and compare it with its classical version, when they both apply. Finally, we prove three main existence results for derived shifted quadratic forms over derived stacks, define ...

  10. Robust Solutions of Uncertain Complex-valued Quadratically Constrained Programs

    Institute of Scientific and Technical Information of China (English)

    Da Chuan XU; Zheng Hai HUANG

    2008-01-01

    In this paper,we discuss complex convex quadratically constrained optimization with uncertain data.Using S-Lemma,we show that the robust counterpart of complex convex quadratically constrained optimization with ellipsoidal or intersection-of-two-ellipsoids uncertainty set leads to a complex semidefinite program.By exploring the approximate S-Lemma,we give a complex semidefinite program which approximates the NP-hard robust counterpart of complex convex quadratic optimization with intersection-of-ellipsoids uncertainty set.

  11. Some Aspects of Quadratic Generalized White Noise Functionals

    Science.gov (United States)

    Si, Si; Hida, Takeyuki

    2009-02-01

    We shall discuss some particular roles of quadratic generalized white noise functionals. First observation is made from the viewpoint of the so-called "la passage du fini à l'infini". We then come to a dual pairing of spaces formed by quadratic generalized white noise functionals. In this line, we can further discuss quadratic forms of differential operators acting on the space of white noise functionals.

  12. Lies and Deception: A Failed Reconciliation

    DEFF Research Database (Denmark)

    Broncano-Berrocal, Fernando

    2013-01-01

    The traditional view of lying says that lying is a matter of intending to deceive others by making statements that one believes to be false. Jennifer Lackey has recently defended the following version of the traditional view: A lies to B just in case (i) A states that p to B, (ii) A believes that...... is false and (iii) A intends to be deceptive to B in stating that p. I argue that, despite all the virtues that Lackey ascribes to her view, conditions (i), (ii) and (iii) are not sufficient for lying.......The traditional view of lying says that lying is a matter of intending to deceive others by making statements that one believes to be false. Jennifer Lackey has recently defended the following version of the traditional view: A lies to B just in case (i) A states that p to B, (ii) A believes that p...

  13. [Psychopathological study of lie motif in schizophrenia].

    Science.gov (United States)

    Otsuka, Koichiro; Kato, Satoshi

    2006-01-01

    The theme of a statement is called "lie motif" by the authors when schizophrenic patients say "I have lied to anybody". We tried to analyse of the psychopathological characteristics and anthropological meanings of the lie motifs in schizophrenia, which has not been thematically examined until now, based on 4 cases, and contrasting with the lie motif (Lügenmotiv) in depression taken up by A. Kraus (1989). We classified the lie motifs in schizophrenia into the following two types: a) the past directive lie motif: the patients speak about their real lie regarding it as a 'petty fault' in their distant past with self-guilty feeling, b) the present directive lie motif: the patients say repeatedly 'I have lied' (about their present speech and behavior), retreating from their previous commitments. The observed false confessions of innocent fault by the patients seem to belong to the present directed lie motif. In comparison with the lie motif in depression, it is characteristic for the lie motif in schizophrenia that the patients feel themselves to already have been caught out by others before they confess the lie. The lie motif in schizophrenia seems to come into being through the attribution process of taking the others' blame on ones' own shoulders, which has been pointed out to be common in the guilt experience in schizophrenia. The others' blame on this occasion is due to "the others' gaze" in the experience of the initial self-centralization (i.e. non delusional self-referential experience) in the early stage of schizophrenia (S. Kato 1999). The others' gaze is supposed to bring about the feeling of amorphous self-revelation which could also be regarded as the guilt feeling without content, to the patients. When the guilt feeling is bound with a past concrete fault, the patients tell the past directive lie motif. On the other hand, when the patients cannot find a past fixed content, and feel their present actions as uncertain and experience them as lies, the

  14. Learning to lie: Effects of practice on the cognitive cost of lying

    Directory of Open Access Journals (Sweden)

    Bram eVan Bockstaele

    2012-11-01

    Full Text Available Cognitive theories on deception posit that lying requires more cognitive resources than telling the truth. In line with this idea, it has been demonstrated that deceptive responses are typically associated with increased response times and higher error rates compared to truthful responses. Although the cognitive cost of lying has been assumed to be resistant to practice, it has recently been shown that people who are trained to lie can reduce this cost. In the present study (n = 42, we further explored the effects of practice on one’s ability to lie by manipulating the proportions of lie and truth-trials in a Sheffield lie test across three phases: Baseline (50% lie, 50% truth, Training (frequent-lie group: 75% lie, 25% truth; control group: 50% lie, 50% truth; and frequent-truth group: 25% lie, 75% truth, and Test (50% lie, 50% truth. The results showed that lying became easier while participants were trained to lie more often and that lying became more difficult while participants were trained to tell the truth more often. Furthermore, these effects did carry over to the test phase, but only for the specific items that were used for the training manipulation. Hence, our study confirms that relatively little practice is enough to alter the cognitive cost of lying, although this effect does not persist over time for non-practiced items.

  15. Deceivers' Responses to Challenges of Their Truthfulness: Difference between Familiar Lies and Unfamiliar Lies.

    Science.gov (United States)

    di Battista, Patrick

    1997-01-01

    Examines whether a lie's cognitive representation affects deceivers' ability to respond to probing. Shows that behavioral changes made in response to probing varied depending on whether the lie was a familiar lie or an unfamiliar lie but that none of these behaviors were related to judges' ratings of truthfulness. (SR)

  16. Quadratic dynamical decoupling with nonuniform error suppression

    Energy Technology Data Exchange (ETDEWEB)

    Quiroz, Gregory; Lidar, Daniel A. [Department of Physics and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States); Departments of Electrical Engineering, Chemistry, and Physics, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States)

    2011-10-15

    We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N{sub 1} and N{sub 2} pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N{sub 1} and N{sub 2}, and near-optimal performance is achieved for general single-qubit interactions when N{sub 1}=N{sub 2}.

  17. The Quadratic Selective Travelling Salesman Problem

    DEFF Research Database (Denmark)

    Thomadsen, Tommy; Stidsen, Thomas K.

    2003-01-01

    complication that each pair of nodes have an associated profit which can be gained only if both nodes are visited. The QSTSP is a subproblem when constructing hierarchical ring networks. We describe an integer linear programming model for the QSTSP. The QSTSP is solved by two construction heuristics...... solutions at a cost of much higher running time. All problems with up to 50 nodes are solved within one hour.......A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...

  18. Compact stars with quadratic equation of state

    CERN Document Server

    Ngubelanga, Sifiso A; Ray, Subharthi

    2015-01-01

    We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.

  19. Low-rank quadratic semidefinite programming

    KAUST Repository

    Yuan, Ganzhao

    2013-04-01

    Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.

  20. Directed animals, quadratic and rewriting systems

    CERN Document Server

    Marckert, Jean-François

    2011-01-01

    A directed animal is a percolation cluster in the directed site percolation model. The aim of this paper is to exhibit a strong relation between in one hand, the problem of computing the generating function $\\G$ of directed animals on the square lattice, counted according to the area and the perimeter, and on the other hand, the problem to find a solution to a system of quadratic equations involving unknown matrices. The matrices solution of this problem can be finite or infinite. We were unable to find finite solutions. We present some solid clues that some infinite explicit matrices, fix points of a rewriting like system are the natural solutions of this system of equations: some strong evidences are given that the problem of finding $\\G$ reduces then to the problem of finding an eigenvector to an explicit infinite matrix. Similar properties are shown for other combinatorial questions concerning directed animals, and for different lattices.

  1. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2002-01-01

    Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which...... is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity of lambda-lifting from O(n 3 log n)toO(n2 log n), where n is the size of the program. Since a lambda-lifter can output...

  2. A SPLITTING METHOD FOR QUADRATIC PROGRAMMING PROBLEM

    Institute of Scientific and Technical Information of China (English)

    魏紫銮

    2001-01-01

    A matrix splitting method is presented for minimizing a quadratic programming (QP)problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate, and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region, and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.

  3. Linear ultrasonic motor using quadrate plate transducer

    Institute of Scientific and Technical Information of China (English)

    Jiamei JIN; Chunsheng ZHAO

    2009-01-01

    A linear ultrasonic motor using a quadrate plate transducer was developed for precision positioning. This motor consists of two pairs of Pb(Zr, Ti)O3 piezo-electric ceramic elements, which are piezoelectrically excited into the second-bending mode of the motor stator's neutral surface in two orthogonal directions, on which the tops of four projections move along an elliptical trajectory, which in turn drives a contacted slider into linear motion via frictional forces. The coincident frequency of the stator is easily obtained for its coincident characteristic dimen-sion in two orthogonal directions. The performance characteristics achieved by the motor are: 1) a maximum linear speed of more than 60 mm/s; 2) a stroke of more than 150 mm; 3) a driving force of more than 5.0 N; and 4) a response time of about 2 ms.

  4. Large-scale sequential quadratic programming algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Eldersveld, S.K.

    1992-09-01

    The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.

  5. Holomorph of Lie color algebras%Lie color代数的全形

    Institute of Scientific and Technical Information of China (English)

    杨恒云

    2007-01-01

    给出Lie color代数全形的一些性质,证明Lie color代数L的全形有分解(H)(L)=L(+)Z(H)(L)(L)的充分必要条件是它是完备Lie color代数.%To the holomorph of Lie color algebras, some properties are studied. A Lie color algebra L is complete if and only if (H)(L) = L(+)Z(H)(L) (L).

  6. Quantum Lie theory a multilinear approach

    CERN Document Server

    Kharchenko, Vladislav

    2015-01-01

    This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin  Lie algebras;  and Shestakov--Umirbaev  operations for the Lie theory of nonassociative products.  Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.

  7. New Heuristic Rounding Approaches to the Quadratic Assignment Problem

    CERN Document Server

    Gharibi, Wajeb

    2011-01-01

    Quadratic assignment problem is one of the great challenges in combinatorial optimization. It has many applications in Operations research and Computer Science. In this paper, the author extends the most-used rounding approach to a one-parametric optimization model for the quadratic assignment problems. A near-optimum parameter is also predestinated. The numerical experiments confirm the efficiency.

  8. Quadratic elongation: A quantitative measure of distortion in coordination polyhedra

    Science.gov (United States)

    Robinson, Kelly F.; Gibbs, G.V.; Ribbe, P.H.

    1971-01-01

    Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elonga tion is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.

  9. Binary GCD like Algorithms for Some Complex Quadratic Rings

    DEFF Research Database (Denmark)

    Agarwal, Saurabh; Frandsen, Gudmund Skovbjerg

    2004-01-01

    binary gcd like algorithms for the ring of integers in and , one now has binary gcd like algorithms for all complex quadratic Euclidean domains. The running time of our algorithms is O(n 2) in each ring. While there exists an O(n 2) algorithm for computing the gcd in quadratic number rings by Erich...

  10. Geometric quadratic stochastic operator on countable infinite set

    Energy Technology Data Exchange (ETDEWEB)

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar [Department of Computational and Theoretical Sciences, Kulliyyah of Science, International Islamic University, Jalan Sultan Ahmad Shah, Bandar InderaMahkota, 25200 Kuantan, Pahang (Malaysia)

    2015-02-03

    In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.

  11. Quadratic Twists of Rigid Calabi–Yau Threefolds Over

    DEFF Research Database (Denmark)

    Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko

    2013-01-01

    We consider rigid Calabi–Yau threefolds defined over Q and the question of whether they admit quadratic twists. We give a precise geometric definition of the notion of a quadratic twists in this setting. Every rigid Calabi–Yau threefold over Q is modular so there is attached to it a certain newfo...

  12. Immunizing Conic Quadratic Optimization Problems Against Implementation Errors

    NARCIS (Netherlands)

    Ben-Tal, A.; den Hertog, D.

    2011-01-01

    We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonali

  13. A Constructive Transition from Linear to Quadratic Functions.

    Science.gov (United States)

    Movshovitz-Hadar, Nitsa

    1993-01-01

    Presents an approach to quadratic functions that draws upon knowledge of linear functions by looking at the product of two linear functions. Then considers the quadratic function as the sum of three monomials. Potential advantages of each approach are discussed. (Contains 17 references.) (MDH)

  14. Approximate *-derivations and approximate quadratic *-derivations on C*-algebras

    Directory of Open Access Journals (Sweden)

    Park Choonkil

    2011-01-01

    Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.

  15. AdS Waves as Exact Solutions to Quadratic Gravity

    CERN Document Server

    Gullu, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram

    2011-01-01

    We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity.

  16. Generalized derivations of Lie triple systems

    Directory of Open Access Journals (Sweden)

    Zhou Jia

    2016-01-01

    Full Text Available In this paper, we present some basic properties concerning the derivation algebra Der (T, the quasiderivation algebra QDer (T and the generalized derivation algebra GDer (T of a Lie triple system T, with the relationship Der (T ⊆ QDer (T ⊆ GDer (T ⊆ End (T. Furthermore, we completely determine those Lie triple systems T with condition QDer (T = End (T. We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.

  17. 3-Leibniz bialgebras (3-Lie bialgebras)

    OpenAIRE

    2016-01-01

    In this paper by use of cohomology complex of $3$-Leibniz algebras, the definitions of Leibniz bialgebras (and Lie bialgebras) are extended for the case of $3$-Leibniz algebras. Many theorems about Leibniz bialgebras are extended and proved for the case of $3$-Leibniz bialgebras ($3$-Lie bialgebras). Moreover a new theorem on the correspondence between $3$-Leibniz bialgebra and its associated Leibniz bialgebra is proved. $3$-Lie bialgebra as particular case of the $3$-Leibniz bialgebra is inv...

  18. Killing Forms of Isotropic Lie Algebras

    CERN Document Server

    Malagon, Audrey

    2010-01-01

    This paper presents a method for computing the Killing form of an isotropic Lie algebra defined over an arbitrary field based on the Killing form of a subalgebra containing its anisotropic kernel. This approach allows for streamlined formulas for many Lie algebras of types E6 and E7 and yields a unified formula for all Lie algebras of inner type E6, including the anisotropic ones.

  19. ALIED: A Theory of Lie Detection

    Directory of Open Access Journals (Sweden)

    Chris N. H. Street

    2016-07-01

    Full Text Available We are very inaccurate lie detectors, and tend to believe what others tell us is the truth more often than we ought to. In fact, studies on lie detection typically describe our tendency to believe others as an error in judgment. Although people may look like hopeless lie detectors, the Adaptive Lie Detector theory (ALIED claims that people are actually making smart, informed judgments. This article explores the ALIED theory and what it means for those wanting to spot a liar.

  20. Computations in finite-dimensional Lie algebras

    Directory of Open Access Journals (Sweden)

    A. M. Cohen

    1997-12-01

    Full Text Available This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System, within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]. This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n×n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra.

  1. Engel Subalgebras of n-Lie Algebras

    Institute of Scientific and Technical Information of China (English)

    Donald W. BARNES

    2008-01-01

    Engel subalgebras of finite-dimensional n Lie algebras are shown to have similar properties to those of Lie algebras.Using these,it is shown that an n Lie algebra,all of whose maximal subalgebras are ideals,is nilpotent.A primitive 2-soluble n Lie algebra is shown to split over its minimal ideal, and all the complements to its minimal ideal are conjugate.A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel,provided that the field has su .ciently many elements. Cartan subalgebras are shown to have a property analogous to intravariance.

  2. QUADRATIC ADMISSIBLE ESTIMATE OF COVARIANCE IN PSEUDO-ELLIPTICAL CONTOURED DISTRIBUTION

    Institute of Scientific and Technical Information of China (English)

    Hengjian CUI; Xiuhong GAO

    2006-01-01

    This article mainly discusses the admissibility of quadratic estimate of covariance in pseudoelliptical distribution. Under the quadratic loss function, the necessary and sufficient conditions that a quadratic estimator is an admissible estimator of covariance in the class of quadratic estimators are obtained. A complete class of the quadratic estimator class is also given.

  3. Counting Quadratic Nonresidues in Shifted Subsets of the Set of Quadratic Nonresidues for Primes p=4k+1

    Directory of Open Access Journals (Sweden)

    Rocío Meza-Moreno

    2015-01-01

    Full Text Available Let p=4k+1 be a prime number and Fp the finite field with p elements. For x∈1,n, Nx will denote the set of quadratic nonresidues less than or equal to x. In this work we calculate the number of quadratic nonresidues in the shifted set N(p-1/2+a.

  4. Approximate Graph Edit Distance in Quadratic Time.

    Science.gov (United States)

    Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst

    2015-09-14

    Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.

  5. A Quadratic Closure for Compressible Turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Futterman, J A

    2008-09-16

    We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.

  6. Optimal power flow using sequential quadratic programming

    Science.gov (United States)

    Nejdawi, Imad M.

    1999-11-01

    Optimal power flow (OPF) is an operational as well as a planning tool used by electric utilities to help them operate their network in the most economic and secure mode of operation. Various algorithms to solve the OPF problem evolved over the past three decades; linear programming (LP) techniques were among the major mathematical programming methods utilized. The linear models of the objective function and the linearization of the constraints are the main features of these techniques. The main advantages of the LP approach are simplicity and speed. Nonlinear programming techniques have been applied to OPF solution. The major drawback is the expensive solution of large sparse systems of equations. This research is concerned with the development of a new OPF solution algorithm using sequential quadratic programming (SQP). In this formulation, a small dense system the size of which is equal to the number of control variables is solved in an inner loop. The Jacobian and Hessian terms are calculated in an outer loop. The total number of outer loop iterations is comparable to those in an ordinary load flow in contrast to 20--30 iterations in other nonlinear methods. In addition, the total number of floating point operations is less than that encountered in direct methods by two orders of magnitude. We also model dispatch over a twenty four-hour time horizon in a transmission constrained power network that includes price-responsive loads where large energy customers can operate their loads in time intervals with lowest spot prices.

