Rigged Hilbert spaces for chaotic dynamical systems
Suchanecki, Z. [International Solvay Institutes for Physics and Chemistry, CP 231, Campus Plaine ULB, Bd. du Triomphe, 1050 Brussels (Belgium)]|[Hugo Steinhaus Center and Institute of Mathematics, Wrocl/aw Technical University, ul. Wybrzeze Wyspianskiego 27, 50-370 Wroclaw (Poland); Antoniou, I. [International Solvay Institutes for Physics and Chemistry, CP 231, Campus Plaine ULB, Bd. du Triomphe, 1050 Brussels (Belgium)]|[Theoretische Natuurkunde Free University of Brussels; Tasaki, S. [International Solvay Institutes for Physics and Chemistry, CP 231, Campus Plaine ULB, Bd. du Triomphe, 1050 Brussels, Belgium and]|[Institute for Fundamental Chemistry 34-4 Takano Nishihiraki-cho Kyoto 606 (Japan); Bandtlow, O.F. [International Solvay Institutes for Physics and Chemistry, CP 231, Campus Plaine ULB, Bd. du Triomphe, 1050 Brussels (Belgium)]|[Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB30HE (United Kingdom)
1996-11-01
We consider the problem of rigging for the Koopman operators of the Renyi and the baker maps. We show that the rigged Hilbert space for the Renyi maps has some of the properties of a strict inductive limit and give a detailed description of the rigged Hilbert space for the baker maps. {copyright} {ital 1996 American Institute of Physics.}
Eigenfunction expansions and scattering theory in rigged Hilbert spaces
Gomez-Cubillo, F [Dpt. de Analisis Matematico, Universidad de Valladolid. Facultad de Ciencias, 47011 Valladolid (Spain)], E-mail: fgcubill@am.uva.es
2008-08-15
The work reviews some mathematical aspects of spectral properties, eigenfunction expansions and scattering theory in rigged Hilbert spaces, laying emphasis on Lippmann-Schwinger equations and Schroedinger operators.
Applications of rigged Hilbert spaces in quantum mechanics and signal processing
Celeghini, E.; Gadella, M.; del Olmo, M. A.
2016-07-01
Simultaneous use of discrete and continuous bases in quantum systems is not possible in the context of Hilbert spaces, but only in the more general structure of rigged Hilbert spaces (RHS). In addition, the relevant operators in RHS (but not in Hilbert space) are a realization of elements of a Lie enveloping algebra and support representations of semigroups. We explicitly construct here basis dependent RHS of the line and half-line and relate them to the universal enveloping algebras of the Weyl-Heisenberg algebra and su(1, 1), respectively. The complete sub-structure of both RHS and of the operators acting on them is obtained from their algebraic structures or from the related fractional Fourier transforms. This allows us to describe both quantum and signal processing states and their dynamics. Two relevant improvements are introduced: (i) new kinds of filters related to restrictions to subspaces and/or the elimination of high frequency fluctuations and (ii) an operatorial structure that, starting from fix objects, describes their time evolution.
Madrid, Rafael de la [Department of Physics, University of California at San Diego, La Jolla, CA 92093 (United States)
2006-04-14
The analytic continuation of the Lippmann-Schwinger bras and kets is obtained and characterized. It is shown that the natural mathematical setting for the analytic continuation of the solutions of the Lippmann-Schwinger equation is the rigged Hilbert space rather than just the Hilbert space. It is also argued that this analytic continuation entails the imposition of a time asymmetric boundary condition upon the group time evolution, resulting in a semigroup time evolution. Physically, the semigroup time evolution is simply a (retarded or advanced) propagator.
Celeghini, Enrico
2014-01-01
Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and allows to obtain the projective algebra io(2). A Rigged Hilbert space is found and a new discrete basis in R obtained. The operators {O[R]} defined on R are shown to belong to the Universal Enveloping Algebra UEA[io(2)] allowing, in this way, their algebraic discussion. Introducing in the half-line a Fourier-like Transform, the procedure is extended to R^+ and can be easily generalized to R^n and to spherical reference systems.
Marmo, G; Simoni, A; Ventriglia, F [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy)
2007-11-15
We present a method of constructing the tomographic probability distributions describing quantum states in parallel with density operators in abstract Hilbert spaces. After the study of an infinite dimensional example, the well known Husimi-Kano quasi-distribution is reconsidered in the new setting and a new tomographic scheme based on coherent states is suggested. Starting from the Sudarshan's diagonal coherent state representation, the associated identity decomposition providing Gram-Schmidt operators is explicitly given.
Sunder, V S
2016-01-01
The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators. .
Alabiso, Carlo
2015-01-01
This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all sub...
EXTENSION OF THE PROJECTION THEOREM ON HILBERT SPACE TO FUZZY HILBERT SPACE OVER FUZZY NUMBER SPACE
K. P. DEEPA; Dr.S.Chenthur Pandian
2012-01-01
In this paper, we extend the projection theorem on Hilbert space to its fuzzy version over fuzzy number space embedded with fuzzy number mapping. To prove this we discuss the concepts of fuzzy Hilbert space over fuzzy number space with fuzzy number mapping. The fuzzy orthogonality, fuzzy orthonormality, fuzzy complemented subset property etc. of fuzzy Hilbert space over fuzzy number space using fuzzy number mapping also been discussed.
Structure of Hilbert space operators
Jiang, Chunlan
2006-01-01
This book exposes the internal structure of non-self-adjoint operators acting on complex separable infinite dimensional Hilbert space, by analyzing and studying the commutant of operators. A unique presentation of the theorem of Cowen-Douglas operators is given. The authors take the strongly irreducible operator as a basic model, and find complete similarity invariants of Cowen-Douglas operators by using K -theory, complex geometry and operator algebra tools. Sample Chapter(s). Chapter 1: Background (153 KB). Contents: Jordan Standard Theorem and K 0 -Group; Approximate Jordan Theorem of Opera
Linear systems and operators in Hilbert space
Fuhrmann, Paul A
2014-01-01
A treatment of system theory within the context of finite dimensional spaces, this text is appropriate for students with no previous experience of operator theory. The three-part approach, with notes and references for each section, covers linear algebra and finite dimensional systems, operators in Hilbert space, and linear systems in Hilbert space. 1981 edition.
Geometrical Underpinning of Finite Dimensional Hilbert space
Revzen, M
2011-01-01
Finite geometry is employed to underpin operators in finite, d, dimensional Hilbert space. The central role of Hilbert space operators that form mutual unbiased bases (MUB) states projectors is exhibited. Interrelation among them revealed through their (finite) dual affine plane geometry (DAPG) underpinning is studied. Transcription to (finite) affine plane geometry (APG) is given and utilized for their interpretation.
Radon Transform for Finite Dimensional Hilbert Space
Revzen, M
2012-01-01
Finite dimensional, d, Hilbert space operators are underpinned with ?nite geometry. The analysis emphasizes a central role for mutual unbiased bases (MUB) states projectors. Interrelation among the Hilbert space operators revealed via their (?nite) dual a?ne plane geometry (DAPG) underpin- ning is studied and utilized in formulating a ?nite dimensional Radon transformation. The ?nite geometry required for our study is outlines.
Geometrical Underpinning of Finite Dimensional Hilbert space
Revzen, M.
2011-01-01
Finite geometry is employed to underpin operators in finite, d, dimensional Hilbert space. The central role of mutual unbiased bases (MUB) states projectors is exhibited. Interrelation among operators in Hilbert space, revealed through their (finite) dual affine plane geometry (DAPG) underpinning is studied. Transcription to (finite) affine plane geometry (APG) is given and utilized for their interpretation.
Introduction to spectral theory in Hilbert space
Helmberg, Gilbert; Koiter, W T
1969-01-01
North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of lin
Hilbert space methods in partial differential equations
Showalter, Ralph E
1994-01-01
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
Theory of linear operators in Hilbert space
Akhiezer, N I
1993-01-01
This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.
Radon Transform in Finite Dimensional Hilbert Space
Revzen, M.
2012-01-01
Novel analysis of finite dimensional Hilbert space is outlined. The approach bypasses general, inherent, difficulties present in handling angular variables in finite dimensional problems: The finite dimensional, d, Hilbert space operators are underpinned with finite geometry which provide intuitive perspective to the physical operators. The analysis emphasizes a central role for projectors of mutual unbiased bases (MUB) states, extending thereby their use in finite dimensional quantum mechani...
Hilbert space theory of classical electrodynamics
RAJAGOPAL A K; GHOSE PARTHA
2016-06-01
Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman–von Neumann–Sudarshan prescription for classical mechanics on Hilbert spaces sans the superselection rule which prohibits interference effects in classical mechanics. This is accomplished by transforming from a set of commutingobservables in one Hilbert space to another set of commuting observables in a larger Hilbert space. This is necessary to clarify the theoretical basis of the much recent work on quantum-like features exhibited by classical optics. Furthermore, following Bondar et al, {\\it Phys. Rev.} A 88, 052108 (2013), it is pointed out that quantum processes that preserve the positivity or nonpositivity of theWigner function can be implemented by classical optics. This may be useful in interpreting quantum information processing in terms of classical optics.
Frames and Bases in Tensor Products of Hilbert Spaces and Hilbert *-Modules
Amir Khosravi; Behrooz Khosravi
2007-02-01
In this article, we study tensor product of Hilbert *-modules and Hilbert spaces. We show that if is a Hilbert -module and is a Hilbert -module, then tensor product of frames (orthonormal bases) for and produce frames (orthonormal bases) for Hilbert $A \\otimes B$-module $E \\otimes F$, and we get more results. For Hilbert spaces and , we study tensor product of frames of subspaces for and , tensor product of resolutions of the identities of and , and tensor product of frame representations for and .
The method of rigged spaces in singular perturbation theory of self-adjoint operators
Koshmanenko, Volodymyr; Koshmanenko, Nataliia
2016-01-01
This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadra...
Coherent states in projected Hilbert spaces
Drummond, P. D.; Reid, M. D.
2016-12-01
Coherent states in a projected Hilbert space have many useful properties. When there are conserved quantities, a representation of the entire Hilbert space is not necessary. The same issue arises when conditional observations are made with postselected measurement results. In these cases, only a part of the Hilbert space needs to be represented, and one can define this restriction by way of a projection operator. Here coherent state bases and normally ordered phase-space representations are introduced for treating such projected Hilbert spaces, including existence theorems and dynamical equations. These techniques are very useful in studying novel optical or microwave integrated photonic quantum technologies, such as boson sampling or Josephson quantum computers. In these cases, states become strongly restricted due to inputs, nonlinearities, or conditional measurements. This paper focuses on coherent phase states, which have especially simple properties. Practical applications are reported on calculating recurrences in anharmonic oscillators, the effects of arbitrary phase noise on Schrödinger cat fringe visibility, and on boson sampling interferometry for large numbers of modes.
More on (,-Normal Operators in Hilbert Spaces
Rasoul Eskandari
2012-01-01
Full Text Available We study some properties of (,-normal operators and we present various inequalities between the operator norm and the numerical radius of (,-normal operators on Banach algebra ℬ(ℋ of all bounded linear operators ∶ℋ→ℋ, where ℋ is Hilbert space.
Invariant Hilbert spaces of holomorphic functions
Faraut, J; Thomas, EGF
1999-01-01
A Hilbert space of holomorphic functions on a complex manifold Z, which is invariant under a group G of holomorphic automorphisms of Z, can be decomposed into irreducible subspaces by using Choquet theory. We give a geometric condition on Z and G which implies that this decomposition is multiplicity
Quantum mechanics in finite dimensional Hilbert space
de la Torre, A C
2002-01-01
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.
Hilbert space for quantum mechanics on superspace
Coulembier, Kevin
2011-01-01
In superspace a realization of sl2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl2-representation is proven. Finally the Heisenberg uncertainty principle for the super Fourier transform is constructed.
Hilbert space for quantum mechanics on superspace
Coulembier, K.; De Bie, H.
2011-06-01
In superspace a realization of {sl}_2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie, and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. (accepted) arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the {sl}_2-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.
Elements of Hilbert spaces and operator theory
Vasudeva, Harkrishan Lal
2017-01-01
The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compressio...
Basis-neutral Hilbert-space analyzers
Martin, Lane; Kondakci, H Esat; Larson, Walker D; Shabahang, Soroush; Jahromi, Ali K; Malhotra, Tanya; Vamivakas, A Nick; Atia, George K; Abouraddy, Ayman F
2016-01-01
Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert space spanned by spatial modes -- a critical task for spatial-mode multiplexing and quantum communication -- basis-specific principles are invoked that are altogether distinct from that of `delay.' Here, we extend the traditional concept of temporal delay to the spatial domain, thereby enabling the analysis of a beam in an arbitrary spatial-mode basis -- exemplified using Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays correspond to optical implementations of fractional transforms; for example, the fractional Hankel transform is the generalized delay associated with the space of Laguerre-Gaussian modes, and an interferometer incorporating such a `delay' obtains modal weights in the associated Hilbert space. By implementing an inherently stable, rec...
Penalty Algorithms in Hilbert Spaces
Jean Pierre DUSSAULT; Hai SHEN; André BANDRAUK
2007-01-01
We analyze the classical penalty algorithm for nonlinear programming in HUbert spaces and obtain global convergence results, as well as asymptotic superlinear convergence order. These convergence results generalize similar results obtained for finite-dimensional problems. Moreover, the nature of the algorithms allows us to solve the unconstrained subproblems in finite-dimensional spaces.
Functional Analysis: Entering Hilbert Space
Hansen, Vagn Lundsgaard
In the second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Map-ping Theorem, the Closed Graph Theorem and the Hahn-Banach The orem. The material on operators between normed vector spaces is further expanded...... of the new material on normed vector spaces and their operators, the book can hopefully serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them....... in a new chapter on Fredholm theory (Chapter 6). Fredholm theory originates in pioneering work of the Swedish mathematician Erik Ivar Fred-holm on integral equations, which inspired the study of a new class of bounded linear operators, known as Fredholm operators. Chapter 6 presents the basic elements...
STATIONARY CONNECTED CURVES IN HILBERT SPACES
Raed Hatamleh
2014-01-01
Full Text Available In this article the structure of non-stationary curves which are stationary connected in Hilbert space is studied using triangular models of non-self-adjoint operator. The concept of evolutionary representability plays here an important role. It is proved that if one of two curves in Hilbert space is evolutionary representable and the curves are stationary connected, then another curve is evolutionary representable too. These curves are studied firstly. The structure of a cross-correlation function in the case when operator, defining the evolutionary representation, has one-dimensional non-Hermitian subspace (the spectrum is discreet and situated in the upper complex half-plane or has infinite multiplicity at zero (Volterra operator is studied.
Rigidity of contractions on Hilbert spaces
Eisner, Tanja
2009-01-01
We study the asymptotic behaviour of contractive operators and strongly continuous semigroups on separable Hilbert spaces using the notion of rigidity. In particular, we show that a "typical" contraction $T$ contains the unit circle times the identity operator in the strong limit set of its powers, while $T^{n_j}$ converges weakly to zero along a sequence $\\{n_j\\}$ with density one. The continuous analogue is presented for isometric ang unitary $C_0$-(semi)groups.
Sparse Signal Recovery in Hilbert Spaces
Pope, Graeme
2012-01-01
This paper reports an effort to consolidate numerous coherence-based sparse signal recovery results available in the literature. We present a single theory that applies to general Hilbert spaces with the sparsity of a signal defined as the number of (possibly infinite-dimensional) subspaces participating in the signal's representation. Our general results recover uncertainty relations and coherence-based recovery thresholds for sparse signals, block-sparse signals, multi-band signals, signals in shift-invariant spaces, and signals in finite unions of (possibly infinite-dimensional) subspaces. Moreover, we improve upon and generalize several of the existing results and, in many cases, we find shortened and simplified proofs.
Quantum Holonomy Theory and Hilbert Space Representations
Aastrup, Johannes
2016-01-01
We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state exist is left for later publications.
Quantum mechanics in an evolving Hilbert space
Artacho, Emilio
2016-01-01
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalisation, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fibre bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge imp...
A distribution space for Hilbert transform and its applications
2008-01-01
In this paper, a new distribution space DH is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that DH is the biggest subspace of D on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for Lp functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations of the space DH are given and a class of useful nonlinear phase signals is shown to be in DH. Finally, the applications of the extended Hilbert transform are discussed.
A distribution space for Hilbert transform and its applications
YANG LiHua
2008-01-01
In this paper, a new distribution space D'H is constructed and the definition of the classical Hilbert transform is extended to it, It is shown that D'H is the biggest subspace of D' on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for Lp functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations of the space DH are given and a class of useful nonlinear phase signals is shown to be in D'H. Finally, the applications of the extended Hilbert transform are discussed.
SpaceTime from Hilbert Space: Decompositions of Hilbert Space as Instances of Time
Noorbala, Mahdiyar
2016-01-01
There has been recent interest in identifying entanglement as the fundamental concept from which space may emerge. We note that the particular way that a Hilbert space is decomposed into tensor factors is important in what the resulting geometry looks like. We then propose that time may be regarded as a variable that parameterizes a family of such decompositions, thus giving rise to a family of spatial geometries. As a proof of concept, this idea is demonstrated in two toy models based on Kitaev's toric code, which feature a dynamical change of dimension and topology.
Quantum mechanics in an evolving Hilbert space
Artacho, Emilio; O'Regan, David D.
2017-03-01
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalization, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fiber bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge implied by a smoothly varying basis set readily connects with Berry's formalism for geometric phases. Generalized expressions for the Berry connection and curvature are obtained for a parameter-dependent occupied Hilbert space spanned by nonorthogonal Wannier functions. The formalism is applicable to basis sets made of atomic-like orbitals and also more adaptative moving basis functions (such as in methods using Wannier functions as intermediate or support bases), but should also apply to other situations in which nonorthogonal functions or related projectors should arise. The formalism is applied to the time-dependent quantum evolution of electrons for moving atoms. The geometric insights provided here allow us to propose new finite-difference time integrators, and also better understand those already proposed.
Quantum holonomy theory and Hilbert space representations
Aastrup, Johannes [Mathematisches Institut, Universitaet Hannover (Germany); Moeller Grimstrup, Jesper [QHT Gruppen, Copenhagen Area (Denmark)
2016-11-15
We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state that generates the representation exist is left for later publications. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Relations between Stochastic and Partial Differential Equations in Hilbert Spaces
I. V. Melnikova
2012-01-01
Full Text Available The aim of the paper is to introduce a generalization of the Feynman-Kac theorem in Hilbert spaces. Connection between solutions to the abstract stochastic differential equation and solutions to the deterministic partial differential (with derivatives in Hilbert spaces equation for the probability characteristic is proved. Interpretation of objects in the equations is given.
Contributions to the extension theory in Hilbert spaces
Sandovici, Valerica Adrian; Sandovici, 27740
2006-01-01
This thesis presents solutions to certain problems in the extension theory in Hilbert spaces. Basically there are three main parts of the thesis corresponding to three objects which are studied. The first part consists of chapter 3 and deals with Lagrangian pairs in a pair of Hilbert spaces. In the
Tools for analysis of Dirac structures on Hilbert spaces
Golo, G.; Iftime, O.V.; Zwart, Heiko J.; van der Schaft, Arjan
2004-01-01
In this paper tools for the analysis of Dirac structures on Hilbert spaces are developed. Some properties are pointed out and two natural representations of Dirac structures on Hilbert spaces are presented. The theory is illustrated on the example of the ideal transmission line.
Hilbert Space Operators in Quantum Physics
Blank, Jiří; Havlíček, Miloslav
2008-01-01
The second edition of this course-tested book provides a detailed and in-depth discussion of the foundations of quantum theory as well as its applications to various systems. The exposition is self-contained; in the first part the reader finds the mathematical background in chapters about functional analysis, operators on Hilbert spaces and their spectral theory, as well as operator sets and algebras. This material is used in the second part to a systematic explanation of the foundations, in particular, states and observables, properties of canonical variables, time evolution, symmetries and various axiomatic approaches. In the third part, specific physical systems and situations are discussed. Two chapters analyze Schrödinger operators and scattering, two others added in the second edition are devoted to new important topics, quantum waveguides and quantum graphs. Some praise for the previous edition: "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands...
Oppio, Marco
2016-01-01
As established by Sol\\`er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this issue from another viewpoint, we argue that there is a fundamental reason why elementary quantum systems are not described in real Hilbert spaces: their symmetry group. We consider an elementary relativistic system within Wigner's approach defined as a faithful irreducible continuous unitary representation of the Poincar\\'e group in a real Hilbert space. We prove that, if the squared-mass operator is non-negative, the system admits a natural, Poincar\\'e invariant and unique up to sign, complex structure which commutes with the whole algebra of observables generated by the representation. All that leads to a physically equivalent formulation in a complex Hilbert space. Differently from what happens in the real picture, here all selfadjoint operators are observables in accor...
Hilbert space, Poincare dodecahedron and golden mean transfiniteness
El Naschie, M.S. [Department of Physics, University of Alexandria, Alexandria (Egypt); Department of Astrophysics, Cairo University (Egypt); Department of Physics, Mansura University (Egypt)
2007-02-15
A rather direct connection between Hilbert space and E-infinity theory is established via an irrational-transfinite golden mean topological probability. Subsequently the ramifications for Kleinian modular spaces and the cosmological Poincare Dodecahedron proposals are considered.
Partial Differential Equations A unified Hilbert Space Approach
Picard, Rainer
2011-01-01
This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. Thefocus on a Hilbert space setting is a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations.This global point of view is takenby focussing on the issues involved in determining the appropriate func
Some remarks about interpolating sequences in reproducing kernel Hilbert spaces
Raghupathi, Mrinal
2011-01-01
In this paper we study two separate problems on interpolation. We first give a new proof of Stout's Theorem on necessary and sufficient conditions for a sequence of points to be an interpolating sequence for the multiplier algebra and for an associated Hilbert space. We next turn our attention to the question of interpolation for reproducing kernel Hilbert spaces on the polydisc and provide a collection of equivalent statements about when it is possible to interpolation in the Schur-Agler class of the associated reproducing kernel Hilbert space.
Analytic Characterization for Hilbert-Schmidt Operators on Fock Space
Cai Shi WANG; Zhi Yuan HUANG; Xiang Jun WANG
2005-01-01
In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism.
Isometric Reflection Vectors and Characterizations of Hilbert Spaces
Donghai Ji
2014-01-01
Full Text Available A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere SX of a Banach space X has nonempty interior in SX, then X is a Hilbert space. Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis.
Space from Hilbert space: Recovering geometry from bulk entanglement
Cao, ChunJun; Carroll, Sean M.; Michalakis, Spyridon
2017-01-01
We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space H into a tensor product of factors, we consider a class of "redundancy-constrained states" in H that generalize the area-law behavior for entanglement entropy usually found in condensed-matter systems with gapped local Hamiltonians. Using mutual information to define a distance measure on the graph, we employ classical multidimensional scaling to extract the best-fit spatial dimensionality of the emergent geometry. We then show that entanglement perturbations on such emergent geometries naturally give rise to local modifications of spatial curvature which obey a (spatial) analog of Einstein's equation. The Hilbert space corresponding to a region of flat space is finite-dimensional and scales as the volume, though the entropy (and the maximum change thereof) scales like the area of the boundary. A version of the ER =EPR conjecture is recovered, in that perturbations that entangle distant parts of the emergent geometry generate a configuration that may be considered as a highly quantum wormhole.
Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
Cao, ChunJun
2016-01-01
We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space $\\mathcal{H}$ into a tensor product of factors, we consider a class of "redundancy-constrained states" in $\\mathcal{H}$ that generalize the area-law behavior for entanglement entropy usually found in condensed-matter systems with gapped local Hamiltonians. Using mutual information to define a distance measure on the graph, we employ classical multidimensional scaling to extract the best-fit spatial dimensionality of the emergent geometry. We then show that entanglement perturbations on such emergent geometries naturally give rise to local modifications of spatial curvature which obey a (spatial) analog of Einstein's equation. The Hilbert space corresponding to a region of flat space is finite-dimensional and scales as the volume, though the entropy (and the maximum change thereof) scales like the area of the boundary. A version of...
Hilbert space renormalization for the many-electron problem
Li, Zhendong
2015-01-01
Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction ansatz, namely the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the 'physical indices' or the coupling rules in the HS-MPS. Alternatively, simply truncating the 'virtual dimension' of the HS-MPS leads to a family of size-extensive wav...
The 2-Hilbert Space of a Prequantum Bundle Gerbe
Bunk, Severin; Szabo, Richard J
2016-01-01
We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier-Douady class is torsion. Analogously to usual prequantisation, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space. These sections are obtained as certain morphism categories in Waldorf's version of the 2-category of line bundle gerbes. We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian. We introduce a dual functor on the sections, which yields a closed structure on the morphisms between bundle gerbes and turns the category of sections into a 2-Hilbert space. We discuss how these 2-Hilbert spaces fit various expectations from higher prequantisation. We then extend the transgression functor to the full 2-category of bundle gerbes and demonstrate its compatibility with the additional structures introduced. We discuss various aspects of Kostant-Souriau prequantisation in this setting, including its dimensional reductio...
Automorphisms of Hilbert space effect algebras
Šemrl, Peter
2015-05-01
Let H be a Hilbert space and E (H) the effect algebra on H. A bijective map φ :E(H)\\to E(H) is called an ortho-order automorphism of E (H) if for every A,B\\in E(H) we have A≤slant B \\Longleftrightarrow φ (A)≤slant φ (B) and φ ({{A}\\bot })=φ {{(A)}\\bot }. The classical theorem of Ludwig states that every such ϕ is of the form φ (A)=UA{{U}*}, A\\in E(H), for some unitary or antiunitary operator U. It is also known that each bijective map on E (H) preserving order and coexistency in both directions is of the same form. Can we improve these two theorems by relaxing the bijectivity assumption and/or replacing the above preserving properties by the weaker assumptions of preserving above relations in one direction only and still get the same conclusion? For both characterizations of automorphisms of effect algebras we will prove the optimal versions and give counterexamples showing the optimality of the obtained results. This research was supported by a grant from ARRS, Slovenia.
Snakes and articulated arms in an Hilbert space
Pelletier, Fernand
2011-01-01
The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [Pe] and [LaPe]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [Ha], [Ro] and proved for a finite dimensional Hilbert space
The Hilbert Inequality in Banach Spaces%Banach空间上的Hilbert不等式
华柳斌; 黎永锦
2011-01-01
Some Hilbert's inequalities in Hilbert spaces and Banach spaces were discussed by inner and functional. The Hilbert spaces and Banach space version of Hilbert's inequalities were established.%利用内积和泛函,在Hilbert空间和Banach空间中讨论Hilbert不等式,建立了抽象空间的Hilbert不等式.
On the Inclusion Relation of Reproducing Kernel Hilbert Spaces
Zhang, Haizhang; Zhao, Liang
2011-01-01
To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established. A full table of inclusion relations among widely-used translation invariant kernels is given. Concrete examples for Hilbert-Schmidt kernels are presented as well. We also discuss the preservation of such a relation under various operations of ...
Hilbert Space of Probability Density Functions Based on Aitchison Geometry
J. J. EGOZCUE; J. L. D(I)AZ-BARRERO; V. PAWLOWSKY-GLAHN
2006-01-01
The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison's ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.
Securing QKD Li01nks in the Full Hilbert Space
Jackson, David J
2004-01-01
Many quantum key distribution analyses examine the link security in a subset of the full Hilbert space that is available to describe the system. In reality, information about the photon state can be embedded in correlations between the polarization space and other dimensions of the Hilbert space in such a way that Eve can determine the polarization of a photon without affecting it. This paper uses the concept of suitability to quantify the available information for Eve, and then describe a systematic way to calculate and measure these possibilities.
ON APPROXIMATION BY SPHERICAL REPRODUCING KERNEL HILBERT SPACES
无
2007-01-01
The spherical approximation between two nested reproducing kernels Hilbert spaces generated from different smooth kernels is investigated. It is shown that the functions of a space can be approximated by that of the subspace with better smoothness. Furthermore, the upper bound of approximation error is given.
Generalized Jordan Semitriple Maps on Hilbert Space Effect Algebras
Qing Yuan
2014-01-01
Full Text Available Let ℰ(H be the Hilbert space effect algebra on a Hilbert space H with dimH≥3, α,β two positive numbers with 2α+β≠1 and Φ:ℰ(H→ℰ(H a bijective map. We show that if Φ(AαBβAα=Φ(AαΦ(BβΦ(Aα holds for all A,B∈ℰ(H, then there exists a unitary or an antiunitary operator U on H such that Φ(A=UAU* for every A∈ℰ(H.
Coarsely Invariant Hilbert Spaces over Infinite Connected Graphs
WANG Qin
2002-01-01
We study in this paper a Hilbert space HV associated with the coarse geometry of an infinite connected graph X(V, E) with vertex set V and edge set E. We show that X(V,E) is uniformly expanding if and only ifl2(V)can be continuously included in HV as a closed subspace,and that the inner product structure of HV is topologically invariant under uniform coarsening of the graph. We also discuss the functorial properties of these Hilbert spaces.
Marshall Space Flight Center High Speed Turbopump Bearing Test Rig
Gibson, Howard; Moore, Chip; Thom, Robert
2000-01-01
The Marshall Space Flight Center has a unique test rig that is used to test and develop rolling element bearings used in high-speed cryogenic turbopumps. The tester is unique in that it uses liquid hydrogen as the coolant for the bearings. This test rig can simulate speeds and loads experienced in the Space Shuttle Main Engine turbopumps. With internal modifications, the tester can be used for evaluating fluid film, hydrostatic, and foil bearing designs. At the present time, the test rig is configured to run two ball bearings or a ball and roller bearing, both with a hydrostatic bearing. The rig is being used to evaluate the lifetimes of hybrid bearings with silicon nitride rolling elements and steel races.