  7. Designing Camera Networks by Convex Quadratic Programming

    KAUST Repository

    Ghanem, Bernard

    2015-05-04

    ​In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport). ​

  8. Linear quadratic regulator for laser beam shaping

    Science.gov (United States)

    Escárate, Pedro; Agüero, Juan C.; Zúñiga, Sebastián; Castro, Mario; Garcés, Javier

    2017-07-01

    The performance of an adaptive optics system depends on multiple factors, including the quality of the laser beam before being projected to the mesosphere. In general, cumbersome procedures are required to optimize the laser beam in terms of amplitude and phase. However, aberrations produced by the optics of the laser beam system are still detected during the operations due to, for example, uncertainty in the utilized models. In this paper we propose the use of feedback to overcome the presence of model uncertainty and disturbances. In particular we use a Linear Quadratic Regulator (LQR) for closed loop laser beam shaping using a setup of two deformable mirrors. The proposed method is studied and simulated to provide an automatic optimization of the Amplitude of the laser beam. The performance of the LQR control algorithm is evaluated via numerical simulations using the root mean square error (RMSE). The results show an effective amplitude correction of the laser system aberrations after 20 iterations of the algorithm, a RMSE less than 0.7 was obtained, with about 140 actuators per mirror and a separation of z=3 [m] among the mirrors.

  9. Equivalence of the generalized Lie-Hori method and the method of averaging. [in celestial mechanics

    Science.gov (United States)

    Ahmed, A. H.; Tapley, B. D.

    1984-01-01

    In this investigation, a comparison is made of two methods for developing perturbation theories for non-canonical dynamical systems. The methods compared are the generalized Lie-Hori method and the method of averaging. In the comparison presented here, the equivalence of the methods up to the second order in the small parameter is shown. However, the approach used can be extended to demonstrate the equivalence for higher orders. To illustrate the equivalence Duffing's equation, the van der Pol equation and the oscillator with quadratic damping problem are solved using each method.

  10. The structure of complex Lie groups

    CERN Document Server

    Lee, Dong Hoon

    2001-01-01

    Complex Lie groups have often been used as auxiliaries in the study of real Lie groups in areas such as differential geometry and representation theory. To date, however, no book has fully explored and developed their structural aspects.The Structure of Complex Lie Groups addresses this need. Self-contained, it begins with general concepts introduced via an almost complex structure on a real Lie group. It then moves to the theory of representative functions of Lie groups- used as a primary tool in subsequent chapters-and discusses the extension problem of representations that is essential for studying the structure of complex Lie groups. This is followed by a discourse on complex analytic groups that carry the structure of affine algebraic groups compatible with their analytic group structure. The author then uses the results of his earlier discussions to determine the observability of subgroups of complex Lie groups.The differences between complex algebraic groups and complex Lie groups are sometimes subtle ...

  11. Classification and identification of Lie algebras

    CERN Document Server

    Snobl, Libor

    2014-01-01

    The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain cl...

  12. Testosterone Administration Reduces Lying in Men

    NARCIS (Netherlands)

    Wibral, M.; Dohmen, T.J.; Klingmüller, Dietrich; Weber, Bernd; Falk, Armin

    2012-01-01

    Lying is a pervasive phenomenon with important social and economic implications. However, despite substantial interest in the prevalence and determinants of lying, little is known about its biological foundations. Here we study a potential hormonal influence, focusing on the steroid hormone

  13. Lie Group Techniques for Neural Learning

    Science.gov (United States)

    2005-01-03

    Lie group techniques for Neural Learning Edinburgh June 2004 Elena Celledoni SINTEF Applied Mathematics, IMF-NTNU Lie group techniques for Neural...ORGANIZATION NAME(S) AND ADDRESS(ES) SINTEF Applied Mathematics, IMF-NTNU 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND

  14. The Killing Forms of Lie Triple Systems

    Institute of Scientific and Technical Information of China (English)

    ZHANG Zhi Xue; GAO Rui

    2009-01-01

    For Lie triple systems in the characteristic zero setting, we obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively, and then investigate the relationship among the Killing forms of a real Lie triple system To, the complexification T of To, and the realification of T.

  15. Matrix Lie Algebras and Integrable Couplings

    Institute of Scientific and Technical Information of China (English)

    ZHANG Yu-Feng; GUO Fu-Kui

    2006-01-01

    Three kinds of higher-dimensional Lie algebras are given which can be used to directly construct integrable couplings of the soliton integrable systems. The relations between the Lie algebras are discussed. Finally, the integrable couplings and the Hamiltonian structure of Giachetti-Johnson hierarchy and a new integrable system are obtained, respectively.

  16. Induced Modules of Restricted Lie Superalgebras

    Institute of Scientific and Technical Information of China (English)

    刘文德

    2005-01-01

    In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established.Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.

  17. On Nambu-Lie 3-algebra representations

    CERN Document Server

    Sochichiu, Corneliu

    2008-01-01

    We propose a recipe to construct matrix representations of Nambu--Lie 3-algebras in terms of irreducible representations of underlying Lie algebra. The case of Euclidean four-dimensional 3-algebra is considered in details. We find that representations of this 3-algebra are not possible in terms of only Hermitian matrices in spite of its Euclidean nature.

  18. Computations in finite-dimensional Lie algebras

    NARCIS (Netherlands)

    Cohen, A.M.; Graaf, W.A. de; Rónyai, L.

    2001-01-01

    This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System), within the computer algebra package GAP. A first sketch of the packagecan be found in Cohen and de Graaf[1]. Since then, in a collaborative

  19. Lie symmetries and 2D Material Physics

    CERN Document Server

    Belhaj, Adil

    2014-01-01

    Inspired from Lie symmetry classification, we establish a correspondence between rank two Lie symmetries and 2D material physics. The material unit cell is accordingly interpreted as the geometry of a root system. The hexagonal cells, appearing in graphene like models, are analyzed in some details and are found to be associated with A_2 and G_2 Lie symmetries. This approach can be applied to Lie supersymmetries associated with fermionic degrees of freedom. It has been suggested that these extended symmetries can offer a new way to deal with doping material geometries. Motivated by Lie symmetry applications in high energy physics, we speculate on a possible connection with (p,q) brane networks used in the string theory compactification on singular Calabi-Yau manifolds.

  20. On nondecomposable positive definite Hermitian forms over imaginary quadratic fields

    Institute of Scientific and Technical Information of China (English)

    ZHU; Fuzu

    2001-01-01

    [1]Mordell, L. J., The representation of a definite quadratic form as a sum of two others, Ann. of Math., 937, 38: 75.[2]Erds, P., Ko Chao, On definite quadratic forms, which are not the sum of two definite or semidefinite forms, Acta Arith., 939, 3: 02.[3]Erds, P., Ko Chao, Some results on definite quadratic forms, J. London Math. Soc., 938, 3: 27.[4]Zhu Fu-zu, Construction of nondecomposable positive definite quadratic forms, Sci. Sinica, Ser. A, 987, 30(): 9.[5]Zhu Fuzu, On nondecomposability and indecomposability of quadratic forms, Sci. Sinica, Ser. A, 988, 3(3): 265.[6]Pleskin, W., Additively indecomposable positive integral quadratic forms, J. Number Theory, 994, 47: 273.[7]Zhu Fuzu, An existence theorem on positive definite unimodular even Hermitian forms, Chinese Ann. of Math., Ser. A, 984, 5: 33.[8]Zhu Fu-Zu, On the construction of positive definite indecomposable unimodular even Hermitian forms, J. Number Theory, 995, 30: 38.[9]O'Meara, O. T., Introduction to Quadratic Forms, Berlin, New York: Springer-Verlag, 973.[10]Zhu Fuzu, Construction of indecomposable definite Hermitian forms, Chinese Ann. of Math., Ser. B, 994, 5: 349.[11]Zhu Fuzu, On nondecomposable Hermitian forms over Gaussian domain, Acta Math. Sinica, New Ser., 998, 4: 447.

  1. Characteristics of the Eysenck Personality Questionnaire Lie Scale and of Extreme Lie Scorers.

    Science.gov (United States)

    Loo, Robert

    1980-01-01

    Results of statistical analyses suggest that high lie-scorers respond honestly, and that the Lie Scale for the Eysenck Personality Inventory may reflect a personality dimension of interest rather than an extraneous and undesirable factor to be eliminated. (Author)

  2. M2 to D2 and vice versa by 3-Lie and Lie bialgebra

    Energy Technology Data Exchange (ETDEWEB)

    Aali-Javanangrouh, M.; Rezaei-Aghdam, A. [Azarbaijan Shahid Madani University, Department of Physics, Faculty of Science, Tabriz (Iran, Islamic Republic of)

    2016-11-15

    Using the concept of a 3-Lie bialgebra, which has recently been defined in arXiv:1604.04475, we construct a Bagger-Lambert-Gustavson (BLG) model for the M2-brane on a Manin triple of a special 3-Lie bialgebra. Then by using the correspondence and the relation between those 3-Lie bialgebra with Lie bialgebra, we reduce this model to an N = (4,4) WZW model (D2-brane), such that its algebraic structure is a Lie bialgebra with one 2-cocycle. In this manner by using the correspondence of the 3-Lie bialgebra and Lie bialgebra (for this special 3-Lie algebra) one can construct the M2-brane from a D2-brane and vice versa. (orig.)

  3. The Cyclicity of the Period Annulus Around the Quadratic Isochronous Center

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    The number of the limit cycles bifurcating in small quadratic perturbations of quadratic systems with an isochronous center is studied, it turns out that the cyclicity of the period annulus around one kind of quadratic isochronous center is two.

  4. A-扩张Lie Rinehart代数%On the A-extended Lie Rinehart Algebras

    Institute of Scientific and Technical Information of China (English)

    陈酌; 祁玉海

    2007-01-01

    The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary,commutative, associative algebra A. It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group, analogous to the well known relationship of Lie algebras and Lie groups.

  5. The Prevalence of Lying in America: Three Studies of Self-Reported Lies

    Science.gov (United States)

    Serota, Kim B.; Levine, Timothy R.; Boster, Franklin J.

    2010-01-01

    This study addresses the frequency and the distribution of reported lying in the adult population. A national survey asked 1,000 U.S. adults to report the number of lies told in a 24-hour period. Sixty percent of subjects report telling no lies at all, and almost half of all lies are told by only 5% of subjects; thus, prevalence varies widely and…

  6. Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra

    Energy Technology Data Exchange (ETDEWEB)

    Movshev, M.V. [Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651 (United States); Schwarz, A., E-mail: schwarz@math.ucdavis.edu [Department of Mathematics, University of California, Davis, CA 95616 (United States); Xu, Renjun [Department of Physics, University of California, Davis, CA 95616 (United States)

    2012-01-11

    We study the homology and cohomology groups of super Lie algebras of supersymmetries and of super Poincare Lie algebras in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions {<=}11. For dimensions D=10,11 we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry Lie algebras.

  7. A Finite Continuation Algorithm for Bound Constrained Quadratic Programming

    DEFF Research Database (Denmark)

    Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.

    1999-01-01

    The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems. The u....... The unique path generated by the minimizers of these problems yields the solution to the original problem for finite values of the approximation parameter. Thus, a finite continuation algorithm is designed. Results of extensive computational experiments are reported....

  8. A Class of Solvable Lie Algebras and Their Hom-Lie Algebra Structures

    Institute of Scientific and Technical Information of China (English)

    LI Xiao-chao; LI Dong-ya; JIN Quan-qin

    2014-01-01

    The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1 as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1. Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.

  9. On the algebraic approach to the time-dependent quadratic Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Urdaneta, Ines; Palma, Alejandro [Instituto de Fisica, Benemerita Universidad Autonoma de Puebla, Puebla (Mexico); Sandoval, Lourdes, E-mail: urdaneta@sirio.ifuap.buap.m [Facultad de Ciencias de la Computacion, Benemerita Universidad Autonoma de Puebla, Puebla (Mexico)

    2010-09-24

    The unitary operator V(t) that diagonalizes the time-dependent quadratic Hamiltonian (TDQH) into a time-dependent harmonic oscillator (TDHO) is obtained using a Lie algebra. The method involves a factorization of the TDQH into a TDHO through a unitary Bogoliubov transformation in terms of creation and annihilation operators with time-dependent coefficients. It is shown that this operator can be easily achieved by means of the factorization, together with the commonly known Wei-Norman theorem. We discuss the conditions under which this unitary operator converges to the evolution operator U(t) of the Schroedinger equation for the TDQH, giving then a straightforward calculation of the evolution operator with respect to the procedures published in the literature.

  10. Compact engineering of path-entangled sources from a monolithic quadratic nonlinear photonic crystal

    CERN Document Server

    Jin, H; Luo, X W; Leng, H Y; Gong, Y X; Zhu, S N

    2013-01-01

    Photonic entangled states lie at the heart of quantum science for the demonstrations of quantum mechanics foundations and supply as a key resource for approaching various quantum technologies. An integrated realization of such states will certainly guarantee a high-degree of entanglement and improve the performance like portability, stability and miniaturization, hence becomes an inevitable tendency towards the integrated quantum optics. Here, we report the compact realization of steerable photonic path-entangled states from a monolithic quadratic nonlinear photonic crystal. The crystal acts as an inherent beam splitter to distribute photons into coherent spatial modes, producing the heralded single-photon even appealing beamlike two-photon path-entanglement, wherein the entanglement is characterized by quantum spatial beatings. Such multifunctional entangled source can be further extended to high-dimensional fashion and multi-photon level as well as involved with other degrees of freedom, which paves a desir...

  11. Introduction to the theory of Lie groups

    CERN Document Server

    Godement, Roger

    2017-01-01

    This textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory. Written by a master of the subject and influential member of the Bourbaki group, the French edition of this textbook has been used by several generations of students. This translation preserves the distinctive style and lively exposition of the original. Requiring only basics of topology and algebra, this book offers an engaging introduction to Lie groups for graduate students and a valuable resource for researchers.

  12. Quasi-big\\`ebres de Lie et cohomologie d'alg\\`ebre de Lie

    CERN Document Server

    Bangoura, Momo

    2010-01-01

    Lie quasi-bialgebras are natural generalisations of Lie bialgebras introduced by Drinfeld. To any Lie quasi-bialgebra structure of finite-dimensional (G, \\mu, \\gamma ,\\phi ?), correspond one Lie algebra structure on D = G\\oplus G*, called the double of the given Lie quasi-bialgebra. We show that there exist on \\Lambda G, the exterior algebra of G, a D-module structure and we establish an isomorphism of D-modules between \\Lambda D and End(\\Lambda G), D acting on \\Lambda D by the adjoint action.

  13. Induced Lie Algebras of a Six-Dimensional Matrix Lie Algebra

    Institute of Scientific and Technical Information of China (English)

    ZHANG Yu-Feng; LIU Jing

    2008-01-01

    By using a six-dimensional matrix Lie algebra [Y.F. Zhang and Y. Wang, Phys. Lett. A 360 (2006) 92], three induced Lie algebras are constructed. One of them is obtained by extending Lie bracket, the others are higher-dimensional complex Lie algebras constructed by using linear transformations. The equivalent Lie algebras of the later two with multi-component forms are obtained as well. As their applications, we derive an integrable coupling and quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations.

  14. Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

    Science.gov (United States)

    Gibson, J. S.; Adamian, A.

    1988-01-01

    An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

  15. Combinatorics on Words in Symbolic Dynamics: The Quadratic Map

    Institute of Scientific and Technical Information of China (English)

    Wan Ji DAI; Kebo L(U); Jun WANG

    2008-01-01

    This paper is contributed to the combinatorial properties of the MSS sequences, which are the periodic kneading words of quadratic maps denned on a interval. An explicit expression of adjacency relations on MSS sequences of given lengths is established.

  16. Modulational stability and dark solitons in periodic quadratic nonlinear media

    DEFF Research Database (Denmark)

    Corney, Joel Frederick; Bang, Ole

    2000-01-01

    We show that stable dark solitons exist in quadratic nonlinear media with periodic linear and nonlinear susceptibilities. We investigate the modulational stability of plane waves in such systems, a necessary condition for stable dark solitons....

  17. Reconsideration on Homogeneous Quadratic Riemann Boundary Value Problem

    Institute of Scientific and Technical Information of China (English)

    Lu Jian-ke

    2004-01-01

    The homogeneous quadratic Riemann boundary value problem (1) with Hǒlder continuous coefficients for the normal case was considered by the author in 1997. But the solutions obtained there are incomplete. Here its general method of solution is obtained.

  18. A Trust-region-based Sequential Quadratic Programming Algorithm

    DEFF Research Database (Denmark)

    Henriksen, Lars Christian; Poulsen, Niels Kjølstad

    This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....

  19. Geometric structure of pseudo-plane quadratic flows

    Science.gov (United States)

    Sun, Che

    2017-03-01

    Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous applications focused on two-dimensional homogeneous fluid, this study examines the geometric structure of three-dimensional quadratic flows in stratified fluid by solving a steady-state pseudo-plane flow model. The complete set of exact solutions reveals that steady quadratic flows have an invariant conic type in the non-rotating frame and a non-rotatory vertical structure in the rotating frame. Three baroclinic solutions with vertically non-aligned formulation disprove an earlier conjecture. All elliptic and hyperbolic solutions, except for the inertial ones, exhibit vertical concentricity. The rich geometry of quadratic flows stands in contrast to the depleted geometry of high-degree polynomial flows. A paradox in the steady solutions of shallow-water reduced-gravity models is also explained.

  20. Finite dimensional semigroup quadratic algebras with minimal number of relations

    CERN Document Server

    Iyudu, Natalia

    2011-01-01

    A quadratic semigroup algebra is an algebra over a field given by the generators $x_1,...,x_n$ and a finite set of quadratic relations each of which either has the shape $x_jx_k=0$ or the shape $x_jx_k=x_lx_m$. We prove that a quadratic semigroup algebra given by $n$ generators and $d\\leq \\frac{n^2+n}{4}$ relations is always infinite dimensional. This strengthens the Golod--Shafarevich estimate for the above class of algebras. Our main result however is that for every $n$, there is a finite dimensional quadratic semigroup algebra with $n$ generators and $\\delta_n$ generators, where $\\delta_n$ is the first integer greater than $\\frac{n^2+n}{4}$. This shows that the above Golod-Shafarevich type estimate for semigroup algebras is sharp.