Hilbert space renormalization for the many-electron problem.
Li, Zhendong; Chan, Garnet Kin-Lic
2016-02-28
Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction Ansatz, namely, the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the "physical indices" or the coupling rules in the HS-MPS. Alternatively, simply truncating the "virtual dimension" of the HS-MPS leads to a family of size-extensive wave function Ansätze that can be used efficiently in variational calculations. We make formal and numerical comparisons between the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI approximations. The analysis and results shed light on fundamental aspects of the efficient representation of many-electron wavefunctions through the renormalization of many-body states.
On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space
Hamdy M. Ahmed
2009-01-01
Full Text Available We study a class of fractional stochastic integrodifferential equations considered in a real Hilbert space. The existence and uniqueness of the Mild solutions of the considered problem is also studied. We also give an application for stochastic integropartial differential equations of fractional order.
Perturbation for Frames for a Subspace of a Hilbert Space
Christensen, Ole; deFlicht, C.; Lennard, C.
1997-01-01
We extend a classical result stating that a sufficiently small perturbation$\\{ g_i \\}$ of a Riesz sequence $\\{ f_i \\}$ in a Hilbert space $H$ is again a Riesz sequence. It turns out that the analog result for a frame does not holdunless the frame is complete. However, we are able to prove a very...
Approximate controllability of semilinear neutral systems in Hilbert spaces
N. I. Mahmudov
2003-01-01
Full Text Available The approximate controllability of semilinear neutral systems in Hilbert spaces is studied using the Schauder fixed point theorem. It is shown that the approximate controllability of the semilinear system under some conditions is implied by the approximate controllability of its linear part.
A geometric approach to quantum control in projective hilbert spaces
Pastorello, Davide
2017-02-01
A quantum theory in a finite-dimensional Hilbert space can be formulated as a proper geometric Hamiltonian theory as explained in [2, 3, 7, 9]. From this point of view a quantum system can be described within a classical-like framework where quantum dynamics is represented by a Hamiltonian flow in the phase space given by a projective Hilbert space. This paper is devoted to investigating how the notion of an accessibility algebra from classical control theory can be applied within the geometric Hamiltonian formulation of quantum mechanics to study controllability of a quantum system. A new characterization of quantum controllability in terms of Killing vector fields w.r.t. the Fubini-Study metric on projective space is also discussed.
Observables and density matrices embedded in dual Hilbert spaces
Prosen, T.; Martignon, L.; Seligman, T. H.
2015-06-01
The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured that we deal with Hilbert spaces although the mathematical background was not entirely clear, particularly, when dealing with bosonic operators. This in turn caused some doubts about the correct way to combine bosonic and fermionic operators or, in other words, regular and Grassmann variables. In this paper we present a formal answer to the problems on a simple and very general basis. We illustrate the resulting construction by revisiting the Bargmann transform and finding the known connection between {{L}}2({{R}}) and the Bargmann-Hilbert space. We pursue this line of thinking one step further and discuss the representations of complex extensions of linear canonical transformations as isometries between dual Hilbert spaces. We then use the formalism to give an explicit formulation for Fock spaces involving both fermions and bosons thus solving the problem at the origin of our considerations.
The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces
Ćurgus, Branko; Dijksma, Aad; Read, Tom
2001-01-01
The boundary eigenvalue problems for the adjoint of a symmetric relation S in a Hilbert space with finite, not necessarily equal, defect numbers, which are related to the selfadjoint Hilbert space extensions of S are characterized in terms of boundary coefficients and the reproducing kernel Hilbert
Hypercyclic Behavior of Translation Operators on Spaces of Analytic Functions on Hilbert Spaces
Zoryana Mozhyrovska
2015-01-01
Full Text Available We consider special Hilbert spaces of analytic functions of many infinite variables and examine composition operators on these spaces. In particular, we prove that under some conditions a translation operator is bounded and hypercyclic.
Precise Asymptotics for Complete Moment Convergence in Hilbert Spaces
Keang Fu; Juan Chen
2012-02-01
Let $\\{X, X_n;n≥ 1\\}$ be a sequence of i.i.d. random variables taking values in a real separable Hilbert space $(H,\\|\\cdot p\\|)$ with covariance operator $\\sum$. Set $S_n=\\sum^n_{i=1}X_i,n≥ 1$. We prove that for 1 < < 2 and $r>1+p/2$, \\begin{multline*}\\lim\\limits_{\\searrow 0}^{(2r-p-2)/(2-p)}\\sum\\limits^∞_{n=1}n^{r/p-2-1/p}E\\{\\|S_n\\|- n^{1/p}\\}+\\\\ =^{-(2r-2-p)/(2-p)}\\frac{p(2-p)}{(r-p)(2r-p-2)}E\\|Y\\|^{2(r-p)/(2-p)},\\end{multline*} where is a Gaussian random variable taking value in a real separable Hilbert space with mean zero and covariance operator , and 2 is the largest eigenvalue of .
Hilbert space structure in quantum gravity: an algebraic perspective
Giddings, Steven B
2015-01-01
If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. This viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of the Hilbert space is problematic. Instead it is better to focus on on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of...
Finite-part singular integral approximations in Hilbert spaces
E. G. Ladopoulos
2004-01-01
Full Text Available Some new approximation methods are proposed for the numerical evaluation of the finite-part singular integral equations defined on Hilbert spaces when their singularity consists of a homeomorphism of the integration interval, which is a unit circle, on itself. Therefore, some existence theorems are proved for the solutions of the finite-part singular integral equations, approximated by several systems of linear algebraic equations. The method is further extended for the proof of the existence of solutions for systems of finite-part singular integral equations defined on Hilbert spaces, when their singularity consists of a system of diffeomorphisms of the integration interval, which is a unit circle, on itself.
Separability criteria with angular and Hilbert space averages
Fujikawa, Kazuo; Oh, C. H.; Umetsu, Koichiro; Yu, Sixia
2016-05-01
The practically useful criteria of separable states ρ =∑kwkρk in d = 2 × 2 are discussed. The equality G(a , b) = 4 [ - ] = 0 for any two projection operators P(a) and P(b) provides a necessary and sufficient separability criterion in the case of a separable pure state ρ = | ψ > Werner state is applied to two photon systems, it is shown that the Hilbert space average can judge its inseparability but not the geometrical angular average.
A construction of full qed using finite dimensional Hilbert space
Francis, Charles
2006-01-01
While causal perturbation theory and lattice regularisation allow treatment of the ultraviolet divergences in qed, they do not resolve the issues of constructive field theory, or show the validity of qed except as a perturbation theory. I present a rigorous construction of quantum and classical electrodynamics from fundamental principles of quantum theory. Hilbert space of dimension N is justified from statements about measurements with finite range and resolution. Using linear combinations o...
Differential representations of dynamical oscillator symmetries in discrete Hilbert space
Andreas Ruffing
2000-01-01
Full Text Available As a very important example for dynamical symmetries in the context of q-generalized quantum mechanics the algebra aa†−q−2a†a=1 is investigated. It represents the oscillator symmetry SUq(1,1 and is regarded as a commutation phenomenon of the q-Heisenberg algebra which provides a discrete spectrum of momentum and space, i.e., a discrete Hilbert space structure. Generalized q-Hermite functions and systems of creation and annihilation operators are derived. The classical limit q→1 is investigated. Finally the SUq(1,1 algebra is represented by the dynamical variables of the q-Heisenberg algebra.
Cantorian spacetime and Hilbert space: Part I-Foundations
Iovane, G. [Dipartimento di Ingegneria dell' Informazione e Matematica Applicata, Universita di Salerno, Via Ponte Don Melillo, 84084 Fisicano, SA (Italy)]. E-mail: iovane@diima.unisa.it
2006-05-15
We are going to show the link between the {epsilon} {sup ({infinity})} Cantorian space and the Hilbert spaces H {sup ({infinity})}. In particular, El Naschie's {epsilon} {sup ({infinity})} is a physical spacetime, i.e. an infinite dimensional fractal space, where time is spacialized and the transfinite nature manifests itself. El Naschie's Cantorian spacetime is an arena where the physics laws appear at each scale in a self-similar way linked to the resolution of the act of observation. By contrast the Hilbert space H {sup ({infinity})} is a mathematical support, which describes the interaction between the observer and the dynamical system under measurement. The present formulation, which is based on the non-classical Cantorian geometry and topology of spacetime, automatically solves the paradoxical outcome of the two-slit experiment and the so-called particle-wave duality. In particular, measurement (i.e. the observation) is equivalent to a projection of {epsilon} {sup ({infinity})} in the Hilbert space built on 3 + 1 Euclidean spacetime. Consequently, the wave-particle duality becomes a mere natural consequence of conducting an experiment in a spacetime with non-classical topological and geometrical structures, while observing and taking measurements in a classical smooth 3 + 1 Euclidean spacetime. In other words, the experimental fact that a wave-particle duality exists is an indirect confirmation of the existence of {epsilon} {sup ({infinity})} and a property of the quantum-classical interface. Another direct consequence of the fact that real spacetime is infinite dimensional hierarchical {epsilon} {sup ({infinity})} is the existence of scaling law R(N), introduced by the author, which generalizes the Compton wavelength. It gives an answer to the problem of segregation of matter at different scales, and shows the role of fundamental constants such as the speed of light and Plank's constant h in the fundamental lengths scale without invoking the
Explicit signal to noise ratio in reproducing kernel Hilbert spaces
Gomez-Chova, Luis; Nielsen, Allan Aasbjerg; Camps-Valls, Gustavo
2011-01-01
This paper introduces a nonlinear feature extraction method based on kernels for remote sensing data analysis. The proposed approach is based on the minimum noise fraction (MNF) transform, which maximizes the signal variance while also minimizing the estimated noise variance. We here propose...... an alternative kernel MNF (KMNF) in which the noise is explicitly estimated in the reproducing kernel Hilbert space. This enables KMNF dealing with non-linear relations between the noise and the signal features jointly. Results show that the proposed KMNF provides the most noise-free features when confronted...
Real analysis measure theory, integration, and Hilbert spaces
Stein, Elias M
2005-01-01
Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After
Invitation to linear operators from matrices to bounded linear operators on a Hilbert space
Furuta, Takayuki
2014-01-01
Most books on linear operators are not easy to follow for students and researchers without an extensive background in mathematics. Self-contained and using only matrix theory, Invitation to Linear Operators: From Matricies to Bounded Linear Operators on a Hilbert Space explains in easy-to-follow steps a variety of interesting recent results on linear operators on a Hilbert space. The author first states the important properties of a Hilbert space, then sets out the fundamental properties of bounded linear operators on a Hilbert space. The final section presents some of the more recent developm
Hilbert space structure in quantum gravity: an algebraic perspective
Giddings, Steven B.
2015-12-01
If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. This viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of the Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of a fundamental role for entanglement.
New Characterizations of Fusion Bases and Riesz Fusion Bases in Hilbert Spaces
Asgari, Mohammad Sadegh
2012-01-01
In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new definition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we define the fusion biorthogonal sequence, Bessel fusion basis, Hilbert fusion basis and obtain some characterizations of them. we study orthonormal fusion systems...
Convex analysis and monotone operator theory in Hilbert spaces
Bauschke, Heinz H
2017-01-01
This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, ma...
Finite-dimensional Hilbert space and frame quantization
Cotfas, Nicolae [Faculty of Physics, University of Bucharest, PO Box 76-54, Post Office 76, Bucharest (Romania); Gazeau, Jean Pierre [Laboratoire APC, Universite Paris Diderot, 10, rue A Domon et L Duquet, 75205 Paris Cedex 13 (France); Vourdas, Apostol, E-mail: ncotfas@yahoo.com, E-mail: gazeau@apc.univ-paris7.fr, E-mail: A.Vourdas@bradford.ac.uk [Department of Computing, University of Bradford, Bradford BD7 1DP (United Kingdom)
2011-04-29
The quantum observables used in the case of quantum systems with finite-dimensional Hilbert space are defined either algebraically in terms of an orthonormal basis and discrete Fourier transformation or by using a continuous system of coherent states. We present an alternative approach to these important quantum systems based on the finite frame quantization. Finite systems of coherent states, usually called finite tight frames, can be defined in a natural way in the case of finite quantum systems. Novel examples of such tight frames are presented. The quantum observables used in our approach are obtained by starting from certain classical observables described by functions defined on the discrete phase space corresponding to the system. They are obtained by using a finite frame and a Klauder-Berezin-Toeplitz-type quantization. Semi-classical aspects of tight frames are studied through lower symbols of basic classical observables.
Construction and coupling of frames in Hilbert spaces with W-metrics
German Escobar
2016-05-01
Full Text Available A definition of frames unitarily equivalent in Hilbert spaces with W-metric is stated, and a characterization is given in terms of their respective analysis operators. From a Hilbert space with a frame we construct a Hilbert space with W-metric and a frame unitarily equivalent to the given one. Finally, we prove that the coupling of two frames is a frame. Resumen. Se definen marcos unitariamente equivalentes en espacios de Hilbert con W-métricas, y se da una caracterización de ellos comparando sus respectivos operadores de análisis. A partir de un espacio de Hilbert con un marco se construye un espacio de Hilbert con W-métrica y un marco unitariamente equivalente al dado. Finalmente, se muestra que el acoplamiento de dos marcos es un marco.
Area integral functions and $H^{\\8}$ functional calculus for sectorial operators on Hilbert spaces
Chen, Zeqian; Sun, Mu
2012-01-01
Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi's results on $H^{\\8}$ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.
Recursive estimation of the conditional geometric median in Hilbert spaces
Cardot, Hervé; Zitt, Pierre-André
2012-01-01
A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirms the interest of this new and fast algorithm when the sample sizes are large. Finally, the ability of these recursive algorithms to deal with very high-dimensional data is illustrated on the robust estimation of television audience profiles conditional on the total time spent watching television over a period of 24 hours.
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
Hamiltonian and physical Hilbert space in polymer quantum mechanics
Corichi, A; Zapata, R J A; Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A.
2006-01-01
In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested, Schroedinger quantum mechanics. The kinematical cornerstone of our framework is the so called polymer representation of the Heisenberg-Weyl (H-W) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schroedinger representation of quantum mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed.
Simulating strongly correlated multiparticle systems in a truncated Hilbert space
Ernst, Thomas; Hallwood, David W.; Gulliksen, Jake; Brand, Joachim [New Zealand Institute for Advanced Study and Centre for Theoretical Chemistry and Physics, Massey University, Private Bag 102904, North Shore, Auckland 0745 (New Zealand); Meyer, Hans-Dieter [Theoretische Chemie, Physikalisch-Chemisches Institut, Universitaet Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg (Germany)
2011-08-15
Representing a strongly interacting multiparticle wave function in a finite product basis leads to errors. Simple rescaling of the contact interaction can preserve the low-lying energy spectrum and long-wavelength structure of wave functions in one-dimensional systems and thus correct for the basis set truncation error. The analytic form of the rescaling is found for a two-particle system where the rescaling is exact. A detailed comparison between finite Hilbert space calculations and exact results for up to five particles show that rescaling can significantly improve the accuracy of numerical calculations in various external potentials. In addition to ground-state energies, the low-lying excitation spectrum, density profile, and correlation functions are studied. The results give a promising outlook for numerical simulations of trapped ultracold atoms.
Chandran, A.; Schulz, M. D.; Burnell, F. J.
2016-01-01
Many phases of matter, including superconductors, fractional quantum Hall fluids and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this article, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned ...
A Hilbert Space setting for higher spin interactions which replaces Gauge Theory
Schroer, Bert
2014-01-01
The recently discovered Hilbert space description of renormalizable interactions of higher spin (equal or bigger than 1) fields requires to replace the pointlocal s=1 vectorpotentials of indefinite metric (Krein space) BRST gauge theory by their stringlike counterpart in Hilbert space. It is shown that the Hilbert space positivity leads to new properties outside the conceptual range of the gauge theoretic description: topological aspects of Wilson loops, induced normalization terms (in particular Mexican hat type potentials for massive vectormesons coupled to Hermitian scalar field) and a possible role of string-localization in confinerment and "darkness".
THE REALIZATION OF MULTIPLIER HILBERT BIMODULE ON BIDUAL SPACE AND TIETZE EXTENSION THEOREM
无
2000-01-01
The multiplier bimodule of Hilbert bimodule is introduced in a way similar to [1],and its realization on a quotient of bidual space and Tietze extension theorem are obtained similar to that in C*-algebra case. As a result,the multiplier bimodule here is also a Hilbert bimodule.
Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
Dittrich, Bianca; Kaminski, Wojciech
2012-01-01
In this and the companion paper a novel holonomy formulation of so called Spin Foam models of lattice gauge gravity are explored. After giving a natural basis for the space of simplicity constraints we define a universal boundary Hilbert space, on which the imposition of different forms of the simplicity constraints can be studied. We detail under which conditions this Hilbert space can be mapped to a Hilbert space of projected spin networks or an ordinary spin network space. These considerations allow to derive the general form of the transfer operators which generates discrete time evolution. We will describe the transfer operators for some current models on the different boundary Hilbert spaces and highlight the role of the simplicity constraints determining the concrete form of the time evolution operators.
Relating Berkovits and $A_\\infty$ Superstring Field Theories; Large Hilbert Space Perspective
Erler, Theodore
2015-01-01
We lift the dynamical field of the $A_\\infty$ superstring field theory to the large Hilbert space by introducing a trivial gauge invariance associated with the eta zero mode. We then provide a field redefinition which relates to the lifted field to the dynamical field of Berkovits' superstring field theory in the large Hilbert space. This generalizes the field redefinition in the small Hilbert space described in earlier works, and is useful for understanding the relation between the gauge symmetries of the theories.
Banan Maayah
2014-01-01
Full Text Available A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge-Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillator’s models.
Mild solutions of semilinear elliptic equations in Hilbert spaces
Federico, Salvatore; Gozzi, Fausto
2017-03-01
This paper extends the theory of regular solutions (C1 in a suitable sense) for a class of semilinear elliptic equations in Hilbert spaces. The notion of regularity is based on the concept of G-derivative, which is introduced and discussed. A result of existence and uniqueness of solutions is stated and proved under the assumption that the transition semigroup associated to the linear part of the equation has a smoothing property, that is, it maps continuous functions into G-differentiable ones. The validity of this smoothing assumption is fully discussed for the case of the Ornstein-Uhlenbeck transition semigroup and for the case of invertible diffusion coefficient covering cases not previously addressed by the literature. It is shown that the results apply to Hamilton-Jacobi-Bellman (HJB) equations associated to infinite horizon optimal stochastic control problems in infinite dimension and that, in particular, they cover examples of optimal boundary control of the heat equation that were not treatable with the approaches developed in the literature up to now.
Quasilinear Inner Product Spaces and Hilbert Quasilinear Spaces
Hacer Bozkurt
2014-01-01
Full Text Available Aseev launched a new branch of functional analysis by introducing the theory of quasilinear spaces in the framework of the topics of norm, bounded quasilinear operators and functionals (Aseev (1986. Furthermore, some quasilinear counterparts of classical nonlinear analysis that lead to such result as Frechet derivative and its applications were examined deal with. This pioneering work causes a lot of results in such applications such as (Rojas-Medar et al. (2005, Talo and Başar (2010, and Nikol'skiĭ (1993. His work has motivated us to introduce the concept of quasilinear inner product spaces. Thanks to this new notion, we obtain some new theorems and definitions which are quasilinear counterparts of fundamental definitions and theorems in linear functional analysis. We claim that some new results related to this concept provide an important contribution to the improvement of quasilinear functional analysis.
Near Subnormality of Weighted Shifts and the Answer to the Hilbert Space Problem 160
WANG Gong-bao
2001-01-01
In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160are presented at the end of the paper.
Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order
Balashov, Maxim V.; Repovš, Dušan,
2011-01-01
We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius.
On the minimizers of calculus of variations problems in Hilbert spaces
Gomes, Diogo A.
2014-01-19
The objective of this paper is to discuss existence, uniqueness and regularity issues of minimizers of one dimensional calculus of variations problem in Hilbert spaces. © 2014 Springer-Verlag Berlin Heidelberg.
Andrei Perjan
2009-07-01
Full Text Available We study the behavior of solutions to perturbed second order abstract evolution equations in Hilbert spaces, when the small parameter, multiplying the second order time derivative, converges to zero.
Nonlocality Proof for Two-Particle Systems in 3 3 Hilbert Space
WU Xiao-Hua; ZONG Hong-Shi; PANG Hou-Rong; WANG Fan
2001-01-01
For a two-particle system in 3 3 Hilbert space, we derive a new type of inequality for local hidden variable model. Using an entangled state, we give a realizable experiment whose joint probabilities violate the inequality.``
Silva, Ralph; Manzano, Gonzalo; Skrzypczyk, Paul; Brunner, Nicolas
2016-09-01
Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relationship between the size of the machine (captured by Hilbert space dimension) and the performance of the machine. Using the concepts of virtual qubits and virtual temperatures, we show that higher dimensional machines can outperform smaller ones. For instance, by considering refrigerators with more levels, lower temperatures can be achieved, as well as higher power. We discuss the optimal design for refrigerators of a given dimension. As a consequence we obtain a statement of the third law in terms of Hilbert space dimension: Reaching absolute zero temperature requires infinite dimension. These results demonstrate that Hilbert space dimension should be considered a thermodynamic resource.
Time-Dependent and/or Nonlocal Representations of Hilbert Spaces in Quantum Theory
M. Znojil
2010-01-01
Full Text Available A few recent innovations of the applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics is discussed in its slightly broadened four-Hilbert-space update. Among applications involving several new scattering and bound-state problems the central role is played by models using apparently non-Hermitian (often called “crypto-Hermitian” Hamiltonians with real spectra. The formalism (originally inspired by the topical need for a mathematically consistent description of tobogganic quantum models is shown to admit even certain unusual nonlocal and/or “moving-frame” representations H(S of the standard physical Hilbert space of wave functions.
How to Derive the Hilbert-Space Formulation of Quantum Mechanics From Purely Operational Axioms
D'Ariano, G M
2006-01-01
In the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of "physical experiment" and assuming "experimental accessibility and simplicity" as specified by five simple Postulates. This accomplishes the program presented in form of conjectures in the previous paper quant-ph/0506034. Pivotal roles are played by the "local observability principle", which reconciles the holism of nonlocality with the reductionism of local observation, and by the postulated existence of "informationally complete observables" and of a "symmetric faithful state". This last notion allows one to introduce an operational definition for the real version of the "adjoint"--i. e. the transposition--from which one can derive a real Hilbert-space structure via either the Mackey-Kakutani or the Gelfand-Naimark-Segal constructions. Here I analyze in detail only the Gelfand-Naimark-Segal construction, which leads to a real Hilbert space structure analogous to that...
Characterizations of g-Frames and g-Riesz Bases in Hilbert Spaces
Yu Can ZHU
2008-01-01
In this paper,we introduce the pre-frame operator Q for the g-frame in a complex Hilbert space,which will play a key role in studying g-frames and g-Riesz bases etc.Using the pre-frame operator Q,we give some necessary and sufficient conditions for a g-Bessel sequence,a g-frame,and a g-Riesz basis in a complex Hilbert space,which have properties similar to those of the Bessel sequence, frame,and Riesz basis respectively.We also obtain the relation between a g-frame and a g-Riesz basis, and the relation of bounds between a g-frame and a g-Riesz basis.Lastly,we consider the stability of a g-frame or a g-Riesz basis for a Hilbert space under perturbation.
Asymptotic behaviour of a family of gradient algorithms in R^d and Hilbert spaces
Pronzato, Luc; Zhigljavsky, Anatoly A
2008-01-01
The asymptotic behaviour of a family of gradient algorithms (including the methods of steepest descent and minimum residues) for the optimisation of bounded quadratic operators in R^d and Hilbert spaces is analyzed. The results obtained generalize those of Akaike (1959) in several directions. First, all algorithms in the family are shown to have the same asymptotic behaviour (convergence to a two-point attractor), which implies in particular that they have similar asymptotic convergence rates. Second, the analysis also covers the Hilbert space case. A detailed analysis of the stability property of the attractor is provided.
Subalakshmi, R. [Department of Mathematics, Bharathiar University, Coimbatore 641 046 (India)], E-mail: suba.ab.bu@gmail.com; Balachandran, K. [Department of Mathematics, Bharathiar University, Coimbatore 641 046 (India)], E-mail: balachandran_k@lycos.com
2009-11-30
Many practical systems in physical and biological sciences have impulsive dynamical behaviours during the evolution process which can be modeled by impulsive differential equations. This paper studies the approximate controllability properties of nonlinear stochastic impulsive integrodifferential and neutral functional stochastic impulsive integrodifferential equations in Hilbert spaces. Assuming the conditions for the approximate controllability of these linear systems we obtain the sufficient conditions for the approximate controllability of these associated nonlinear stochastic impulsive integrodifferential systems in Hilbert spaces. The results are obtained by using the Nussbaum fixed-point theorem. Finally, two examples are presented to illustrate the utility of the proposed result.
The Construction of Hilbert Spaces over the Non-Newtonian Field
Uğur Kadak
2014-01-01
the novel presentations probably lead most naturally to the development of the non-Newtonian calculi. In this paper we introduce vector spaces over real and complex non-Newtonian field with respect to the *-calculus which is a branch of non-Newtonian calculus. Also we give the definitions of real and complex inner product spaces and study Hilbert spaces which are special type of normed space and complete inner product spaces in the sense of *-calculus. Furthermore, as an example of Hilbert spaces, first we introduce the non-Cartesian plane which is a nonlinear model for plane Euclidean geometry. Secondly, we give Euclidean, unitary, and sequence spaces via corresponding norms which are induced by an inner product. Finally, by using the *-norm properties of complex structures, we examine Cauchy-Schwarz and triangle inequalities.
Convergence of a general iterative method for nonexpansive mappings in Hilbert spaces
Cho, Yeol Je; Qin, Xiaolong
2009-06-01
In this paper, we introduce a modified Ishikawa iterative process for approximating a fixed point of nonexpansive mappings in Hilbert spaces. We establish some strong convergence theorems of the general iteration scheme under some mild conditions. The results improve and extend the corresponding results of many others.
Discrimination and synthesis of recursive quantum states in high-dimensional Hilbert spaces
Simon, David S.; Fitzpatrick, Casey A.; Sergienko, Alexander V.
2015-04-01
We propose an interferometric method for statistically discriminating between nonorthogonal states in high-dimensional Hilbert spaces for use in quantum information processing. The method is illustrated for the case of photon orbital angular momentum (OAM) states. These states belong to pairs of bases that are mutually unbiased on a sequence of two-dimensional subspaces of the full Hilbert space, but the vectors within the same basis are not necessarily orthogonal to each other. Over multiple trials, this method allows distinguishing OAM eigenstates from superpositions of multiple such eigenstates. Variations of the same method are then shown to be capable of preparing and detecting arbitrary linear combinations of states in Hilbert space. One further variation allows the construction of chains of states obeying recurrence relations on the Hilbert space itself, opening a new range of possibilities for more abstract information-coding algorithms to be carried out experimentally in a simple manner. Among other applications, we show that this approach provides a simplified means of switching between pairs of high-dimensional mutually unbiased OAM bases.
On the quasiuniqueness of solutions of degenerate equations in Hilbert space
Vladimir Schuchman
1988-01-01
Full Text Available In this paper, we study the quasiuniqueness (i.e., f1≐f2 if f1−f2 is flat, the function f(t being called flat if, for any K>0, t−kf(t→0 as t→0 for ordinary differential equations in Hilbert space. The case of inequalities is studied, too.
On the physical Hilbert space of $QCD_2$ in the decoupled formulation
Cabra, D C
1997-01-01
We consider the QCD$_2$ partition function in the non-local, decoupled formulation and systematically establish which subset of the nilpotent Noether charges is required to vanish on the physical states. The implications for the Hilbert space structure are also examined.
Growth estimates for $\\exp(A^{-1}t)$ on a Hilbert space
Zwart, H.J.
2007-01-01
Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on the Hilbert space $H$. Since $A^{-1}$ is a bounded operator, it is the infinitesimal generator of a strongly continuous semigroup. In this paper we show that the growth of this semigroup is bounded by
Existence Results for Impulsive Neutral Stochastic Evolution Inclusions in Hilbert Space
Han Wen NING; Bin LIU
2011-01-01
This paper is concerned with the existence of mild solutions of a class of impulsive neutral stochastic evolution inclusions in Hilbert space in the case where the right hand side is convex or nonconvex-valued.The results are obtained by using two fixed point theorems for multivalued mappings and evolution system theory.
Approximation of Besov vectors by Paley-Wiener vectors in Hilbert spaces
Pesenson, Isaac Z
2011-01-01
We develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data representation, compression, denoising and visualization. These tasks are of great importance to machine learning, complex data analysis and computer vision.
Approximately dual frames in Hilbert spaces and applications to Gabor frames
Christensen, Ole; Laugesen, Richard S.
2011-01-01
Approximately dual frames are studied in the Hilbert space setting. Approximate duals are easier to construct than classical dual frames, and can be tailored to yield almost perfect reconstruction. Bounds on the deviation from perfect reconstruction are obtained for approximately dual frames cons...