  1. Quadratic measurement and conditional state preparation in an optomechanical system

    DEFF Research Database (Denmark)

    A. Brawley, George; Vanner, Michael A.; Bowen, Warwick P.;

    2014-01-01

    We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator.......We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator....

  2. An Interval Maximum Entropy Method for Quadratic Programming Problem

    Institute of Scientific and Technical Information of China (English)

    RUI Wen-juan; CAO De-xin; SONG Xie-wu

    2005-01-01

    With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the maximum entropy function, provide the region deletion test rules and design an interval maximum entropy algorithm for quadratic programming problem. The convergence of the method is proved and numerical results are presented. Both theoretical and numerical results show that the method is reliable and efficient.

  3. On wave-packet dynamics in a decaying quadratic potential

    DEFF Research Database (Denmark)

    Møller, Klaus Braagaard; Henriksen, Niels Engholm

    1997-01-01

    We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics.......We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics....

  4. DERIVATIVES OF EIGENPAIRS OF SYMMETRIC QUADRATIC EIGENVALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    Derivatives of eigenvalues and eigenvectors with respect to parameters in symmetric quadratic eigenvalue problem are studied. The first and second order derivatives of eigenpairs are given. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the quadratic eigenvalue problem, and the use of state space representation is avoided, hence the cost of computation is greatly reduced. The efficiency of the presented method is demonstrated by considering a spring-mass-damper system.

  5. Scale-Invariant Rotating Black Holes in Quadratic Gravity

    Directory of Open Access Journals (Sweden)

    Guido Cognola

    2015-07-01

    Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.

  6. Ideal Class Groups and Subgroups of Real Quadratic Function Fields

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    In this paper, we study the real quadratic function fields K=k(D), given a necessary and sufficient condition for the ideal class group H(K) of any real quadratic function field K to have a cyclic subgroup of order n, and obtained eight series of such fields. The ideal class numbers h(OK) of K in the series all have a factor n.

  7. Burgers' turbulence problem with linear or quadratic external potential

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.

    2005-01-01

    We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....

  8. On Integers, Primes and UniqueFactorization in Quadratic Fields

    OpenAIRE

    Hedenlund, Alice

    2013-01-01

    Abstract. This thesis will deal with quadratic elds. The prob- lem is to study such elds and their properties including, but not limited to, determining integers, nding primes and deciding which quadratic elds have unique factorization. The goal is to get famil- iar with these concepts and to provide a starting point for students with an interest in algebra to explore eld extensions and inte- gral closures in relation to elementary number theory. The reader will be assumed to have a basic kn...

  9. Stability of a Generalized Quadratic Functional Equation in Schwartz Distributions

    Institute of Scientific and Technical Information of China (English)

    Jae-Young CHUNG

    2009-01-01

    We consider the Hyers-Ulam stability problem of the generalized quadratic functional equation u(o)A+v(o)B-2w(o)P1-2k(o)P2=0, which is a distributional version of the classical generalized quadratic functional equation f(x + y) + g(x - y) - 2h(x) - 2k(y) = 0.

  10. Quadratic function approaching method for magnetotelluric soundingdata inversion

    Energy Technology Data Exchange (ETDEWEB)

    Liangjun, Yan; Wenbao, Hu; Zhang, Keni

    2004-04-05

    The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.

  11. On the use of simplex methods in constructing quadratic models

    Institute of Scientific and Technical Information of China (English)

    Qing-hua ZHOU

    2007-01-01

    In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces. And the quadratic model is solved in the new subspaces. The motivation is to use the information disclosed by the former steps to construct more promising directions. For most tested problems, the number of function evaluations have been reduced obviously through our algorithms.

  12. The Frattini Subalgebra of Restricted Lie Superalgebras

    Institute of Scientific and Technical Information of China (English)

    Liang Yun CHEN; Dao Ji MENG; Yong Zheng ZHANG

    2006-01-01

    In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra (L, [p]). We show first that if L = A1 (⊙) A2 (⊙) … (⊙) An, then φp (L) = φp (A1) + φp (A2) +… +φp (An),where each Ai is a p-ideal of L. We then obtain two results: F(L) = φ(L) = J(L) = L(1) if and only if L is nilpotent; Fp(L) and F(L) are nilpotent ideals of L if L is solvable. In addition, necessary and sufficient conditions are found for φp-free restricted Lie superalgebras. Finally, we discuss the relationships of E-p-restricted Lie superalgebras and E-restricted Lie superalgebras.

  13. Linearization from Complex Lie Point Transformations

    Directory of Open Access Journals (Sweden)

    Sajid Ali

    2014-01-01

    Full Text Available Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs which have Lie algebras of maximum dimension d, with d≤4. We identify such a class by employing complex structure on the manifold that defines the geometry of differential equations. Furthermore we provide a geometrical construction of the procedure adopted that provides an analogue in R3 of the linearizability criteria in R2.

  14. Lie Superalgebras arising from bosonic representation

    CERN Document Server

    Jing, Naihuan

    2012-01-01

    A 2-toroidal Lie superalgebra is constructed using bosonic fields and a ghost field. The superalgebra contains $osp(1|2n)^{(1)}$ as a distinguished subalgebra and behaves similarly to the toroidal Lie superalgebra of type $B(0, n)$. Furthermore this algebra is a central extension of the algebra $osp(1|2n)\\otimes \\mathbb C[s, s^{-1}, t,t^{-1}]$.

  15. Noncommutative geometry with graded differential Lie algebras

    Science.gov (United States)

    Wulkenhaar, Raimar

    1997-06-01

    Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the Connes-Lott prescription of noncommutative geometry, differs from that, however, by the implementation of unitary Lie algebras instead of associative * -algebras. The general scheme is presented in detail and is applied to functions ⊗ matrices.

  16. Post-Lie algebras and factorization theorems

    Science.gov (United States)

    Ebrahimi-Fard, Kurusch; Mencattini, Igor; Munthe-Kaas, Hans

    2017-09-01

    In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable completions of) those Hopf algebras. Of particular interest is the case of post-Lie algebras defined in terms of solutions of modified classical Yang-Baxter equations. In this setting we will study factorization properties of the aforementioned group-like elements.

  17. Constructing semisimple subalgebras of semisimple Lie algebras

    CERN Document Server

    de Graaf, Willem A

    2010-01-01

    Algorithms are described that help with obtaining a classification of the semisimple subalgebras of a given semisimple Lie algebra, up to linear equivalence. The algorithms have been used to obtain classifications of the semisimple subalgebras of the simple Lie algebras of ranks <= 8. These have been made available as a database inside the SLA package of GAP4. The subalgebras in this database are explicitly given, as well as the inclusion relations among them.

  18. Lie Admissible Non-Associative Algebras

    Institute of Scientific and Technical Information of China (English)

    H.Mohammad Ahmadi; Ki-Bong Nam; Jonathan Pakinathan

    2005-01-01

    A non-associative ring which contains a well-known associative ring or Lie ring is interesting. In this paper, a method to construct a Lie admissible non-associative ring is given; a class of simple non-associative algebras is obtained; all the derivations of the non-associative simple N0,0,1 algebra defined in this paper are determined; and finally, a solid algebra is defined.

  19. Central extension of graded Lie algebras

    CERN Document Server

    Welte, Angelika

    2010-01-01

    In this thesis we describe the universal central extension of two important classes of so-called root-graded Lie algebras defined over a commutative associative unital ring $k.$ Root-graded Lie algebras are Lie algebras which are graded by the root lattice of a locally finite root system and contain enough $\\mathfrak{sl}_2$-triples to separate the homogeneous spaces of the grading. Examples include the infinite rank analogs of the simple finite-dimensional complex Lie algebras. \\\\ In the thesis we show that in general the universal central extension of a root-graded Lie algebra $L$ is not root-graded anymore, but that we can measure quite easily how far it is away from being so, using the notion of degenerate sums, introduced by van der Kallen. We then concentrate on root-graded Lie algebras which are graded by the root systems of type $A$ with rank at least 2 and of type $C$. For them one can use the theory of Jordan algebras.

  20. Random action of compact Lie groups and minimax estimation of a mean pattern

    CERN Document Server

    Bigot, Jérémie; Gadat, Sebastien

    2011-01-01

    This paper considers the problem of estimating a mean pattern in the setting of Grenander's pattern theory. Shape variability in a data set of curves or images is modeled by the random action of elements in a compact Lie group on an infinite dimensional space. In the case of observations contaminated by an additive Gaussian white noise, it is shown that estimating a reference template in the setting of Grenander's pattern theory falls into the category of deconvolution problems over Lie groups. To obtain this result, we build an estimator of a mean pattern by using Fourier deconvolution and harmonic analysis on compact Lie groups. In an asymptotic setting where the number of observed curves or images tends to infinity, we derive upper and lower bounds for the minimax quadratic risk over Sobolev balls. This rate depends on the smoothness of the density of the random Lie group elements representing shape variability in the data, which makes a connection between estimating a mean pattern and standard deconvoluti...

  1. A transient, quadratic nodal method for triangular-Z geometry

    Energy Technology Data Exchange (ETDEWEB)

    DeLorey, T.F.

    1993-06-01

    Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.

  2. Quadratic 0-1 programming: Geometric methods and duality analysis

    Science.gov (United States)

    Liu, Chunli

    The unconstraint quadratic binary problem (UBQP), as a classical combinatorial problem, finds wide applications in broad field and human activities including engineering, science, finance, etc. The NP-hardness of the combinatorial problems makes a great challenge to solve the ( UBQP). The main purpose of this research is to develop high performance solution method for solving (UBQP) via the geometric properties of the objective ellipse contour and the optimal solution. This research makes several contributions to advance the state-of-the-art of geometric approach of (UBQP). These contributions include both theoretical and numerical aspects as stated below. In part I of this dissertation, certain rich geometric properties hidden behind quadratic 0-1 programming are investigated. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 0-1 optimization problems by investigating geometric features of the ellipse contour of a (perturbed) convex quadratic function. These findings further lead to some new optimality conditions for quadratic 0-1 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branch-and-bound type, we obtain promising preliminary computational results. In part II of this dissertation, we present new results of the duality gap between the binary quadratic optimization problem and its Lagrangian dual. We first derive a necessary and sufficient condition for the zero duality gap and discuss its relationship with the polynomial solvability of the problem. We then characterize the zeroness of duality gap by the distance, delta, between the binary set and certain affine space C. Finally, we discuss a computational procedure of the distance delta. These results provide new insights into the duality gap and polynomial solvability of binary quadratic optimization problems.

  3. A twisted generalization of Lie-Yamaguti algebras

    CERN Document Server

    Gaparayi, Donatien

    2010-01-01

    A twisted generalization of Lie-Yamaguti algebras, called Hom-Lie-Yamaguti algebras, is defined. Hom-Lie-Yamaguti algebras generalize Hom-Lie triple systems (and susequently ternary Hom-Nambu algebras) and Hom-Lie algebras in the same way as Lie-Yamaguti algebras generalize Lie triple systems and Lie algebras. It is shown that the category of Hom-Lie-Yamaguti algebras is closed under twisting by self-morphisms. Constructions of Hom-Lie-Yamaguti algebras from classical Lie-Yamaguti algebras and Malcev algebras are given. It is observed that, when the ternary operation of a Hom-Lie-Yamaguti algebra expresses through its binary one in a specific way, then such a Hom-Lie-Yamaguti algebra is a Hom-Malcev algebra.

  4. Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

    Energy Technology Data Exchange (ETDEWEB)

    Ibarra-Sierra, V.G.; Sandoval-Santana, J.C. [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F. (Mexico); Cardoso, J.L. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Kunold, A., E-mail: akb@correo.azc.uam.mx [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico)

    2015-11-15

    We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a

  5. Detecting true lies:police officers' ability to detect suspects' lies

    OpenAIRE

    Mann, Samantha; Vrij, Aldert; Bull, Ray

    2004-01-01

    Ninety-nine police officers, not identified in previous research as belonging to groups which are superior in lie detection, attempted to detect truths and lies told by suspects during their videotaped police interviews. Accuracy rates were higher than typically found in deception research and reached levels similar to those obtained by specialized lie detectors in previous research. Accuracy was positively correlated with perceived experience in interviewing suspects and with mentioning cues...

  6. Lie n-algebras of BPS charges

    CERN Document Server

    Sati, Hisham

    2015-01-01

    We uncover higher algebraic structures on Noether currents and BPS charges. It is known that equivalence classes of conserved currents form a Lie algebra. We show that at least for target space symmetries of higher parameterized WZW-type sigma-models this naturally lifts to a Lie (p+1)-algebra structure on the Noether currents themselves. Applied to the Green-Schwarz-type action functionals for super p-brane sigma-models this yields super Lie (p+1)-algebra refinements of the traditional BPS brane charge extensions of supersymmetry algebras. We discuss this in the generality of higher differential geometry, where it applies also to branes with (higher) gauge fields on their worldvolume. Applied to the M5-brane sigma-model we recover and properly globalize the M-theory super Lie algebra extension of 11-dimensional superisometries by 2-brane and 5-brane charges. Passing beyond the infinitesimal Lie theory we find cohomological corrections to these charges in higher analogy to the familiar corrections for D-brane...

  7. Riemannian manifolds as Lie-Rinehart algebras

    Science.gov (United States)

    Pessers, Victor; van der Veken, Joeri

    2016-07-01

    In this paper, we show how Lie-Rinehart algebras can be applied to unify and generalize the elementary theory of Riemannian geometry. We will first review some necessary theory on a.o. modules, bilinear forms and derivations. We will then translate some classical theory on Riemannian geometry to the setting of Rinehart spaces, a special kind of Lie-Rinehart algebras. Some generalized versions of classical results will be obtained, such as the existence of a unique Levi-Civita connection, inducing a Levi-Civita connection on a submanifold, and the construction of spaces with constant sectional curvature.

  8. Split-octonion Lie 3-algebra

    CERN Document Server

    Jardino, Sergio

    2010-01-01

    We extend the concept of a generalized Lie 3-algebra, known to octonions $\\mathbb{O}$, to split-octonions $\\mathbb{SO}$. In order to do that, we introduce a notational device that unifies the two elements product of both of the algebras. We have also proved that $\\mathbb{SO}$ is a Malcev algebra and have recalculated known relations for the structure constants in terms of the introduced structure tensor. An application of the split Lie $3-$algebra to a Bagger and Lambert gauge theory is also discussed.

  9. Integrability of Lie Systems Through Riccati Equations

    Science.gov (United States)

    Cariñena, José F.; de Lucas, Javier

    Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides us with a unified geometrical viewpoint that allows us to analyse some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalised to describe integrability conditions for any Lie system. Finally, we show the usefulness of our treatment in order to study the problem of the linearisability of Riccati equations.

  10. Integrability of Lie systems through Riccati equations

    CERN Document Server

    Cariñena, José F

    2010-01-01

    Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides us with a unified geometrical viewpoint that allows us to analyse some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalised to describe integrability conditions for any Lie system. Finally, we show the usefulness of our treatment in order to study the problem of the linearisability of Riccati equations.

  11. Quiver Gauge theories from Lie Superalgebras

    CERN Document Server

    Belhaj, A

    2012-01-01

    We discuss quiver gauge models with matter fields based on Dynkin diagrams of Lie superalgebra structures. We focus on A(1,0) case and we find first that it can be related to intersecting complex cycles with genus $g$. Using toric geometry, A(1,0) quivers are analyzed in some details and it is shown that A(1,0) can be used to incorporate fundamental fields to a product of two unitary factor groups. We expect that this approach can be applied to other kinds of Lie superalgebras;

  12. Spiders for rank 2 Lie algebras

    CERN Document Server

    Kuperberg, G

    1996-01-01

    A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. We define certain combinatorial spiders by generators and relations that are isomorphic to the representation theories of the three rank two simple Lie algebras, namely A2, B2, and G2. They generalize the widely-used Temperley-Lieb spider for A1. Among other things, they yield bases for invariant spaces which are probably related to Lusztig's canonical bases, and they are useful for computing quantities such as generalized 6j-symbols and quantum link invariants.

  13. Lie algebra contractions and separation of variables

    CERN Document Server

    Vinternits, P; Pogosyan, G S; Sissakian, A N

    2001-01-01

    The concept of analytical Lie group contractions is introduced to relate the separation of variables in space of constant nonzero curvature to separation in Euclidean or pseudo-Euclidean spaces. The contraction parameter is introduced explicitly into the basis of the Lie algebra, the Laplace-Beltrami operator, the complete set of commuting operators, the coordinates themselves and into the solutions. This enables to obtain asymptotic formulae connecting special functions related to the groups O(n) and O(n,1) to those related to Euclidean and pseudo-Euclidean groups

  14. Lie Point Symmetries of Differential-Difference Equations

    Institute of Scientific and Technical Information of China (English)

    DING Wei; TANG Xiao-Yan

    2004-01-01

    In this paper, the classical Lie group approach is extended to find some Lie point symmetries of differentialdifference equations. It reveals that the obtained Lie point symmetries can constitute a Kac-Moody-Virasoro algebra.

  15. The generalized quadratic knapsack problem. A neuronal network approach.

    Science.gov (United States)

    Talaván, Pedro M; Yáñez, Javier

    2006-05-01

    The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.

  16. Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

    Energy Technology Data Exchange (ETDEWEB)

    Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar

    2016-06-15

    We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.

  17. The quadratic reciprocity law a collection of classical proofs

    CERN Document Server

    Baumgart, Oswald

    2015-01-01

    This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.

  18. Parametric localized modes in quadratic nonlinear photonic structures

    DEFF Research Database (Denmark)

    Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole;

    2001-01-01

    We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi2) nonlinear interfaces embedded in a linear layered structure-a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear...... interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...... in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media....

  19. On Volterra quadratic stochastic operators with continual state space

    Energy Technology Data Exchange (ETDEWEB)

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar [Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University, Jalan Sultan Ahmad Shah, Bandar Indera Mahkota, 25200 Kuantan, Pahang (Malaysia)

    2015-05-15

    Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.

  20. Amalgamated Products of Ore and Quadratic Extensions of Rings

    CERN Document Server

    Johnson, Garrett

    2012-01-01

    We study the ideal theory of amalgamated products of Ore and quadratic extensions over a base ring R. We prove an analogue of the Hilbert Basis theorem for an amalgamated product Q of quadratic extensions and determine conditions for when the one-sided ideals of Q are principal or doubly-generated. We also determine conditions that make Q a principal ideal ring. Finally, we show that the double affine Hecke algebra $H_{q,t}$ associated to the general linear group GL_2(k) (here, k is a field with characteristic not 2) is an amalgamated product of quadratic extensions over a three-dimensional quantum torus and give an explicit isomorphism. In this case, it follows that $H_{q,t}$ is a noetherian ring.

  1. A Projection Neural Network for Constrained Quadratic Minimax Optimization.

    Science.gov (United States)

    Liu, Qingshan; Wang, Jun

    2015-11-01

    This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.

  2. The Lie Algebras in which Every Subspace s Its Subalgebra

    Institute of Scientific and Technical Information of China (English)

    WU MING-ZHONG

    2009-01-01

    In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g+Cidg, where g is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete.

  3. Lie, truth, lie: the role of task switching in a deception context.

    Science.gov (United States)

    Debey, Evelyne; Liefooghe, Baptist; De Houwer, Jan; Verschuere, Bruno

    2015-05-01

    A cornerstone of the task switching literature is the finding that task performance is typically slower and more error-prone when the task switches than when it repeats. So far, deception research has largely ignored that such cognitive switch costs should also emerge when switching between truth telling and lying, and may affect the cognitive cost of lying as reflected in higher prefrontal brain activity and slower and less accurate responding compared to truth telling. To get a grasp on the relative size of the switch costs associated with lying and truth telling, the current study had participants perform a reaction time-based deception task, in which they alternated between lying and telling the truth to yes/no questions that were related to activities performed in the lab (Experiment 1) or neutral autobiographical facts (Experiment 2). In both experiments, the error and reaction time switch costs were found to be equally large for switching from truth telling to lying and from lying to truth telling. This symmetry in switch costs can be explained from the hypothesis that lying requires a first step of truth telling, and demonstrates that task switching does not contribute to the cognitive cost of lying when the repetition/switch ratio is balanced. Theoretical and methodological implications are considered.

  4. Lying in Business : Insights from Hannah Arendt’s ‘Lying in Politics’

    NARCIS (Netherlands)

    Eenkhoorn, P.; Graafland, J.J.

    2010-01-01

    The famous political philosopher Hannah Arendt develops several arguments why truthfulness cannot be counted among the political virtues. This article shows that similar arguments apply to lying in business. Based on Hannah Arendt’s theory, we distinguish five reasons why lying is a structural tempt

  5. Teaching the Truth about Lies to Psychology Students: The Speed Lying Task

    Science.gov (United States)

    Pearson, Matthew R.; Richardson, Thomas A.

    2013-01-01

    To teach the importance of deception in everyday social life, an in-class activity called the "Speed Lying Task" was given in an introductory social psychology class. In class, two major research findings were replicated: Individuals detected deception at levels no better than expected by chance and lie detection confidence was unrelated…

  6. Lying in Business : Insights from Hannah Arendt’s ‘Lying in Politics’

    NARCIS (Netherlands)

    Eenkhoorn, P.; Graafland, J.J.

    2010-01-01

    The famous political philosopher Hannah Arendt develops several arguments why truthfulness cannot be counted among the political virtues. This article shows that similar arguments apply to lying in business. Based on Hannah Arendt’s theory, we distinguish five reasons why lying is a structural tempt

  7. Lying in Business : Insights from Hannah Arendt’s ‘Lying in Politics’

    NARCIS (Netherlands)

    Eenkhoorn, P.; Graafland, J.J.

    2010-01-01

    The famous political philosopher Hannah Arendt develops several arguments why truthfulness cannot be counted among the political virtues. This article shows that similar arguments apply to lying in business. Based on Hannah Arendt’s theory, we distinguish five reasons why lying is a structural

  8. Teaching the Truth about Lies to Psychology Students: The Speed Lying Task

    Science.gov (United States)

    Pearson, Matthew R.; Richardson, Thomas A.

    2013-01-01

    To teach the importance of deception in everyday social life, an in-class activity called the "Speed Lying Task" was given in an introductory social psychology class. In class, two major research findings were replicated: Individuals detected deception at levels no better than expected by chance and lie detection confidence was unrelated…

  9. Why Do Lie-Catchers Fail? A Lens Model Meta-Analysis of Human Lie Judgments

    Science.gov (United States)

    Hartwig, Maria; Bond, Charles F., Jr.

    2011-01-01

    Decades of research has shown that people are poor at detecting lies. Two explanations for this finding have been proposed. First, it has been suggested that lie detection is inaccurate because people rely on invalid cues when judging deception. Second, it has been suggested that lack of valid cues to deception limits accuracy. A series of 4…

  10. Convergence properties of the softassign quadratic assignment algorithm.

    Science.gov (United States)

    Rangarajan, A; Vuille, A; Mjolsness, E

    1999-08-15

    The softassign quadratic assignment algorithm is a discrete-time, continuous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its convergence properties have not been studied. Here, we construct discrete-time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.

  11. Robust quadratic assignment problem with budgeted uncertain flows

    Directory of Open Access Journals (Sweden)

    Mohammad Javad Feizollahi

    2015-12-01

    Full Text Available We consider a generalization of the classical quadratic assignment problem, where material flows between facilities are uncertain, and belong to a budgeted uncertainty set. The objective is to find a robust solution under all possible scenarios in the given uncertainty set. We present an exact quadratic formulation as a robust counterpart and develop an equivalent mixed integer programming model for it. To solve the proposed model for large-scale instances, we also develop two different heuristics based on 2-Opt local search and tabu search algorithms. We discuss performance of these methods and the quality of robust solutions through extensive computational experiments.

  12. Selectable linear or quadratic coupling in an optomechanical system

    CERN Document Server

    Xuereb, André

    2012-01-01

    There has been much interest recently in the analysis of optomechanical systems incorporating dielectric nano- or microspheres inside a cavity field. We analyse here the situation when one of the mirrors of the cavity itself is also allowed to move. We reveal that the interplay between the two oscillators yields a cross-coupling that results in, e.g., appreciable cooling and squeezing of the motion of the sphere, despite its nominal quadratic coupling. We also discuss a simple modification that would allow this cross-coupling to be removed at will, thereby yielding a purely quadratic coupling for the sphere.

  13. The size of quadratic $p$-adic linearization disks

    OpenAIRE

    Lindahl, Karl-Olof

    2013-01-01

    We find the exact radius of linearization disks at indifferent fixed points of quadratic maps in $\\mathbb{C}_p$. We also show that the radius is invariant under power series perturbations. Localizing all periodic orbits of these quadratic-like maps we then show that periodic points are not the only obstruction for linearization. In so doing, we provide the first known examples in the dynamics of polynomials over $\\mathbb{C}_p$ where the boundary of the linearization disk does not contain any ...

  14. On the use of simplex methods in constructing quadratic models

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In this paper,we investigate the quadratic approximation methods.After studying the basic idea of simplex methods,we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces.And the quadratic model is solved in the new subspaces.The motivation is to use the information disclosed by the former steps to construct more promising directions.For most tested problems,the number of function evaluations have been reduced obviously through our algorithms.

  15. New robust chaotic system with exponential quadratic term

    Institute of Scientific and Technical Information of China (English)

    Bao Bo-Cheng; Li Chun-Biao; Xu Jian-Peing; Liu Zhong

    2008-01-01

    This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term.This system can display a double-scroll chaotic attractor with only two equilibria,and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent.Some basic dynamical properties and chaotic behaviour of novel attractor are studied.By numerical simulation,this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviottrs by a constant controller.

  16. Approximation algorithms for indefinite complex quadratic maximization problems

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    In this paper,we consider the following indefinite complex quadratic maximization problem: maximize zHQz,subject to zk ∈ C and zkm = 1,k = 1,...,n,where Q is a Hermitian matrix with trQ = 0,z ∈ Cn is the decision vector,and m 3.An (1/log n) approximation algorithm is presented for such problem.Furthermore,we consider the above problem where the objective matrix Q is in bilinear form,in which case a 0.7118 cos mπ 2approximation algorithm can be constructed.In the context of quadratic optimization,various extensions and connections of the model are discussed.

  17. Simultaneous quadratic performance stabilization for linear time-delay systems

    Institute of Scientific and Technical Information of China (English)

    Chen Yuepeng; Zhou Zude; Liu Huanbin; Zhang Qingling

    2006-01-01

    A newly designed approach of simultaneous stabilization is given for linear discrete time-delay systems. The problem of stabilization for a collection of systems is discussed initially. Adequate condition are obtained in terms of linear matrix inequalities (LMIs) which are independent of time delays such that the resultant collection of discrete time-delay systems are stable with an upper bound of the quadratic performance index. Subsequently, controllers are designed such that the resultant closed-loop discrete time-delay systems are simultaneously stabilized with the upper bound of the quadratic performance index. Finally,a numerical example is given to illustrate the design method.

  18. PORTAL SUPPLY TO CAUDATE LOBE AND QUADRATE LOBE OF LIVER

    Directory of Open Access Journals (Sweden)

    Maheswari

    2015-09-01

    Full Text Available The precise knowledge of intra hepatic branching pattern of portal vein to caudate lobe and quadrate lobe is important for Gastroenterologist during hepatic segmental and subsegmental resection. The study was done in 47 adult human liver specimens. In this study methods like Manual dissection and Contrast study were used. During this study the portal branches to caudate l obe, Quadrate lobe and accessory branches to segment IV in addition to its branches were observed. The results were compared with previous studies

  19. Sparse Signal Recovery from Quadratic Measurements via Convex Programming

    OpenAIRE

    Li, Xiaodong; Voroninski, Vladislav

    2012-01-01

    In this paper we consider a system of quadratic equations ||^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be underdetermined, i.e., m < n. We prove that if there exists a sparse solution x, i.e., at most k components of x are non-zero, then by solving a convex optimization program, we can solve for x up to a multiplicative constant with high probability, provided that k

  20. Exact solutions to quadratic gravity generated by a conformal method

    CERN Document Server

    Pravda, Vojtech; Podolsky, Jiri; Svarc, Robert

    2016-01-01

    We study the role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one non-linear partial differential equation for the conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. We show that all spacetimes conformal to Kundt are either Kundt or Robinson--Trautmann, and we provide explicit Kundt and Robinson--Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.

  1. Hiding an Inconvenient Truth : Lies and Vagueness

    NARCIS (Netherlands)

    Serra Garcia, M.; van Damme, E.E.C.; Potters, J.J.M.

    2010-01-01

    When truth conflicts with e¢ ciency, can verbal communication destroy efficiency? Or are lies or vagueness used to hide inconvenient truths? We consider a sequential 2-player public good game in which the leader has private information about the value of the public good. This value can be low, high,

  2. Are 'Lying Compositions' Detrimental To Student Growth?

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    @@ A greater number of primary school students are inventing stories and telling lies when they are supposed to be writing about personal experiences. The Chengdu Business Daily said, of 40 pupils in a grade-four class, 30 wrote about how they struggled with human traffickers or thieves, and 26 pupils admitted they made the stories up.

  3. Lie Algebra of Noncommutative Inhomogeneous Hopf Algebra

    CERN Document Server

    Lagraa, M

    1997-01-01

    We construct the vector space dual to the space of right-invariant differential forms construct from a first order differential calculus on inhomogeneous quantum group. We show that this vector space is equipped with a structure of a Hopf algebra which closes on a noncommutative Lie algebra satisfying a Jacobi identity.

  4. SAYD modules over Lie-Hopf algebras

    CERN Document Server

    Rangipour, B

    2011-01-01

    In this paper a general van Est type isomorphism is established. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one correspondence between stable-anti-Yetter-Drinfeld (SAYD) modules over the total Lie algebra and SAYD modules over the associated Hopf algebra. In contrast to the non-general case done in our previous work, here the van Est isomorphism is found at the first level of a natural spectral sequence, rather than at the level of complexes. It is proved that the Connes-Moscovici Hopf algebras do not admit any finite dimensional SAYD modules except the unique one-dimensional one found by Connes- Moscovici in 1998. This is done by extending our techniques to work with the infinite dimensional Lie algebra of formal vector fields. At the end, the one to one correspondence is applied to construct a highly nontrivial four dimensional SAYD module over the Schwarzian Hopf algebra. We then illustrate...

  5. Happiness lies somewhere in your brain

    Institute of Scientific and Technical Information of China (English)

    梅寒

    2007-01-01

    <正> When I was a kid,I defined happinessas being able to afford anything that was de-sired and thus I came up with the conclusionthat happiness lies in the possession of mon-ey.Time turned me tall and smart,also,able

  6. Lie algebras and linear differential equations.

    Science.gov (United States)

    Brockett, R. W.; Rahimi, A.

    1972-01-01

    Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.

  7. On Split Lie Triple Systems II

    Indian Academy of Sciences (India)

    Antonio J Calderón Martín; M Forero Piulestán

    2010-04-01

    In [4] it is studied that the structure of split Lie triple systems with a coherent 0-root space, that is, satisfying $[T_0,T_0,T]=0$ and $[T_0,T_,T_0]≠ 0$ for any nonzero root and where $T_0$ denotes the 0-root space and $T_$ the -root space, by showing that any of such triple systems with a symmetric root system is of the form $T=\\mathcal{U}+\\sum_j I_j$ with $\\mathcal{U}$ a subspace of the 0-root space $T_0$ and any $I_j$ a well described ideal of , satisfying $[I_j,T,I_k]=0$ if $j≠ k$. It is also shown in [4] that under certain conditions, a split Lie triple system with a coherent 0-root space is the direct sum of the family of its minimal ideals, each one being a simple split Lie triple system, and the simplicity of is characterized. In the present paper we extend these results to arbitrary split Lie triple systems with no restrictions on their 0-root spaces.

  8. SAYD Modules over Lie-Hopf Algebras

    Science.gov (United States)

    Rangipour, Bahram; Sütlü, Serkan

    2012-11-01

    In this paper a general van Est type isomorphism is proved. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one correspondence between stable-anti-Yetter-Drinfeld (SAYD) modules over the total Lie algebra and those modules over the associated Hopf algebra. In contrast to the non-general case done in our previous work, here the van Est isomorphism is proved at the first level of a natural spectral sequence, rather than at the level of complexes. It is proved that the Connes-Moscovici Hopf algebras do not admit any finite dimensional SAYD modules except the unique one-dimensional one found by Connes-Moscovici in 1998. This is done by extending our techniques to work with the infinite dimensional Lie algebra of formal vector fields. At the end, the one to one correspondence is applied to construct a highly nontrivial four dimensional SAYD module over the Schwarzian Hopf algebra. We then illustrate the whole theory on this example. Finally explicit representative cocycles of the cohomology classes for this example are calculated.

  9. Clustered Self Organising Migrating Algorithm for the Quadratic Assignment Problem

    Science.gov (United States)

    Davendra, Donald; Zelinka, Ivan; Senkerik, Roman

    2009-08-01

    An approach of population dynamics and clustering for permutative problems is presented in this paper. Diversity indicators are created from solution ordering and its mapping is shown as an advantage for population control in metaheuristics. Self Organising Migrating Algorithm (SOMA) is modified using this approach and vetted with the Quadratic Assignment Problem (QAP). Extensive experimentation is conducted on benchmark problems in this area.

  10. Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.

    Science.gov (United States)

    Wang, Di; Kleinberg, Robert D

    2009-11-28

    Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.

  11. A new heuristic for the quadratic assignment problem

    OpenAIRE

    Zvi Drezner

    2002-01-01

    We propose a new heuristic for the solution of the quadratic assignment problem. The heuristic combines ideas from tabu search and genetic algorithms. Run times are very short compared with other heuristic procedures. The heuristic performed very well on a set of test problems.

  12. HOMOCLINIC CYCLES OF A QUADRATIC SYSTEM DESCRIBED BY QUARTIC CURVES

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    This paper is devoted to discussing the topological classification of the quartic invariant algebraic curves for a quadratic system. We obtain sufficient and necessary conditions which ensure that the homoclinic cycle of the system is defined by the quartic invariant algebraic curve. Finally, the corresponding global phase diagrams are drawn.

  13. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

    DEFF Research Database (Denmark)

    Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip

    2016-01-01

    We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...

  14. Positivity and storage functions for quadratic differential forms

    NARCIS (Netherlands)

    Trentelman, Hendrikus; Willems, Jan C.

    1996-01-01

    Differential equations and one-variable polynomial matrices play an essential role in describing dynamics of systems. When studying functions of the dynamical variables or specifying performance criteria in optimal control, we invariably encounter quadratic expressions in the variables and their der

  15. Canonical realization of Bondi-Metzner-Sachs symmetry: Quadratic Casimir

    Science.gov (United States)

    Gomis, Joaquim; Longhi, Giorgio

    2016-01-01

    We study the canonical realization of Bondi-Metzner-Sacks symmetry for a massive scalar field introduced by Longhi and Materassi [J. Math. Phys. 40, 480 (1999)]. We construct an invariant scalar product for the generalized momenta. As a consequence we introduce a quadratic Casimir with the supertranslations.