New Hybrid Iterative Schemes for an Infinite Family of Nonexpansive Mappings in Hilbert Spaces
Guo Baohua
2010-01-01
Full Text Available We propose some new iterative schemes for finding common fixed point of an infinite family of nonexpansive mappings in a Hilbert space and prove the strong convergence of the proposed schemes. Our results extend and improve ones of Nakajo and Takahashi (2003.
A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces
Singthong Urailuk
2010-01-01
Full Text Available We introduce a new general iterative method by using the -mapping for finding a common fixed point of a finite family of nonexpansive mappings in the framework of Hilbert spaces. A strong convergence theorem of the purposed iterative method is established under some certain control conditions. Our results improve and extend the results announced by many others.
Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space
Bracken, A. J.
2002-01-01
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Classical mechanics can now be viewed as a deformation of quantum mechanics. The forms of semiquantum approximations to classical mechanics are indicated.
Schroer, Bert
2016-01-01
The Hilbert space formulation of interacting spin 1 vector-potentials stands in an interesting contrast with the point-local Krein space setting.of gauge theory. Already in the absence of interactions the Wilson loop in a Hilbert space setting has a topological property which is missing in the gauge theoretic description (Haag duality, Aharonov-Bohm effect); the conceptual differences increase in the presence of interactions. The Hilbert space positivity weakens the causal localization properties if interacting fields from point- to string-like, but it also improves the short distance properties in that the scale dimensions of string-local fields fields is independent of spin. This makes it possible to find interaction densities within the power-counting bound of renormalizability for any spin, But for string-local interacting fields there is a new requirement (existence of a L,V pair) which has no analog for point-local fields.It insures the preservation of string-localization in higher orders and secures th...
The Construction of Hilbert Spaces over the Non-Newtonian Field
Uğur Kadak; Hakan Efe
2014-01-01
Although there are many excellent ways to present the principle of the classical calculus, the novel presentations probably lead most naturally to the development of the non-Newtonian calculi. In this paper we introduce vector spaces over real and complex non-Newtonian field with respect to the *-calculus which is a branch of non-Newtonian calculus. Also we give the definitions of real and complex inner product spaces and study Hilbert spaces which are special type of normed space and complet...
A Quantitative Version of the Bishop-Phelps Theorem for Operators in Hilbert Spaces
Li Xin CHENG; Yun Bai DONG
2012-01-01
In this paper,with the help of spectral integral,we show a quantitative version of the Bishop-Phelps theorem for operators in complex Hilbert spaces.Precisely,let H be a complex Hilbert space and 0 ＜ ε ＜ 1/2. Then for every bounded linear operator T:H → H and x0 ∈ H with ‖T‖ =1 =‖x0‖ such that ‖Txo‖ ＞ 1 -ε,there exist xε ∈ H and a bounded linear operator S:H → Hwith ‖S‖ =1 =‖xε‖ such that ‖Sxε‖=1,‖xε-x0‖≤√2ε+4√2ε,‖S-T‖≤√2ε.
Corrections to nucleon capture cross sections computed in truncated Hilbert spaces
Acharya, B.; Ekström, A.; Odell, D.; Papenbrock, T.; Platter, L.
2017-03-01
Nucleon capture cross sections enter various astrophysical processes. The measurement of proton capture on nuclei at astrophysically relevant low energies is a challenge, and theoretical computations in this long-wavelength regime are sensitive to the long-distance asymptotics of the wave functions. A theoretical foundation for estimating and correcting errors introduced in capture cross sections due to Hilbert space truncation has so far been lacking. We derive extrapolation formulas that relate the infrared regularized capture amplitudes to the infinite basis limit and demonstrate their efficacy for proton-proton fusion. Our results are thus relevant to current calculations of few-body capture reactions such as proton-proton fusion or proton capture on the deuteron, and they also open the way for the use of ab initio many-body wave functions represented in finite Hilbert spaces in precision calculations of nucleon capture on heavier nuclei.
Precise asymptotics in the law of the logarithm for random fields in Hilbert space
FU Ke-ang; ZHANG Li-xin
2007-01-01
Consider the positive d-dimensional lattice Zd+ (d≥2) with partial ordering ≤, let {XK; K∈Zd+} be i.i.d. random variables taking values in a real separable Hilbert space (H, ‖·‖) with mean zero and covariance operator ∑, and set partial sums SN =∑K≤NXK, K, N ∈ Zd+. Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε↘0 by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of (Gut and Spǎtaru, 2003).
Vacuum GR in Chang--Soo variables: Hilbert space structure in anisotropic minisuperspace
Ita, Eyo
2009-01-01
In this paper we address the major criticism of the pure Kodama state, namely its normalizability and its existence within a genuine Hilbert space of states, by recasting Ashtekar's general relativity into set of new variables attributed to Chang--Soo/CDJ. While our results have been shown for anisotropic minisuperspace, we reserve a treatment of the full theory for a following paper which it is hoped should finally bring this issue to a close. We have performed a canonical treatment of these new variables from the level of the classical/quantum algebra of constraints, all the way to the construction of the Hilbert space of states, and have demonstrated their relevance to the principle of the semiclassical-quantum correspondence. It is hoped that these new variables and their physical interpretation should provide a new starting point for investigations in classical and quantum GR and in the construction of a consistent quantum theory.
Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces
Arnon Ploymukda
2016-01-01
Full Text Available We introduce the notion of Khatri-Rao product for operator matrices acting on the direct sum of Hilbert spaces. This notion generalizes the tensor product and Hadamard product of operators and the Khatri-Rao product of matrices. We investigate algebraic properties, positivity, and monotonicity of the Khatri-Rao product. Moreover, there is a unital positive linear map taking Tracy-Singh products to Khatri-Rao products via an isometry.
Relating Berkovits and $A_\\infty$ Superstring Field Theories; Small Hilbert Space Perspective
Erler, Theodore
2015-01-01
In a previous paper it was shown that the recently constructed action for open superstring field theory based on $A_\\infty$ algebras can be re-written in Wess-Zumino-Witten-like form, thus establishing its relation to Berkovits' open superstring field theory. In this paper we explain the relation between these two theories from a different perspective which emphasizes the small Hilbert space, and in particular the relation between the $A_\\infty$ structures on both sides.
On the System of Nonlinear Mixed Implicit Equilibrium Problems in Hilbert Spaces
Yeol Je Cho
2010-01-01
Full Text Available We use the Wiener-Hopf equations and the Yosida approximation notions to prove the existence theorem of a system of nonlinear mixed implicit equilibrium problems (SMIE in Hilbert spaces. The algorithm for finding a solution of the problem (SMIE is suggested; the convergence criteria and stability of the iterative algorithm are discussed. The results presented in this paper are more general and are viewed as an extension, refinement, and improvement of the previously known results in the literature.
Multiple-Set Split Feasibility Problems for κ-Strictly Pseudononspreading Mapping in Hilbert Spaces
Jing Quan
2013-01-01
Full Text Available The purpose of this paper is to prove some weak and strong convergence theorems for solving the multiple-set split feasibility problems for κ-strictly pseudononspreading mapping in infinite-dimensional Hilbert spaces by using the proposed iterative method. The main results presented in this paper extend and improve the corresponding results of Xu et al. (2006, of Osilike et al. (2011, and of many other authors.
On Nyman, Beurling and Baez-Duarte's Hilbert Space Reformulation of the Riemann Hypothesis
Bhaskar Bagchi
2006-05-01
There has been a surge of interest of late in an old result of Nyman and Beurling giving a Hilbert space formulation of the Riemann hypothesis. Many authors have contributed to this circle of ideas, culminating in a beautiful refinement due to Baez-Duarte. The purpose of this little survey is to dis-entangle the resulting web of complications, and reveal the essential simplicity of the main results.
Wiśnicki, Andrzej
2012-01-01
Suppose that S is a left amenable semitopological semigroup. We prove that if $\\{T_{t}: t \\in S \\}$ is a uniformly k-Lipschitzian semigroup on a bounded closed and convex subset C of a Hilbert space and $k<\\sqrt{2}$, then the set of fixed points of this semigroup is a H\\"{o}lder continuous retract of C. This gives a qualitative complement to the Ishihara-Takahashi fixed point existence theorem.
Beta-gamma system, pure spinors and Hilbert series of arc spaces
Bhamidipati, Chandrasekhar [School of Basic Sciences, Indian Institute of Technology Bhubaneswar,Bhubaneswar 751 007 (India); Ray, Koushik [Department of Theoretical Physics, Indian Association for the Cultivation of Science,Calcutta 700 032 (India)
2015-01-14
Algorithms are presented for calculating the partition function of constrained beta-gamma systems in terms of the generating functions of the individual fields of the theory, the latter obtained as the Hilbert series of the arc space of the algebraic variety defined by the constraint. Examples of a beta-gamma system on a complex surface with an A{sub 1} singularity and pure spinors are worked out and compared with existing results.
Samia Bushnaq
2014-01-01
Full Text Available We present a new version of the reproducing kernel Hilbert space method (RKHSM for the solution of systems of fractional integrodifferential equations. In this approach, the solution is obtained as a convergent series with easily computable components. Several illustrative examples are given to demonstrate the effectiveness of the present method. The method described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus.
Fast-forward scaling in a finite-dimensional Hilbert space
TAKAHASHI, Kazutaka
2014-01-01
Time evolution of quantum systems is accelerated by the fast-forward scaling. We reformulate the method to study systems in a finite-dimensional Hilbert space. For several simple systems, we explicitly construct the acceleration potential. We also use our formulation to accelerate the adiabatic dynamics. Applying the method to the transitionless quantum driving, we find that the fast-forward potential can be understood as a counterdiabatic term.
Dynamics of a harmonic oscillator in a finite-dimensional Hilbert space
Kuang Leman (CCAST (World Lab.), Beijing, BJ (China) Dept. of Physics and Inst. of Physics, Hunan Normal Univ. (China)); Wang Fabo (Dept. of Physics, Hunan Normal Univ. (China)); Zhou Yanguo (Dept. of Physics, Hunan Normal Univ. (China))
1993-11-29
Some dynamical properties of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are studied. The time evolution of the position and momentum operators and the second-order quadrature squeezing are investigated in detail. It is shown that the coherent states of the FDHSHO are not the minimum uncertainty states of the position and momentum operators of the FDHSHO. It is found that the second-order squeezing of the quadrature operators vanishes and reappears periodically in the time evolution. (orig.)
Approximation of Nearest Common Fixed Point of Nonexpansive Mappings in Hilbert Spaces
Shi Sheng ZHANG; H. W. JOSEPH LEE; Chi Kin CHAN
2007-01-01
The purpose of this paper is to study the convergence problem of the iteration schemexn+1=λn+1y + (1-λn+1)Tn+1Xn for a family of infinitely many nonexpansive mappings T1, T2,…ina Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly tothe nearest common fixed point of this family of nonexpansive mappings. The results presented in thispaper extend and improve some recent results.
A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method
Mustafa Inc
2013-01-01
Full Text Available We propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have also been studied to demonstrate the accuracy of the present method. Results of numerical examples show that the presented method is effective.
Approximate controllability of neutral stochastic integrodifferential systems in Hilbert spaces
Krishnan Balachandran
2008-12-01
Full Text Available In this paper sufficient conditions are established for the controllability of a class of neutral stochastic integrodifferential equations with nonlocal conditions in abstract space. The Nussbaum fixed point theorem is used to obtain the controllability results, which extends the linear system to the stochastic settings with the help of compact semigroup. An example is provided to illustrate the theory.
The Born rule from a consistency requirement on hidden measurements in complex Hilbert space
Aerts, S
2002-01-01
We formalize the hidden measurement approach within the very general notion of an interactive probability model. We narrow down the model by assuming the state space of a physical entity is a complex Hilbert space and introduce the principle of consistent interaction which effectively partitions the space of apparatus states. The normalized measure of the set of apparatus states that interact with a pure state giving rise to a fixed outcome is shown to be in accordance with the probability obtained using the Born rule.
Moduli Structures, Separability of the Kinematic Hilbert Space and Frames in Loop Quantum Gravity
Carvalho, Bruno
2016-01-01
We reassess the problem of separability of the kinematic Hilbert space in loop quantum gravity under a new mathematical point of view. We use the formalism of frames, a tool used in signal analysis, in order to remove the redundancy of the moduli structures in high valence graphs, without resorting to set extension of diffeomorphism group. For this, we introduce a local redundancy which encodes the concentration of frame vectors on the tangent spaces $T_pM$ around points of intersections $p$ of smooth loops $\\alpha$ in $\\mathbb{R}^{3}$.
Mourad Kerboua
2014-12-01
Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.
Minimal sufficient positive-operator valued measure on a separable Hilbert space
Kuramochi, Yui, E-mail: kuramochi.yui.22c@st.kyoto-u.ac.jp [Department of Nuclear Engineering, Kyoto University, 6158540 Kyoto (Japan)
2015-10-15
We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert space to be separable, we show that for a given POVM, a sufficient statistic called a Lehmann-Scheffé-Bahadur statistic induces a minimal sufficient POVM. We also show that every POVM has an equivalent minimal sufficient POVM and that such a minimal sufficient POVM is unique up to relabeling neglecting null sets. We apply these results to discrete POVMs and information conservation conditions proposed by the author.
Representation Theorem for Stochastic Differential Equations in Hilbert Spaces and its Applications
Viorica Mariela Ungureanu
2006-12-01
Full Text Available In this survey we recall the results obtained in [Ungureanu,Electronic Journal of Qualitative Theory of Differential Equations, 2004] where we gave a representation theorem for the solutions of stochastic differential equations in Hilbert spaces. Using this representation theorem we obtained deterministic characterizations of exponential stability and uniform observability in [Ungureanu,Electronic Journal of Qualitative Theory of Differential Equations, 2004], [Ungureanu, Operator Theory: Advances and Applications, Birkhauser Verlag Basel, 2005] and we will prove a result of Datko type concerning the exponential dichotomy of stochastic equations.
Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces
Juguo Su
2012-01-01
Full Text Available The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.
Hilbert-space factorization is a limited and expensive information-processing resource
Fields, Chris
2014-01-01
By taking the need for quantum reference frames into account, it is shown that Hilbert-space factorization is a dissipative process requiring on the order of kT to reduce by one bit an observer's uncertainty in the provenance of a classically-recorded observational outcome. This cost is neglected in standard treatments of decoherence that assume that observational outcomes are obtained by interacting with a collection of degrees of freedom identified a priori. Treating this cost explicitly leads to a natural measure of the probability of any particular quantum reference frame.
Corrections to nucleon capture cross sections computed in truncated Hilbert spaces
Acharya, B; Odell, D; Papenbrock, T; Platter, L
2016-01-01
Nucleon capture cross sections enter various astrophysical processes. The measurement of proton capture on nuclei at astrophysically relevant low energies is a challenge, and the precise theoretical computation in this long-wavelength regime requires us to understand the corrections due to finite Hilbert spaces. We derive extrapolation formulas that relate the infrared regularized capture amplitudes to the infinite basis limit and demonstrate their efficacy for proton-proton fusion. Our results are thus relevant to current calculations of few-body capture reactions such as proton-proton fusion or proton capture on the deuteron, and also open the way for a more precise understanding of nucleon capture on heavier nuclei.
Hilbert space of curved \\beta\\gamma systems on quadric cones
Aisaka, Yuri
2008-01-01
We clarify the structure of the Hilbert space of curved \\beta\\gamma systems defined by a quadratic constraint. The constraint is studied using intrinsic and BRST methods, and their partition functions are shown to agree. The quantum BRST cohomology is non-empty only at ghost numbers 0 and 1, and there is a one-to-one mapping between these two sectors. In the intrinsic description, the ghost number 1 operators correspond to the ones that are not globally defined on the constrained surface. Extension of the results to the pure spinor superstring is discussed in a separate work.
Bogdanov, Yu I; Gavrichenko, A K
2011-01-01
A throughout study of statistical characteristics of fidelity in different protocols of quantum tomography is given. We consider protocols based on geometry of platonic solids and other polyhedrons with high degree of symmetry such as fullerene and its dual polyhedron. Characteristics of fidelity in different protocols are compared to the theoretical level of the minimum possible level of fidelity loss. Tomography of pure and mixed states in Hilbert spaces of different dimension is analyzed. Results of this work could be used for a better control of quantum gates and quantum states in quantum information technologies.
Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study
Botelho, Luiz Carlos Lobato
2010-01-01
We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent advection, etc. - and subject to deterministic or stochastic (white noise) stirrings. In order to achieve such goal, we use the powerful results of compacity on functional Lp spaces (the Aubin-Lion Theorem). We use such results to write a path-integral solution for this problem. Additionally, we present the rigourous functional integral solutions for the Linear Diffussion equation defined in Infinite-Dimensional Spaces (Separable Hilbert Spaces). These further results are presented in order to be useful to understand Polymer cylindrical surfaces probability distributions and functionals on String theory.
Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space
Athalye, Vivek; Uecker, Martin
2013-01-01
In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient non-Cartesian sampling schemes. As shown here, reconstruction from samples at arbitrary locations can be understood as approximation of vector-valued functions from the acquired samples and formulated using a Reproducing Kernel Hilbert Space (RKHS) with a matrix-valued kernel defined by the spatial sensitivities of the receive coils. This establishes a formal connection between approximation theory and parallel imaging. Theoretical tools from approximation theory can then be used to understand reconstruction in k-space and to extend the analysis of the effects of samples selection beyond the traditional g-factor noise analysis to both noise amplification and approximation errors. This is demonstrated wit...
Quantum-optical states in finite-dimensional Hilbert space; 1, General formalism
Miranowicz, A; Imoto, N; Miranowicz, Adam; Leonski, Wieslaw; Imoto, Nobuyuki
2001-01-01
The interest in quantum-optical states confined in finite-dimensional Hilbert spaces has recently been stimulated by the progress in quantum computing, quantum-optical state preparation and measurement techniques, in particular, by the development of the discrete quantum-state tomography. In the first part of our review we present two essentially different approaches to define harmonic oscillator states in the finite-dimensional Hilbert spaces. One of them is related to the truncation scheme of Pegg, Phillips and Barnett [Phys. Rev. Lett. 81, 1604 (1998)] -- the so-called quantum scissors device. The second method corresponds to the truncation scheme of Leo\\'nski and Tana\\'s [Phys. Rev. A 49, R20 (1994)]. We propose some new definitions of the states related to these truncation schemes and find their explicit forms in the Fock representation. We discuss finite-dimensional generalizations of coherent states, phase coherent states, displaced number states, Schr\\"odinger cats, and squeezed vacuum. We show some i...
Zhu Jiuyun (Department of Physics, Hunan Normal University, Hunan 410006 (China)); Kuang Leman (Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin 300071 (China) Department of Physics and Institute of Physics, Hunan Normal University, Hunan 410081 (China))
1994-10-03
The even and odd coherent states (CSs) of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are constructed and some properties of these states are studied. Their quadrature squeezing and amplitude-squared squeezing are investigated in detail. It is shown that, while the squeezing behaviour of the even and odd CSs of the FDHSHO approaches that of the even and odd CSs of the usual harmonic oscillator as the dimension of the Hilbert space tends to infinity, this behaviour is nontrivally different if the dimension of the Hilbert space is finite. In the latter case, it is found that the even and odd CSs exhibit both amplitude-squared squeezing and quadrature squeezing. ((orig.))
Hilbert series for moduli spaces of instantons on ℂ{sup 2}/ℤ{sub n}
Dey, Anindya [Theory Group and Texas Cosmology Center, Department of Physics,University of Texas at Austin, Austin, TX 78712 (United States); Hanany, Amihay [Theoretical Physics Group, The Blackett Laboratory, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom); Mekareeya, Noppadol [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut),Föhringer Ring 6, 80805 München (Germany); Theory Group, Physics Department, CERN,CH-1211, Geneva 23 (Switzerland); Rodríguez-Gómez, Diego [Department of Physics, Universidad de Oviedo,Avda. Calvo Sotelo 18, 33007, Oviedo (Spain); Seong, Rak-Kyeong [Theoretical Physics Group, The Blackett Laboratory, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom); School of Physics, Korea Institute for Advanced Study,85 Hoegi-ro, Seoul 130-722 (Korea, Republic of)
2014-01-31
We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A{sub n−1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiver descriptions do indeed agree, as expected.
Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
Dey, Anindya; Mekareeya, Noppadol; Rodríguez-Gómez, Diego; Seong, Rak-Kyeong
2014-01-01
We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A_{n-1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiv...
Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
Dey, Anindya; Mekareeya, Noppadol; Rodríguez-Gómez, Diego; Seong, Rak-Kyeong
2014-01-01
We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A_{n-1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiv...
Fano, Guido
2017-01-01
This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result...
Cheng, Ching-An; Huang, Han-Pang; Hsu, Huan-Kun; Lai, Wei-Zh; Cheng, Chih-Chun
2016-07-01
We investigate the modeling of inverse dynamics without prior kinematic information for holonomic rigid-body robots. Despite success in compensating robot dynamics and friction, general inverse dynamics models are nontrivial. Rigid-body models are restrictive or inefficient; learning-based models are generalizable yet require large training data. The structured kernels address the dilemma by embedding the robot dynamics in reproducing kernel Hilbert space. The proposed kernels autonomously converge to rigid-body models but require fewer samples; with a semi-parametric framework that incorporates additional parametric basis for friction, the structured kernels can efficiently model general rigid-body robots. We tested the proposed scheme in simulations and experiments; the models that consider the structure of function space are more accurate.
Gravitational instanton in Hilbert space and the mass of high energy elementary particles
El Naschie, M.S
2004-06-01
While the theory of relativity was formulated in real spacetime geometry, the exact formulation of quantum mechanics is in a mathematical construction called Hilbert space. For this reason transferring a solution of Einstein's field equation to a quantum gravity Hilbert space is far of being a trivial problem. On the other hand {epsilon}{sup ({infinity}}{sup )} spacetime which is assumed to be real is applicable to both, relativity theory and quantum mechanics. Consequently, one may expect that a solution of Einstein's equation could be interpreted more smoothly at the quantum resolution using the Cantorian {epsilon}{sup ({infinity}}{sup )} theory. In the present paper we will attempt to implement the above strategy to study the Eguchi-Hanson gravitational instanton solution and its interpretation by 't Hooft in the context of quantum gravity Hilbert space as an event and a possible solitonic 'extended' particle. Subsequently we do not only reproduce the result of 't Hooft but also find the mass of a fundamental 'exotic' symplictic-transfinite particle m{approx_equal}1.8 MeV as well as the mass M{sub x} and M (Planck) which are believed to determine the GUT and the total unification of all fundamental interactions respectively. This may be seen as a further confirmation to an argument which we put forward in various previous publications in favour of an alternative mass acquisition mechanism based on unification and duality considerations. Thus even in case that we never find the Higgs particle experimentally, the standard model would remain substantially intact as we can appeal to tunnelling and unification arguments to explain the mass. In fact a minority opinion at present is that finding the Higgs particle is not a final conclusive argument since one could ask further how the Higgs particle came to its mass which necessitates a second Higgs field. By contrast the present argument could be viewed as an ultimate theory
Berry-Esseen's central limit theorem for non-causal linear processes in Hilbert space
Machkouri, Mohamed EL
2010-01-01
Let $H$ be a real separable Hilbert space and $(a_k)_{k\\in\\mathbb{Z}}$ a sequence of bounded linear operators from $H$ to $H$. We consider the linear process $X$ defined for any $k$ in $\\mathbb{Z}$ by $X_k=\\sum_{j\\in\\mathbb{Z}}a_j(\\varepsilon_{k-j})$ where $(\\varepsilon_k)_{k\\in\\mathbb{Z}}$ is a sequence of i.i.d. centered $H$-valued random variables. We investigate the rate of convergence in the CLT for $X$ and in particular we obtain the usual Berry-Esseen's bound provided that $\\sum_{j\\in\\mathbb{Z}}\\vert j\\vert\\|a_j\\|_{\\mathcal{L}(H)}<+\\infty$ and $\\varepsilon_0$ belongs to $L_H^{\\infty}$.
Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces
Cho Yeol
2011-01-01
Full Text Available Abstract In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed variational inequalities problems, it is clear that it cannot be directly applied to the problems that we have considered in this paper because of φ and g. 2000 AMS Subject Classification: 47H05; 47H09; 47J25; 65J15.
Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors
Vanfleteren, Diederik; Bultinck, Patrick; Ayers, Paul W; Waroquier, Michel; 10.1063/1.3521493
2011-01-01
A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges.
Mean-Field Backward Stochastic Evolution Equations in Hilbert Spaces and Optimal Control for BSPDEs
Ruimin Xu
2014-01-01
Full Text Available We obtain the existence and uniqueness result of the mild solutions to mean-field backward stochastic evolution equations (BSEEs in Hilbert spaces under a weaker condition than the Lipschitz one. As an intermediate step, the existence and uniqueness result for the mild solutions of mean-field BSEEs under Lipschitz condition is also established. And then a maximum principle for optimal control problems governed by backward stochastic partial differential equations (BSPDEs of mean-field type is presented. In this control system, the control domain need not to be convex and the coefficients, both in the state equation and in the cost functional, depend on the law of the BSPDE as well as the state and the control. Finally, a linear-quadratic optimal control problem is given to explain our theoretical results.
A spectral-based numerical method for Kolmogorov equations in Hilbert spaces
Delgado-Vences, Francisco; Flandoli, Franco
2016-08-01
We propose a numerical solution for the solution of the Fokker-Planck-Kolmogorov (FPK) equations associated with stochastic partial differential equations in Hilbert spaces. The method is based on the spectral decomposition of the Ornstein-Uhlenbeck semigroup associated to the Kolmogorov equation. This allows us to write the solution of the Kolmogorov equation as a deterministic version of the Wiener-Chaos Expansion. By using this expansion we reformulate the Kolmogorov equation as an infinite system of ordinary differential equations, and by truncating it we set a linear finite system of differential equations. The solution of such system allow us to build an approximation to the solution of the Kolmogorov equations. We test the numerical method with the Kolmogorov equations associated with a stochastic diffusion equation, a Fisher-KPP stochastic equation and a stochastic Burgers equation in dimension 1.
3D Hilbert Space Filling Curves in 3D City Modeling for Faster Spatial Queries
Ujang, Uznir; Antón Castro, Francesc/François; Azri, Suhaibah;
2014-01-01
are presented in this paper. The advantages of implementing space-filling curves in 3D city modeling will improve data retrieval time by means of optimized 3D adjacency, nearest neighbor information and 3D indexing. The Hilbert mapping, which maps a sub-interval of the ([0,1]) interval to the corresponding...... method, retrieving portions of and especially searching these 3D city models, will not be done optimally. Even though current developments are based on an open data model allotted by the Open Geospatial Consortium (OGC) called CityGML, its XML-based structure makes it challenging to cluster the 3D urban...... web standards. However, these 3D city models consume much more storage compared to two dimensional (2 D) spatial data. They involve extra geometrical and topological information together with semantic data. Without a proper spatial data clustering method and its corresponding spatial data access...
A Remark on the Unitary Group of a Tensor Product of Finite-Dimensional Hilbert Spaces
K R Parthasarathy
2003-02-01
Let $H_i, 1 ≤ i ≤ n$ be complex finite-dimensional Hilbert spaces of dimension $d_i, 1 ≤ i ≤ n$ respectively with $d_i ≥ 2$ for every . By using the method of quantum circuits in the theory of quantum computing as outlined in Nielsen and Chuang [2] and using a key lemma of Jaikumar [1] we show that every unitary operator on the tensor product $H = H_1 \\otimes H_2 \\otimes\\ldots \\otimes H_n$ can be expressed as a composition of a finite number of unitary operators living on pair products $H_i \\otimes H_j, 1 ≤ i, j ≤ n$. An estimate of the number of operators appearing in such a composition is obtained.
Strong Metrizability for Closed Operators and the Semi-Fredholm Operators between Two Hilbert Spaces
Mohammed Benharrat
2015-08-01
Full Text Available To be able to refine the completion of C(H1, H2, the of set all closed densely defined linear operators between two Hilbert spaces H1 and H2, we define in this paper some new strictly stronger metrics than the gap metric g and we characterize the closure with respect to theses metrics of the subset L(H1, H2 of bounded elements of C(H1, H2. In addition, several operator norm inequalities concerning the equivalence of some metrics on L(H1, H2 are presented. We also establish the semi-Fredholmness and Fredholmness of unbounded in terms of bounded pure contractions.
Blanchard, Philippe
2015-01-01
The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three main parts. Part I is a brief introduction to distribution theory, in which elements from the theories of ultradistributions and hyperfunctions are considered in addition to some deeper results for Schwartz distributions, thus providing a comprehensive introduction to the theory of generalized functions. P...
Divide and conquer the Hilbert space of translation-symmetric spin systems.
Weisse, Alexander
2013-04-01
Iterative methods that operate with the full Hamiltonian matrix in the untrimmed Hilbert space of a finite system continue to be important tools for the study of one- and two-dimensional quantum spin models, in particular in the presence of frustration. To reach sensible system sizes such numerical calculations heavily depend on the use of symmetries. We describe a divide-and-conquer strategy for implementing translation symmetries of finite spin clusters, which efficiently uses and extends the "sublattice coding" of H. Q. Lin [Phys. Rev. B 42, 6561 (1990)]. With our method, the Hamiltonian matrix can be generated on-the-fly in each matrix vector multiplication, and problem dimensions beyond 10^{11} become accessible.