  16. A Unified Approach to Teaching Quadratic and Cubic Equations.

    Science.gov (United States)

    Ward, A. J. B.

    2003-01-01

    Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

  17. Second Order Backward Stochastic Differential Equations with Quadratic Growth

    CERN Document Server

    Dylan, Possamai

    2012-01-01

    We prove the existence and uniqueness of a solution for one-dimensionnal second order backward stochastic differential equations introduced by Soner, Touzi and Zhang (2010), with a bounded terminal condition and a generator which is continuous with quadratic growth in z. We also prove a Feyman-Kac formula and a probabilistic representation for fully nonlinear PDEs in this setting.

  18. Bandit-Inspired Memetic Algorithms for Solving Quadratic Assignment Problems

    NARCIS (Netherlands)

    Puglierin, Francesco; Drugan, Madalina M.; Wiering, Marco

    2013-01-01

    In this paper we propose a novel algorithm called the Bandit-Inspired Memetic Algorithm (BIMA) and we have applied it to solve different large instances of the Quadratic Assignment Problem (QAP). Like other memetic algorithms, BIMA makes use of local search and a population of solutions. The novelty

  19. The Quadratic Assignment Problem is Easy for Robinsonian Matrices

    NARCIS (Netherlands)

    Laurent, M.; Seminaroti, M.

    2014-01-01

    We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form QAP(A;B), by showing that the identity permutation is optimal when A and B are respectively a Robinson similarity and dissimilarity matrix and one of A or B is a Toeplitz matrix. A Robinson (dis)

  20. A bilinear programming solution to the quadratic assignment problem

    NARCIS (Netherlands)

    J.F. Kaashoek (Johan); J.H.P. Paelinck (Jean)

    1999-01-01

    textabstractThe quadratic assignment problem (QAP) or maximum acyclical graph problem is well documented (see e.g. Pardalos and Wolkowicz, 1994). One of the authors has published some material, in which it was tried, by structuring the problem additionally, to bring it as closely as possible in the

  1. The quadratic assignment problem is easy for robinsonian matrices

    NARCIS (Netherlands)

    Laurent, M.; Seminaroti, M.

    2015-01-01

    We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans–Beckman form QAP(A,B), by showing that the identity permutation is optimal when AA and BB are respectively a Robinson similarity and dissimilarity matrix and one of AA or BB is a Toeplitz matrix. A Robinson (

  2. Solving quadratic programming problems by delayed projection neural network.

    Science.gov (United States)

    Yang, Yongqing; Cao, Jinde

    2006-11-01

    In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network.

  3. A Result on Output Feedback Linear Quadratic Control

    NARCIS (Netherlands)

    Engwerda, J.C.; Weeren, A.J.T.M.

    2006-01-01

    In this note we consider the static output feedback linear quadratic control problem.We present both necessary and sufficient conditions under which this problem has a solution in case the involved cost depend only on the output and control variables.This result is used to present both necessary and

  4. Nonlocal description of X waves in quadratic nonlinear materials

    DEFF Research Database (Denmark)

    Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole

    2006-01-01

    We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...

  5. ON WEIGHTED GENERALIZED FUNCTIONS ASSOCIATED WITH QUADRATIC FORMS

    Directory of Open Access Journals (Sweden)

    E. L. Shishkina

    2016-12-01

    Full Text Available In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with the Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with the Bessel operator.

  6. Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales

    Institute of Scientific and Technical Information of China (English)

    ZHANG JI; LIU ZHEN-XIN

    2011-01-01

    In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△ = A(t)x on time scales.Moreover, for the nonlinear perturbed equation x△ = A(t)x + f(t,x) we give the instability of the zero solution when f is sufficiently small.

  7. Radar Rainfall Estimation using a Quadratic Z-R equation

    Science.gov (United States)

    Hall, Will; Rico-Ramirez, Miguel Angel; Kramer, Stefan

    2016-04-01

    The aim of this work is to test a method that enables the input of event based drop size distributions to alter a quadratic reflectivity (Z) to rainfall (R) equation that is limited by fixed upper and lower points. Results will be compared to the Marshall-Palmer Z-R relation outputs and validated by a network of gauges and a single polarisation weather radar located close to Essen, Germany. The time window over which the drop size distribution measurements will be collected is varied to note any effect on the generated quadratic Z-R relation. The new quadratic algorithm shows some distinct improvement over the Marshall-Palmer relationship through multiple events. The inclusion of a minimum number of Z-R points helped to decrease the associated error by defaulting back to the Marshall-Palmer equation if the limit was not reached. More research will be done to discover why the quadratic performs poorly in some events as there appears to be little correlation between number of drops or mean rainfall amount and the associated error. In some cases it seems the spatial distribution of the disdrometers has a significant effect as a large percentage of the rain bands pass to the north of two of the three disdrometers, frequently in a slightly north-easterly direction. However during widespread precipitation events the new algorithm works very well with reductions compared to the Marshall-Palmer relation.

  8. ANOTHER LOOK AT LINEAR-QUADRATIC OPTIMIZATION PROBLEMS OVER TIME

    NARCIS (Netherlands)

    NIEUWENHUIS, JW

    1995-01-01

    We will study deterministic quadratic optimization problems over time with linear constraints by means of the behavioral approach of linear systems as developed by Willems (1986, 1989). We will start with a simple example from economics and embed this in a general framework. Then we will develop the

  9. Entanglement entropy of fermionic quadratic band touching model

    Science.gov (United States)

    Chen, Xiao; Cho, Gil Young; Fradkin, Eduardo

    2014-03-01

    The entanglement entropy has been proven to be a useful tool to diagnose and characterize strongly correlated systems such as topologically ordered phases and some critical points. Motivated by the successes, we study the entanglement entropy (EE) of a fermionic quadratic band touching model in (2 + 1) dimension. This is a fermionic ``spinor'' model with a finite DOS at k=0 and infinitesimal instabilities. The calculation on two-point correlation functions shows that a Dirac fermion model and the quadratic band touching model both have the asymptotically identical behavior in the long distance limit. This implies that EE for the quadratic band touching model also has an area law as the Dirac fermion. This is in contradiction with the expectation that dense fermi systems with a finite DOS should exhibit LlogL violations to the area law of entanglement entropy (L is the length of the boundary of the sub-region) by analogy with the Fermi surface. We performed numerical calculations of entanglement entropies on a torus of the lattice models for the quadratic band touching point and the Dirac fermion to confirm this. The numerical calculation shows that EE for both cases satisfy the area law. We further verify this result by the analytic calculation on the torus geometry. This work was supported in part by the NSF grant DMR-1064319.

  10. Finding the Best Quadratic Approximation of a Function

    Science.gov (United States)

    Yang, Yajun; Gordon, Sheldon P.

    2011-01-01

    This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

  11. Kronecker limit formula for real quadratic number fields(III)

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    For a kind of L-function of the real quadratic number fields, we prove a Kronecker limit formula which generalized a result of Hecke. And taking an example we give an interesting identity on a fundamental unit of such a field.

  12. A realised volatility measurement using quadratic variation and ...

    African Journals Online (AJOL)

    the instantaneous volatility does not change too much as a result of a weighted average ... method is also based on quadratic variation theory, but the underlying return model is ..... [3] Barndorff-Nielsen OE & Shepard N, 2001, Non-Gaussian ...

  13. The strong law of large numbers for random quadratic forms

    NARCIS (Netherlands)

    Mikosch, T

    1996-01-01

    The paper establishes strong laws of large numbers for the quadratic forms [GRAPHICS] and the bilinear forms [GRAPHICS] where X = (X(n)) is a sequence of independent random variables and Y = (Y-n) is an independent copy of it. In the case of independent identically distributed symmetric p-stable ran

  14. Confidence set interference with a prior quadratic bound. [in geophysics

    Science.gov (United States)

    Backus, George E.

    1989-01-01

    Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

  15. Optimization with quadratic support functions in nonconvex smooth optimization

    Science.gov (United States)

    Khamisov, O. V.

    2016-10-01

    Problem of global minimization of twice continuously differentiable function with Lipschitz second derivatives over a polytope is considered. We suggest a branch and bound method with polytopes as partition elements. Due to the Lipschitz property of the objective function we can construct a quadratic support minorant at each point of the feasible set. Global minimum of of this minorant provides a lower bound of the objective over given partition subset. The main advantage of the suggested method consists in the following. First quadratic minorants usually are nonconvex and we have to solve auxiliary global optimization problem. This problem is reduced to a mixed 0-1 linear programming problem and can be solved by an advanced 0-1 solver. Then we show that the quadratic minorants are getting convex as soon as partition elements are getting smaller in diameter. Hence, at the final steps of the branch and bound method we solve convex auxiliary quadratic problems. Therefore, the method accelerates when we are close to the global minimum of the initial problem.

  16. Stochastic level-value approximation for quadratic integer convex programming

    Institute of Scientific and Technical Information of China (English)

    PENG Zheng; WU Dong-hua

    2008-01-01

    We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and re-port some numerical results to illuminate its effectiveness.

  17. Semismooth Newton method for quadratic programs with bound constraints

    Science.gov (United States)

    Daryina, A. N.; Izmailov, A. F.

    2009-10-01

    Convex quadratic programs with bound constraints are proposed to be solved by applying a semismooth Newton method to the corresponding variational inequality. Computational experiments demonstrate that, for strongly convex problems, this approach can be considerably more efficient than more traditional approaches.

  18. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

    DEFF Research Database (Denmark)

    Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip

    2016-01-01

    We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...

  19. Sub-quadratic decoding of one-point hermitian codes

    DEFF Research Database (Denmark)

    Nielsen, Johan Sebastian Rosenkilde; Beelen, Peter

    2015-01-01

    We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power...

  20. Cosmological Vorticity in a Gravity with Quadratic Order Curvature Couplings

    CERN Document Server

    Hwang, J

    1998-01-01

    We analyse the evolution of the rotational type cosmological perturbation in a gravity with general quadratic order gravitational coupling terms. The result is expressed independently of the generalized nature of the gravity theory, and is simply interpreted as a conservation of the angular momentum.

  1. The strong law of large numbers for random quadratic forms

    NARCIS (Netherlands)

    Mikosch, T

    1996-01-01

    The paper establishes strong laws of large numbers for the quadratic forms [GRAPHICS] and the bilinear forms [GRAPHICS] where X = (X(n)) is a sequence of independent random variables and Y = (Y-n) is an independent copy of it. In the case of independent identically distributed symmetric p-stable

  2. Dimension of the $c$-nilpotent multiplier of Lie algebras

    Indian Academy of Sciences (India)

    MEHDI ARASKHAN; MOHAMMAD REZA RISMANCHIAN

    2016-08-01

    The purpose of this paper is to derive some inequalities for dimension of the $c$-nilpotent multiplier of finite dimensional Lie algebras and their factor Lie algebras. We further obtain an inequality between dimensions of $c$-nilpotent multiplier of Lie algebra $L$ and tensor product of a central ideal by its abelianized factor Lie algebra

  3. Legitimate lies : The relationship between omission, commission, and cheating

    NARCIS (Netherlands)

    Pittarello, Andrea; Rubaltelli, Enrico; Motro, Daphna

    2016-01-01

    Across four experiments, we show that when people can serve their self-interest, they are more likely to refrain from reporting the truth ( lie of omission) than actively lie ( lie of commission). We developed a novel online "Heads or Tails" task in which participants can lie to win a monetary prize

  4. Whittaker categories and strongly typical Whittaker modules for Lie superalgebras

    CERN Document Server

    Bagci, Irfan; Wiesner, Emilie

    2012-01-01

    Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra according to the action of an appropriate sub-superalgebra; and, for basic classical Lie superalgebras of type I, a description of the strongly typical simple Whittaker modules.

  5. A Local Characterization of Lie Homomorphisms of Nest Algebras

    Institute of Scientific and Technical Information of China (English)

    YANG Miao-xia; ZHANG Jian-hua

    2014-01-01

    In this paper, linear maps preserving Lie products at zero points on nest algebras are studied. It is proved that every linear map preserving Lie products at zero points on any finite nest algebra is a Lie homomorphism. As an application, the form of a linear bijection preserving Lie products at zero points between two finite nest algebras is obtained.

  6. Lie symmetries for equations in conformal geometries

    CERN Document Server

    Hansraj, S; Msomi, A M; Govinder, K S

    2005-01-01

    We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been found in practice. We use the method of Lie analysis of differential equations to obtain new group invariant solutions to conformally related Petrov type D spacetimes. Four cases arise depending on the nature of the Lie symmetry generator. In three cases we are in a position to solve the master field equation in terms of elementary functions. In the fourth case special solutions in terms of Bessel functions are obtained. These solutions contain known models as special cases.

  7. Geodesic models generated by Lie symmetries

    CERN Document Server

    Abebe, G Z; Govinder, K S

    2014-01-01

    We study the junction condition relating the pressure to the heat flux at the boundary of a shearing and expanding spherically symmetric radiating star when the fluid particles are travelling in geodesic motion. The Lie symmetry generators that leave the junction condition invariant are identified and the optimal system is generated. We use each element of the optimal system to transform the partial differential equation to an ordinary differential equation. New exact solutions, which are group invariant under the action of Lie point infinitesimal symmetries, are found. We obtain families of traveling wave solutions and self-similar solutions, amongst others. The gravitational potentials are given in terms of elementary functions, and the line elements can be given explicitly in all cases. We show that the Friedmann dust model is regained as a special case, and we can connect our results to earlier investigations.

  8. Analytic factorization of Lie group representations

    DEFF Research Database (Denmark)

    Gimperlein, Heiko; Krötz, Bernhard; Lienau, Christoph

    2012-01-01

    For every moderate growth representation (p,E)(p,E) of a real Lie group G on a Fréchet space, we prove a factorization theorem of Dixmier–Malliavin type for the space of analytic vectors E¿E¿. There exists a natural algebra of superexponentially decreasing analytic functions A(G)A(G), such that E......¿=¿(A(G))E¿E¿=¿(A(G))E¿. As a corollary we obtain that E¿E¿ coincides with the space of analytic vectors for the Laplace–Beltrami operator on G.......For every moderate growth representation (p,E)(p,E) of a real Lie group G on a Fréchet space, we prove a factorization theorem of Dixmier–Malliavin type for the space of analytic vectors E¿E¿. There exists a natural algebra of superexponentially decreasing analytic functions A(G)A(G), such that E...

  9. Harmonic analysis on exponential solvable Lie groups

    CERN Document Server

    Fujiwara, Hidenori

    2015-01-01

    This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated alge...

  10. Constructions of Lie algebras and their modules

    CERN Document Server

    Seligman, George B

    1988-01-01

    This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. T...

  11. ON THE PRIMARY DECOMPOSITION THEOREM OF MODULAR LIE SUPERALGEBRAS

    Institute of Scientific and Technical Information of China (English)

    CHEN LIANGYUN; MENG DAOJI

    2005-01-01

    This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primry decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras (see [5, 6]). Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.

  12. Abstract Lie groups and locally compact topological groups

    Directory of Open Access Journals (Sweden)

    Jacek Lech

    2004-05-01

    Full Text Available We introduce a notion of abstract Lie group by means of the mapping which plays the role of the evolution operator. We show some basic properties of such groups very similar to the fundamentals of the infinite dimensional Lie theory. Next we give remarkable examples of abstract Lie groups which are not necessarily usual Lie groups. In particular, by making use of Yamabe theorem we prove that any locally compact topological group admits the structure of abstract Lie group and that the Lie algebra and the exponential mapping of it coincide with those determined by the Lie group structure.

  13. k-symplectic formalism on Lie algebroids

    Energy Technology Data Exchange (ETDEWEB)

    De Leon, M; De Diego, D Martin [Instituto de Ciencias Matematicas (CSIC-UAM-UC3M-UCM) C/Serrano 123, 28006 Madrid (Spain); Salgado, M; Vilarino, S [Departamento de XeometrIa e TopoloxIa, Facultade de Matematicas, Universidade de Santiago de Compostela, 15782-Santiago de Compostela (Spain)], E-mail: mdeleon@imaff.cfmac.csic.es, E-mail: d.martin@imaff.cfmac.csic.es, E-mail: modesto.salgado@usc.es, E-mail: silvia.vilarino@usc.es

    2009-09-25

    In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of k-symplectic geometry. We discuss the relation between the Lagrangian and Hamiltonian descriptions through a convenient notion of Legendre transformation. The theory is a natural generalization of the standard one; in addition, other interesting examples are studied, in particular, systems with symmetry and Poisson-sigma models.

  14. How to Lie with Bad Data

    OpenAIRE

    De Veaux, Richard D.; Hand, David J.

    2005-01-01

    As Huff’s landmark book made clear, lying with statistics can be accomplished in many ways. Distorting graphics, manipulating data or using biased samples are just a few of the tried and true methods. Failing to use the correct statistical procedure or failing to check the conditions for when the selected method is appropriate can distort results as well, whether the motives of the analyst are honorable or not. Even when the statistical procedure and motives are correct, bad data can produce ...

  15. Lies, Incentives and Self-confidence

    OpenAIRE

    Maggian, Valeria

    2013-01-01

    The present thesis is composed by three chapters, each of them making contributions to three distinct topics in behavioral Economics. The chapters can thus be read independently from each other. The first chapter concerns an experimental analysis which aim is to examine the development of social preferences with respect to age and how they are related with lying behavior of children. The second chapter investigates the role of reciprocity in exacerbating inefficient and opportunistic behavior...