Extension of Wirtinger's Calculus in Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS
Bouboulis, Pantelis
2010-01-01
Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space. However, so far, the emphasis has been on batch techniques. It is only recently, that online techniques have been considered in the context of adaptive signal processing tasks. Moreover, these efforts have only been focussed on and real valued data sequences. To the best of our knowledge, no kernel-based strategy has been developed, so far, that is able to deal with complex valued signals. In this paper, we present a general framework to attack the problem of adaptive filtering of complex signals, using either real reproducing kernels, taking advantage of a technique called \\textit{complexification} of real RKHSs, or complex reproducing kernels, highlighting the use of the complex gaussian kernel. In order to derive gradients of operators that need to be defined on the associat...
A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces
Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)
2017-06-15
We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.
Weakly Ordered A-Commutative Partial Groups of Linear Operators Densely Defined on Hilbert Space
Jirí Janda
2013-01-01
Full Text Available The notion of a generalized effect algebra is presented as a generalization of effect algebra for an algebraic description of the structure of the set of all positive linear operators densely defined on a Hilbert space with the usual sum of operators. The structure of the set of not only positive linear operators can be described with the notion of a weakly ordered partial commutative group (wop-group.Due to the non-constructive algebraic nature of the wop-group we introduce its stronger version called a weakly ordered partial a-commutative group (woa-group. We show that it also describes the structure of not only positive linear operators.
Bath-induced correlations in an infinite-dimensional Hilbert space
Nizama, Marco; Cáceres, Manuel O.
2017-09-01
Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T> 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.
Strong Metrizability for Closed Operators and the Semi-Fredholm Operators between Two Hilbert Spaces
Mohammed Benharrat
2015-08-01
Full Text Available To be able to refine the completion of C(H1, H2, the of set all closed densely defined linear operators between two Hilbert spaces H1 and H2, we define in this paper some new strictly stronger metrics than the gap metric g and we characterize the closure with respect to theses metrics of the subset L(H1, H2 of bounded elements of C(H1, H2. In addition, several operator norm inequalities concerning the equivalence of some metrics on L(H1, H2 are presented. We also establish the semi-Fredholmness and Fredholmness of unbounded in terms of bounded pure contractions.
Construction and coupling of frames in Hilbert spaces with W-metrics
German Escobar
2016-01-01
Full Text Available Se definen marcos unitariamente equivalentes en espacios de Hilbert con W-métricas, y se da una caracterización de ellos comparando sus respectivos operadores de análisis. A partir de un espacio de Hilbert con un marco se construye un espacio de Hilbert con W-métrica y un marco unitariamente equivalente al dado. Finalmente, se muestra que el acoplamiento de dos marcos es un marco.
Shi-sheng ZHANG; Ruo-feng RAO; Jia-lin HUANG
2009-01-01
The main purpose of this paper is to study a new iterative algorithm for finding a common element of the set of solutions for a generalized equilibrium problem and the set of fixed points for a κ-strict pseudocontractive mapping in the Hilbert space.The presented results extend and improve the corresponding results reported in the literature.
A note on stability of the integral-differential equation of the hyperbolic type in a Hilbert space
Ashyraliyev, M.
2008-01-01
In this paper, the initial-value problem for integral-differential equation of the hyperbolic type in a Hilbert space H is considered. The unique solvability of this problem is established. The stability estimates for the solution of this problem are obtained. The difference scheme approximately sol
Hilbert空间H中G-框架的扰动%Perturbations of G-Frames in Hilbert Spaces
姚喜妍
2008-01-01
In this paper,we discuss the properties of g-frames and g-frame operators for Hilbert spaces by utilizing the method of operator theory.Furthermore,we study perturbations of g-frames,and obtain some meaningful results.
Group-theoretical approach to the construction of bases in 2{sup n}-dimensional Hilbert space
Garcia, A.; Romero, J. L.; Klimov, A. B., E-mail: klimov@cencar.udg.mx [Universidad de Guadalajara, Departamento de Fisica (Mexico)
2011-06-15
We propose a systematic procedure to construct all the possible bases with definite factorization structure in 2{sup n}-dimensional Hilbert space and discuss an algorithm for the determination of basis separability. The results are applied for classification of bases for an n-qubit system.
2010-07-01
... Elimination System (NPDES) permit issued in accordance with section 402 of the Clean Water Act and 40 CFR... 33 Navigation and Navigable Waters 2 2010-07-01 2010-07-01 false Platform machinery space drainage... machinery space drainage on oceangoing fixed and floating drilling rigs and other platforms. (a) No...
Santhanam, Thalanayar S [Department of Physics Saint Louis University, Missouri, MO 63103 (United States); Santhanam, Balu [Department of Electrical and Computer Engineering, MSC01 1100 1, University of New Mexico Albuquerque, NM 87131-0001 (United States)], E-mail: santhats@slu.edu, E-mail: bsanthan@ece.unm.edu
2009-05-22
Quantum mechanics of a linear harmonic oscillator in a finite-dimensional Hilbert space satisfying the correct equations of motion is studied. The connections to Weyl's formulation of the algebra of bounded unitary operators in finite space as well as to a truncated quantized linear harmonic oscillator are discussed. It is pointed out that the discrete Fourier transformation (DFT) plays a central role in determining the actual form of the position, the momentum, the number and the Hamiltonian operators. The explicit form of these operators in different bases is exhibited for some low values of the dimension of the Hilbert space. In this formulation, it is shown that the Hamiltonian is indeed the logarithm of the DFT and that by modifying Weyl's framework to include position and momentum operators with non-uniformly spaced spectra the equations of motion are satisfied.
Chen, Xiaoman
2003-01-01
The seminal 1989 work of Douglas and Paulsen on the theory of analytic Hilbert modules precipitated a number of major research efforts. This in turn led to some intriguing and valuable results, particularly in the areas of operator theory and functional analysis. With the field now beginning to blossom, the time has come to collect those results under one cover. Written by two of the most active and often-cited researchers in the field, Analytic Hilbert Modules reports on the progress made by the authors and others, including the characteristic space theory, rigidity, the equivalence problem, the Arveson modules, extension theory, and reproducing Hilbert spaces on n-dimensional complex space.
Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space
Strauss, Y; Eisenberg, E
2000-01-01
We show that models for the quantum Lax-Phillips theory of scattering and unstable systems can be constructed for which the evolution is pointwise on a time axis that can be put into correspondence with laboratory time; in the Lax-Phillips free translation representation the evolution operator acts as a smooth kernel, thus satisfying the condition for a nontrivial relation between the singularities of the S-matrix and the spectrum of the generator of the semigroup describing resonance decay. We show, furthermore, that the Lax-Phillips S-matrix is unitarily related to the S-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable $\\sigma$ of the Lax-Phillips theory. Analytic continuation in $\\sigma$ to find the null space has some of the properties of a method developed some time ago for application to dilation analytic potentials, but, in Lax-Phillips theory, results in a resonant state which lies in the original Hilbert space of states. We work out an illustrativ...
On the continuity of the map square root of nonnegative isomorphisms in Hilbert spaces
Jeovanny de Jesus Muentes Acevedo
2015-06-01
Full Text Available Let H be a real (or complex Hilbert space. Every nonnegative operator L ∈ L(H admits a unique nonnegative square root R ∈ L(H, i.e., a nonnegative operator R ∈ L(H such that R2 = L. Let GL+ S (H be the set of nonnegative isomorphisms in L(H. First we will show that GL+ S (H is a convex (real Banach manifold. Denoting by L1/2 the nonnegative square root of L. In [3], Richard Bouldin proves that L1/2 depends continuously on L (this proof is non-trivial. This result has several applications. For example, it is used to find the polar decomposition of a bounded operator. This polar decomposition allows us to determine the positive and negative spectral subespaces of any self-adjoint operator, and moreover, allows us to define the Maslov index. The autor of the paper under review provides an alternative proof (and a little more simplified that L1/2 depends continuously on L, and moreover, he shows that the map is a homeomorphism. Resumen. Sea H un espacio de Hilbert real (o complejo. Todo operador no negativo L ∈ L(H admite una única raíz cuadrada no negativa R ∈ L(H, esto es, un operador no negativo R ∈ L(H tal que R2 = L. Sea GL+ S (H el conjunto de los isomorfismos no negativos en L(H. Primero probaremos que GL+ S (H es una variedad de Banach (real. Denotando como L1/2 la raíz cuadrada no negativa de L, en [3] Richard Bouldin prueba que L1/2 depende continuamente de L (esta prueba es no trivial. Este resultado tiene varias aplicaciones. Por ejemplo, es usado para encontrar la descomposición polar de un operador limitado. Esta descomposición polar nos lleva a determinar los subespacios espectrales positivos y negativos de cualquier operador autoadjunto, y además, lleva a definir el índice de Máslov. El autor de este artículo da una prueba alternativa (y un poco más simplificada de que L1/2 depende continuamente de L, y además, prueba que la aplicación es un homeomorfismo
A differential equation for Lerch's transcendent and associated symmetric operators in Hilbert space
Kaplitskii, V M [Southern Federal University, Rostov-on-Don (Russian Federation)
2014-08-01
The function Ψ(x,y,s)=e{sup iy}Φ(−e{sup iy},s,x), where Φ(z,s,v) is Lerch's transcendent, satisfies the following two-dimensional formally self-adjoint second-order hyperbolic differential equation, where s=1/2+iλ. The corresponding differential expression determines a densely defined symmetric operator (the minimal operator) on the Hilbert space L{sub 2}(Π), where Π=(0,1)×(0,2π). We obtain a description of the domains of definition of some symmetric extensions of the minimal operator. We show that formal solutions of the eigenvalue problem for these symmetric extensions are represented by functional series whose structure resembles that of the Fourier series of Ψ(x,y,s). We discuss sufficient conditions for these formal solutions to be eigenfunctions of the resulting symmetric differential operators. We also demonstrate a close relationship between the spectral properties of these symmetric differential operators and the distribution of the zeros of some special analytic functions analogous to the Riemann zeta function. Bibliography: 15 titles.
Simulating the Generalized Gibbs Ensemble (GGE): A Hilbert space Monte Carlo approach
Alba, Vincenzo
By combining classical Monte Carlo and Bethe ansatz techniques we devise a numerical method to construct the Truncated Generalized Gibbs Ensemble (TGGE) for the spin-1/2 isotropic Heisenberg (XXX) chain. The key idea is to sample the Hilbert space of the model with the appropriate GGE probability measure. The method can be extended to other integrable systems, such as the Lieb-Liniger model. We benchmark the approach focusing on GGE expectation values of several local observables. As finite-size effects decay exponentially with system size, moderately large chains are sufficient to extract thermodynamic quantities. The Monte Carlo results are in agreement with both the Thermodynamic Bethe Ansatz (TBA) and the Quantum Transfer Matrix approach (QTM). Remarkably, it is possible to extract in a simple way the steady-state Bethe-Gaudin-Takahashi (BGT) roots distributions, which encode complete information about the GGE expectation values in the thermodynamic limit. Finally, it is straightforward to simulate extensions of the GGE, in which, besides the local integral of motion (local charges), one includes arbitrary functions of the BGT roots. As an example, we include in the GGE the first non-trivial quasi-local integral of motion.
On Quantile Regression in Reproducing Kernel Hilbert Spaces with Data Sparsity Constraint.
Zhang, Chong; Liu, Yufeng; Wu, Yichao
2016-04-01
For spline regressions, it is well known that the choice of knots is crucial for the performance of the estimator. As a general learning framework covering the smoothing splines, learning in a Reproducing Kernel Hilbert Space (RKHS) has a similar issue. However, the selection of training data points for kernel functions in the RKHS representation has not been carefully studied in the literature. In this paper we study quantile regression as an example of learning in a RKHS. In this case, the regular squared norm penalty does not perform training data selection. We propose a data sparsity constraint that imposes thresholding on the kernel function coefficients to achieve a sparse kernel function representation. We demonstrate that the proposed data sparsity method can have competitive prediction performance for certain situations, and have comparable performance in other cases compared to that of the traditional squared norm penalty. Therefore, the data sparsity method can serve as a competitive alternative to the squared norm penalty method. Some theoretical properties of our proposed method using the data sparsity constraint are obtained. Both simulated and real data sets are used to demonstrate the usefulness of our data sparsity constraint.
WEAK AND STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES
Yu Miao
2008-08-01
Full Text Available In a real {sc Hilbert} space $H$, starting from an arbitrary initialpoint $x_0in H$, an iterative process is defined as follows:$x_{n+1}=a_nx_n+(1-a_nT^{lambda_{n+1}}_fy_n$, $y_n= b_nx_n+(1-b_nT^{eta_{n}}_gx_n$, $nge 0$, where$T^{lambda_{n+1}}_f x= Tx-lambda_{n+1} mu_f f(Tx$,$T^{eta_{n}}_g x= Tx-eta_{n} mu_g g(Tx$, ($forall xinH$, $T: Ho H$ a nonexpansive mappingwith $F(T eemptyset$ and $f$ (resp. $g$ $: Ho H$ an$eta_f$ (resp. $eta_g$-strongly monotone and $k_f$ (resp. $k_g$-Lipschitzianmapping, ${a_n}subset(0,1$, ${b_n}subset(0,1$ and ${lambda_n}subset[0,1$,${eta_n}subset[0,1$. Under some suitable conditions, severalconvergence results of the sequence ${x_n}$ are shown.
Representation of quantum mechanical resonances in the Lax-Phillips Hilbert space
Strauss, Y. [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Horwitz, L. P. [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Eisenberg, E. [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
2000-01-01
We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the Lax-Phillips S-matrix is unitarily related to the S-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable σ of the Lax-Phillips theory. Analytic continuation in σ has some of the properties of a method developed some time ago for application to dilation analytic potentials. We work out an illustrative example using a Lee-Friedrichs model for the underlying dynamical system.
Niemiec, Piotr
2011-01-01
An \\textit{ideal} of $N$-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with respect to ideals) for $N$-tuples of closed densely defined linear operators acting in a common (arbitrary) Hilbert space are presented. Algebraic and order (with respect to containment) properties of the class $CDD_N$ of all unitary equivalence classes of such $N$-tuples are established and certain ideals in $CDD_N$ are distinguished. It is proved that infinite operations in $CDD_N$ may be reconstructed from the direct sum operation of a pair. \\textit{Prime decomposition} in $CDD_N$ is proposed and its (in a sense) uniqueness is established. The issue of classification of ideals in $CDD_N$ (up to isomorphism) is discussed. A model for $CDD_N$ is described and its concrete realization is presented. A new partial order of $N$-tuples of operators is introduced and its fundamental...
Dimensions of subspaces of a Hilbert space and index of the semi-Fredholm operator
马吉溥
1996-01-01
Let 2" denote the set of all closed subspaces of the Hilbert space H. The generalized dimension, dim gH0 for any , is introduced. Then an order is defined in [2H], the set of generalized dimensions of 2H. It makes [2H] totally ordered such that 0
Ioan Boţ, Radu; Hofmann, Bernd
2016-12-01
In the literature on singular perturbation (Lavrentiev regularization) for the stable approximate solution of operator equations with monotone operators in the Hilbert space the phenomena of conditional stability and local well-posedness or ill-posedness are rarely investigated. Our goal is to present some studies which try to bridge this gap. So we present new results on the impact of conditional stability on error estimates and convergence rates for the Lavrentiev regularization and distinguish for linear problems well-posedness and ill-posedness in a specific manner motivated by a saturation result. Taking into account that the behavior of the bias (regularization error in the noise-free case) is crucial, general convergence rates, including logarithmic rates, are derived for linear operator equations by means of the method of approximate source conditions. This allows us to extend well-known convergence rate results for the Lavrentiev regularization that were based on general source conditions to the case of non-selfadjoint linear monotone forward operators for which general source conditions fail. Examples presenting the self-adjoint multiplication operator as well as the non-selfadjoint fractional integral operator and Cesàro operator illustrate the theoretical results. Extensions to the nonlinear case under specific conditions on the nonlinearity structure complete the paper.
Stability for a New Class of GNOVI with (γG,λ-Weak-GRD Mappings in Positive Hilbert Spaces
Hong Gang Li
2016-01-01
Full Text Available By using ordered fixed point theory, we set up a new class of GNOVI structures (general nonlinear ordered variational inclusions with (γG,λ-weak-GRD mappings, discuss an existence theorem of solution, consider a perturbed Ishikawa iterative algorithm and the convergence of iterative sequences generated by the algorithm, and show the stability of algorithm for GNOVI structures in positive Hilbert spaces. The results in the instrument are obtained.
Real Operator Algebras on a Complex Hilbert Space%复Hilbert空间上的实算子代数
李炳仁
2009-01-01
We study real operator algebras on a complex Hilbert space H. From H, we can get a real Hilbert space H_r. Further, we have a complex Hilbert space H_(rc)= H_r+iH_r. Through this process, we prove the following. If A and M are uniformly closed and weakly closed real * operator algebras on H respectively, then their complex span A + iA and M + iM are (complex) C*-algebra and (complex) von Neumann algebra on H, respectively. Here, we don't need the condition: A∩iA = {0}, M∩iM = {0}. So our result is a generalization of Stormer's result.%本文研究在一个复Hilbert空间H上的实算子代数.从H可以得到一个实Hilbert空间Hr珥,进而又有一个复Hilbert空间H_(rc)=H_r+iH_r.通过这个过程,证明了如下结果.如果A,M分别是H上一致闭的,弱闭的实*算子代数,则它们的复扩张A+iA,M4-iM分别是日上的(复)C~*代数,(复)von Neumann代数.这里,不需要条件A∩iA={0},MniM={0}.因此,我们的结果是Stormer结果的推广.
Mohammad W. Alomari
2014-01-01
Full Text Available Several new error bounds for the Čebyšev functional under various assumptions are proved. Applications for functions of self-adjoint operators on complex Hilbert spaces are provided as well.
Filippov, S N
2010-01-01
The columns of $d^2 \\times N$ matrices are shown to create different kinds of sets of $N$ operators acting on $d$-dimensional Hilbert space. This construction corresponds to formalism of star-product of the operator symbols. The known bases are shown to be partial cases of generic formulas obtained by using $d^2 \\times d^2$ matrices as the source for constructing the arbitrary bases. The known examples of the SIC, MUB and phase-space descriptions of qubit states are considered from the viewpoint of a developed unified approach. Qubit examples are given in detail.
Chang, Weng-Long; Ren, Ting-Ting; Feng, Mang
2015-01-01
In this paper, it is shown that the proposed quantum algorithm for implementing Boolean circuits generated from the DNA-based algorithm solving the vertex-cover problem of any graph G with m edges and n vertices is the optimal quantum algorithm. Next, it is also demonstrated that mathematical solutions of the same biomolecular solutions are represented in terms of a unit vector in the finite-dimensional Hilbert space. Furthermore, for testing our theory, a nuclear magnetic resonance (NMR) experiment of three quantum bits to solve the simplest vertex-cover problem is completed.
The coupled-cluster approach to quantum many-body problem in a three-Hilbert-space reinterpretation
Bishop, Raymond F
2013-01-01
The quantum many-body bound-state problem in its computationally successful coupled cluster method (CCM) representation is reconsidered. In conventional practice one factorizes the ground-state wave functions $|\\Psi\\rangle= e^S |\\Phi\\rangle$ which live in the "physical" Hilbert space ${\\cal H}^{(P)}$ using an elementary ansatz for $|\\Phi\\rangle$ plus a formal expansion of $S$ in an operator basis of multi-configurational creation operators. In our paper a reinterpretation of the method is proposed. Using parallels between the CCM and the so called quasi-Hermitian, alias three-Hilbert-space (THS), quantum mechanics, the CCM transition from the known microscopic Hamiltonian (denoted by usual symbol $H$), which is self-adjoint in ${\\cal H}^{(P)}$, to its effective lower-case isospectral avatar $\\hat{h}=e^{-S} H e^S$, is assigned a THS interpretation. In the opposite direction, a THS-prescribed, non-CCM, innovative reinstallation of Hermiticity is shown to be possible for the CCM effective Hamiltonian $\\hat{h}$, ...
Invariant Robust 3-D Face Recognition based on the Hilbert Transform in Spectral Space
Eric Paquet
2006-04-01
Full Text Available One of the main objectives of face recognition is to determine whether an acquired face belongs to a reference database and to subsequently identify the corresponding individual. Face recognition has application in, for instance, forensic science and security. A face recognition algorithm, to be useful in real applications, must discriminate in between individuals, process data in real-time and be robust against occlusion, facial expression and noise.A new method for robust recognition of three-dimensional faces is presented. The method is based on harmonic coding, Hilbert transform and spectral analysis of 3-D depth distributions. Experimental results with three-dimensional faces, which were scanned with a laser scanner, are presented. The proposed method recognises a face with various facial expressions in the presence of occlusion, has a good discrimination, is able to compare a face against a large database of faces in real-time and is robust against shot noise and additive noise.
On orthogonal systems in Hilbert C*-modules
Landi, Giovanni; PAVLOV, Alexander
2009-01-01
Analogues for Hilbert C*-modules of classical results of Fourier series theory in Hilbert spaces are considered. Relations between different properties of orthogonal and orthonormal systems for Hilbert C*-modules are studied with special attention paid on the differences with the well-known Hilbert space situation.
Mayet-Godowski Hilbert Lattice Equations
Megill, Norman D.; Pavicic, Mladen
2006-01-01
Several new results in the field of Hilbert lattice equations based on states defined on the lattice as well as novel techniques used to arrive at these results are presented. An open problem of Mayet concerning Hilbert lattice equations based on Hilbert-space-valued states is answered.
Royden's lemma in infinite dimensions and Hilbert-Hartogs manifolds
Ivashkovich, S
2011-01-01
We prove the Royden's Lemma for complex Hilbert manifolds, i.e., that a holomorphic imbedding of the closure of a finite dimensional, strictly pseudoconvex domain into a complex Hilbert manifold extends to a biholomorphic mapping onto a product of this domain with the unit ball in Hilbert space. This reduces several problems concerning complex Hilbert manifolds to open subsets of a Hilbert space. As an illustration we prove some results on generalized loop spaces of complex manifolds.
赋范线性空间中的Hilbert型积分不等式%Hilbert-type Integral Inequalities in Normed Linear Spaces
匡继昌
2013-01-01
基于利用一个积分恒等式的新技巧,建立了赋范线性空间中新的Hilbert型积分不等式.这些新的结果包含了n维欧氏空间中n重积分的Hilbert型积分不等式作为其特殊情形.%In this paper we employ a new technique based on an integral identity to study some new Hilbert-type integral inequalities in normed linear spaces. These new results include the corresponding multiple Hilbert-type integral inequalities in Rn as special cases.
Muhammad Ashfaq Ahmad; Lin Jie; Qian Yan; Ma Zhi-Min; Ma Ai-Qun; Liu Shu-Tian
2007-01-01
This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.
Effect of Adding a Regenerator to Kornhauser's MIT "Two-Space" (Gas-Spring+Heat Exchanger) Test Rig
Ebiana, Asuquo B.; Gidugu, Praveen
2008-01-01
This study employed entropy-based second law post-processing analysis to characterize the various thermodynamic losses inside a 3-space solution domain (gas spring+heat exchanger+regenerator) operating under conditions of oscillating pressure and oscillating flow. The 3- space solution domain is adapted from the 2-space solution domain (gas spring+heat exchanger) in Kornhauser's MIT test rig by modifying the heat exchanger space to include a porous regenerator system. A thermal nonequilibrium model which assumes that the regenerator porous matrix and gas average temperatures can differ by several degrees at a given axial location and time during the cycle is employed. An important and primary objective of this study is the development and application of a thermodynamic loss post-processor to characterize the major thermodynamic losses inside the 3-space model. It is anticipated that the experience gained from thermodynamic loss analysis of the simple 3-space model can be extrapolated to more complex systems like the Stirling engine. It is hoped that successful development of loss post-processors will facilitate the improvement of the optimization capability of Stirling engine analysis codes through better understanding of the heat transfer and power losses. It is also anticipated that the incorporation of a successful thermal nonequilibrium model of the regenerator in Stirling engine CFD analysis codes, will improve our ability to accurately model Stirling regenerators relative to current multidimensional thermal-equilibrium porous media models.
Coherent States for generalized oscillator with finite-dimensional Hilbert space
Borzov, Vadim V.; Damaskinsky, Eugene V.
2006-01-01
The construction of oscillator-like systems connected with the given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of the systems with finite-dimensional state space. As example we consider the generalized oscillator connected with Krawtchouk polynomials.
Truncated Hilbert space approach to the 2d $\\phi^{4}$ theory
Bajnok, Z
2015-01-01
We apply the massive analogue of the truncated conformal space approach to study the two dimensional $\\phi^{4}$ theory in finite volume. We focus on the broken phase and determine the finite size spectrum of the model numerically. We compare these results against semi-classical analysis and the Bethe-Yang spectrum.
张丽丽
2012-01-01
In this paper, our aim is to discuss the topological place of the space of fuzzy compacta in its Naturnal Hilbert cube compactification. By using the topological characterization of the pseudoboundary in the Hilbert cube, we show that the space of fuzzy compacta is a pseudointerior of its Hilbert cube compact if ication.%以讨论模糊紧空间在其一个自然的Hilbert方体紧化中的拓扑位置为目的,利用Hilbert方体中伪边界的拓扑刻画,得出模糊紧空间是其Hilbert方体紧化的伪内部.
Potoček, Václav; Miatto, Filippo M.; Mirhosseini, Mohammad; Magaña-Loaiza, Omar S.; Liapis, Andreas C.; Oi, Daniel K. L.; Boyd, Robert W.; Jeffers, John
2015-10-01
In 1924 David Hilbert conceived a paradoxical tale involving a hotel with an infinite number of rooms to illustrate some aspects of the mathematical notion of "infinity." In continuous-variable quantum mechanics we routinely make use of infinite state spaces: here we show that such a theoretical apparatus can accommodate an analog of Hilbert's hotel paradox. We devise a protocol that, mimicking what happens to the guests of the hotel, maps the amplitudes of an infinite eigenbasis to twice their original quantum number in a coherent and deterministic manner, producing infinitely many unoccupied levels in the process. We demonstrate the feasibility of the protocol by experimentally realizing it on the orbital angular momentum of a paraxial field. This new non-Gaussian operation may be exploited, for example, for enhancing the sensitivity of NOON states, for increasing the capacity of a channel, or for multiplexing multiple channels into a single one.
Potoček, Václav; Miatto, Filippo M; Mirhosseini, Mohammad; Magaña-Loaiza, Omar S; Liapis, Andreas C; Oi, Daniel K L; Boyd, Robert W; Jeffers, John
2015-10-16
In 1924 David Hilbert conceived a paradoxical tale involving a hotel with an infinite number of rooms to illustrate some aspects of the mathematical notion of "infinity." In continuous-variable quantum mechanics we routinely make use of infinite state spaces: here we show that such a theoretical apparatus can accommodate an analog of Hilbert's hotel paradox. We devise a protocol that, mimicking what happens to the guests of the hotel, maps the amplitudes of an infinite eigenbasis to twice their original quantum number in a coherent and deterministic manner, producing infinitely many unoccupied levels in the process. We demonstrate the feasibility of the protocol by experimentally realizing it on the orbital angular momentum of a paraxial field. This new non-Gaussian operation may be exploited, for example, for enhancing the sensitivity of NOON states, for increasing the capacity of a channel, or for multiplexing multiple channels into a single one.
Feynman's Operational Calculus and the Stochastic Functional Calculus in Hilbert Space
Jefferies, Brian
2010-01-01
Let $A_1, A_2$ be bounded linear operators acting on a Banach space $E$. A pair $(\\mu_1, \\mu_2)$ of continuous probability measures on $[0,1]$ determines a functional calculus $f \\rightarrowtail f_{\\mu1,|mu2}(A_1, A_2)$ for analytic functions $f$ by weighting all possible orderings of operator products of $A_1$ and $A_2$ via the probability measures $\\mu_1$ and $\\mu_2$. For example, $f \\rightarrowtail f_{\\mu,\\mu}(A_1, A_2)$ is the Weyl functional calculus with equally weighted operator produc...
Truncated Hilbert space approach to the 2d ϕ{sup 4} theory
Bajnok, Zoltan [MTA Lendület Holographic QFT Group, Wigner Research Centre for Physics,Konkoly Thege Miklós út 29-33, Budapest (Hungary); Lajer, Marton [Roland Eötvös University,Pázmány Péter sétány 1/A, Budapest (Hungary)
2016-10-11
We apply the massive analogue of the truncated conformal space approach to study the two dimensional ϕ{sup 4} theory in finite volume. We focus on the broken phase and determine the finite size spectrum of the model numerically. We interpret the results in terms of the Bethe-Yang spectrum, from which we extract the infinite volume masses and scattering matrices for various couplings. We compare these results against semiclassical analysis and perturbation theory. We also analyze the critical point of the model and confirm that it is in the Ising universality class.
Examples of bosonic de Finetti states over finite dimensional Hilbert spaces
Gottlieb, A D
2005-01-01
According to the Quantum de Finetti Theorem, locally normal infinite particle states with Bose-Einstein symmetry can be represented as mixtures of infinite tensor powers of vector states. This note presents examples of infinite-particle states with Bose-Einstein symmetry that arise as limits of Gibbs ensembles on finite dimensional spaces, and displays their de Finetti representations. We consider Gibbs ensembles for systems of bosons in a finite dimensional setting and discover limits as the number of particles tends to infinity, provided the temperature is scaled in proportion to particle number.
Truncated Hilbert Space Approach for the 1+1D phi^4 Theory
CERN. Geneva
2016-01-01
(an informal seminar, not a regular string seminar) We used the massive analogue of the truncated conformal space approach to study the broken phase of the 1+1 dimensional scalar phi^4 model in finite volume, similarly to the work by S. Rychkov and L. Vitale. In our work, the finite size spectrum was determined numerically using an effective eigensolver routine, which was followed by a simple extrapolation in the cutoff energy. We analyzed both the periodic and antiperiodic sectors. The results were compared with semiclassical and Bethe-Yang results as well as perturbation theory. We obtained the coupling dependence of the infinite volume breather and kink masses for moderate couplings. The results fit well with semiclassics and perturbative estimations, and confirm the conjecture of Mussardo that at most two neutral excitations can exist in the spectrum. We believe that improving our method with the renormalization procedure of Rychkov et al. enables to measure further interesting quantities such as decay ra...
Ali Hadi Abdulwahid
2016-12-01
Full Text Available Nowadays, the use of distributed generation (DG has increased because of benefits such as increased reliability, reduced losses, improvement in the line capacity, and less environmental pollution. The protection of microgrids, which consist of generation sources, is one of the most crucial concerns of basic distribution operators. One of the key issues in this field is the protection of microgrids against permanent and temporary failures by improving the safety and reliability of the network. The traditional method has a number of disadvantages. The reliability and stability of a power system in a microgrid depend to a great extent on the efficiency of the protection scheme. The application of Artificial Intelligence approaches was introduced recently in the protection of distribution networks. The fault detection method depends on differential relay based on Hilbert Space-Based Power (HSBP theory to achieve fastest primary protection. It is backed up by a total harmonic distortion (THD detection method that takes over in case of a failure in the primary method. The backup protection would be completely independent of the main protection. This is rarely attained in practice. This paper proposes a new algorithm to improve protection performance by adaptive network-based fuzzy inference system (ANFIS. The protection can be obtained in a novel way based on this theory. An advantage of this algorithm is that the protection system operates in fewer than two cycles after the occurrence of the fault. Another advantage is that the error detection is not dependent on the selection of threshold values, and all types of internal fault can identify and show that the algorithm operates correctly for all types of faults while preventing unwanted tripping, even if the data were distorted by current transformer (CT saturation or by data mismatches. The simulation results show that the proposed circuit can identify the faulty phase in the microgrid quickly and
Benjawan Rodjanadid
2013-12-01
Full Text Available In this paper, we introduce an iterative method for finding a common element of the set of solutions of a generalized mixed equilibrium problem (GMEP, the solutions of a general system of equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Then, we prove that the sequence converges strongly to a common element of the above three sets. Furthermore, we apply our result to prove four new strong convergence theorems in fixed point problems, mixed equilibrium problems, generalized equilibrium problems , equilibrium problems and variational inequality.
Rig it right! Maya animation rigging concepts
O'Hailey, Tina
2013-01-01
Rigging a character can be a complicated undertaking. Move from a bi-pedal character to a quad- or poly-pedal and, well, things just got real. Where do you begin? Unlike all of those button-pushing manuals out there, Rig it Right! breaks down rigging so that you can achieve a fundamental understanding of the concept, allowing you to rig more intuitively in your own work. Veteran animation professor Tina O'Hailey will get you up and rigging in a matter of hours with step-by-step tutorials covering multiple animation control types, connection methods, interactive skinning, Blend
Biddlecombe, George
1990-01-01
The best manual ever produced on rigging a sailing ship, based on extensively revised and updated 1848 edition prepared by Biddlecombe, Master in the Royal Navy. Complete definition of terms, on-shore operations, process of rigging ships, reeving the running rigging and bending sails, rigging brigs, yachts and small vessels, more. 17 plates.
Review of photonic Hilbert transformers
Chaotan SIMA
2013-01-01
This paper reviews the demonstrations of photonic Hilbert transformers （PHTs）, describing their progress and recent developments. The physical operating principles of PHTs including fractional Hilbert transformers are discussed, together with device applications in all-optical signal processing. Versatile approaches to realize PHTs are discussed, e.g., discrete free space optics, fiber-based schemes and integrated planar geometry. The numerical designs and experimental performances of these PHTs are analyzed in terms of spectral quality, operating bandwidth, system integration, and mechanical and thermal stability. Recent developments of the monolithically integrated photonic Hilbert transform （HT） devices include directional couplers and planar Bragg gratings which allow all-optical single-sideband （SSB） suppression and sideband switching.
Hilbert Series for Theories with Aharony Duals
Hanany, Amihay; Kim, Hyungchul; Park, Jaemo; Seong, Rak-Kyeong
2015-01-01
The algebraic structure of moduli spaces of 3d N=2 supersymmetric gauge theories is studied by computing the Hilbert series which is a generating function that counts gauge invariant operators in the chiral ring. These U(N_c) theories with N_f flavors have Aharony duals and their moduli spaces receive contributions from both mesonic and monopole operators. In order to compute the Hilbert series, recently developed techniques for Coulomb branch Hilbert series in 3d N=4 are extended to 3d N=2. The Hilbert series computation leads to a general expression of the algebraic variety which represents the moduli space of the U(N_c) theory with N_f flavors and its Aharony dual theory. A detailed analysis of the moduli space is given, including an analysis of the various components of the moduli space.
Barik, Sailen
2016-01-01
RIG-I (retinoic acid-inducible gene 1) is an archetypal member of the cytoplasmic DEAD-box dsRNA helicase family (RIG-I-like receptors or RLRs), the members of which play essential roles in the innate immune response of the metazoan cell. RIG-I functions as a pattern recognition receptor that detects nonself RNA as a pathogen-associated molecular pattern (PAMP). However, the exact molecular nature of the viral RNAs that act as a RIG-I ligand has remained a mystery and a matter of debate. In this article, we offer a critical review of the actual viral RNAs that act as PAMPs to activate RIG-I, as seen from the perspective of a virologist, including a recent report that the viral Leader-read-through transcript is a novel and effective RIG-I ligand.
The moduli spaces of $3d$ ${\\cal N} \\ge 2$ Chern-Simons gauge theories and their Hilbert series
Cremonesi, Stefano; Zaffaroni, Alberto
2016-01-01
We present a formula for the Hilbert series that counts gauge invariant chiral operators in a large class of 3d ${\\cal N} \\ge 2$ Yang-Mills-Chern-Simons theories. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background. We provide a general formula for the case of abelian theories, where nonperturbative corrections are absent, and consider a few examples of nonabelian theories where nonperturbative corrections are well understood. We also analyze in detail nonabelian ABJ(M) theories as well as worldvolume theories of M2-branes probing Calabi-Yau fourfold and hyperK\\"ahler twofold singularities with ${\\cal N} = 2$ and ${\\cal N} = 3$ supersymmetry.
Hilbert, completeness and geometry
Giorgio Venturi
2011-11-01
Full Text Available This paper aims to show how the mathematical content of Hilbert's Axiom of Completeness consists in an attempt to solve the more general problem of the relationship between intuition and formalization. Hilbert found the accordance between these two sides of mathematical knowledge at a logical level, clarifying the necessary and sufficient conditions for a good formalization of geometry. We will tackle the problem of what is, for Hilbert, the definition of geometry. The solution of this problem will bring out how Hilbert's conception of mathematics is not as innovative as his conception of the axiomatic method. The role that the demonstrative tools play in Hilbert's foundational reflections will also drive us to deal with the problem of the purity of methods, explicitly addressed by Hilbert. In this respect Hilbert's position is very innovative and deeply linked to his modern conception of the axiomatic method. In the end we will show that the role played by the Axiom of Completeness for geometry is the same as the Axiom of Induction for arithmetic and of Church-Turing thesis for computability theory. We end this paper arguing that set theory is the right context in which applying the axiomatic method to mathematics and we postpone to a sequel of this work the attempt to offer a solution similar to Hilbert's for the completeness of set theory.
2013-01-01
David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations. Ten essays are devoted to the analysis of classical as well as modern proof theory; three papers on the mathematical roots of Hilbert's work precede the analytical core, and three final essays exploit an open philosophical horizon for reflection on the nature of mathematics in the 21st century.
2010-01-01
Motivados por el estudio de espacios de Hilbert asociados a sistemas físicos y la construcción de modelos como el espacio cociente del ultraproducto de estructuras, se ha establecido la teoría de los haces de estructuras topológicas como una extensión natural de la teoría de los haces de estructuras de primer orden, desarrollada por Caicedo y otros. Se analiza el problema de la completes de Cauchy en los casos que la topología sobre cada fibra es inducida por una métrica. Esta discusión lleva...
A CHARACTERIZATION OF SIGNED GENERALIZED FRAMES IN A HILBERT SPACE%Hilbert空间H中带符号广义框架的一个刻画
姚喜妍
2006-01-01
本文研究了可分的Hilbert空间H中带符号广义框架,利用算子理论方法,给出了H中一族向量{hm}m∈M是一个带符号广义框架当且仅当带符号广义框架的框架算子的正部S+和负部S-是有界线性算子,讨论了H中带符号广义框架的框架算子S的可逆性,并且得到了H中每个向量f关于带符号广义框架{h~m}m∈M和其对偶带符号广义框架{m}m∈M的表示式.%In this paper, we study signed generalized frames in a separable Hilbert space H. Using operator-theoretic methods, we give that a family of vectors {hm}m∈M for H is a signed generalized frame if and only if positive and negative parts S+, S- of the signed generalized frame operators S are bounded linear operators. We also discuss that the signed generalized frame operators S is invertible for every f∈H, and obtain the signed generalized frame representation, with respect to a signed generalized frame {hm}m∈M and its dual signed generalized frame {(h~)m}m∈M.
Sánchez, C M; Levstein, P R; Buljubasich, L; Pastawski, H M; Chattah, A K
2016-06-13
In this work, we overview time-reversal nuclear magnetic resonance (NMR) experiments in many-spin systems evolving under the dipolar Hamiltonian. The Loschmidt echo (LE) in NMR is the signal of excitations which, after evolving with a forward Hamiltonian, is recovered by means of a backward evolution. The presence of non-diagonal terms in the non-equilibrium density matrix of the many-body state is directly monitored experimentally by encoding the multiple quantum coherences. This enables a spin counting procedure, giving information on the spreading of an excitation through the Hilbert space and the formation of clusters of correlated spins. Two samples representing different spin systems with coupled networks were used in the experiments. Protons in polycrystalline ferrocene correspond to an 'infinite' network. By contrast, the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline in the nematic mesophase represents a finite proton system with a hierarchical set of couplings. A close connection was established between the LE decay and the spin counting measurements, confirming the hypothesis that the complexity of the system is driven by the coherent dynamics.
F. O. Isiogugu
2016-01-01
Full Text Available The strong convergence of a hybrid algorithm to a common element of the fixed point sets of multivalued strictly pseudocontractive-type mappings and the set of solutions of an equilibrium problem in Hilbert spaces is obtained using a strict fixed point set condition. The obtained results improve, complement, and extend the results on multivalued and single-valued mappings in the contemporary literature.
Orthogonal apartments in Hilbert Grassmannians
Pankov, Mark
2015-01-01
Let $H$ be an infinite-dimensional complex Hilbert space and let ${\\mathcal L}(H)$ be the logic formed by all closed subspaces of $H$. For every natural $k$ we denote by ${\\mathcal G}_{k}(H)$ the Grassmannian consisting of $k$-dimensional subspaces. An orthogonal apartment of ${\\mathcal G}_{k}(H)$ is the set consisting of all $k$-dimensional subspaces spanned by subsets of a certain orthogonal base of $H$. Orthogonal apartments can be characterized as maximal sets of mutually compatible eleme...
Petrosky, T.; Hashimoto, K.; Kanki, K.; Tanaka, S.
2017-10-01
Irreversible process of a weakly coupled one-dimensional quantum perfect Lorentz gas is studied on the basis of the fundamental laws of physics in terms of the complex spectral analysis associated with the resonance state of the Liouvillian. Without any phenomenological operations, such as a coarse-graining of space-time or a truncation of the higher order correlation, we obtained irreversible processes on a purely dynamical basis in all space and time scale including the microscopic atomic interaction range that is much smaller than the mean-free-length. The list of development of the complex spectral analysis of the Hamiltonian (instead of the Liouvillian) in quantum optical systems and in quantum nano-devices is also presented.
Cardot, Hervé; Zitt, Pierre-André
2011-01-01
With the progress of measurement apparatus and the development of automatic sensors it is not unusual anymore to get thousands of samples of observations taking values in high dimension spaces such as functional spaces. In such large samples of high dimensional data, outlying curves may not be uncommon and even a few individuals may corrupt simple statistical indicators such as the mean trajectory. We focus here on the estimation of the geometric median which is a direct generalization of the real median and has nice robustness properties. The geometric median being defined as the minimizer of a simple convex functional that is differentiable everywhere when the distribution has no atoms, it is possible to estimate it with online gradient algorithms. Such algorithms are very fast and can deal with large samples. Furthermore they also can be simply updated when the data arrive sequentially. We state the almost sure consistency and the L2 rates of convergence of the stochastic gradient estimator as well as the ...
Learning Inverse Rig Mappings by Nonlinear Regression.
Holden, Daniel; Saito, Jun; Komura, Taku
2016-11-11
We present a framework to design inverse rig-functions - functions that map low level representations of a character's pose such as joint positions or surface geometry to the representation used by animators called the animation rig. Animators design scenes using an animation rig, a framework widely adopted in animation production which allows animators to design character poses and geometry via intuitive parameters and interfaces. Yet most state-of-the-art computer animation techniques control characters through raw, low level representations such as joint angles, joint positions, or vertex coordinates. This difference often stops the adoption of state-of-the-art techniques in animation production. Our framework solves this issue by learning a mapping between the low level representations of the pose and the animation rig. We use nonlinear regression techniques, learning from example animation sequences designed by the animators. When new motions are provided in the skeleton space, the learned mapping is used to estimate the rig controls that reproduce such a motion. We introduce two nonlinear functions for producing such a mapping: Gaussian process regression and feedforward neural networks. The appropriate solution depends on the nature of the rig and the amount of data available for training. We show our framework applied to various examples including articulated biped characters, quadruped characters, facial animation rigs, and deformable characters. With our system, animators have the freedom to apply any motion synthesis algorithm to arbitrary rigging and animation pipelines for immediate editing. This greatly improves the productivity of 3D animation, while retaining the flexibility and creativity of artistic input.
Hilbert space and quantum mechanics
Gallone, Franco
2015-01-01
The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Pref...
Realization Theory in Hilbert Space
1985-07-01
Furthermore, a sufficient condition is that G(t) e R P x m is locally of bounded variation and satisfies an estimate of the form (6.10) VAR G r Me wt [0...not be of bounded variation . In the same way there exist time invariant, causal, linear input-output operators T which cannot be represented in the form...6.12) Tu(t) - f d(s)u(t-s) , t e R 0 for some matrix function U(t) of bounded variation . -29- " " " """. r . .................. .. . . . iliI
Quantum mechanics in Hilbert space
Prugovecki, Eduard
2006-01-01
A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas.This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the
Gorenstein Hilbert Coefficients
Khoury, Sabine El
2012-01-01
We prove upper and lower bounds for all the coefficients in the Hilbert Polynomial of a graded Gorenstein algebra $S=R/I$ with a quasi-pure resolution over $R$. The bounds are in terms of the minimal and the maximal shifts in the resolution of $R$ . These bounds are analogous to the bounds for the multiplicity found in \\cite{S} and are stronger than the bounds for the Cohen Macaulay algebras found in \\cite{HZ}.
Fractional vortex Hilbert's Hotel
Gbur, Greg
2015-01-01
We demonstrate how the unusual mathematics of transfinite numbers, in particular a nearly perfect realization of Hilbert's famous hotel paradox, manifests in the propagation of light through fractional vortex plates. It is shown how a fractional vortex plate can be used, in principle, to create any number of "open rooms," i.e. topological charges, simultaneously. Fractional vortex plates are therefore demonstrated to create a singularity of topological charge, in which the vortex state is completely undefined and in fact arbitrary.
Glasner, Eli
2010-01-01
Returning to a classical question in Harmonic Analysis we strengthen an old result of Walter Rudin. We show that there exists a weakly almost periodic function on the group of integers Z which is not in the norm-closure of the algebra B(Z) of Fourier-Stieltjes transforms of measures on the circle, the dual group of Z, and which is recurrent. We also show that there is a Polish monothetic group which is reflexively but not Hilbert representable.
Braun, Gabriel; Narboux, Julien
2012-01-01
International audience; In this paper, we report on the formal proof that Hilbert's axiom system can be derived from Tarski's system. For this purpose we mechanized the proofs of the first twelve chapters of Schwabauser, Szmielew and Tarski's book: Metamathematische Methoden in der Geometrie. The proofs are checked formally within classical logic using the Coq proof assistant. The goal of this development is to provide clear foundations for other formalizations of geometry and implementations...
Seres, Gyula
2016-01-01
Manipulating prices in auctions raises antitrust concerns. Collusion lowers the revenue of the auctioneer and creates information rents. Bid rigging is a prevalent phenomenon and the affected market is enormous. Public procurement amounts to between 10 and 25 percent of national GDP in industrialize
Heisenberg model and Rigged Configurations
Giri, Pulak Ranjan
2015-01-01
We show a correspondence of all the solutions of the spin-1/2 isotropic Heisenberg model for N=12 to the rigged configurations based on the comparison of the set of Takahashi quantum numbers in lexicographical order with the set of riggings of the rigged configurations in co-lexicographical order.
Takesaki-Takai Duality Theorem in Hilbert C*-Modules
Mao Zheng GUO; Xiao Xia ZHANG
2004-01-01
In this paper, we generalize the Takesaki-Takai duality theorem in Hilbert C*-modules;that is to say, if (H, V, U) is a Kac-system, where H is a Hilbert space, V is a multiplicative unitary operator on H (×) H and U is a unitary operator on H, and if E is an (j)-compatible Hilbert (A)-module,then E × (j∧) × (j) (≌) E (×) K(H), where K(H) is the set of all compact operators on H, and (j) and (j) are Hopf C*-algebras corresponding to the Kac-system (H, V, U).
Hilbert C*-模中本原理想子模的一些性质%Some properties of primitive ideal submodules in Hilbert C*-modules
杨功林; 纪培胜
2014-01-01
给出了Hilbert C*-模中本原理想子模的定义，研究了Hilbert C*-模的本原理想子模空间以及谱空间的一些性质，所得结果推广和改进了已有的结果。%The definition of the primitive ideal submodules in Hilbert C*-modules is given.Some properties of primi-tive ideal submodule space and the spectrum space in Hilbert C*-modules are studied.It is shown that these results ex-tend and improve the existing results.
Decomposition theorems for Hilbert modular newforms
Linowitz, Benjamin
2011-01-01
Let $\\mathscr{S}_k^+(\\cn,\\Phi)$ denote the space generated by Hilbert modular newforms (over a fixed totally real field $K$) of weight $k$, level $\\cn$ and Hecke character $\\Phi$. We show how to decompose $\\mathscr{S}_k^+(\\cn,\\Phi)$ into direct sums of twists of other spaces of newforms. This sheds light on the behavior of a newform under a character twist: the exact level of the twist of a newform, when such a twist is itself a newform, and when a newform may be realized as the twist of a primitive newform. These results were proven for elliptic modular forms by Hijikata, Pizer and Shemanske by employing a formula for the trace of the Hecke operator $T_k(n)$. We obtain our results not by employing a more general formula for the trace of Hecke operators on spaces of Hilbert modular forms, but instead by using basic properties of newforms which were proven for elliptic modular forms by Li, and Atkin and Li, and later extended to Hilbert modular forms by Shemanske and Walling.
A Riemann-Hilbert approach to Painleve IV
Put, M. van der; Top, J.
2013-01-01
The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painleve equation. One obtains a Riemann-Hilbert correspondence between moduli spaces of rank two connections on P-1 and moduli spaces for the monodromy data. The moduli spaces for these connections are identified with Okamoto-Painleve va
A Riemann-Hilbert approach to Painleve IV
Put, M. van der; Top, J.
2013-01-01
The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painleve equation. One obtains a Riemann-Hilbert correspondence between moduli spaces of rank two connections on P-1 and moduli spaces for the monodromy data. The moduli spaces for these connections are identified with Okamoto-Painleve va
Gamow, not Hilbert: The Architect of Hilbert's Grand Hotel
Kragh, Helge
2014-01-01
What is known as "Hilbert's hotel" is a story of an imaginary hotel with infinitely many rooms that illustrates the bizarre consequences of assuming an actual infinity of objects or events. Since the 1970s it has been used in a variety of arguments, some of them relating to cosmology and others to philosophy and theology. It turns out that the name is a misnomer, as Hilbert was not responsible for the story. The originator was George Gamow, who invented the hotel in 1947, jokingly attributing it to Hilbert. Although well known, the counter-intuitive hotel only attracted wide interest in the 1970s, first in philosophical and theological contexts. The paper outlines the origin and early history of what might be called the Gamow-Hilbert hotel paradox.
Deep water challenges for drilling rig design
Roth, M. [Transocean Sedco Forex, Houston, TX (United States)
2001-07-01
Drilling rigs designed for deep water must meet specific design considerations for harsh environments. The early lessons for rig design came from experiences in the North Sea. Rig efficiency and safety considerations must include structural integrity, isolated/redundant ballast controls, triple redundant DP systems, enclosed heated work spaces, and automated equipment such as bridge cranes, pipe handling gear, offline capabilities, subsea tree handling, and computerized drill floors. All components must be designed to harmonize man and machine. Some challenges which are unique to Eastern Canada include frequent storms and fog, cold temperature, icebergs, rig ice, and difficult logistics. This power point presentation described station keeping and mooring issues in terms of dynamic positioning issues. The environmental influence on riser management during forced disconnects was also described. Design issues for connected deep water risers must insure elastic stability, and control deflected shape. The design must also keep stresses within acceptable limits. Codes and standards for stress limits, flex joints and tension were also presented. tabs., figs.
Glenn Extreme Environments Rig (GEER) Independent Review
Jankovsky, Robert S.; Smiles, Michael D.; George, Mark A.; Ton, Mimi C.; Le, Son K.
2015-01-01
The Chief of the Space Science Project Office at Glenn Research Center (GRC) requested support from the NASA Engineering and Safety Center (NESC) to satisfy a request from the Science Mission Directorate (SMD) Associate Administrator and the Planetary Science Division Chief to obtain an independent review of the Glenn Extreme Environments Rig (GEER) and the operational controls in place for mitigating any hazard associated with its operation. This document contains the outcome of the NESC assessment.
National Aeronautics and Space Administration — The three goals of this IRAD are:1.1 Research and develop the Hilbert-Huang Transform for 2D second and last component – the Hilbert Spectral Analysis for 2D...
Pressure rig for repetitive casting
Vasquez, Peter (Inventor); Hutto, William R. (Inventor); Philips, Albert R. (Inventor)
1989-01-01
The invention is a pressure rig for repetitive casting of metal. The pressure rig performs like a piston for feeding molten metal into a mold. Pressure is applied to an expandable rubber diaphragm which expands like a balloon to force the metal into the mold. A ceramic cavity which holds molten metal is lined with blanket-type insulating material, necessitating only a relining for subsequent use and eliminating the lengthy cavity preparation inherent in previous rigs. In addition, the expandable rubber diaphragm is protected by the insulating material thereby decreasing its vulnerability to heat damage. As a result of the improved design the life expectancy of the pressure rig contemplated by the present invention is more than doubled. Moreover, the improved heat protection has allowed the casting of brass and other alloys with higher melting temperatures than possible in the conventional pressure rigs.
Soileau, Kerry M.; Baicy, John W.
2008-01-01
Rig Diagnostic Tools is a suite of applications designed to allow an operator to monitor the status and health of complex networked systems using a unique interface between Java applications and UNIX scripts. The suite consists of Java applications, C scripts, Vx- Works applications, UNIX utilities, C programs, and configuration files. The UNIX scripts retrieve data from the system and write them to a certain set of files. The Java side monitors these files and presents the data in user-friendly formats for operators to use in making troubleshooting decisions. This design allows for rapid prototyping and expansion of higher-level displays without affecting the basic data-gathering applications. The suite is designed to be extensible, with the ability to add new system components in building block fashion without affecting existing system applications. This allows for monitoring of complex systems for which unplanned shutdown time comes at a prohibitive cost.
The high order Schwarz-Pick lemma on complex Hilbert balls
无
2010-01-01
In this paper we prove a high order Schwarz-Pick lemma for holomorphic mappings between unit balls in complex Hilbert spaces.In addition,a Schwarz-Pick estimate for high order Fréchet derivatives of a holomorphic function f of a Hilbert ball into the right half-plane is obtained.
Hoisting and Rigging (Formerly Hoisting and Rigging Manual)
NONE
1995-06-01
This standard is intended as a reference document to be used by supervisors, line managers, safety personnel, equipment operators, and any other personnel responsible for safety of hoisting and rigging operations at DOE sites. It quotes or paraphrases the US OSHA and ANSI requirements. It also encompasses, under one cover,hoisting and rigging requirements, codes, standards, and regulations, eliminating the need to maintain extensive (and often incomplete) libraries of hoisting and rigging standards throughout DOE. The standard occasionally goes beyond the minimum general industry standards established by OSHA and ANSI, and also delineates the more stringent requirements necessary to accomplish the complex, diversified, critical, and often hazardous hoisting and rigging work found with the DOE complex.
Hilbert complexes of nonlinear elasticity
Angoshtari, Arzhang; Yavari, Arash
2016-12-01
We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.
On the 5d instanton index as a Hilbert series
Rodríguez-Gómez, Diego, E-mail: d.rodriguez.gomez@uniovi.es [Department of Physics, Universidad de Oviedo, Avda. Calvo Sotelo 18, 33007 Oviedo (Spain); Zafrir, Gabi, E-mail: gabizaf@techunix.technion.ac.il [Department of Physics, Technion, Israel Institute of Technology, Haifa 32000 (Israel)
2014-01-15
The superconformal index for N=2 5d theories contains a non-perturbative part arising from 5d instantonic operators which coincides with the Nekrasov instanton partition function. In this article, for pure gauge theories, we elaborate on the relation between such instanton index and the Hilbert series of the instanton moduli space. We propose a non-trivial identification of fugacities allowing the computation of the instanton index through the Hilbert series. We show the agreement of our proposal with existing results in the literature, as well as use it to compute the exact index for a pure U(1) gauge theory.
Lectures on Hilbert modular varieties and modular forms
Goren, Eyal Z
2001-01-01
This book is devoted to certain aspects of the theory of p-adic Hilbert modular forms and moduli spaces of abelian varieties with real multiplication. The theory of p-adic modular forms is presented first in the elliptic case, introducing the reader to key ideas of N. M. Katz and J.-P. Serre. It is re-interpreted from a geometric point of view, which is developed to present the rudiments of a similar theory for Hilbert modular forms. The theory of moduli spaces of abelian varieties with real multiplication is presented first very explicitly over the complex numbers. Aspects of the general theory are then exposed, in particular, local deformation theory of abelian varieties in positive characteristic. The arithmetic of p-adic Hilbert modular forms and the geometry of moduli spaces of abelian varieties are related. This relation is used to study q-expansions of Hilbert modular forms, on the one hand, and stratifications of moduli spaces on the other hand. The book is addressed to graduate students and non-exper...
Hilbert manifold structure for asymptotically hyperbolic relativistic initial data
Fougeirol, Jérémie
2016-01-01
We provide a Hilbert manifold structure {\\`a} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{\\'e} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.
A support theorem for Hilbert schemes of planar curves
Migliorini, Luca
2011-01-01
Consider a family of integral complex locally planar curves whose relative Hilbert scheme of points is smooth. The decomposition theorem of Beilinson, Bernstein, and Deligne asserts that the pushforward of the constant sheaf on the relative Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension. It follows that the perverse filtration on the cohomology of the compactified Jacobian of an integral plane curve encodes the cohomology of all Hilbert schemes of points on the curve. Globally, it follows that a family of such curves with smooth relative compactified Jacobian ("moduli space of D-branes") in an irreducible curve class on a Calabi-Yau threefold will contribute equally to the BPS invariants in the formulation of Pandharipande and Thomas, and in the formulation of Hosono, Saito, and Takahashi.
Topological freeness for Hilbert bimodules
Kwasniewski, Bartosz
2014-01-01
It is shown that topological freeness of Rieffel’s induced representation functor implies that any C*-algebra generated by a faithful covariant representation of a Hilbert bimodule X over a C*-algebra A is canonically isomorphic to the crossed product A ⋊ X ℤ. An ideal lattice description and a s...
Balázs, András
2003-06-01
In the present paper, some physical considerations of the biological symbol-matter problem is exposed. First of all, the physical concept of quantum dynamical internal measuremental robustness is discussed. In this context, the significance of introducing affine molecular Hilbert spaces, the original (primordeal) internal quantum measurement, and the global constraining nature of time-inversion symmetry restoring, as a special restoration force, is discussed at some length. It is pointed out, as a summary, that global robustness of the internal dynamics of quantum measurements is due to two basic factors: on one hand, the global constraining nature of the chosen specific (symmetry-) restoring force, and on the other, the individual robustness of the discrete local internal measuremental interactions. The second condition is supposed to follow from a system-internalised ("objective") Bohr-type Copenhagen interpretation of quantum mechanics, corresponding, in an external context, to the Generalized Complementarity Principle of Bohr and Elsasser. It is not claimed, however, that this latter problem has been, as yet, satisfactorily settled physically. In fact, if it were, it would amount to a specifically biological quantum theory of internal measurement, which had to be rooted in the original primordeal global internal measurement, amounting to the origin of the genetic code.