  16. Spherical functions on affine Lie groups

    CERN Document Server

    Etingof, P; Kirillov, A A; Pavel Etingof; Igor Frenkel; Alexander Kirillov Jr

    1994-01-01

    We show that the space of holomorphic functions of a fixed degree on an affine Lie group which take values in a finite-dimensional representation of this group and are equivariant with respect to (twisted) conjugacy coin- cides with the space of conformal blocks of the Wess-Zumino-Witten conformal field theory on an elliptic curve with punctures, or, equivalently,with the space of states of the Chern-Simons topological field theory in genus 1. This provides a group-theoretic realization of the Segal modular functor for elliptic curves. We also show that the the radial part of the second order Laplace operator on an affine Lie group acting in the space of equivariant functions coincides with the operator defining the Knizhnik-Zamolodchikov connection on conformal blocks on elliptic curves, and its eigenfunctions coincide with the correlation functions of conformal blocks. At the critical value of the degree (minus the dual Coxeter number of the underlying simple Lie algebra) there exist higher order Laplace op...

  17. COMPLETE LIE ALGEBRAS WITH l-STEP NILPOTENT RADICALS

    Institute of Scientific and Technical Information of China (English)

    高永存; 孟道冀

    2002-01-01

    The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by using the modules of simple Lie algebras. The quotient algebras of this new constructed Lie algebras are non-solvable complete Lie algebras with l-step nilpotent radicals.

  18. Lie algebras with given properties of subalgebras and elements

    CERN Document Server

    Zusmanovich, Pasha

    2011-01-01

    Results about the following classes of finite-dimensional Lie algebras over a field of characteristic zero are presented: anisotropic (i.e., Lie algebras for which each adjoint operator is semisimple), regular (i.e., Lie algebras in which each nonzero element is regular in the sense of Bourbaki), minimal nonabelian (i.e., nonabelian Lie algebras all whose proper subalgebras are abelian), and algebras of depth 2 (i.e., Lie algebras all whose proper subalgebras are abelian or minimal nonabelian).

  19. Classification of filiform Lie algebras of order 3

    Science.gov (United States)

    Navarro, Rosa María

    2016-12-01

    Lie algebras of order 3 constitute a generalization of Lie algebras and superalgebras. Throughout this paper the classification problem of filiform Lie algebras of order 3 is considered and therefore this work is a continuation papers seen in the literature. We approach this classification by extending Vergne's result for filiform Lie algebras and by considering algebras of order 3 of high nilindex. We find the expression of the law to which any elementary filiform Lie algebra of order 3 is isomorphic.

  20. Lie color 代数的商代数%Algebras of quotients of Lie color algebras

    Institute of Scientific and Technical Information of China (English)

    裴凤; 周建华

    2004-01-01

    介绍了Lie color 代数的一些性质,如素性、半素性、非退化性等.给出了Lie color 代数的商代数以及弱商代数的概念,并把Lie color 代数的素性和半素性推广到它的商代数上.利用没有非零零化子的理想对Lie color 代数的商代数进行刻画,证明了:若L是Lie color 代数Q的子代数,则Q是L的商代数当且仅当Q理想吸收于L.通过具体构造证明了每一个半素Lie color 代数都有极大商代数,并给出这个极大商代数的等价刻画.

  1. Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson-Lie groups

    Science.gov (United States)

    Abedi-Fardad, J.; Rezaei-Aghdam, A.; Haghighatdoost, Gh.

    2017-01-01

    We classify all four-dimensional real Lie bialgebras of symplectic type and obtain the classical r-matrices for these Lie bialgebras and Poisson structures on all the associated four-dimensional Poisson-Lie groups. We obtain some new integrable models where a Poisson-Lie group plays the role of the phase space and its dual Lie group plays the role of the symmetry group of the system.

  2. MODIFIED BERNOULLI ITERATION METHODS FOR QUADRATIC MATRIX EQUATION

    Institute of Scientific and Technical Information of China (English)

    Zhong-Zhi Bai; Yong-Hua Gao

    2007-01-01

    We construct a modified Bernoulli iteration method for solving the quadratic matrix equation AX2+BX+C=0,where A,B and C are square matrices.This method is motivated from the Gauss-Seidel iteration for solving linear systems and the ShermanMorrison-Woodbury formula for updating matrices.Under suitable conditions, we prove the local linear convergence of the Dew method.An algorithm is presented to find the solution of the quadratic matrix equation and some numerical results are given to show the feasibility and the effectiveness of the algorithm.In addition,we also describe and analyze the block version of the modified Bernoulli iteration method.

  3. Gravitomagnetic effects in quadratic gravity with a scalar field

    CERN Document Server

    Finch, Andrew

    2016-01-01

    The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.

  4. Induced motion of domain walls in multiferroics with quadratic interaction

    Energy Technology Data Exchange (ETDEWEB)

    Gerasimchuk, Victor S., E-mail: viktor.gera@gmail.com [National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremohy Avenue 37, 03056 Kiev (Ukraine); Shitov, Anatoliy A., E-mail: shitov@mail.ru [Donbass National Academy of Civil Engineering, Derzhavina Street 2, 86123 Makeevka, Donetsk Region (Ukraine)

    2013-10-15

    We theoretically study the dynamics of 180-degree domain wall of the ab-type in magnetic materials with quadratic magnetoelectric interaction in external alternating magnetic and electric fields. The features of the oscillatory and translational motions of the domain walls and stripe structures depending on the parameters of external fields and characteristics of the multiferroics are discussed. The possibility of the domain walls drift in a purely electric field is established. - Highlights: • We study DW and stripe DS in multiferroics with quadratic magnetoelectric interaction. • We build up the theory of oscillatory and translational (drift) DW and DS motion. • DW motion can be caused by crossed alternating electric and magnetic fields. • DW motion can be caused by alternating “pure” electric field. • DW drift velocity is formed by the AFM and Dzyaloshinskii interaction terms.

  5. Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates

    CERN Document Server

    Rand, Alexander; Bajaj, Chandrajit

    2011-01-01

    We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon satisfying simple geometric criteria, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n+1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called `serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

  6. QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

    Science.gov (United States)

    Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

    2014-01-01

    We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

  7. Quadratic differentials in low genus: exceptional and non-varying

    CERN Document Server

    Chen, Dawei

    2012-01-01

    We give an algebraic way of distinguishing the components of the exceptional strata of quadratic differentials in genus three and four. The complete list of these strata is (9, -1), (6,3,-1), (3,3,3, -1) in genus three and (12), (9,3), (6,6), (6,3,3) and (3,3,3,3) in genus four. This result is part of a more general investigation of disjointness of Teichmueller curves with divisors of Brill-Noether type on the moduli space of curves. As a result we show that for many strata of quadratic differentials in low genus the sum of Lyapunov exponents for the Teichmueller geodesic flow is the same for all Teichmueller curves in that stratum.

  8. QUADRATIC INVARIANTS AND SYMPLECTIC STRUCTURE OF GENERAL LINEAR METHODS

    Institute of Scientific and Technical Information of China (English)

    Ai-guo Xiao; Shou-fu Li; Min Yang

    2001-01-01

    In this paper, we present some invariants and conservation laws of general linear methods applied to differential equation systems. We show that the quadratic invariants and symplecticity of the systems can be extended to general linear methods by a tensor product, and show that general linear methods with the matrix M=0 inherit in an extended sense the quadratic invariants possessed by the differential equation systems being integrated and preserve in an extended sense the symplectic structure of the phase space in the integration of Hamiltonian systems. These unify and extend existing relevant results on Runge-Kutta methods, linear multistep methods and one-leg methods. Finally, as special cases of general linear methods, we examine multistep Runge-Kutta methods, one-leg methods and linear two-step methods in detail.

  9. Large Deviation Principle for Benedicks-Carleson Quadratic Maps

    Science.gov (United States)

    Chung, Yong Moo; Takahasi, Hiroki

    2012-11-01

    Since the pioneering works of Jakobson and Benedicks & Carleson and others, it has been known that a positive measure set of quadratic maps admit invariant probability measures absolutely continuous with respect to Lebesgue. These measures allow one to statistically predict the asymptotic fate of Lebesgue almost every initial condition. Estimating fluctuations of empirical distributions before they settle to equilibrium requires a fairly good control over large parts of the phase space. We use the sub-exponential slow recurrence condition of Benedicks & Carleson to build induced Markov maps of arbitrarily small scale and associated towers, to which the absolutely continuous measures can be lifted. These various lifts together enable us to obtain a control of recurrence that is sufficient to establish a level 2 large deviation principle, for the absolutely continuous measures. This result encompasses dynamics far from equilibrium, and thus significantly extends presently known local large deviations results for quadratic maps.

  10. On Jannsen's conjecture for Hecke characters of imaginary quadratic fields

    CERN Document Server

    Bars, Francesc

    2007-01-01

    We present a collection of results on a conjecture of Jannsen about the $p$-adic realizations associated to Hecke characters over an imaginary quadratic field $K$ of class number 1. The conjecture is easy to check for Galois groups purely of local type. We prove the conjecture under a geometric regularity condition for the imaginary quadratic field $K$ at $p$, which is related to the property that a global Galois group is purely of local type. Without this regularity assumption at $p$, we present a review of the known situations in the critical case and in the non-critical case for the realizations associated to Hecke characters over $K$. We relate the conjecture to the non-vanishing of some concrete non-critical values of the associated $p$-adic $L$-function of the Hecke character. Finally, we prove that the conjecture follows from a general conjecture on Iwasawa theory for almost all Tate twists.

  11. Identity-based signature scheme based on quadratic residues

    Institute of Scientific and Technical Information of China (English)

    CHAI ZhenChuan; CAO ZhenFu; DONG XiaoLei

    2007-01-01

    Identity-based (ID-based) cryptography has drawn great concerns in recent years, and most of ID-based schemes are constructed from bilinear parings. Therefore, ID-based scheme without pairing is of great interest in the field of cryptography. Up to now,there still remains a challenge to construct ID-based signature scheme from quadratic residues. Thus, we aim to meet this challenge by proposing a concrete scheme. In this paper, we first introduce the technique of how to calculate a 2lth root of a quadratic residue, and then give a concrete ID-based signature scheme using such technique.We also prove that our scheme is chosen message and ID secure in the random oracle model, assuming the hardness of factoring.

  12. Time-Inconsistent Stochastic Linear--Quadratic Control

    CERN Document Server

    Hu, Ying; Zhou, Xun Yu

    2011-01-01

    In this paper, we formulate a general time-inconsistent stochastic linear--quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we find an explicit equilibrium control. As an application, we then consider a mean-variance portfolio selection model in a complete financial market where the risk-free rate is a deterministic function of time but all the other market parameters are possibly stochastic processes. Applying the general sufficient condition, we obtain explicit equilibrium strategies when the risk premium is both deterministic and stochastic.

  13. A Special Role of Boolean Quadratic Polytopes among Other Combinatorial Polytopes

    Directory of Open Access Journals (Sweden)

    A. N. Maksimenko

    2016-01-01

    Full Text Available We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set, 3-assignment. For comparing two families of polytopes we use the following method. We say that a family

  14. A new semidefinite programming relaxation for the quadratic assignment problem and its computational perspectives

    NARCIS (Netherlands)

    de Klerk, E.; Sotirov, R.; Truetsch, U.

    2015-01-01

    Recent progress in solving quadratic assignment problems (QAPs) from the QAPLIB (Quadratic Assignment Problem Library) test set has come from mixed-integer linear or quadratic programming models that are solved in a branch-and-bound framework. Semidefinite programming (SDP) bounds for QAPs have also

  15. UNIFORM SUPERAPPROXIMATION OF THE DERIVATIVE OF TETRAHEDRAL QUADRATIC FINITE ELEMENT APPROXIMATION

    Institute of Scientific and Technical Information of China (English)

    Jing-hong Liu; Qi-ding Zhu

    2005-01-01

    In this paper,we will prove the derivative of tetrahedral quadratic finite element approximation is superapproximate to the derivative of the quadratic Lagrange interpolant of the exact solution in the L∞-norm, which can be used to enhance the accuracy of the derivative of tetrahedral quadratic finite element approximation to the derivative of the exact solution.

  16. A Hamiltonian-based solution to the linear quadratic consensus control problem

    NARCIS (Netherlands)

    Weiss, M.

    2012-01-01

    The Linear Quadratic Consensus Control (LQCC) problem is a relaxation of the classical Linear Quadratic Regulation (LQR) problem, that consists of asymptotically driving the state of the system to a "consensus" point in which all coordinates are equal, in such a way that a quadratic cost function on

  17. Quadratic and Cubic Nonlinear Oscillators with Damping and Their Applications

    Science.gov (United States)

    Li, Jibin; Feng, Zhaosheng

    We apply the qualitative theory of dynamical systems to study exact solutions and the dynamics of quadratic and cubic nonlinear oscillators with damping. Under certain parametric conditions, we also consider the van der Waals normal form, Chaffee-Infante equation, compound Burgers-KdV equation and Burgers-KdV equation for explicit representations of kink-profile wave solutions and unbounded traveling wave solutions.

  18. Solving the Quadratic Assignment Problem by a Hybrid Algorithm

    Directory of Open Access Journals (Sweden)

    Aldy Gunawan

    2011-01-01

    Full Text Available This paper presents a hybrid algorithm to solve the Quadratic Assignment Problem (QAP. The proposed algorithm involves using the Greedy Randomized Adaptive Search Procedure (GRASP to obtain an initial solution, and then using a combined Simulated Annealing (SA and Tabu Search (TS algorithm to improve the solution. Experimental results  indicate that the hybrid algorithm is able to obtain good quality solutions for QAPLIB test problems within reasonable computation time.

  19. Developing A Combined Strategy For Solving Quadratic Assignment Problem

    Directory of Open Access Journals (Sweden)

    Faiz Ahyaningsih

    2015-08-01

    Full Text Available Abstract The quadratic assigment problem QAP is one of the most interesting and most challenging combinatorial optimization problems in existence. In this paper we propose a random point strategy to get a starting point and then we use a combination methods to get optimal solution. As a computational experience weve solved QAP 30 x 30 adopted from Nugent and backboard wiring problem 42 amp61620 42 adopted from Skorin-Kapov.

  20. A new genetic representation for quadratic assignment problem

    Directory of Open Access Journals (Sweden)

    Kratica Jozef

    2011-01-01

    Full Text Available In this paper, we propose a new genetic encoding for well known Quadratic Assignment Problem (QAP. The new encoding schemes are implemented with appropriate objective function and modified genetic operators. The numerical experiments were carried out on the standard QAPLIB data sets known from the literature. The presented results show that in all cases proposed genetic algorithm reached known optimal solutions in reasonable time.

  1. Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

    Science.gov (United States)

    Acikmese, Ahmet Behcet; Corless, Martin

    2004-01-01

    We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

  2. A Riccati approach for constrained linear quadratic optimal control

    Science.gov (United States)

    Sideris, Athanasios; Rodriguez, Luis A.

    2011-02-01

    An active-set method is proposed for solving linear quadratic optimal control problems subject to general linear inequality path constraints including mixed state-control and state-only constraints. A Riccati-based approach is developed for efficiently solving the equality constrained optimal control subproblems generated during the procedure. The solution of each subproblem requires computations that scale linearly with the horizon length. The algorithm is illustrated with numerical examples.

  3. Linear Quadratic Controller with Fault Detection in Compact Disk Players

    DEFF Research Database (Denmark)

    Vidal, Enrique Sanchez; Hansen, K.G.; Andersen, R.S.

    2001-01-01

    The design of the positioning controllers in Optical Disk Drives are today subjected to a trade off between an acceptable suppression of external disturbances and an acceptable immunity against surfaces defects. In this paper an algorithm is suggested to detect defects of the disk surface combined...... with an observer and a Linear Quadratic Regulator. As a result, the mentioned trade off is minimized and the playability of the tested compact disk player is considerably enhanced....

  4. On a linear-quadratic problem with Caputo derivative

    Directory of Open Access Journals (Sweden)

    Dariusz Idczak

    2016-01-01

    Full Text Available In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.

  5. Information sets as permutation cycles for quadratic residue codes

    Directory of Open Access Journals (Sweden)

    Richard A. Jenson

    1982-01-01

    Full Text Available The two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1,   (p+1/2] extended binary quadratic residue code, O(p, properly contains PSL(2,p. These codes have some of their information sets represented as permutation cycles from Aut(Q(p. Analysis proves that all information sets of Q(7 are so represented but those of Q(23 are not.

  6. A quadratic rate of asymptotic regularity for CAT(0)-spaces

    OpenAIRE

    Leustean, Laurentiu

    2005-01-01

    In this paper we obtain a quadratic bound on the rate of asymptotic regularity for the Krasnoselski-Mann iterations of nonexpansive mappings in CAT(0)-spaces, whereas previous results guarantee only exponential bounds. The method we use is to extend to the more general setting of uniformly convex hyperbolic spaces a quantitative version of a strengthening of Groetsch's theorem obtained by Kohlenbach using methods from mathematical logic (so-called ``proof mining'').

  7. Adomian solution of a nonlinear quadratic integral equation

    Directory of Open Access Journals (Sweden)

    E.A.A. Ziada

    2013-04-01

    Full Text Available We are concerned here with a nonlinear quadratic integral equation (QIE. The existence of a unique solution will be proved. Convergence analysis of Adomian decomposition method (ADM applied to these type of equations is discussed. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of Adomian’s series solution. Two methods are used to solve these type of equations; ADM and repeated trapezoidal method. The obtained results are compared.

  8. Almost-Riemannian Geometry on Lie Groups

    OpenAIRE

    Ayala, Victor; Jouan, Philippe

    2015-01-01

    A simple Almost-Riemmanian Structure on a Lie group G is defined by a linear vector field and dim(G)-1 left-invariant ones. We state results about the singular locus, the abnormal extremals and the desingularization of such ARS's, and these results are illustrated by examples on the 2D affine and the Heisenberg groups.These ARS's are extended in two ways to homogeneous spaces, and a necessary and sufficient condition for an ARS on a manifold to be equivalent to a general ARS on a homogeneous ...