邓宏贵; 朱从旭
2001-01-01
该文运用数值计算方法研究了有限维希尔伯特空间谐振子偶相干态的非经典特性.研究表明.在有限维情景，偶相干态不仅出现振幅正交分量压缩，而且出现振幅平方压缩和反聚束效应.随着维数s减少，出现两种压缩的区域均缩小且压缩强度减弱；而出现反聚束效应的区域却变大且反聚束程度加强.%The nonclassical properties of even coherent states in a finite-dimensional Hilbert spaces (FDHS) case are studied by numerical method . It is found that, not only quadrature squeezing but also amplitude-squeezing and antibunching effects exist in the states. With the number of dimension reducing, both quadrate squeezing and amplitudesqueezing effects are weakened,but the antibunching effect is Enhanced.
Perturbations of Standard Generalized Frames in Hilbert W*-Module%HILBERT W*-模上标准广义框架的摄动
付焕坤; 孟彬; 董芳芳
2011-01-01
In this paper, the stability of Hilbert W*-modular standard generalized frames under perturbations are studied intensively by using operator-theoretic-methods, and some useful conditions of perturbation and results which are similar to the frames in Hilbert space are given.%该文主要用算子理论的方法详细讨论了Hilbert W*-模中标准广义框架的摄动性,且给出了类似于Hilbert空间中的很有用的摄动条件和相应结论.
卢道明
2008-01-01
Using the numerical method,the antibunching effects of a new kind of odd and even nonlinear CO- herent states in a finite-dimensional Hilbert space are studied.The results show that the new kind of odd non- 1inear coherent state exhibits antibunching effect and the new kind of even nonlinear coherent state does not exhibits antibunching effect in a finite-dimensional Hilbert space.%利用数值计算方法,研究了有限维Hilbert空间一种新的奇偶非线性相干态的反聚束效应.研究结果表明:各有限维Hilbert空间新的偶非线性相干态均不出现反聚束效应.但各有限维Hilbert空间新的奇非线性相干态均可出现反聚束效应.
闫明刚; 刘海防; 陈汝栋
2009-01-01
在希尔伯特空间,我们引入一个新的迭代序列来逼近广义均衡问题和有限组扩张映像的不动点的公共元素.相应推广了 Satoru Takahashi,Wararu Takahashif Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space,Nonlinear Analysis 69(2008)0250-1033
Compatibility and Schur Complements of Operators on Hilbert C*-Module
Xiaochun FANG; Jing YU
2011-01-01
Let E be a Hilbert C*-module, and (J) be an orthogonally complemented closed submodule of E. The authors generalize the definitions of (J)-complementability and (J)compatibility for general (adjointable) operators from Hilbert space to Hilbert C*-module,and discuss the relationship between each other. Several equivalent statements about (J)complementability and (J)-compatibility, and several representations of Schur complements of (J)-complementable operators (especially, of (J)-compatible operators and of positive (J)compatible operators) on a Hilbert C*-module are obtained. In addition, the quotient property for Schur complements of matrices is generalized to the quotient property for Schur complements of (J)-complementable operators and (J)*-complementable operators on a Hilbert C*-module.
Digital watermarking : An approach based on Hilbert transform
Agarwal, Rashmi; Santhanam, M S; Srinivas, K; Venugopalan, K
2010-01-01
Most of the well known algorithms for watermarking of digital images involve transformation of the image data to Fourier or singular vector space. In this paper, we introduce watermarking in Hilbert transform domain for digital media. Generally, if the image is a matrix of order $m$ by $n$, then the transformed space is also an image of the same order. However, with Hilbert transforms, the transformed space is of order $2m$ by $2n$. This allows for more latitude in storing the watermark in the host image. Based on this idea, we propose an algorithm for embedding and extracting watermark in a host image and analytically obtain a parameter related to this procedure. Using extensive simulations, we show that the algorithm performs well even if the host image is corrupted by various attacks.
PNNL Hoisting and Rigging Manual
Haynie, Todd O.; Fullmer, Michael W.
2008-12-29
This manual describes the safe and cost effective operation, inspection, maintenance, and repair requirements for cranes, hoists, fork trucks, slings, rigging hardware, and hoisting equipment. It is intended to be a user's guide to requirements, codes, laws, regulations, standards, and practices that apply to Pacific Northwest National Laboratory (PNNL) and its subcontractors.
Hoisting and rigging manual: Uncontrolled document
NONE
1991-05-01
This document is a draft copy of a Hoisting and Rigging Manual for the Department of Energy. The manual is divided into ten chapters. The chapter titles follow: terminology and definitions; operator training and qualification; overhead and gantry cranes; mobile cranes; forklift trucks; hoists; hooks; wire rope, slings, and rigging accessories; construction hoisting and rigging equipment requirements; references.
Rotary Engine Friction Test Rig Development Report
2011-12-01
5 4. Friction Rig Development 7 5. AutoCAD ...Figure 4. Engine friction test rig AutoCAD model. ........................................................................8 Figure 5. Engine...top dead center. 8 5. AutoCAD Model Development A model of the rotary engine friction test rig was developed to determine the optimal
Balázs, András
2006-08-01
A physical (affine Hilbert spaces) frame is developed for the discussion of the interdependence of the problem of the origin (symbolic assignment) of the genetic code and a possible endophysical (a kind of "internal") quantum measurement in an explicite way, following the general considerations of Balázs (Balázs, A., 2003. BioSystems 70, 43-54; Balázs, A., 2004a. BioSystems 73, 1-11). Using the Everett (a dynamic) interpretation of quantum mechanics, both the individual code assignment and the concatenated linear symbolism is discussed. It is concluded that there arises a skewed quantal probability field, with a natural dynamic non-linearity in codon assignment within the physical model adopted (essentially corresponding to a much discussed biochemical frame of self-catalyzed binding (charging) of t RNA like proto RNAs (ribozymes) with amino acids). This dynamic specific molecular complex assumption of individual code assignment, and the divergence of the code in relation to symbol concatenation, are discussed: our frame supports the former and interpret the latter as single-type codon (triplet), also unambiguous and extended assignment, selection in molecular evolution, corresponding to converging towards the fixedpoint of the internal dynamics of measurement, either in a protein- or RNA-world. In this respect, the general physical consequence is the introduction of a fourth rank semidiagonal energy tensor (see also Part II) ruling the internal dynamics as a non-linear in principle second-order one. It is inferred, as a summary, that if the problem under discussion could be expressed by the concepts of the Copenhagen interpretation of quantum mechanics in some yet not quite specified way, the matter would be particularly interesting with respect to both the origin of life and quantum mechanics, as a dynamically supported natural measurement-theoretical split between matter ("hardware") and (internal) symbolism ("software") aspects of living matter.
张勇; 王维玺
2000-01-01
构造了有限维希尔伯特空间偶奇q-相干态,并通过数值计算研究了它们的高阶反聚束效应,分析了空间维数和形变参数q对反聚束效应的影响.%Even and odd q-coherent states in a finite-dimensional Hilbert space are constructed. Their antibunching effects are studied through the numerical method, and the function of the dimension of space and deformation parameter q to the antibunching effect is analyzed.
Equivalence of Quotient Hilbert Modules
Ronald G Douglas; Gadadhar Misra
2003-08-01
Let $\\mathcal{M}$ be a Hilbert module of holomorphic functions over a natural function algebra $\\mathcal{A}()$, where $ \\subseteq \\mathbb{C}^m$ is a bounded domain. Let $\\mathcal{M}_0 \\subseteq \\mathcal{M}$ be the submodule of functions vanishing to order on a hypersurface $\\mathcal{Z} \\subseteq $. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modules $\\mathcal{Q} = \\mathcal{M} \\ominus \\mathcal{M}_0$. The invariants are given explicitly in the particular case of = 2.
CHEN JIECHENG; DING YONG; FAN DASHAN
2003-01-01
The authors define the directional hyper Hilbert transform and give its mixed norm estimate.The similar conclusions for the directional fractional integral of one dimension are also obtainedin this paper. As an application of the above results, the authors give the Lp-boundedness for aclass of the hyper singular integrals and the fractional integrals with variable kernel. Moreover,as another application of the above results, the authors prove the dimension free estimate forthe hyper Riesz transform. This is an extension of the related result obtained by Stein.
An image encryption algorithm utilizing julia sets and hilbert curves.
Sun, Yuanyuan; Chen, Lina; Xu, Rudan; Kong, Ruiqing
2014-01-01
Image encryption is an important and effective technique to protect image security. In this paper, a novel image encryption algorithm combining Julia sets and Hilbert curves is proposed. The algorithm utilizes Julia sets' parameters to generate a random sequence as the initial keys and gets the final encryption keys by scrambling the initial keys through the Hilbert curve. The final cipher image is obtained by modulo arithmetic and diffuse operation. In this method, it needs only a few parameters for the key generation, which greatly reduces the storage space. Moreover, because of the Julia sets' properties, such as infiniteness and chaotic characteristics, the keys have high sensitivity even to a tiny perturbation. The experimental results indicate that the algorithm has large key space, good statistical property, high sensitivity for the keys, and effective resistance to the chosen-plaintext attack.
Orthogonal apartments in Hilbert Grassmannians. Finite-dimensional case
Pankov, Mark
2015-01-01
Let $H$ be a complex Hilbert space of finite dimension $n\\ge 3$. Denote by ${\\mathcal G}_{k}(H)$ the Grassmannian consisting of $k$-dimensional subspaces of $H$. Every orthogonal apartment of ${\\mathcal G}_{k}(H)$ is defined by a certain orthogonal base of $H$ and consists of all $k$-dimensional subspaces spanned by subsets of this base. For $n\
Contractive Hilbert modules and their dilations over natural function algebras
Douglas, Ronald G; Sarkar, Jaydeb
2009-01-01
In this note, we show that quasi-free Hilbert modules R defined over natural function algebras satisfying a certain positivity condition, defined via the hereditary functional calculus, admit a dilation (actually a co-extension) to the Hardy module over the polydisk. An explicit realization of the dilation space is given along with the isometric embedding of the module R in it. Some consequences of this basic fact is then explored in the case of several natural function algebras.
Quantum Hilbert matrices and orthogonal polynomials
Andersen, Jørgen Ellegaard; Berg, Christian
2009-01-01
Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|matrices...... of reciprocal Fibonacci numbers called Filbert matrices. We find a formula for the entries of the inverse quantum Hilbert matrix....
Quantum mechanics: why complex Hilbert space?
Cassinelli, G; Lahti, P
2017-11-13
We outline a programme for an axiomatic reconstruction of quantum mechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).
Hilbert space methods for partial differential equations
Ralph E. Showalter
1994-09-01
Full Text Available This book is an outgrowth of a course which we have given almost periodically over the last eight years. It is addressed to beginning graduate students of mathematics, engineering, and the physical sciences. Thus, we have attempted to present it while presupposing a minimal background: the reader is assumed to have some prior acquaintance with the concepts of ``linear'' and ``continuous'' and also to believe $L^2$ is complete. An undergraduate mathematics training through Lebesgue integration is an ideal background but we dare not assume it without turning away many of our best students. The formal prerequisite consists of a good advanced calculus course and a motivation to study partial differential equations.
Physics of the Hilbert Book Model
Leunen, Hans van
2014-07-01
The Hilbert Book Model is the name of a personal project of the author. The model is deduced from a foundation that is based on quantum logic and that is subsequently extended with trustworthy mathematical methods. What is known from conventional physics is used as a guideline, but the model is not based on the methodology of contemporary physics. In this way the model can reach deeper into the basement of physics. The ambition of the model is rather modest. It limits its scope to the lowest levels of the physical hierarchy. Thus fields and elementary particles are treated in fair detail, but composites are treated marginally and only some aspects of cosmology are touched. Still the model dives into the origins of gravitation and inertia and explains the diversity of the elementary particles. It explains what photons are and introduces a lower level of physical objects and a new kind of ultra-high frequency waves that carry information about their emitters. It explains entanglement and the Pauli principle. Above all the HBM introduces a new way of looking at space and time. Where contemporary physics applies the spacetime model, the HBM treats space and progression as a paginated model.
The Hilbert transform: Applications to atomic spectra
Whittaker, K A; Hughes, I G; Adams, C S
2014-01-01
In many areas of physics, the Kramers-Kronig (KK) relations are used to extract information about the real part of the optical response of a medium from its imaginary counterpart. In this paper we discuss an alternative but mathematically equivalent approach based on the Hilbert transform. We apply the Hilbert transform to transmission spectra to find the group and refractive indices of a Cs vapor, and thereby demonstrate how the Hilbert transform allows indirect measurement of the refractive index, group index and group delay whilst avoiding the use of complicated experimental set ups.
A new concept drilling hoisting systems rigs
Jan Artymiuk
2006-10-01
Full Text Available In rig constructions two nev designs have been introduced apart from the conventional hoisting system. The first one is the Maritime Hydraulics A.S RamRig© drilling concept, based on hydraulic cylinders as actuators powered by up to 3.4 MW of hydraulic power in a closed loop hydraulic system. This synthesis of the well-known technology allows for the use of integrated active and passive heave compensation, as well as the storing and reuse of energy from the lowering phase of an operation. The RamRig concept makes mechanical brakes and clutches obsolete, since hoisting and lowering of the load is controlled solely by the closed loop hydraulics. This decreases the number of critical mechanical components in the hoisting system to a minimum. Safe handling and emergency shut down of extreme amounts of hydraulic power is taking care of by cartridge valves, which make rerouting of hydraulic power possible with minor losses of transferred effect.The second is a new land rig concept based on a patented rack & pinion drive system with a new generation of rigs which can instantly switch between the workover, drilling and the snubbing operations. The new rig concept has a direct drive, thus no drill line. The mobilization time is reduced as the rig has fewer truck loads, a faster rig up and a higher automation level. One land rig currently under construction will be the world’s first single operator unit, with a full pipe handling capability and a fully automated control system. The rig is fully equipped with the 250 T top drive which can be used for the rotation and snubbing, the purpose designed snubbing slips and other features supporting the multifunctional well operations. The paper will focus on features related to the land rig under construction, and how it may reduce the operational cost and improve the well performance.
Hyperbolic monotonicity in the Hilbert ball
Reich Simeon
2006-01-01
Full Text Available We first characterize -monotone mappings on the Hilbert ball by using their resolvents and then study the asymptotic behavior of compositions and convex combinations of these resolvents.
29 CFR 1918.54 - Rigging gear.
2010-07-01
... 29 Labor 7 2010-07-01 2010-07-01 false Rigging gear. 1918.54 Section 1918.54 Labor Regulations...) SAFETY AND HEALTH REGULATIONS FOR LONGSHORING Vessel's Cargo Handling Gear § 1918.54 Rigging gear. (a... other alternate device shall be provided to allow trimming of the gear and to prevent employees...
China-made Rigs Enter International Market
Zhang Yongze; Chen Liren
2006-01-01
@@ Nowadays, China's drilling equipment manufacturing has formed into a sophisticated industrial chain, playing an indispensable role in supporting China's petroleum industry. Especially in recent years, apart from satisfying the requirements of domestic onshore drilling operations,the state-of-the-art drilling equipments like offshore modular drilling rigs, 9000 meter ultra-deep rigs have also been successfully manufactured, this, together with the wholesale export of electric drilling rigs to the overseas market, has ranked China as a primary manufacturer of drilling equipments in the world. China can now wholesale produce series of onshore and offshore drilling equipment with rig production of nearly 200 per year.The production capacity accounts for 20%-25% of the world total. In addition to satisfying domestic market,China made onshore drilling rigs have also gained great competitive advantages in the international market.
Fitts, R.L.; Crowhurst, M.E. (Market Research and Analysis, Reed Tool Co., Houston, TX (US))
1990-10-01
According to this report, sharp and encouraging movement toward a balance between rig supply and demand is becoming apparent. During the past year, contractors reported the number of rigs available for drilling in the U.S. fell by 222 (8.7%). Contractors also reported that rigs meeting the census definition of active increased by 233 (16.1%). Highlights of the 1990 census, presented by the authors, include: The available U.S. fleet now stands at 2,320 rigs, the lowest since 1976. Last year's count was 2,542. The census active count of 1,677 rigs is the highest since 1985 and up from 1,444 last year. Rig utilization increased to 72%, up from the 57% a year ago. The number of rig owners declined from 558 to 500. More than 190 companies have left the drilling business since 1987. About 6.5% of last year's fleet was cannibalized or auctioned as parts.
朱从旭; 邓宏贵
2000-01-01
The amplitude-squared squeezing of odd coherent state in a finite-dimensional Hilbert spaces (FDHS) case are studied by numerical method. It is found that amplitude-squared squeezing properties exist in these states, and the properties are different from those of usual odd coherent states. but the results tend to those of usual odd coherent states when the number of dimension tend to ∞.%运用数值计算方法研究了有限维希尔伯特(Hilbert)空间谐振子奇相干态的振幅平方压缩特性.研究表明，在有限维情景，奇相干态存在振幅平方压缩效应，并展现了与通常无限维奇相干态截然不同的振幅平方压缩特性；而当维数足够大时，与通常奇相干态的结果趋于一致.
Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms
Kokilashvili V
1997-01-01
Full Text Available As is well known, invariant operators with a shift can be bounded from into only if . We show that the case might also hold for weighted spaces. We derive the sufficient conditions for the validity of strong (weak type inequalities for the Hilbert transform when . The examples of couple of weights which guarantee the fulfillness of two-weighted strong (weak type inequalities for singular integrals are presented. The method of proof of the main results allows us to generalize the results of this paper to the singular integrals which are defined on homogeneous groups. The Fourier multiplier theorem is also proved.
Body Language Advanced 3D Character Rigging
Allen, Eric; Fong, Jared; Sidwell, Adam G
2011-01-01
Whether you're a professional Character TD or just like to create 3D characters, this detailed guide reveals the techniques you need to create sophisticated 3D character rigs that range from basic to breathtaking. Packed with step-by-step instructions and full-color illustrations, Body Language walks you through rigging techniques for all the body parts to help you create realistic and believable movements in every character you design. You'll learn advanced rigging concepts that involve MEL scripting and advanced deformation techniques and even how to set up a character pipeline.
On Certain Theoretical Developments Underlying the Hilbert-Huang Transform
Kizhner, Semion; Blank, Karin; Flatley, Thomas; Huang, Norden E.; Petrick, David; Hestness, Phyllis
2006-01-01
One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real-value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a nearly orthogonal derived from the data (adaptive) basis. The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2-D processing using Field Programmable Gate Array (FPGA
On the Hilbert-Huang Transform Theoretical Developments
Kizhner, Semion; Blank, Karin; Flatley, Thomas; Huang, Norden E.; Patrick, David; Hestnes, Phyllis
2005-01-01
One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as linearity, of being stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposition data, the HHT allows spectrum analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a near orthogonal adaptive basis, a basis that is derived from the data. The IMFs can be further analyzed for spectrum interpretation by the classical Hilbert Transform. A new engineering spectrum analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications post additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs near orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the developments of new HHT processing options, such as real-time and 2-D processing using Field Programmable
On the Hilbert-Huang Transform Data Processing System Development
Kizhner, Semion; Flatley, Thomas P.; Huang, Norden E.; Cornwell, Evette; Smith, Darell
2003-01-01
One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). The Fourier view of nonlinear mechanics that had existed for a long time, and the associated FFT (fairly recent development), carry strong a-priori assumptions about the source data, such as linearity and of being stationary. Natural phenomena measurements are essentially nonlinear and nonstationary. A very recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT) proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using the Empirical Mode Decomposition (EMD) followed by the Hilbert Transform of the empirical decomposition data (HT), the HHT allows spectrum analysis of nonlinear and nonstationary data by using an engineering a-posteriori data processing, based on the EMD algorithm. This results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF) that can be further analyzed for spectrum interpretation by the classical Hilbert Transform. This paper describes phase one of the development of a new engineering tool, the HHT Data Processing System (HHTDPS). The HHTDPS allows applying the "T to a data vector in a fashion similar to the heritage FFT. It is a generic, low cost, high performance personal computer (PC) based system that implements the HHT computational algorithms in a user friendly, file driven environment. This paper also presents a quantitative analysis for a complex waveform data sample, a summary of technology commercialization efforts and the lessons learned from this new technology development.
Espaços de Hilbert de reprodução e a Transformada de Laplace
2016-01-01
Este trabalho tem o objetivo de estudar os espaços de Hilbert de reprodução, propriedades espectrais da transformada de Laplace e um método para obtenção da transformada de Laplace inversa. This work aims to study the Hilbert spaces, espectral properties of the Laplace transform, and a method for obtaining the inverse Laplace transform.
How Hilbert has found the Einstein equations before Einstein and forgeries of Hilbert's page proofs
Ebner, D W
2006-01-01
A succinct chronology is given around Nov 1915, when the explicit field equations of General Relativity have been found. Evidence, unearthed by D.Wuensch, that a decisive document of Hilbert has been mutilated in recent years with the intention to distort the historical truth is reviewed and discussed. The procedure how Hilbert has found before Einstein the correct equations "easily without calculation" by invariant-theoretical arguments is identified for the first time. However, Hilbert has based his derivation on an incorrect or at least not yet formally proved invariant theoretical fact.
刘英
2011-01-01
Abstract:We introduce an iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of two asymptotically nonexpansive mappings in Hilbert spaces and then obtain a strong convergence theorem.Our results improve and extend the corresponding results announced by many others.%本文在Hilbert空间中引进了一迭代方法来逼近两个集合的公共元素,这两个集合分别是一类广义平衡问题的解集和两个渐近非扩张映射公共不动点集.得到一强收敛定理,所得结果提高和推广了许多作者的相应结果.
陈静仁; 王玉文
2012-01-01
This paper studies Hilbert space has a closed range of densely defined closed linear operator Moore-Penorse orthogonal generalized inverse of the perturbation,and in this paper, the first class, second class of perturbations on the basis of the definition perturbation in the third and fourth categories, and the nature and conclusions.%主要研究Hilbert空间具有闭值域的稠定闭线性算子的Moore-Penrose正交广义逆的扰动,并且在原有的第一类,第二类扰动的基础上定义了第三类和第四类扰动,并得到了相应的性质和结论.
Generating and Analyzing N-dimensional Hilbert Cell
FENG Yucai; LI Chenyang
2005-01-01
In this paper, two algorithms are presented for generating two code scan lists of an N-dimensional Hilbert cell, and a formal proof of the backward encoding algorithm is given. On the basis of the self-simi-larity properties of a Hilbert curve, this paper gives a novel algorithm for generating a static evolvement rule table through analyzing a Hilbert cell. By looking up the static evolvement rule table, the N-dimensional Hilbert mappings are efficiently implemented.
Experimental Investigation of a Direct Methanol Fuel Cell with Hilbert Fractal Current Collectors
Jing-Yi Chang
2014-01-01
Full Text Available The Hilbert curve is a continuous type of fractal space-filling curve. This fractal curve visits every point in a square grid with a size of 2×2, 4×4, or any other power of two. This paper presents Hilbert fractal curve application to direct methanol fuel cell (DMFC current collectors. The current collectors are carved following first, second, and third order Hilbert fractal curves. These curves give the current collectors different free open ratios and opening perimeters. We conducted an experimental investigation into DMFC performance as a function of the free open ratio and opening perimeter on the bipolar plates. Nyquist plots of the bipolar plates are made and compared using electrochemical impedance spectroscopy (EIS experiments to understand the phenomena in depth. The results obtained in this paper could be a good reference for future current collector design.
Hilbert modules associated to parabolically induced representations of semisimple Lie groups
Clare, Pierre
2009-01-01
Given a measured space X with commuting actions of two groups G and H satisfying certain conditions, we construct a Hilbert C*(H)-module E(X) equipped with a left action of C*(G), which generalises Rieffel's construction of inducing modules. Considering G to be a semisimple Lie group and H to be the Levi component L of a parabolic subgroup P=LN, the Hilbert module associated to X=G/N encodes the P-series representations of G coming from parabolic subgroups associated to P. We provide several descriptions of this Hilbert module, corresponding to the classical pictures of P-series. We then characterise the bounded operators on E(G/N) that commute to the left action of C*(G) as central multipliers of C*(L) and interpret this result as a globalised generic irreducibility theorem. Finally, we establish the convergence of intertwining integrals on a dense subset of E(G/N).
Hilbert's axiomatic method and Carnap's general axiomatics.
Stöltzner, Michael
2015-10-01
This paper compares the axiomatic method of David Hilbert and his school with Rudolf Carnap's general axiomatics that was developed in the late 1920s, and that influenced his understanding of logic of science throughout the 1930s, when his logical pluralism developed. The distinct perspectives become visible most clearly in how Richard Baldus, along the lines of Hilbert, and Carnap and Friedrich Bachmann analyzed the axiom system of Hilbert's Foundations of Geometry—the paradigmatic example for the axiomatization of science. Whereas Hilbert's axiomatic method started from a local analysis of individual axiom systems in which the foundations of mathematics as a whole entered only when establishing the system's consistency, Carnap and his Vienna Circle colleague Hans Hahn instead advocated a global analysis of axiom systems in general. A primary goal was to evade, or formalize ex post, mathematicians' 'material' talk about axiom systems for such talk was held to be error-prone and susceptible to metaphysics. Copyright © 2015 Elsevier Ltd. All rights reserved.
HILBERT-DIRAC OPERATORS IN CLIFFORD ANALYSIS
F.BRACKX; H.DE SCHEPPER
2005-01-01
Around the central theme of "square root" of the Laplace operator it is shown that the classical Riesz potentials of the first and of the second kind allow for an explicit expression of so-called Hilbert-Dirac convolution operators involving natural and complex powers of the Dirac operator.
A relative Hilbert-Mumford criterion
Gulbrandsen, Martin G.; Halle, Lars Halvard; Hulek, Klaus
2015-01-01
We generalize the classical Hilbert-Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative situation of an equivariant, projective morphism X -> Spec A to a noetherian k-algebra A. We also extend the classical...
Applications of the Hilbert-Huang Transform
Huang, Norden E.; Zukor, Dorothy J. (Technical Monitor)
2001-01-01
A new method, the Hilbert-Huang Transform, has been developed for analyzing nonlinear and nonstationary data. The key part of the method is the Empirical Mode Decomposition with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An M is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies'as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. With this technique we can examine the detailed dynamics characteristics of a nonlinear system through the instantaneous frequency rather than harmonics. Thus it constitutes a new view of the nonlinear dynamics. Examples of classic nonlinear equations and other nonlinear and nonstationary data sets will be used as examples to illustrate the advantage of the application of this new data analysis method.
Hilbert's Sixteenth Problem and Its Generalization
无
2001-01-01
This paper deals with Hilbert's 16th problem and its generalizations. The configurations of all closed branches of an algebraic curve of degree n are discussed. The maximum number of sheets for an algebraic equation of degree n and the maximum number of limit cycles for a planar algebraic autonomous system are achieved. The author also considers different generalizations and some related problems.
On Equivariant Embedding of Hilbert C^* modules
Goswami, Debashish
2007-01-01
We prove that an arbitrary (not necessarily countably generated) Hilbert $G$-$\\cla$ module on a G-C^* algebra $\\cla$ admits an equivariant embedding into a trivial $G-\\cla$ module, provided G is a compact Lie group and its action on $\\cla$ is ergodic.
On Equivariant Embedding of Hilbert $C^*$ modules
Goswami, Debashish
2007-01-01
We prove that an arbitrary (not necessarily countably generated) Hilbert $G$-$\\cla$ module on a $G-C^*$ algebra $\\cla$ admits an equivariant embedding into a trivial $G-\\cla$ module, provided $G$ is a compact Lie group and its action on $\\cla$ is ergodic.
On Equivariant Embedding of Hilbert * Modules
Debashish Goswami
2009-02-01
We prove that an arbitrary (not necessarily countably generated) Hilbert $G-\\mathcal{A}$ module on a -* algebra $\\mathcal{A}$ admits an equivariant embedding into a trivial $G-\\mathcal{A}$ module, provided is a compact Lie group and its action on $\\mathcal{A}$ is ergodic.
Optical Micro- and Nanofiber Pulling Rig
Ward, J M; Le, Vu H; Chormaic, S Nic
2014-01-01
We review the method of producing adiabatic optical micro- and nanofibers using a hydrogen/oxygen flame brushing technique. The flame is scanned along the fiber, which is being simultaneously stretched by two translation stages. The tapered fiber fabrication is reproducible and yields highly adiabatic tapers with either exponential or linear profiles. Details regarding the setup of the flame brushing rig and the various parameters used are presented. Information available from the literature is compiled and further details that are necessary to have a functioning pulling rig are included. This should enable the reader to fabricate various taper profiles, while achieving adiabatic transmission of ~ 99% for fundamental mode propagation. Using this rig, transmissions greater than 90% for higher order modes in an optical nanofiber have been obtained.
Dirac-orthogonality in the space of tempered distributions
Carfì, David
2003-04-01
The main goal of this paper is the realization that some formal basic results and definitions of the mathematical formalism of the quantum mechanics have a solid mathematical basis. In particular, we justify the so-called "delta" normalization in the continuous case introduced by Dirac (P.A.M. Dirac, The principles of Quantum Mechanics, Clarendon Press, Oxford, 1930, pp. 66-68), works that are of fundamental importance in the foundation of the modern quantum physics. This formal mathematical tool had not, until now, a rigorous counterpart, neither in the area of the rigged Hilbert spaces theory. It is possible to find a systematic application of the above mentioned formal tool in (W. Pauli, Wellenmechanik, 1958), (R. Shankar, Principles of Quantum Mechanics, Plenum Press, New York, 1994) and others.