  9. The graded Lie algebra of general relativity

    CERN Document Server

    Reiterer, Michael

    2014-01-01

    We construct a graded Lie algebra in which a solution to the vacuum Einstein equations is any element of degree 1 whose bracket with itself is zero. Each solution generates a cochain complex, whose first cohomology is linearized gravity about that solution. We gauge-fix to get a smaller cochain complex with the same cohomologies (deformation retraction). The new complex is much smaller, it consists of the solution spaces of linear homogeneous wave equations (symmetric hyperbolic equations). The algorithm that produces these gauges and wave equations is both for linearized gravity and the full Einstein equations. The gauge groupoid is the groupoid of rank 2 complex vector bundles.

  10. New sequential quadratic programming algorithm with consistent subproblems

    Institute of Scientific and Technical Information of China (English)

    贺国平; 高自友; 赖炎连

    1997-01-01

    One of the most interesting topics related to sequential quadratic programming algorithms is how to guarantee the consistence of all quadratic programming subproblems. In this decade, much work trying to change the form of constraints to obtain the consistence of the subproblems has been done The method proposed by De O. Panto-ja J F A and coworkers solves the consistent problem of SQP method, and is the best to the authors’ knowledge. However, the scale and complexity of the subproblems in De O. Pantoja’s work will be increased greatly since all equality constraints have to be changed into absolute form A new sequential quadratic programming type algorithm is presented by means of a special ε-active set scheme and a special penalty function. Subproblems of the new algorithm are all consistent, and the form of constraints of the subproblems is as simple as one of the general SQP type algorithms. It can be proved that the new method keeps global convergence and local superhnear convergence.

  11. Measurement of quadratic electrogyration effect in castor oil

    Science.gov (United States)

    Izdebski, Marek; Ledzion, Rafał; Górski, Piotr

    2015-07-01

    This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.

  12. Parameter Optimization of Linear Quadratic Controller Based on Genetic Algorithm

    Institute of Scientific and Technical Information of China (English)

    LI Jimin; SHANG Chaoxuan; ZOU Minghu

    2007-01-01

    The selection of weighting matrix in design of the linear quadratic optimal controller is an important topic in the control theory. In this paper, an approach based on genetic algorithm is presented for selecting the weighting matrix for the optimal controller. Genetic algorithm is adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and genetic. In this algorithm, the fitness function is used to evaluate individuals and reproductive success varies with fitness. In the design of the linear quadratic optimal controller, the fitness function has relation to the anticipated step response of the system. Not only can the controller designed by this approach meet the demand of the performance indexes of linear quadratic controller, but also satisfy the anticipated step response of close-loop system. The method possesses a higher calculating efficiency and provides technical support for the optimal controller in engineering application. The simulation of a three-order single-input single-output (SISO) system has demonstrated the feasibility and validity of the approach.

  13. Fermionic realisations of simple Lie algebras

    CERN Document Server

    de Azcárraga, J A

    2000-01-01

    We study the representation ${\\cal D}$ of a simple compact Lie algebra $\\g$ of rank l constructed with the aid of the hermitian Dirac matrices of a (${\\rm dim} \\g$)-dimensional euclidean space. The irreducible representations of $\\g$ contained in ${\\cal D}$ are found by providing a general construction on suitable fermionic Fock spaces. We give full details not only for the simplest odd and even cases, namely su(2) and su(3), but also for the next (${dim} \\g$)-even case of su(5). Our results are far reaching: they apply to any $\\g$-invariant quantum mechanical system containing ${\\rm dim} \\g$ fermions. Another reason for undertaking this study is to examine the role of the $\\g$-invariant fermionic operators that naturally arise. These are given in terms of products of an odd number of gamma matrices, and include, besides a cubic operator, (l-1) fermionic scalars of higher order. The latter are constructed from the Lie algebra cohomology cocycles, and must be considered to be of theoretical significance simila...

  14. Family of N-dimensional superintegrable systems and quadratic algebra structures

    Science.gov (United States)

    Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong

    2016-01-01

    Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide applications in modern physics and connection to many domains in pure and applied mathematics. We overview two new families of superintegrable Kepler-Coulomb systems with non-central terms and superintegrable Hamiltonians with double singular oscillators of type (n, N — n) in N-dimensional Euclidean space. We present their quadratic and polynomial algebras involving Casimir operators of so(N + 1) Lie algebras that exhibit very interesting decompositions Q(3) ⊕ so(N — 1), Q(3) ⊕ so(n) ⊕ so(N — n) and the cubic Casimir operators. The realization of these algebras in terms of deformed oscillator enables the determination of a finite dimensional unitary representation. We present algebraic derivations of the degenerate energy spectra of these systems and relate them with the physical spectra obtained from the separation of variables.

  15. Uncertainty Principles on Two Step Nilpotent Lie Groups

    Indian Academy of Sciences (India)

    S K Ray

    2001-08-01

    We extend an uncertainty principle due to Cowling and Price to two step nilpotent Lie groups, which generalizes a classical theorem of Hardy. We also prove an analogue of Heisenberg inequality on two step nilpotent Lie groups.

  16. Pants on fire: the electrophysiological signature of telling a lie.

    Science.gov (United States)

    Pfister, Roland; Foerster, Anna; Kunde, Wilfried

    2014-01-01

    Even though electroencephalography has played a prominent role for lie detection via personally relevant information, the electrophysiological signature of active lying is still elusive. We addressed this signature with two experiments in which participants helped a virtual police officer to locate a knife. Crucially, before this response, they announced whether they would lie or tell the truth about the knife's location. This design allowed us to study the signature of lie-telling in the absence of rare and personally significant oddball stimuli that are typically used for lie detection via electrophysiological markers, especially the P300 component. Our results indicate that active lying attenuated P300 amplitudes as well as N200 amplitudes for such non-oddball stimuli. These results support accounts that stress the high cognitive demand of lie-telling, including the need to suppress the truthful response and to generate a lie.

  17. A kind of signature scheme based on class groups of quadratic fields

    Institute of Scientific and Technical Information of China (English)

    董晓蕾; 曹珍富

    2004-01-01

    Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic fields remained open, because of the difficulty of computing class numbers of quadratic fields. In this paper, according to our researches on quadratic fields, we construct the first digital signature scheme in ideal class groups of quadratic fields, using q as modulus, which denotes the prime divisors of ideal class numbers of quadratic fields. Security of the new signature scheme is based fully on CL-DLP. This paper also investigates realization of the scheme, and proposes the concrete technique. In addition, the technique introduced in the paper can be utilized to realize signature schemes of other kinds.

  18. Lie symmetries and differential galois groups of linear equations

    NARCIS (Netherlands)

    Oudshoorn, W.R.; Put, M. van der

    2002-01-01

    For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In co

  19. 33 CFR 401.92 - Wintering and lying-up.

    Science.gov (United States)

    2010-07-01

    ... 33 Navigation and Navigable Waters 3 2010-07-01 2010-07-01 false Wintering and lying-up. 401.92... OF TRANSPORTATION SEAWAY REGULATIONS AND RULES Regulations General § 401.92 Wintering and lying-up. No vessel shall winter within the Seaway or lie-up within the Seaway during the navigation...

  20. Lie Pseudogroups à la Cartan from a Modern Perspective

    NARCIS (Netherlands)

    Yudilevich, O.

    2016-01-01

    In 1904-05, the mathematician Élie Cartan published two pioneer papers in which he introduced a structure theory for Lie pseudogroups. Lie pseudogroups are mathematical objects that appear in both differential geometry and in the theory of differential equations as local symmetries of geometric stru

  1. Graded Lie Algebra Generating of Parastatistical Algebraic Relations

    Institute of Scientific and Technical Information of China (English)

    JING Si-Cong; YANG Wei-Min; LI Ping

    2001-01-01

    A new kind of graded Lie algebra (We call it Z2,2 graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable Bose subspace of the Z2,2 graded Lie algebra and using relevant generalized Jacobi identities, we generate the whole algebraic structure of parastatistics.

  2. Extremal projectors for contragredient Lie (super)symmetries (short review)

    CERN Document Server

    Tolstoy, V N

    2010-01-01

    A brief review of the extremal projectors for contragredient Lie (super)symmetries (finite-dimensional simple Lie algebras, basic classical Lie superalgebras, infinite-dimensional affine Kac-Moody algebras and superalgebras, as well as their quantum $q$-analogs) is given. Some bibliographic comments on the applications of extremal projectors are presented.

  3. Focal sampling of cow lying behaviour for automated welfare assessment

    NARCIS (Netherlands)

    Mattachini, G.; Riva, E.; Bisaglia, C.; Pompe, J.C.A.M.; Provolo, G.

    2013-01-01

    the objective of the current study was to determine the number of focal animals required to represent the daily lying behaviour of a herd of lactating dairy cows. the study was carried out at 3 commercial dairy farms. the lying time (h/d) and number of lying bouts (n/d) of 15 ± 3 focal dairy cows,

  4. Universal representations of Lie algebras by coderivations

    OpenAIRE

    Petracci, Emanuela

    2003-01-01

    A class of representations of a Lie superalgebra (over a commutative superring) in its symmetric algebra is studied. As an application we get a direct and natural proof of a strong form of the Poincare'-Birkhoff-Witt theorem, extending this theorem to a class of nilpotent Lie superalgebras. Other applications are presented. Our results are new already for Lie algebras.

  5. Lie symmetry algebra of one-dimensional nonconservative dynamical systems

    Institute of Scientific and Technical Information of China (English)

    Liu Cui-Mei; Wu Run-Heng; Fu Jing-Li

    2007-01-01

    Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1-1 mapping,the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.

  6. Central Extension for the Triangular Derivation Lie Algebra

    Institute of Scientific and Technical Information of China (English)

    Chunming LI; Ping XU

    2012-01-01

    In this paper,we study a class of subalgebras of the Lie algebra of vector fields on n-dimensional torus,which are called the Triangular derivation Lie algebra.We give the structure and the central extension of Triangular derivation Lie algebra.

  7. Construction of Difference Equations Using Lie Groups

    Energy Technology Data Exchange (ETDEWEB)

    Axford, R.A.

    1998-08-01

    The theory of prolongations of the generators of groups of point transformations to the grid point values of dependent variables and grid spacings is developed and applied to the construction of group invariant numerical algorithms. The concepts of invariant difference operators and generalized discrete sources are introduced for the discretization of systems of inhomogeneous differential equations and shown to produce exact difference equations. Invariant numerical flux functions are constructed from the general solutions of first order partial differential equations that come out of the evaluation of the Lie derivatives of conservation forms of difference schemes. It is demonstrated that invariant numerical flux functions with invariant flux or slope limiters can be determined to yield high resolution difference schemes. The introduction of an invariant flux or slope limiter can be done so as not to break the symmetry properties of a numerical flux-function.

  8. [Counter-acception or abort and lie].

    Science.gov (United States)

    Maruani, G

    1979-09-01

    In this very short but fiery and violent paper against abortion the author states that most women seeking abortion are actually lying to themselves, pretending they want something which, in reality, they do not want, i.e. an abortion. The laws regulating abortion in most countries are such that a woman is practically forbidden to make an independent decision, despite, or because of the number of counseling sessions and of meetings with doctors that she must go through. Radio, television, newspapers and magazines, friends and relatives, all contribute to make of abortion a run-of-the-mill operation, while it should be seen as scandal, and as the total negation of any maternal instinct.

  9. Lie algebraic noncommuting structures from reparametrisation symmetry

    CERN Document Server

    Gangopadhyay, S

    2007-01-01

    We extend our earlier work of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. We show explicitly (in contrast to the earlier results in our paper \\cite{sg}) that for some special choices of the reparametrisation parameter $\\epsilon$, one can obtain space-space noncommuting structures which are Lie-algebraic in form even in the case of the relativistic free particle. The connection of these structures with the existing models in the literature is also briefly discussed. Further, there exists some values of $\\epsilon$ for which the noncommutativity in the space-space sector can be made to vanish. As a matter of internal consistency of our approach, we also study the angular momentum algebra in details.

  10. On Quantum Lie Nilpotency of Order 2

    Directory of Open Access Journals (Sweden)

    E. A. Kireeva

    2016-01-01

    Full Text Available The paper investigates the free algebras of varieties of associative algebras modulo identities of quantum Lie nilpotency of order 1 and 2. Let q be an invertible element of the ground field K (or of its extension. The element[x,y]q = xy-qyxof the free associative algebra is called a quantum commutator. We consider the algebras modulo identities                                                           [x,y]q = 0                                             (1and                                                      [[x,y]q ,z]q = 0.                                       (2It is natural to consider the aforementioned algebras as the quantum analogs of commutative algebras and algebras of Lie nilpotency of order 2. The free algebras of the varieties of associative algebras modulo the identity of Lie nilpotency of order 2, that is the identity[[x,y] ,z] =0,where [x,y]=xy-yx is a Lie commutator, are of great interest in the theory of algebras with polynomial identities, since it was proved by A.V.Grishin for algebras over fields of characteristic 2, and V.V.Shchigolev for algebras over fields of characteristic p>2, that these algebras contain non-finitely generated T-spaces.We prove in the paper that the algebras modulo identities (1 and (2 are nilpotent in the usual sense and calculate precisely the nilpotency order of these algebras. More precisely, we prove that the free algebra of the variety of associative algebras modulo identity (1 is nilpotent of order 2 if q ≠ ± 1, and nilpotent of order 3 if q = - 1 and the characteristic of K is not equal to 2. It is also proved that the free algebra of the variety of associative algebras modulo identity (2 is nilpotent of order 3 if q3 ≠ 1, q ≠ ± 1, nilpotent of order 4 if q3 = 1, q ≠ 1, and nilpotent of

  11. Detecting Children's Lies: Are Parents Accurate Judges of Their Own Children's Lies?

    Science.gov (United States)

    Talwar, Victoria; Renaud, Sarah-Jane; Conway, Lauryn

    2015-01-01

    The current study investigated whether parents are accurate judges of their own children's lie-telling behavior. Participants included 250 mother-child dyads. Children were between three and 11 years of age. A temptation resistance paradigm was used to elicit a minor transgressive behavior from the children involving peeking at a forbidden toy and…

  12. Detecting Children's Lies: Are Parents Accurate Judges of Their Own Children's Lies?

    Science.gov (United States)

    Talwar, Victoria; Renaud, Sarah-Jane; Conway, Lauryn

    2015-01-01

    The current study investigated whether parents are accurate judges of their own children's lie-telling behavior. Participants included 250 mother-child dyads. Children were between three and 11 years of age. A temptation resistance paradigm was used to elicit a minor transgressive behavior from the children involving peeking at a forbidden toy and…

  13. Exact solution of the classical mechanical quadratic Zeeman effect

    Indian Academy of Sciences (India)

    Sambhu N Datta; Anshu Pandey

    2007-06-01

    We address the curious problem of quadratic Zeeman effect at the classical mechanical level. The problem has been very well understood for decades, but an analytical solution of the equations of motion is still to be found. This state of affairs persists because the simultaneous presence of the Coulombic and quadratic terms lowers the dynamical symmetry. Energy and orbital angular momentum are still constants of motion. We find the exact solutions by introducing the concept of an image ellipse. The quadratic effect leads to a dilation of space–time, and a one-to-one correspondence is observed for pairs of physical quantities like energy and angular momentum, and the maximum and minimum distances from the Coulomb center for the Zeeman orbit and the corresponding pairs for the image ellipse. Thus, instead of finding additional conserved quantities, we find constants of motion for an additional dynamics, namely, the image problem. The trajectory is open, in agreement with Bertrand's theorem, but necessarily bound. A stable unbound trajectory does not exist for real values of energy and angular momentum. The radial distance, the angle covered in the plane of the orbit, and the time are uniquely determined by introducing further the concept of an image circle. While the radial distance is defined in a closed form as a transcendental function of the image-circular angle, the corresponding orbit angle and time variables are found in the form of two convergent series expansions. The latter two variables are especially contracted, thereby leading to a precession of the open cycles around the Coulomb center. It is expected that the space–time dilation effect observed here would somehow influence the solution of the quantum mechanical problem at the non-relativistic level.

  14. Vacuum solutions of Bianchi cosmologies in quadratic gravity

    Energy Technology Data Exchange (ETDEWEB)

    Deus, Juliano Alves de; Muller, Daniel [Universidade de Brasilia (UnB), DF (Brazil)

    2011-07-01

    Full text: In this work we solve numerically the vacuum solutions of field equations of Bianchi homogeneous universes in the context of Semiclassical theory. Our interest is to study the quadratic theory of gravity with regard in the cosmological description of our universe in periods of intense fields. Bianchi cosmologies are anisotropic homogeneous cosmological models, but can include the isotropic models as particular cases (Bianchi I, VII and IX include homogeneous and isotropic Friedmann models plane, hyperbolic and spherical, respectively). Homogeneous models are good cosmological representations of our universe. With focus in solutions for intense fields, like the early universe, where isotropy is not necessarily required, the adopted scenario is the vacuum solutions, where the geometry is dominant in determining the gravitation. Still following in this way, the Semiclassical theory, which considers quantum matter fields propagating in classical geometrical background, is addressed to give the field equations. This formalism leads to fourth-order ordinary differential equations, in contrast to second-order equations from General Relativity. The Lagrangian of the theory is quadratic in the Ricci scalar and in the Ricci tensor. The equations system is highly non-linear and can be only numerically solved, except perhaps for few particular cases. We obtained numerical solutions for Bianchi V II{sub A} evolving to Minkowski and to de Sitter solutions, and also to singularities. The both first and second solutions were obtained choosing initial conditions near from respective exact vacuum solutions from Einstein theory, which are also exact solutions of the quadratic theory. Other Bianchi types are still under study. (author)

  15. Creepers: Real quadratic orders with large class number

    Science.gov (United States)

    Patterson, Roger

    2007-03-01

    Shanks's sequence of quadratic fields Q(sqrt{S_{n}}) where S_{n}=(2^n+1)^2 + 2^{n+2} instances a class of quadratic fields for which the class number is large and, therefore, the continued fraction period is relatively short. Indeed, that period length increases linearly with n, that is: in arithmetic progression. The fields have regulator O(n^2). In the late nineties, these matters intrigued Irving Kaplansky, and led him to compute period length of the square root of sequences a^2x^{2n}+bx^{n}+c for integers a, b, c, and x. In brief, Kap found unsurprisingly that, generically, triples (a,b,c) are `leapers': they yield sequences with period length increasing at exponential rate. But there are triples yielding sequences with constant period length, Kap's `sleepers'. Finally, there are triples, as exemplified by the Shanks's sequence, for which the period lengths increase in arithmetic progression. Felicitously, Kaplansky called these `creepers'. It seems that the sleepers and creepers are precisely those for which one is able to detail the explicit continued fraction expansion for all n. Inter alia, this thesis noticeably extends the known classes of creepers and finds that not all are `kreepers' (of the shape identified by Kaplansky) and therefore not of the shape of examples studied by earlier authors looking for families of quadratic number fields with explicitly computable unit and of relatively large regulator. The work of this thesis includes the discovery of old and new families of hyperelliptic curves of increasing genus g and torsion divisor of order O(g^2). It follows that the apparent trichotomy leaper/sleeper/creeper coincides with the folk belief that the just-mentioned torsion is maximum possible.