Ergonomic exposure on a drilling rig
Jensen, Carsten; Jensen, Chris
, absence from work due to other health problems may not show a similar trend towards lower absenteeism. Sickness absence was reported by Maersk Contractors to have increased among their drilling rig personnel in the Danish Sector of the North Sea from 2000 to 2004 (Steffensen 2005). Their statistics were....... In a relatively old study on American drilling rigs it was indicated that lower back problems was a frequent cause of absence (Clemmer et al. 1991). Most of the incidents causing lower back injuries were associated with heavy lifting or pushing/pulling objects by roustabouts, floorhands, derrickmen and welders...
Design and Characterization of a Centrifugal Compressor Surge Test Rig
2011-01-01
A detailed description of a new centrifugal compressor surge test rig is presented. The objective of the design and development of the rig is to study the surge phenomenon in centrifugal compression systems and to investigate a novel method of surge control by active magnetic bearing servo actuation of the impeller axial tip clearance. In this paper, we focus on the design, initial setup, and testing of the rig. The latter two include the commissioning of the rig and the experimental characte...
Status of the Combined Cycle Engine Rig
Saunders, Dave; Slater, John; Dippold, Vance
2009-01-01
Status for the past year is provided of the turbine-based Combined-Cycle Engine (CCE) Rig for the hypersonic project. As part of the first stage propulsion of a two-stage-to-orbit vehicle concept, this engine rig is designed with a common inlet that supplies flow to a turbine engine and a dual-mode ramjet / scramjet engine in an over/under configuration. At Mach 4 the inlet has variable geometry to switch the airflow from the turbine to the ramjet / scramjet engine. This process is known as inlet mode-transition. In addition to investigating inlet aspects of mode transition, the rig will allow testing of turbine and scramjet systems later in the test series. Fully closing the splitter cowl "cocoons" the turbine engine and increases airflow to the scramjet duct. The CCE Rig will be a testbed to investigate integrated propulsion system and controls technology objectives. Four phases of testing are planned to 1) characterize the dual inlet database, 2) collect inlet dynamics using system identification techniques, 3) implement an inlet control to demonstrate mode-transition scenarios and 4) demonstrate integrated inlet/turbine engine operation through mode-transition. Status of the test planning and preparation activities is summarized with background on the inlet design and small-scale testing, analytical CFD predictions and some details of the large-scale hardware. The final stages of fabrication are underway.
Largest Contract for Rig Export Wound up Successfully
无
2003-01-01
@@ In mid-November, the last drilling rig, typed ZJ50DBA,of the 10-rig deal was packed and transported to Uzbekistan from Chuanyou Guanghan Honghua Co Ltd, a drilling equipment producer under Sichuan Petroleum Administration Bureau, putting an end to China's largest contract for export of drilling rigs.
Three Dimensional Measurements by Deflectometry and Double Hilbert Transform
Na, Silin; Yu, Younghun
2016-01-01
An improved phase retrieval method based Hilbert transform is introduced to quantitatively calculate the phase distribution from distorted fringe pattern. Also phase measurement deflectomety are widely used in specular type samples. The background noise or bias should be suppressed prior to apply Hilbert transform. A method for suppression background noise double Hilbert transform is presented, which requires only one image. The method is easy to implement, and it is able to conducting automated fast measurements. We have demonstrated the double Hilbert transform method to retrieve the phase and background suppression by computer simulation and experiment in phase measuring deflectometry method.
Lossless compression of medical images using Hilbert scan
Sun, Ziguang; Li, Chungui; Liu, Hao; Zhang, Zengfang
2007-12-01
The effectiveness of Hilbert scan in lossless medical images compression is discussed. In our methods, after coding of intensities, the pixels in a medical images have been decorrelated with differential pulse code modulation, then the error image has been rearranged using Hilbert scan, finally we implement five coding schemes, such as Huffman coding, RLE, lZW coding, Arithmetic coding, and RLE followed by Huffman coding. The experiments show that the case, which applies DPCM followed by Hilbert scan and then compressed by the Arithmetic coding scheme, has the best compression result, also indicate that Hilbert scan can enhance pixel locality, and increase the compression ratio effectively.
Nested Hilbert schemes on surfaces: Virtual fundamental class
Gholampour, Amin; Sheshmani, Artan; Yau, Shing-Tung
2017-01-01
We construct natural virtual fundamental classes for nested Hilbert schemes on a nonsingular projective surface S. This allows us to define new invariants of S that recover some of the known important cases such as Poincare invariants of Durr-Kabanov-Okonek and the stable pair invariants of Kool......-Thomas. In the case of the nested Hilbert scheme of points, we can express these invariants in terms of integrals over the products of Hilbert scheme of points on S, and relate them to the vertex operator formulas found by Carlsson-Okounkov. The virtual fundamental classes of the nested Hilbert schemes play a crucial...
Trogdon, Thomas; Deconinck, Bernard
2013-05-01
We derive a Riemann-Hilbert problem satisfied by the Baker-Akhiezer function for the finite-gap solutions of the Korteweg-de Vries (KdV) equation. As usual for Riemann-Hilbert problems associated with solutions of integrable equations, this formulation has the benefit that the space and time dependence appears in an explicit, linear and computable way. We make use of recent advances in the numerical solution of Riemann-Hilbert problems to produce an efficient and uniformly accurate numerical method for computing all periodic and quasi-periodic finite-genus solutions of the KdV equation.
Davide Barbieri
2016-12-01
Full Text Available This is a joint work with E. Hernández, J. Parcet and V. Paternostro. We will discuss the structure of bases and frames of unitary orbits of discrete groups in invariant subspaces of separable Hilbert spaces. These invariant spaces can be characterized, by means of Fourier intertwining operators, as modules whose rings of coefficients are given by the group von Neumann algebra, endowed with an unbounded operator valued pairing which defines a noncommutative Hilbert structure. Frames and bases obtained by countable families of orbits have noncommutative counterparts in these Hilbert modules, given by countable families of operators satisfying generalized reproducing conditions. These results extend key notions of Fourier and wavelet analysis to general unitary actions of discrete groups, such as crystallographic transformations on the Euclidean plane or discrete Heisenberg groups.
Ben Salem, Samira; Bacha, Khmais; Chaari, Abdelkader
2012-09-01
In this work we suggest an original fault signature based on an improved combination of Hilbert and Park transforms. Starting from this combination we can create two fault signatures: Hilbert modulus current space vector (HMCSV) and Hilbert phase current space vector (HPCSV). These two fault signatures are subsequently analysed using the classical fast Fourier transform (FFT). The effects of mechanical faults on the HMCSV and HPCSV spectrums are described, and the related frequencies are determined. The magnitudes of spectral components, relative to the studied faults (air-gap eccentricity and outer raceway ball bearing defect), are extracted in order to develop the input vector necessary for learning and testing the support vector machine with an aim of classifying automatically the various states of the induction motor.
Concerning the Hilbert 16th problem
Ilyashenko, Yu; Il'yashenko, Yu
1995-01-01
This book examines qualitative properties of vector fields in the plane, in the spirit of Hilbert's Sixteenth Problem. Two principal topics explored are bifurcations of limit cycles of planar vector fields and desingularization of singular points for individual vector fields and for analytic families of such fields. In addition to presenting important new developments in this area, this book contains an introductory paper which outlines the general context and describes connections between the papers in the volume. The book will appeal to researchers and graduate students working in the qualit
Further Results on Hilbert's Tenth Problem
Sun, Zhi-Wei
2017-01-01
Hilbert's Tenth Problem (HTP) asked for an algorithm to test whether an arbitrary polynomial Diophantine equation with integer coefficients has solutions over the ring $\\mathbb Z$ of the integers. This was finally solved by Matiyasevich negatively in 1970. In this paper we obtain some further results on HTP over $\\mathbb Z$. We show that there is no algorithm to determine for any $P(z_1,\\ldots,z_9)\\in\\mathbb Z[z_1,\\ldots,z_9]$ whether the equation $P(z_1,\\ldots,z_9)=0$ has integral solutions ...
Bethe's quantum numbers and rigged configurations
Anatol N. Kirillov
2016-04-01
Full Text Available We propose a method to determine the quantum numbers, which we call the rigged configurations, for the solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg model under the periodic boundary condition. Our method is based on the observation that the sums of Bethe's quantum numbers within each string behave particularly nicely. We confirm our procedure for all solutions for length 12 chain (totally 923 solutions.
Development of Magnetorheological Engine Mount Test Rig
Md Yunos Mohd Razali; Harun Mohamad Hafiz; Sariman M.Z.; Mat Yamin A.K.
2017-01-01
Ride comfort is an important factor in any road vehicle performance. Nonetheless, passenger ride comfort is sometimes affected by the vibrations resulting from the road irregularities. Vehicle ride comfort is also often compromised by engine vibration. Engine mount is one of the devices which act as vibration isolator from unwanted vibration from engine to the driver and passengers. This paper explains the development of the test rig used for laboratory testing of Magnetorheological (MR) engi...
唐金芳
2011-01-01
By using the Fan-KKM lemma,the existence and uniqueness of solution of the auxiliary problem for GEP is derived. A iterative method for finding a common element of the set of solution of a generalized equilibrium problem and the set of fixed points for an infinite family of nonexpansive mappings in a Hilbert space is induced. Under suitable conditions a strong convergence theorem is proved. The results presented in the paper extend and improved some recent results.%在Hilbert空间中,用Fan-KKM定理导出了广义平衡问题的辅助问题的解的存在性和唯一性,讨论了寻找广义平衡问题和一族非扩张映象的公共不动点集的迭代序列,证明此序列强收敛于这两个集合的公共元.本文结论改进了一些近期结果.
高文娟; 何中全
2014-01-01
In Hilbert Spaces, by using the FA N-KKM theorem,the existence and uniqueness of solu-tions of the auxiliary problem for generalized equilibrium-like problem is derived. Under suitable conditions, it is proven that a new hybrid iterative scheme converge strongly to a common element of the set of solutions of a generalized equilibrium-like problem and the set of fixed points of a k- strict pseudo-contraction map-ping.%在Hilbert空间中，用FAN-KKM定理导出了广义似平衡问题的辅助问题的解的存在性和唯一性，在适当的条件下，引入和研究了一种新的混合迭代序列，用以寻求广义似平衡问题的解集与一个k-严格伪压缩映象的不动点集的公共元。
Computers make rig life extension an option
NONE
1996-10-01
The worldwide semisubmersible drilling rig fleet is approaching retirement. But replacement is not an attractive option even though dayrates are reaching record highs. In 1991, Schlumberger Sedco Forex managers decided that an alternative might exist if regulators and insurers could be convinced to extend rig life expectancy through restoration. Sedco Forex chose their No. 704 semisubmersible, an 18-year North Sea veteran, to test their process. The first step was to determine what required restoration, meaning fatigue life analysis of each weld on the huge vessel. If inspected, the task would be unacceptably time-consuming and of questionable accuracy. Instead a suite of computer programs modeled the stress seen by each weld, statistically estimated the sea states seen by the rig throughout its North Sea service and calibrated a beam-element model on which to run their computer simulations. The elastic stiffness of the structure and detailed stress analysis of each weld was performed with ANSYS, a commercially available finite-element analysis program. The use of computer codes to evaluate service life extension is described.
RIEMANN-HILBERT PROBLEMS OF DEGENERATE HYPERBOLIC SYSTEM
无
2010-01-01
This paper is concerned with the Riemann-Hilbert problems of degenerate hyperbolic system in two general domains, where the boundary curves are given by the parameter equations of the arc length s. We prove the existence and uniqueness of solutions to the Riemann-Hilbert problems by conformal deformations. The corre-sponding representations of solutions to the problems are also presented.
Aeroelastic Flight Data Analysis with the Hilbert-Huang Algorithm
Brenner, Martin J.; Prazenica, Chad
2006-01-01
This report investigates the utility of the Hilbert Huang transform for the analysis of aeroelastic flight data. It is well known that the classical Hilbert transform can be used for time-frequency analysis of functions or signals. Unfortunately, the Hilbert transform can only be effectively applied to an extremely small class of signals, namely those that are characterized by a single frequency component at any instant in time. The recently-developed Hilbert Huang algorithm addresses the limitations of the classical Hilbert transform through a process known as empirical mode decomposition. Using this approach, the data is filtered into a series of intrinsic mode functions, each of which admits a well-behaved Hilbert transform. In this manner, the Hilbert Huang algorithm affords time-frequency analysis of a large class of signals. This powerful tool has been applied in the analysis of scientific data, structural system identification, mechanical system fault detection, and even image processing. The purpose of this report is to demonstrate the potential applications of the Hilbert Huang algorithm for the analysis of aeroelastic systems, with improvements such as localized online processing. Applications for correlations between system input and output, and amongst output sensors, are discussed to characterize the time-varying amplitude and frequency correlations present in the various components of multiple data channels. Online stability analyses and modal identification are also presented. Examples are given using aeroelastic test data from the F-18 Active Aeroelastic Wing airplane, an Aerostructures Test Wing, and pitch plunge simulation.
Dedekind and Hilbert on the foundations of the deductive sciences
Klev, A.M.
2011-01-01
We offer an interpretation of the words and works of Richard Dedekind and the David Hilbert of around 1900 on which they are held to entertain diverging views on the structure of a deductive science. Firstly, it is argued that Dedekind sees the beginnings of a science in concepts, whereas Hilbert se
Bharti, Omesh Kumar; Madhusudana, Shampur Narayan; Wilde, Henry
2017-02-22
An increasing number of dog bite victims were being presented to public hospitals in Himachal Pradesh in 2014 amidst virtual non availability of any rabies immunoglobulin (RIG). Only a small quantity of equine rabies immunoglobulin (eRIG) was available from the government owned Central Research Institute (CRI) Kasauli. This available eRIG was used in 269 patients as an emergency response and only for local infiltration of severe bite wounds by suspected rabid dogs. This was followed by rabies vaccination, using the WHO approved intra-dermal Thai Red Cross Society vaccination schedule. A subgroup of 26 patients were later identified who had been severely bitten by laboratory confirmed rabid dogs. They were followed for more than one year and all were found to be alive.
关于Banach共轭算子和Hilbert共轭算子的讨论%Discussion on Banach conjugate operator and Hilbert conjugate operator
杨纪华; 李艳秋
2014-01-01
Banach conjugate operator and Hilbert conjugate operator are two very important concepts in functional analysis. Hilbert space is a special Banach space,but the conjugate operator in Hilbert space does not follow the definition of conjugate operator in Banach space,and thevast majority textbooks don′t explain the reasons for this definition.Described the reason why conjugate operator in Hilbert space does not follow the definition of conjugate operator in Banach space,and discussed the relationship between the two operators.%Banach共轭算子和Hilbert共轭算子是泛函分析中两个非常重要的概念．Hilbert 空间是特殊的Banach空间，但Hilbert空间上的共轭算子没有沿用Banach空间上共轭算子的定义，并且绝大数教材都没有说明这样定义的原因．阐述了Hilbert空间上的共轭算子没有沿用Banach空间上共轭算子定义的原因，并讨论Hilbert空间中这两种算子的关系.
Endurance test on IR rig for RI production
Chung, Heung June; Youn, Y. J.; Han, H. S.; Hong, S. B.; Cho, Y. G.; Ryu, J. S
2000-12-01
This report presents the pressure drop, vibration and endurance test results for IR rig for RI production which were desigened and fabricated by KAERI. From the pressure drop test results, it is noted that the flow rate through the IR rig corresponding to the pressure drop of 200 kPa is measured to be about 3.12 kg/sec. Vibration frequency for the IR rig ranges from 13 to 17 Hz. RMS(Root Mean Square) displacement for the IR rig is less than 30 {mu}m, and the maximum displacement is less than 110{mu}m. These experimental results show that the design criteria of IR rig meet the HANARO limit conditions. Endurance test results show that the appreciable fretting wear for the IR rig does not occur, however tiny trace of wear between contact points is observed.
Parameter identification using the Hilbert transform
Allison, A; Allison, Andrew; Abbott, Derek
2002-01-01
Many physical systems can be adequately modelled using a second order approximation. The problem of plant identification reduces to the problem of estimating the position of a single pair of complex conjugate poles. One approach to the problem is to apply the method of least squares to the time domain data. This type of computation is best carried out in "batch" mode and applies to an entire data set. Another approach would be to design an adaptive filter and to use autoregressive, AR, techniques. This would be well suited to continuous real-time data and could track slow changes on the underlying plant. I this paper we present a very fast but approximate technique for the estimation of the position of a single pair of complex conjugate poles, using the Hilbert transform to reconstruct the analytic signal.
Hilbert Transform Applied to Separation of Waves
孙鹤泉; 王永学; 彭静萍
2002-01-01
The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is ap-plicable to both regular and irregular trains of waves. The wave data series measured with two wave gauges in the experi-ments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily ob-tained. The arrival of reflected waves can also be detected for improvement of the accuracy of the reflection coefficient.The reflection performance of the physical model can be estimated exactly without calculation of wave height and phasedifference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conduct-ed and compared with Goda's method and satisfactory results are obtained.
Electrotechnical complex of drill rig with adjustable electric drives
Nikulin Oleg; Shabanov Vitaliy
2017-01-01
The paper considers the electrotechnical complex of a drill rig with adjustable electric drives of the main mechanisms. A computer model has been developed for the electrical complex of the drill rig, which allows studying processes in case of interruptions in the power supply system, changes in the technological parameters of drilling, etc. The article presents the simulation results for short circuits in the power supply system of the drilling rig and for drilling a well.
Electrotechnical complex of drill rig with adjustable electric drives
Nikulin Oleg
2017-01-01
Full Text Available The paper considers the electrotechnical complex of a drill rig with adjustable electric drives of the main mechanisms. A computer model has been developed for the electrical complex of the drill rig, which allows studying processes in case of interruptions in the power supply system, changes in the technological parameters of drilling, etc. The article presents the simulation results for short circuits in the power supply system of the drilling rig and for drilling a well.
Innovative technology for a cost-effective land rig
Mehra, S.; Bryce, T.
1996-05-01
Sedco Forex has recently completed a new land drilling rig, currently deployed in Gabon, that integrates well construction activities with multiskilling to create cost savings across the board in drilling operations. Historically, operators have produced a comprehensive tender package specifying strictly the type and size of individual rig components and the number of personnel required to drill. In this case, the drilling contractor provides a fit-for-purpose rig, consistent with field location, well profile, operator`s priorities, and local constraints.
The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link
Oblomkov, Alexei; Shende, Vivek
2012-01-01
We conjecture an expression for the dimensions of the Khovanov-Rozansky HOMFLY homology groups of the link of a plane curve singularity in terms of the weight polynomials of Hilbert schemes of points scheme-theoretically supported on the singularity. The conjecture specializes to our previous conjecture relating the HOMFLY polynomial to the Euler numbers of the same spaces upon setting t = -1. By generalizing results of Piontkowski on the structure of compactified Jacobians to the case of Hilbert schemes of points, we give an explicit prediction of the HOMFLY homology of a (k, n) torus knot as a certain sum over diagrams. The Hilbert scheme series corresponding to the summand of the HOMFLY homology with minimal "a" grading can be recovered from the perverse filtration on the cohomology of the compactified Jacobian. In the case of (k,n) torus knots, this space furnishes the unique finite dimensional simple representation of the rational spherical Cherednik algebra with central character k/n. Up to a conjectura...
Who Dominates the Semi-submersible Rig Market?
Yang Qingxia; Liu Chengming; LiangYuanhua
2011-01-01
Currently, the US and Europe are the centers for the design of semi-submersible rigs.The American company FRIEDE & GOLDMAN was founded in the 1950s. At present, over 100 mobile offshore drilling units and production platforms in the world are designed by this company, which mainly has two types of deepwater semi-submersible rig, F&GExD and MillenniumSA. F&GExD is the semi-submersible rig of the sixth generation and its operational depth can reach up to 3050m. MillenniumSA is semi-submersible rig of the fifth and half generation with an operational depth of 2400m.
Multifunctional Testing Rig for Machinery Safety Equipment
Vöth Stefan
2017-01-01
Full Text Available At the Centre of Drive and Lifting Technology ZAFT of Technische Hochschule Georg Agricola a new testing device will be available. The device is suitable for testing drivetrain components like safety clutches and hoist safety components like snag protection devices. In focus are continuous tests with regard to fatigue as well as transient tests with regard to switching characteristics. The article gives information on requirements on the testing rig out of the main purpose and out of the given environment. Furthermore concept, main data and engineering design of this equipment are demonstrated. Aspects and first results of the mechanical assembly are shown.
Field Demonstraton of Existing Microhole Coiled Tubing Rig (MCTR) Technology
Kent Perry; Samih Batarseh; Sheriff Gowelly; Thomas Hayes
2006-05-09
The performance of an advanced Microhole Coiled Tubing Rig (MCTR) has been measured in the field during the drilling of 25 test wells in the Niobrara formation of Western Kansas and Eastern Colorado. The coiled tubing (CT) rig designed, built and operated by Advanced Drilling Technologies (ADT), was documented in its performance by GTI staff in the course of drilling wells ranging in depth from 500 to nearly 3,000 feet. Access to well sites in the Niobrara for documenting CT rig performance was provided by Rosewood Resources of Arlington, VA. The ADT CT rig was selected for field performance evaluation because it is one of the most advanced commercial CT rig designs that demonstrate a high degree of process integration and ease of set-up and operation. Employing an information collection protocol, data was collected from the ADT CT rig during 25 drilling events that encompassed a wide range of depths and drilling conditions in the Niobrara. Information collected included time-function data, selected parametric information indicating CT rig operational conditions, staffing levels, and field observations of the CT rig in each phase of operation, from rig up to rig down. The data obtained in this field evaluation indicates that the ADT CT rig exhibited excellent performance in the drilling and completion of more than 25 wells in the Niobrara under varied drilling depths and formation conditions. In the majority of the 25 project well drilling events, ROP values ranged between 300 and 620 feet per hour. For all but the lowest 2 wells, ROP values averaged approximately 400 feet per hour, representing an excellent drilling capability. Most wells of depths between 500 and 2,000 feet were drilled at a total functional rig time of less than 16 hours; for wells as deep at 2,500 to 3,000 feet, the total rig time for the CT unit is usually well under one day. About 40-55 percent of the functional rig time is divided evenly between drilling and casing/cementing. The balance of
Field Demonstraton of Existing Microhole Coiled Tubing Rig (MCTR) Technology
Kent Perry; Samih Batarseh; Sheriff Gowelly; Thomas Hayes
2006-05-09
The performance of an advanced Microhole Coiled Tubing Rig (MCTR) has been measured in the field during the drilling of 25 test wells in the Niobrara formation of Western Kansas and Eastern Colorado. The coiled tubing (CT) rig designed, built and operated by Advanced Drilling Technologies (ADT), was documented in its performance by GTI staff in the course of drilling wells ranging in depth from 500 to nearly 3,000 feet. Access to well sites in the Niobrara for documenting CT rig performance was provided by Rosewood Resources of Arlington, VA. The ADT CT rig was selected for field performance evaluation because it is one of the most advanced commercial CT rig designs that demonstrate a high degree of process integration and ease of set-up and operation. Employing an information collection protocol, data was collected from the ADT CT rig during 25 drilling events that encompassed a wide range of depths and drilling conditions in the Niobrara. Information collected included time-function data, selected parametric information indicating CT rig operational conditions, staffing levels, and field observations of the CT rig in each phase of operation, from rig up to rig down. The data obtained in this field evaluation indicates that the ADT CT rig exhibited excellent performance in the drilling and completion of more than 25 wells in the Niobrara under varied drilling depths and formation conditions. In the majority of the 25 project well drilling events, ROP values ranged between 300 and 620 feet per hour. For all but the lowest 2 wells, ROP values averaged approximately 400 feet per hour, representing an excellent drilling capability. Most wells of depths between 500 and 2,000 feet were drilled at a total functional rig time of less than 16 hours; for wells as deep at 2,500 to 3,000 feet, the total rig time for the CT unit is usually well under one day. About 40-55 percent of the functional rig time is divided evenly between drilling and casing/cementing. The balance of
A New Fast Approximate Hilbert Transform with Different Applications
Abdulnasir Hossen
2012-08-01
Full Text Available A new and fast approximate Hilbert transform based on subband decomposition is presented. This new algorithm is called the subband (SB-Hilbert transform. The reduction in complexity is obtained for narrow-band signal applications by considering only the band of most energy. Different properties of the SB-Hilbert transform are discussed with simulation examples. The new algorithm is compared with the full band Hilbert transform in terms of complexity and accuracy. The aliasing errors taking place in the algorithm are found by applying the Hilbert transform to the inverse FFT (time signal of the aliasing errors of the SB-FFT of the input signal. Different examples are given to find the analytic signal using SB-Hilbert transform with a varying number of subbands. Applications of the new algorithm are given in single-sideband amplitude modulation and in demodulating frequency-modulated signals in communication systems.Key Words: Fast Algorithms, Hilbert Transform, Analytic Signal Processing.
Ondra, V.; Sever, I. A.; Schwingshackl, C. W.
2017-01-01
This paper presents a method for detection and characterisation of structural non-linearities from a single frequency response function using the Hilbert transform in the frequency domain and artificial neural networks. A frequency response function is described based on its Hilbert transform using several common and newly introduced scalar parameters, termed non-linearity indexes, to create training data of the artificial neural network. This network is subsequently used to detect the existence of non-linearity and classify its type. The theoretical background of the method is given and its usage is demonstrated on different numerical test cases created by single degree of freedom non-linear systems and a lumped parameter multi degree of freedom system with a geometric non-linearity. The method is also applied to several experimentally measured frequency response functions obtained from a cantilever beam with a clearance non-linearity and an under-platform damper experimental rig with a complex friction contact interface. It is shown that the method is a fast and noise-robust means of detecting and characterising non-linear behaviour from a single frequency response function.
Characteristic classes of Hilbert schemes of points via symmetric products
Cappell, Sylvain; Ohmoto, Toru; Schuermann, Joerg; Yokura, Shoji
2012-01-01
We obtain a formula for the generating series of (the push-forward under the Hilbert-Chow morphism of) the Hirzebruch homology characteristic classes of the Hilbert schemes of points for a smooth quasi-projective variety of arbitrary pure dimension. This result is based on a geometric construction of a motivic exponentiation generalizing the notion of motivic power structure, as well as on a formula for the generating series of the Hirzebruch homology characteristic classes of symmetric products. We apply the same methods for the calculation of generating series formulae for the Hirzebruch classes of the push-forwards of "virtual motives" of Hilbert schemes of a threefold. As corollaries, we obtain counterparts for the MacPherson (and Aluffi) Chern classes of Hilbert schemes of a smooth quasi-projective variety (resp. for threefolds). For a projective Calabi-Yau threefold, the latter yields a Chern class version of the dimension zero MNOP conjecture.
The Kieffer dough and gluten extensibility rig - An experimental evaluation
Dunnewind, B.; Sliwinski, E.L.; Grolle, K.; Vliet, T. van
2003-01-01
Load-extension tests on flour dough are widely used by plant breeders, millers and bakers. The 'Kieffer dough and gluten extensibility rig' is a small-scale version of the Brabender extensograph, in which test pieces of about 0.4 g are extended. With the Kieffer rig, lower strain rates can be applie
The Hilbert schemes of locally Cohen-Macaulay curves in P^3 may after all be connected
Lella, Paolo
2011-01-01
Progress on the problem whether the Hilbert schemes of locally Cohen-Macaulay curves in projective 3 space are connected has been hampered by the lack of an answer to a question that was raised by Robin Hartshorne in his paper "On the connectedness of the Hilbert scheme of curves in projective 3 space" Comm. Algebra 28 (2000) and more recently in the open problems list of the 2010 AIM workshop Components of Hilbert Schemes available at http://aimpl.org/hilbertschemes: does there exist a flat irreducible family of curves whose general member is a union of d disjoint lines on a smooth quadric surface and whose special member is a locally Cohen-Macaulay curve in a double plane? In this paper we give a positive answer to this question: for every d, we construct a family with the required properties, whose special fiber is an extremal curve in the sense of Martin-Deschamps and Perrin. From this we conclude that every effective divisor in a smooth quadric surface is in the connected component of its Hilbert scheme ...
Did Einstein "Nostrify" Hilbert's Final Form of the Field Equations for General Relativity?
Weinstein, Galina
2014-01-01
Einstein's biographer Albrecht F\\"olsing explained: Einstein presented his field equations on November 25, 1915, but six days earlier, on November 20, Hilbert had derived the identical field equations for which Einstein had been searching such a long time. On November 18 Hilbert had sent Einstein a letter with a certain draft, and F\\"olsing asked about this possible draft: "Could Einstein, casting his eye over this paper, have discovered the term which was still lacking in his own equations, and thus 'nostrified' Hilbert?" Historical evidence support a scenario according to which Einstein discovered his final field equations by "casting his eye over" his own previous works. In November 4, 1915 Einstein wrote the components of the gravitational field and showed that a material point in a gravitational field moves on a geodesic line in space-time, the equation of which is written in terms of the Christoffel symbols. Einstein found it advantageous to use for the components of the gravitational field the Christof...
LETTER TO THE EDITOR: Explicit finite inverse Hilbert transforms
You, Jiangsheng; Zeng, Gengsheng L.
2006-06-01
Recently, Noo and coworkers discovered an explicit inversion formula for the finite Hilbert transform, which is very important to accurate reconstruction from truncated projections. This letter presents two formulae for the finite inverse Hilbert transform using some elementary complex variable analysis. The new formulae do not contain the constant C and the singular endpoints that exist in the formula in Noo et al (2004 Phys. Med. Biol. 49 3903-23).