  16. Solving the quadratic assignment problem with clues from nature.

    Science.gov (United States)

    Nissen, V

    1994-01-01

    This paper describes a new evolutionary approach to solving quadratic assignment problems. The proposed technique is based loosely on a class of search and optimization algorithms known as evolution strategies (ES). These methods are inspired by the mechanics of biological evolution and have been applied successfully to a variety of difficult problems, particularly in continuous optimization. The combinatorial variant of ES presented here performs very well on the given test problems as compared with the standard 2-Opt heuristic and results with simulated annealing and tabu search. Extensions for practical applications in factory layout are described.

  17. Two Reformulations for the Dynamic Quadratic Assignment Problem

    Directory of Open Access Journals (Sweden)

    Sirirat Muenvanichakul

    2010-01-01

    Full Text Available Problem statement: The Dynamic Quadratic Assignment Problem (DQAP, an NP-hard problem, is outlined and reformulated in two alternative models: Linearized model and logic-based model. Approach: The solution methods for both models based on combinatorial methods (Benders’ Decomposition and Approximate Dynamic Programming and constraint logic programming, respectively, are proposed. Results: Proofs of model equivalence and solution methodology are presented. Conclusion: Both proposed models are more simplified leading to possible hybrid adaptations of existing techniques for more practical approaches.

  18. STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    This paper studies a stochastic linear quadratic optimal control problem (LQ problem, for short), for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. The authors introduce the stochastic Riccati equation for the LQ problem. This is a backward SDE with a complicated nonlinearity and a singularity. The local solvability of such a backward SDE is established, which by no means is obvious. For the case of deterministic coefficients, some further discussions on the Riccati equations have been carried out. Finally, an illustrative example is presented.

  19. Restart-Based Genetic Algorithm for the Quadratic Assignment Problem

    Science.gov (United States)

    Misevicius, Alfonsas

    The power of genetic algorithms (GAs) has been demonstrated for various domains of the computer science, including combinatorial optimization. In this paper, we propose a new conceptual modification of the genetic algorithm entitled a "restart-based genetic algorithm" (RGA). An effective implementation of RGA for a well-known combinatorial optimization problem, the quadratic assignment problem (QAP), is discussed. The results obtained from the computational experiments on the QAP instances from the publicly available library QAPLIB show excellent performance of RGA. This is especially true for the real-life like QAPs.

  20. Gilmore-Lawler bound of quadratic assignment problem

    Institute of Scientific and Technical Information of China (English)

    Yong XIA

    2008-01-01

    The Gilmore-Lawler bound (GLB) is one of the well-known lower bound of quadratic assignment problem (QAP). Checking whether GLB is tight is an NP-complete problem. In this article, based on Xia and Yuan linearization technique, we provide an upper bound of the complexity of this problem, which makes it pseudo-polynomial solvable. We also pseudo-polynomially solve a class of QAP whose GLB is equal to the optimal objec-tive function value, which was shown to remain NP-hard.

  1. A Solution Proposal To Indefinite Quadratic Interval Transportation Problem

    Directory of Open Access Journals (Sweden)

    Hasan Dalman

    2013-12-01

    Full Text Available The data of real world applications generally cannot be expressed strictly. An efficient way of handling this situation is expressing the data as intervals. Thus, this paper focus on the Indefinite Quadratic Interval Transportation Problem (IQITP in which all the parameters i.e. cost and risk coefficients of the objective function, supply and demand quantities are expressed as intervals. A Taylor series approach is presented for the solution of IQITP by means of the expression of intervals with its left and right limits. Also a numerical example is executed to illustrate the procedure.

  2. Neural network for solving convex quadratic bilevel programming problems.

    Science.gov (United States)

    He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

    2014-03-01

    In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network.

  3. Rigorous Performance Bounds for Quadratic and Nested Dynamical Decoupling

    CERN Document Server

    Xia, Yuhou; Lidar, Daniel A

    2011-01-01

    We present rigorous performance bounds for the quadratic dynamical decoupling (QDD) pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumption of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.

  4. Analysis of electroperforated materials using the quadrat counts method

    Energy Technology Data Exchange (ETDEWEB)

    Miranda, E; Garzon, C; Garcia-Garcia, J [Departament d' Enginyeria Electronica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona (Spain); MartInez-Cisneros, C; Alonso, J, E-mail: enrique.miranda@uab.cat [Departament de Quimica AnalItica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona (Spain)

    2011-06-23

    The electroperforation distribution in thin porous materials is investigated using the quadrat counts method (QCM), a classical statistical technique aimed to evaluate the deviation from complete spatial randomness (CSR). Perforations are created by means of electrical discharges generated by needle-like tungsten electrodes. The objective of perforating a thin porous material is to enhance its air permeability, a critical issue in many industrial applications involving paper, plastics, textiles, etc. Using image analysis techniques and specialized statistical software it is shown that the perforation locations follow, beyond a certain length scale, a homogeneous 2D Poisson distribution.

  5. Bianchi $VII_A$ solutions of quadratic gravity

    CERN Document Server

    de Deus, Juliano A

    2011-01-01

    It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "open" model $H^ 3$ for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity.

  6. Quadratic controller syntheses for the steam generator water level

    Energy Technology Data Exchange (ETDEWEB)

    Arzelier, D.; Daafouz, J.; Bernussou, J.; Garcia, G

    1998-06-01

    The steam generator water level, (SGWL), control problem in the pressurized water reactor of a nuclear power plant is considered from robust control techniques point of view. The plant is a time-varying system with a non minimum phase behavior and an unstable open-loop response. The time-varying nature of the plant due to change in operating power is taken into account by including slowly time-varying uncertainty in the model. A linear Time-Invariant, (LTI) guaranteed cost quadratic stabilizing controller is designed in order to address some of the particular issues arising for such a control problem. (author) 17 refs.

  7. SPEECH EMOTION RECOGNITION USING MODIFIED QUADRATIC DISCRIMINATION FUNCTION

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Quadratic Discrimination Function(QDF)is commonly used in speech emotion recognition,which proceeds on the premise that the input data is normal distribution.In this Paper,we propose a transformation to normalize the emotional features,then derivate a Modified QDF(MQDF) to speech emotion recognition.Features based on prosody and voice quality are extracted and Principal Component Analysis Neural Network (PCANN) is used to reduce dimension of the feature vectors.The results show that voice quality features are effective supplement for recognition.and the method in this paper could improve the recognition ratio effectively.

  8. FaSa: A Fast and Stable Quadratic Placement Algorithm

    Institute of Scientific and Technical Information of China (English)

    HOU WenTing(侯文婷); HONG XianLong(洪先龙); WU WeiMin(吴为民); CAI YiCi(蔡懿慈)

    2003-01-01

    Placement is a critical step in VLSI design because it dominates overall speed andquality of design flow. In this paper, a new fast and stable placement algorithm called FaSa is pro-posed. It uses quadratic programming model and Lagrange multiplier method to solve placementproblems. And an incremental LU factorization method is used to solve equations for speeding up.The experimental results show that FaSa is very stable, much faster than previous algorithms andits total wire length is comparable with other algorithms.

  9. Quadratic growth and stability in convex programming problems

    OpenAIRE

    Bonnans, J. Frederic; Ioffe, Alexander D.

    1994-01-01

    Projet PROMATH; Given a convex program with $C^2$ functions and a convex set $S$ of solutions to the problem, we give a second order condition which guarantees that the problem does not have solutions outside of $S$. This condition is interpreted as a characterization for the quadratic growth of the cost function. The crucial role in the proofs is played by a theorem describing a certain uniform regularity property of critical cones in smooth convex programs. We apply these results to the dis...

  10. Asymmetric Simple Exclusion Process with Open Boundaries and Quadratic Harnesses

    Science.gov (United States)

    Bryc, Włodek; Wesołowski, Jacek

    2017-04-01

    We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses. We use our representation to prove the large deviations principle for the total number of particles in the system. We use the generator of the Markov process to show how explicit formulas for the average occupancy of a site arise for special choices of parameters. We also give similar representations for limits of stationary measures as the number of sites tends to infinity.

  11. Linear and quadratic in temperature resistivity from holography

    CERN Document Server

    Ge, Xian-Hui; Wu, Shang-Yu; Wu, Shao-Feng

    2016-01-01

    We present a new black hole solution in the Lifshitz spacetime with a hyperscaling violating factor. We analytically compute all of the DC thermoelectric conductivities in this theory. We find that both the linear-T and quadratic-T contributions to the resistivity can be realized, indicating that a more detailed comparison with experimental phenomenology can be performed in this scenario. At zero temperature, the Lorenz ratios are a constant, obeying the Wiedemann-Franz law, indications of a Fermi-liquid ground state.

  12. Automorphisms of Strong Homotopy Lie Algebras of Local Observables

    CERN Document Server

    Ritter, Patricia

    2015-01-01

    There is a well-established procedure of assigning a strong homotopy Lie algebra of local observables to a multisymplectic manifold which can be regarded as part of a categorified Poisson structure. For a 2-plectic manifold, the resulting Lie 2-algebra is isomorphic to a sub Lie 2-algebra of a natural Lie 2-algebra structure on an exact Courant algebroid. We generalize this statement to arbitrary n-plectic manifolds and study automorphisms on the arising Lie n-algebras. Our observations may be useful in studying the quantization problem on multisymplectic manifolds.

  13. Determinantal formulae for the Casimir operators of inhomogeneous Lie algebras

    Energy Technology Data Exchange (ETDEWEB)

    Campoamor-Stursberg, Rutwig [Dpto. Geometria y Topologia, Fac CC Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias, 3, E-28040 Madrid (Spain)

    2006-03-10

    Contractions of Lie algebras are combined with the classical matrix method of Gel'fand to obtain matrix formulae for the Casimir operators of inhomogeneous Lie algebras. The method is presented for the inhomogeneous pseudo-unitary Lie algebras Iu(p,q). This procedure is extended to contractions of Iu(p,q) isomorphic to an extension by a derivation of the inhomogeneous special pseudo-unitary Lie algebras Isu(p-1,q), providing an additional analytical method to obtain their invariants. Further, matrix formulae for the invariants of other inhomogeneous Lie algebras are presented.

  14. Restricted and quasi-toral restricted Lie-Rinehart algebras

    Directory of Open Access Journals (Sweden)

    Sun Bing

    2015-09-01

    Full Text Available In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension should be.

  15. Nonlinear effects of winter sea ice on the survival probabilities of Adélie penguins.

    Science.gov (United States)

    Ballerini, Tosca; Tavecchia, Giacomo; Olmastroni, Silvia; Pezzo, Francesco; Focardi, Silvano

    2009-08-01

    The population dynamics of Antarctic seabirds are influenced by variations in winter sea ice extent and persistence; however, the type of relationship differs according to the region and the demographic parameter considered. We used annual presence/absence data obtained from 1,138 individually marked birds to study the influence of environmental and individual characteristics on the survival of Adélie penguins Pygoscelis adeliae at Edmonson Point (Ross Sea, Antarctica) between 1994 and 2005. About 25% of 600 birds marked as chicks were reobserved at the natal colony. The capture and survival rates of Adélie penguins at this colony increased with the age of individuals, and five age classes were identified for both parameters. Mean adult survival was 0.85 (SE = 0.01), and no effect of sex on survival was evident. Breeding propensity, as measured by adult capture rates, was close to one, indicating a constant breeding effort through time. Temporal variations in survival were best explained by a quadratic relationship with winter sea ice extent anomalies in the Ross Sea, suggesting that for this region optimal conditions are intermediate between too much and too little winter sea ice. This is likely the result of a balance between suitable wintering habitat and food availability. Survival rates were not correlated with the Southern Oscillation Index. Low adult survival after a season characterized by severe environmental conditions at breeding but favorable conditions during winter suggested an additional mortality mediated by the reproductive effort. Adélie penguins are sensitive indicators of environmental changes in the Antarctic, and the results from this study provide insights into regional responses of this species to variability in winter sea ice habitat.

  16. Pro-Lie Groups: A Survey with Open Problems

    Directory of Open Access Journals (Sweden)

    Karl H. Hofmann

    2015-07-01

    Full Text Available A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a complete category. It includes each finite-dimensional Lie group, each locally-compact group that has a compact quotient group modulo its identity component and, thus, in particular, each compact and each connected locally-compact group; it also includes all locally-compact Abelian groups. This paper provides an overview of the structure theory and the Lie theory of pro-Lie groups, including results more recent than those in the authors’ reference book on pro-Lie groups. Significantly, it also includes a review of the recent insight that weakly-complete unital algebras provide a natural habitat for both pro-Lie algebras and pro-Lie groups, indeed for the exponential function that links the two. (A topological vector space is weakly complete if it is isomorphic to a power RX of an arbitrary set of copies of R. This class of real vector spaces is at the basis of the Lie theory of pro-Lie groups. The article also lists 12 open questions connected to pro-Lie groups.

  17. Electroweak vacuum stability and finite quadratic radiative corrections

    Energy Technology Data Exchange (ETDEWEB)

    Masina, Isabella [Ferrara Univ. (Italy). Dipt. di Fisica e Scienze della Terra; INFN, Sezione di Ferrara (Italy); Southern Denmark Univ., Odense (Denmark). CP3-Origins; Southern Denmark Univ., Odense (Denmark). DIAS; Nardini, Germano [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Quiros, Mariano [Institucio Catalana de Recerca i Estudis Avancats (ICREA), Barcelona (Spain); IFAE-IAB, Barcelona (Spain)

    2015-07-15

    If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale Λ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative Ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales the cutoff is not unique and each SM sector has its own UV cutoff Λ{sub i}. We have performed this calculation assuming the Minimal Supersymmetric Standard Model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs Λ{sub i}, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the Focus Point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.

  18. On the Content Bound for Real Quadratic Field Extensions

    Directory of Open Access Journals (Sweden)

    Robert G. Underwood

    2012-12-01

    Full Text Available Let K be a finite extension of Q and let S = {ν} denote the collection of K normalized absolute values on K. Let V+K denote the additive group of adeles over K and let K ≥0   c : V + → R denote the content map defined as c({aν } = Q K   ν ∈S ν (aν for {aν } ∈ V+K A classical result of J. W. S. Cassels states that there is a constant c > 0 depending only on the field K  with the following property: if {aν } ∈ V+K with c({aν }  > c, then there exists a non-zero element b  ∈ K for which ν (b ≤ ν (aν , ∀ν  ∈ S. Let cK be the greatest lower bound of the set of all c that satisfy this property. In the case that K is a real quadratic extension there is a known upper bound for cK due to S. Lang. The purpose of this paper is to construct a new upper bound for cK in the case that K has class number one. We compare our new bound with Lang’s bound for various real quadratic extensions and find that our new bound is better than Lang’s in many instances.

  19. Creepers: Real quadratic orders with large class number

    CERN Document Server

    Patterson, R

    2007-01-01

    Shanks's sequence of quadratic fields $\\Q(\\sqrt{S_{n}})$ where $S_{n}=(2^n+1)^2 + 2^{n+2}$ instances a class of quadratic fields for which the class number is large and, therefore, the continued fraction period is relatively short. Indeed, that period length increases linearly with $n$, that is: in arithmetic progression. The fields have regulator $O(n^2)$. In the late nineties, these matters intrigued Irving Kaplansky, and led him to compute period length of the square root of sequences $a^2x^{2n}+bx^{n}+c$ for integers $a$, $b$, $c$, and $x$. In brief, Kap found unsurprisingly that, generically, triples $(a,b,c)$ are `leapers': they yield sequences with period length increasing at exponential rate. But there are triples yielding sequences with constant period length, Kap's `sleepers'. Finally, there are triples, as exemplified by the Shanks's sequence, for which the period lengths increase in arithmetic progression. Felicitously, Kaplansky called these `creepers'. It seems that the sleepers and creepers are...

  20. Local Points on Quadratic Twists of X_0(N)

    CERN Document Server

    Ozman, Ekin

    2009-01-01

    Let X^d(N) be the quadratic twist of the modular curve X_0(N) through the Atkin-Lehner involution w_N and a quadratic extension Q(\\sqrt{d})/Q. The points of X^d(N)(Q) are precisely the Q(\\sqrt{d})-rational points of X_0(N) that are fixed by \\sigma composition w_N, where \\sigma is the generator of Gal(Q(\\sqrt{d})/Q).Ellenberg asked the following question: For which d and N does X^d(N) have rational points over every completion of Q? Given (N,d,p) we give necessary and sufficient conditions for the existence of a Q_p-rational point on X^d(N), whenever p is not simultaneously ramified in Q(\\sqrt{d}) and Q(\\sqrt{-N}), answering Ellenberg's question for all odd primes p when (N,d)=1. The main theorem yields a population of curves which have local points everywhere but no points over Q; in several cases we show that this obstruction to the Hasse Principle is explained by the Brauer-Manin obstruction.