Advanced Hot Section Materials and Coatings Test Rig
Dan Davis
2006-09-30
Phase I of the Hyperbaric Advanced Hot Section Materials & Coating Test Rig Program has been successfully completed. Florida Turbine Technologies has designed and planned the implementation of a laboratory rig capable of simulating the hot gas path conditions of coal gas fired industrial gas turbine engines. Potential uses of this rig include investigations into environmental attack of turbine materials and coatings exposed to syngas, erosion, and thermal-mechanical fatigue. The principle activities during Phase 1 of this project included providing several conceptual designs for the test section, evaluating various syngas-fueled rig combustor concepts, comparing the various test section concepts and then selecting a configuration for detail design. Conceptual definition and requirements of auxiliary systems and facilities were also prepared. Implementation planning also progressed, with schedules prepared and future project milestones defined. The results of these tasks continue to show rig feasibility, both technically and economically.
Nonlinear vibrating system identification via Hilbert decomposition
Feldman, Michael; Braun, Simon
2017-02-01
This paper deals with the identification of nonlinear vibration systems, based on measured signals for free and forced vibration regimes. Two categories of time domain signal are analyzed, one of a fast inter-modulation signal and a second as composed of several mono-components. To some extent, this attempts to imitate analytic studies of such systems, with its two major analysis groups - the perturbation and the harmonic balance methods. Two appropriate signal processing methods are then investigated, one based on demodulation and the other on signal decomposition. The Hilbert Transform (HT) has been shown to enable effective and simple methods of analysis. We show that precise identification of the nonlinear parameters can be obtained, contrary to other average HT based methods where only approximation parameters are obtained. The effectiveness of the proposed methods is demonstrated for the precise nonlinear system identification, using both the signal demodulation and the signal decomposition methods. Following the exposition of the tools used, both the signal demodulation as well as decomposition are applied to classical examples of nonlinear systems. Cases of nonlinear stiffness and damping forces are analyzed. These include, among other, an asymmetric Helmholtz oscillator, a backlash with nonlinear turbulent square friction, and a Duffing oscillator with dry friction.
Wind Turbine Gearbox Fault Diagnosis Based on Improved EEMD and Hilbert Square Demodulation
Huanguo Chen
2017-01-01
Full Text Available The rapid expansion of wind farms has accelerated research into improving the reliability of wind turbines to reduce operational and maintenance costs. A critical component in wind turbine drive-trains is the gearbox, which is prone to different types of failures due to long-term operation under tough environments, variable speeds and alternating loads. To detect gearbox fault early, a method is proposed for an effective fault diagnosis by using improved ensemble empirical mode decomposition (EEMD and Hilbert square demodulation (HSD. The method was verified numerically by implementing the scheme on the vibration signals measured from bearing and gear test rigs. In the implementation process, the following steps were identified as being important: (1 in order to increase the accuracy of EEMD, a criterion of selecting the proper resampling frequency for raw vibration signals was developed; (2 to select the fault related intrinsic mode function (IMF that had the biggest kurtosis index value, the resampled signal was decomposed into a series of IMFs; (3 the selected IMF was demodulated by means of HSD, and fault feature information could finally be obtained. The experimental results demonstrate the merit of the proposed method in gearbox fault diagnosis.
Endothelial RIG-I activation impairs endothelial function
Asdonk, Tobias, E-mail: tobias.asdonk@ukb.uni-bonn.de [Department of Medicine/Cardiology, University of Bonn, Sigmund-Freud-Str. 25, 53105 Bonn (Germany); Motz, Inga; Werner, Nikos [Department of Medicine/Cardiology, University of Bonn, Sigmund-Freud-Str. 25, 53105 Bonn (Germany); Coch, Christoph; Barchet, Winfried; Hartmann, Gunther [Institute for Clinical Chemistry and Clinical Pharmacology, University of Bonn, Sigmund-Freud-Str. 25, 53105 Bonn (Germany); Nickenig, Georg; Zimmer, Sebastian [Department of Medicine/Cardiology, University of Bonn, Sigmund-Freud-Str. 25, 53105 Bonn (Germany)
2012-03-30
Highlights: Black-Right-Pointing-Pointer RIG-I activation impairs endothelial function in vivo. Black-Right-Pointing-Pointer RIG-I activation alters HCAEC biology in vitro. Black-Right-Pointing-Pointer EPC function is affected by RIG-I stimulation in vitro. -- Abstract: Background: Endothelial dysfunction is a crucial part of the chronic inflammatory atherosclerotic process and is mediated by innate and acquired immune mechanisms. Recent studies suggest that pattern recognition receptors (PRR) specialized in immunorecognition of nucleic acids may play an important role in endothelial biology in a proatherogenic manner. Here, we analyzed the impact of endothelial retinoic acid inducible gene I (RIG-I) activation upon vascular endothelial biology. Methods and results: Wild type mice were injected intravenously with 32.5 {mu}g of the RIG-ligand 3pRNA (RNA with triphosphate at the 5 Prime end) or polyA control every other day for 7 days. In 3pRNA-treated mice, endothelium-depended vasodilation was significantly impaired, vascular oxidative stress significantly increased and circulating endothelial microparticle (EMP) numbers significantly elevated compared to controls. To gain further insight in RIG-I dependent endothelial biology, cultured human coronary endothelial cells (HCAEC) and endothelial progenitor cells (EPC) were stimulated in vitro with 3pRNA. Both cells types express RIG-I and react with receptor upregulation upon stimulation. Reactive oxygen species (ROS) formation is enhanced in both cell types, whereas apoptosis and proliferation is not significantly affected in HCAEC. Importantly, HCAEC release significant amounts of proinflammatory cytokines in response to RIG-I stimulation. Conclusion: This study shows that activation of the cytoplasmatic nucleic acid receptor RIG-I leads to endothelial dysfunction. RIG-I induced endothelial damage could therefore be an important pathway in atherogenesis.
Development of Magnetorheological Engine Mount Test Rig
Md Yunos Mohd Razali
2017-01-01
Full Text Available Ride comfort is an important factor in any road vehicle performance. Nonetheless, passenger ride comfort is sometimes affected by the vibrations resulting from the road irregularities. Vehicle ride comfort is also often compromised by engine vibration. Engine mount is one of the devices which act as vibration isolator from unwanted vibration from engine to the driver and passengers. This paper explains the development of the test rig used for laboratory testing of Magnetorheological (MR engine mount characterization. MR engine mount was developed to investigate the vibration isolation process. An engine mount test machine was designed to measure the displacement, relative velocity and damper force with respect to current supply to characterize the hysteresis behavior of the damper and as force tracking control of the MR engine mount.
Investigating Knowledge Transfer Mechanisms for Oil Rigs
Vianello, Giovanna; Ahmed, Saeema
2009-01-01
of lessons learnt from one rig to the next, and the actual situation emerged. Various approaches for transferring knowledge were elicited and analysed with regard to the types of knowledge that were transferred and the context in which they were used. This study indicates factors that should be considered......It is widely recognized, both in industry and academia, that clear strategies in knowledge transfer positively influence the success of a firm. A firm should support the transfer of knowledge by standardizing communication channels within and across departments, based upon personalization......, codification or a combination of these two strategies. The characteristics of the business influence the choice of communication channels used for knowledge transfer. This paper presents a case study exploring the transfer of knowledge within and across projects, specifically the transfer of service knowledge...
Investigating Knowledge Transfer Mechanisms for Oil Rigs
Vianello, Giovanna; Ahmed, Saeema
2009-01-01
It is widely recognized, both in industry and academia, that clear strategies in knowledge transfer positively influence the success of a firm. A firm should support the transfer of knowledge by standardizing communication channels within and across departments, based upon personalization......, codification or a combination of these two strategies. The characteristics of the business influence the choice of communication channels used for knowledge transfer. This paper presents a case study exploring the transfer of knowledge within and across projects, specifically the transfer of service knowledge...... in the case of complex machinery. The strategies used for knowledge transfer were analysed and compared with the expected transfer mechanisms, similarities and differences were investigated and are described. A family of four identical rigs for offshore drilling was the selected case. The transfer...
Mao, Ning; Yao, Yuping; Hata, Mitsuhiko; Wada, Masashi; Kanaoka, Chikao
2008-01-01
VDI type-1 rig and JIS rig are the two major testing rigs for cleanable fabric filters. We measured the filter cleaning performance using these rigs and the results were compared in order to characterize the two testing methods. The filter performance tests showed that the filter cleaning efficiency measured with VDI type-1 rig is higher than that with JIS rig. During pulse jet cleaning, JIS rig gave a higher peak pressure and a shorter time period of pulse jet compared to VDI type-1 rig. A n...
Tractor accelerated test on test rig
M. Mattetti
2013-09-01
Full Text Available The experimental tests performed to validate a tractor prototype before its production, need a substantial financial and time commitment. The tests could be reduced using accelerated tests able to reproduce on the structural part of the tractor, the same damage produced on the tractor during real life in a reduced time. These tests were usually performed reproducing a particular harsh condition a defined number of times, as for example using a bumpy road on track to carry out the test in any weather condition. Using these procedures the loads applied on the tractor structure are different with respect to those obtained during the real use, with the risk to apply loads hard to find in reality. Recently it has been demonstrated how, using the methodologies designed for cars, it is possible to also expedite the structural tests for tractors. In particular, automotive proving grounds were recently successfully used with tractors to perform accelerated structural tests able to reproduce the real use of the machine with an acceleration factor higher than that obtained with the traditional methods. However, the acceleration factor obtained with a tractor on proving grounds is in any case reduced due to the reduced speed of the tractors with respect to cars. In this context, the goal of the paper is to show the development of a methodology to perform an accelerated structural test on a medium power tractor using a 4 post test rig. In particular, several proving ground testing conditions have been performed to measure the loads on the tractor. The loads obtained were then edited to remove the not damaging portion of signals, and finally the loads obtained were reproduced in a 4 post test rig. The methodology proposed could be a valid alternative to the use of a proving ground to reproduce accelerated structural tests on tractors.
One analysis of aerodynamic characteristics of sloop rig; Sloop rig no kuriki tokusei no ichikaiseki
Shinkai, A.; Iyoda, H. [Kyushu University, Fukuoka (Japan). Faculty of Engineering
1996-10-01
A sloop which is one form of rigs of sail boats was analyzed of its basic aerodynamic characteristics by using the vortex distribution method. This solution method consists of an algorithm to derive a given pressure distribution on thin sail surface based on the vortex distribution method, and an algorithm to derive sail shapes from the given pressure distribution under a hypothesis of using flexible thin sails. An example of the calculation results showed distribution in an angular distance of pressure difference coefficients which act on each of the two sails, and showed the case where trim angle is changed and seven other parameters are fixed. With respect to control of trim angle which has close correlation with basic performance of the sloop rig, how the increase in the trim angle releases the main sail from aerodynamically adverse effect to which the main sail is subjected was shown. Furthermore, in order to estimate simply the performance of the sloop rig, a series calculation was executed and a chart was prepared which can estimate simply how a maximum thrust can be generated. 17 refs., 12 figs., 1 tab.
基于R实现Hilbert-Huang变换%Based on Hilbert-Huang Transform R to Achieve
马娜
2013-01-01
Hilbert-Huang Transform (HHT) is a new deal with the nonlinear, non-stationary time-frequency analysis method. It has been used in finance, biotechnology, telecommunications and other fields. This article discusses the Hilbert-Huang trans-form the basic principles and methods, and the open source environment to achieve based on R Hilbert-Huang transform, the fi-nal use of financial high-frequency data for the experiment and results are given.%Hilbert-Huang变换（HHT）是一种新型的处理非线性、非平稳信号的时频分析方法。它已经被应用在金融、生物、通信等多个领域。该文讨论了Hilbert-Huang变换的基本原理及实现方法，并基于R开源环境实现Hilbert-Huang变换，最后采用金融高频数据进行实验并给出结果。
Preparation of entangled states through Hilbert space engineering
Lin, Y; Reiter, F; Tan, T R; Bowler, R; Wan, Y; Keith, A; Knill, E; Glancy, S; Coakley, K; Sørensen, A S; Leibfried, D; Wineland, D J
2016-01-01
Entangled states are a crucial resource for quantum-based technologies such as quantum computers and quantum communication systems (1,2). Exploring new methods for entanglement generation is important for diversifying and eventually improving current approaches. Here, we create entanglement in atomic ions by applying laser fields to constrain the evolution to a restricted number of states, in an approach that has become known as "quantum Zeno dynamics" (3-5). With two trapped $^9\\rm{Be}^+$ ions, we obtain Bell state fidelities up to $0.990^{+2}_{-5}$, with three ions, a W-state (6) fidelity of $0.910^{+4}_{-7}$ is obtained. Compared to other methods of producing entanglement in trapped ions, this procedure is relatively insensitive to certain imperfections such as fluctuations in laser intensity, laser frequency, and ion-motion frequencies.
On stochastic fractional Volterra equations in Hilbert space
Karczewska, Anna; Lizama, Carlos
2006-01-01
In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties of stochastic convolutions are given. The paper provides a sufficient condition for a stochastic convolution to be a strong solution to a stochastic Volterra equation.
Renorms and topological linear contractions on Hilbert spaces
施茂祥; 谭炳均; 陈国强
1999-01-01
Properties of and the relationships between (topological) proper contractions, (topological) strict contractions and (topological) contractions are investigated, Explicit renorms are constructed so that all operators in a (finite or countable) family or a semigroup simultaneously become proper contractions or strict contractions. Some results are obtained for operator weighted shifts or operator weighted continuous shifts to be topological strict contractions.
Controllability of quasilinear stochastic evolution equations in Hilbert spaces
P. Balasubramaniam
2001-01-01
Full Text Available Controllability of the quasilinear stochastic evolution equation is studied using semigroup theory and a stochastic version of the well known fixed point theorem. An application to stochastic partial differential equations is given.
Detecting dimensional crossover and finite Hilbert space through entanglement entropies
Garagiola, Mariano; Cuestas, Eloisa; Pont, Federico M.; Serra, Pablo; Osenda, Omar
2016-01-01
The information content of the two-particle one- and two-dimensional Calogero model is studied using the von Neumann and R\\'enyi entropies. The one-dimensional model is shown to have non-monotonic entropies with finite values in the large interaction strength limit. On the other hand, the von Neumann entropy of the two-dimensional model with isotropic confinement is a monotone increasing function of the interaction strength which diverges logarithmically. By considering an anisotropic confine...
APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES
Amir KHOSRAVI; Morteza MIRZAEE AZANDARYANI
2014-01-01
In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.
Introduction to partial differential equations and Hilbert space methods
Gustafson, Karl E
1997-01-01
Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.
A power recirculating test rig for ball screw endurance tests
Giberti Hermes
2016-01-01
Full Text Available A conceptual design of an innovative test rig for endurance tests of ball screws is presented in this paper. The test rig layout is based on the power recirculating principle and it also allows to overtake the main critical issues of the ball screw endurance tests. Among these there are the high power required to make the test, the lengthy duration of the same and the high loads between the screw and the frame that holds it. The article describes the test rig designed scheme, the kinematic expedients to be adopted in order to obtain the required performance and functionality and the sizing procedure to choose the actuation system.
Application of the Hilbert-Huang Transform to the Search for Gravitational Waves
Camp, Jordan B.; Cannizzo, John K.; Numata, Kenji
2007-01-01
We present the application of a novel method of time-series analysis, the Hilbert-Huang Transform, to the search for gravitational waves. This algorithm is adaptive and does not impose a basis set on the data, and thus the time-frequency decomposition it provides is not limited by time-frequency uncertainty spreading. Because of its high time-frequency resolution it has important applications to both signal detection and instrumental characterization. Applications to the data analysis of the ground and space based gravitational wave detectors, LIGO and LISA, are described.
Diagonalization of a self-adjoint operator acting on a Hilbert module
Parfeny P. Saworotnow
1985-01-01
Full Text Available For each bounded self-adjoint operator T on a Hilbert module H over an H*-algebra A there exists a locally compact space m and a certain A-valued measure μ such that H is isomorphic to L2(μ⊗A and T corresponds to a multiplication with a continuous function. There is a similar result for a commuting family of normal operators. A consequence for this result is a representation theorem for generalized stationary processes.
Application of the Hilbert-Huang Transform to Financial Data
Huang, Norden
2005-01-01
A paper discusses the application of the Hilbert-Huang transform (HHT) method to time-series financial-market data. The method was described, variously without and with the HHT name, in several prior NASA Tech Briefs articles and supporting documents. To recapitulate: The method is especially suitable for analyzing time-series data that represent nonstationary and nonlinear phenomena including physical phenomena and, in the present case, financial-market processes. The method involves the empirical mode decomposition (EMD), in which a complicated signal is decomposed into a finite number of functions, called "intrinsic mode functions" (IMFs), that admit well-behaved Hilbert transforms. The HHT consists of the combination of EMD and Hilbert spectral analysis. The local energies and the instantaneous frequencies derived from the IMFs through Hilbert transforms can be used to construct an energy-frequency-time distribution, denoted a Hilbert spectrum. The instant paper begins with a discussion of prior approaches to quantification of market volatility, summarizes the HHT method, then describes the application of the method in performing time-frequency analysis of mortgage-market data from the years 1972 through 2000. Filtering by use of the EMD is shown to be useful for quantifying market volatility.
Application of Three-dimensional Hilbert Curve in Image Scrambling%三维Hilbert曲线在图像置乱中的应用
万里红; 孙燮华; 林旭亮
2011-01-01
研究三维Hilbert曲线基元在空间中的24种形态,提出一种基于基元分形走向的n阶三维Hilbert曲线生成算法,将图像像素点存入到一个空间立方体数组中,按三维Hilbert曲线遍历顺序对空间立方体中的像素点进行顺序扫描存储,从而实现图像置乱处理.实验结果表明,相比二维Hilbert曲线,三维Hilbert曲线置乱具有更强的图像置乱度和更高的图像加密安全性.%This paper researches twenty-four space forms of three-dimensional Hilbert curve primitives, and proposes a n-order three-dimensional Hilbert curve generation algorithm based on the orientation of the primitives.It puts the pixels into a space cube array, sequentially scans them and stores them based on the traversal sequence of three-dimensional Hilbert to realize image scrambling.Experimental results show that three-dimensional Hilbert curve scrambling has a stronger image scrambling degree and higher encryption security compared with the two-dimensional Hilbert curve.
Five-Axis, Three-Magnetic-Bearing Dynamic Spin Rig
Morrison, Carlos R.; Provenza, Andrew; Kurkov, Anatole; Mehmed, Oral; Johnson, Dexter; Montague, Gerald; Duffy, Kirsten; Jansen, Ralph
2005-01-01
The Five-Axis, Three-Magnetic-Bearing Dynamic Spin Rig is an apparatus for vibration testing of turbomachine blades in a vacuum at rotational speeds from 0 to 40,000 rpm. This rig includes (1) a vertically oriented shaft on which is mounted an assembly comprising a rotor holding the blades to be tested, (2) two actively controlled heteropolar radial magnetic bearings at opposite ends of the shaft, and (3) an actively controlled magnetic thrust bearing at the upper end of the shaft. This rig is a more capable successor to a prior apparatus, denoted the Dynamic Spin Rig (DSR), that included a vertically oriented shaft with a mechanical thrust bearing at the upper end and a single actively controlled heteropolar radial magnetic bearing at the lower end.
China-made Oil Rigs Well Sold on International Market
无
2003-01-01
@@ By the end of July, ChinaPetroleum Technology Development Company (CPTDC), one of CNPC's subsidiaries, has cumulatively sold 26 oil drilling rigs worth more than US$200 million in the past three years.
46 CFR 162.050-17 - Separator test rig.
2010-10-01
... operate; and (4) Have either bypass piping to its suction side or a throttle valve or orifice on its discharge side. (c) The inlet piping of the test rig must be sized so that— (1) Influent water flows at...
Testing for voter rigging in small polling stations
Jiménez, Raúl; Klimek, Peter
2016-01-01
Since the 1970s there has been a large number of countries that combine formal democratic institutions with authoritarian practices. Although in such countries the ruling elites may receive considerable voter support they often employ several manipulation tools to control election outcomes. A common practice of these regimes is the coercion and mobilization of a significant amount of voters to guarantee the electoral victory. This electoral irregularity is known as voter rigging, distinguishing it from vote rigging, which involves ballot stuffing or stealing. Here we develop a statistical test to quantify to which extent the results of a particular election display traces of voter rigging. Our key hypothesis is that small polling stations are more susceptible to voter rigging, because it is easier to identify opposing individuals, there are less eye witnesses, and supposedly less visits from election observers. We devise a general statistical method for testing whether voting behavior in small polling station...
Technical specification for IR rig manufacture
Han Hyon Soo; Cho, W. K.; Kim, S. D.; Park, U. J.; Hong, S. B.; Yoo, K. M
2000-10-01
IR Rig is one of the equipments are required in HANARO core for a radioisotope target. The various conditions like high radiation, high heat, rapid flow and vibration may cause swelling, Brittleness and acceleration of corrosion in HANARO core. These specific problems can be prevented and the safety of such equipment are prerequisite as well as durableness and surveillance. Therefore, the selection of material has to be made on the basis of small cross-section area, low energy emission by the gamma ray due to the absorption of neutron and short half life. The body is consist of aluminum and Inconel-750 was used for the internal spring(coil) which is known to be durable. The whole production process including the purchase of accessory, mechanical processing, welding and assembly was carried out according to the standard procedure to meet the requirement. A design, manufacture, utilization of reactor core and the other relevant uses were fit to class ''T'' to certify the whole process as general. And design, fabrication, analytical test, materials and accessory were carried out based on the ASME, ASTM, ANSI, AWS, JIS and KS standard.
Endoscopic PIV measurements in a low pressure turbine rig
Kegalj, Martin; Schiffer, Heinz-Peter [Technische Universitaet Darmstadt (Germany). Department of Gas Turbines and Aerospace Propulsion
2009-10-15
Particle-Image-Velocimetry (PIV) is a useful way to acquire information about the flow in turbomachinery. Several premises have to be fulfilled to achieve high-quality data, for example, optical access, low vibrations and low reflections. However, not all test facilities comply with these requirements. If there is no optical access to the test area, measurements cannot be performed. The use of borescopic optics is a possible solution to this issue, as the access required is very small. Several different techniques can be used to measure the three components of the velocity vector, one of which is Stereo-PIV. These techniques require either large optical access from several viewing angles or highly complex setups. Orthogonal light sheet orientations in combination with borescopic optics using Planar-PIV can deliver sufficient information about the flow. This study will show the feasibility of such an approach in an enclosed test area, such as the interblade space in a Low-Pressure-Turbine-Rig. The results from PIV will be compared with data collected with conventional techniques, such as the Five-Hole-Probe and the 2-component Hot-Wire-Anemometry. An analysis of time- and phase-averaged data will be performed. (orig.)
Hilbert's epsilon as an Operator of Indefinite Committed Choice
Wirth, Claus-Peter
2009-01-01
Paul Bernays and David Hilbert carefully avoided overspecification of Hilbert's epsilon-operator and axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the epsilon-operator underspecified. In the meanwhile, there have been several suggestions for semantics of the epsilon as a choice operator. After reviewing the literature on semantics of Hilbert's epsilon operator, we propose a new semantics with the following features: We avoid overspecification (such as right-uniqueness), but admit indefinite choice, committed choice, and classical logics. Moreover, our semantics for the epsilon supports proof search optimally and is natural in the sense that it does not only mirror some cases of referential interpretation of indefinite articles in natural language, but may also contribute to philosophy of language. Finally, we ask the question whether our epsilon within our free-variable framework can serve as a paradigm useful in the specification and computation of seman...
Fundamental normal surfaces and the enumeration of Hilbert bases
Burton, Benjamin A
2011-01-01
Normal surfaces are a key tool in computational knot theory and 3-manifold topology, and have featured in significant computational breakthroughs in recent years. Despite this, there has been little practical progress on algorithms that use fundamental normal surfaces, which are described in terms of a Hilbert basis for a pointed rational cone on a high-dimensional integer lattice. In this paper we develop and implement several algorithms to enumerate fundamental normal surfaces, by merging domain-specific techniques from normal surface theory with classical Hilbert basis algorithms. The most successful of these combines a maximal admissible face decomposition with the primal Hilbert basis algorithm of Bruns, Ichim and Koch, and in many cases can solve 168-dimensional enumeration problems (based on 24-tetrahedron knot complements) in a matter of hours. As an application, we use this new algorithm to compute 164 previously unknown crosscap numbers in the KnotInfo database of knot invariants.
Hilbert-值半鞅序列的弱收敛%Week Convergence of Hilbert-valued Semimartingale Sequence
李亮坤; 彭运佳; 谢颖超
2000-01-01
本文在条件UT下研究了Hilbert-值半鞅序列到连续Hilbert-值半鞅的收敛性,并在弱收敛的条件下研究了形如 Xn=∫10an(Xn,s)dYn,+∫10bn(Xn,s)dAns,Xn0=0(A)n≥1随机微分方程的稳定性,其中Yn和An分别为Hilbert-值半鞅和分量为增过程的Hilbert-值有限变差过程.%The convergence of Hilbert-valued semimartingales to continuous semimartingales are discussed under the condition UT. And the stability of stochastic differential equations of typeXn=∫10an(Xn,s)dYn,+∫10bn(Xn,s)dAns,Xn0=0(A)n≥1 is discussed under jointly weak convergence of driving processes {(Yn,An)}n≥1},where Yn and An are H-valued semimartingale and H-valued finite variation with every component being increasing process,respectively.
Fusion Frames and -Frames in Banach Spaces
Amir Khosravi; Behrooz Khosravi
2011-05-01
Fusion frames and -frames in Hilbert spaces are generalizations of frames, and frames were extended to Banach spaces. In this article we introduce fusion frames, -frames, Banach -frames in Banach spaces and we show that they share many useful properties with their corresponding notions in Hilbert spaces. We also show that -frames, fusion frames and Banach -frames are stable under small perturbations and invertible operators.
Gastrostomy insertion: comparing the options - PEG, RIG or PIG?
Laasch, H.-U. E-mail: hul@smtr.nhs.uk; Wilbraham, L.; Bullen, K.; Marriott, A.; Lawrance, J.A.L.; Johnson, R.J.; Lee, S.H.; England, R.E.; Gamble, G.E.; Martin, D.F
2003-05-01
AIM: To compare percutaneous endoscopic gastrostomy (PEG) with radiologically inserted gastrostomy (RIG) and assess a hybrid gastrostomy technique (per-oral image-guided gastrostomy, PIG). MATERIALS AND METHODS: Fifty PEGs and 50 RIGs performed in three centres were prospectively compared and the endoscopic findings of 200 PEGs reviewed. A fluoroscopy-guided technique was modified to place 20 F over-the-wire PEG-tubes in 60 consecutive patients. RESULTS: Technical success was 98%, 100% and 100% for PEG, RIG and PIG, respectively. Antibiotic prophylaxis significantly reduced stoma infection for orally placed tubes (p=0.02). Ten out of 50 (20%) small-bore RIG tubes blocked. Replacement tubes were required in six out of 50 PEGs (12%), 10 out of 50 RIGs (20%), but no PIGs (p<0.001). No procedure-related complications occurred. The function of radiologically placed tubes was significantly improved with the larger PIG (p<0.001), with similar wound infection rates. PIG was successful in 24 patients where endoscopic insertion could not be performed. Significant endoscopic abnormalities were found in 42 out of 200 PEG patients (21%), all related to peptic disease. Insignificant pathology was found in 8.5%. CONCLUSION: PIG combines advantages of both traditional methods with a higher success and lower re-intervention rate. Endoscopy is unlikely to detect clinically relevant pathology other than peptic disease. PIG is a very effective gastrostomy method; it has better long-term results than RIG and is successful where conventional PEG has failed.
Radial Hilbert transform with Laguerre-Gaussian spatial filters.
Guo, Cheng-Shan; Han, Yu-Jing; Xu, Jian-Bo; Ding, Jianping
2006-05-15
We analyze the point spread function (PSF) of the image processing system for radial Hilbert transform and propose a novel spiral phase filter, called the Laguerre-Gaussian spatial filter (LGSF). Theoretical analysis and real experiments show that the LGSF possesses some advantages in comparison with the conventional spiral phase plate (SPP). For example, the PSF of the imaging system with a LGSF presents smaller suboscillations than that with the conventional SPP, which allows us to realize a radial Hilbert transform for achieving a high contrast edge enhancement with high resolution.
Hilbert series for constructing Lagrangians: Expanding the phenomenologist's toolbox
Lehman, Landon; Martin, Adam
2015-05-01
This paper presents the Hilbert series technique to a wider audience in the context of constructing group-invariant Lagrangians. This technique provides a fast way to calculate the number of operators of a specified mass dimension for a given field content and is a useful cross-check on more well-known group theoretical methods. In addition, at least when restricted to invariants without derivatives, the Hilbert series technique supplies a robust way of counting invariants in scenarios which, due to the large number of fields involved or to high-dimensional group representations, are intractable by traditional methods. We work out several practical examples.
Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
Lehman, Landon
2015-01-01
This note presents the Hilbert series technique to a wider audience in the context of constructing group-invariant Lagrangians. This technique provides a fast way to calculate the number of operators of a specified mass dimension for a given field content, and is a useful cross check on more well-known group theoretical methods. In addition, at least when restricted to invariants without derivatives, the Hilbert series technique supplies a robust way of counting invariants in scenarios which, due to the large number of fields involved or to high dimensional group representations, are intractable by traditional methods. We work out several practical examples.
Hilbert格上正算子的谱%The Spectrum of Positive Operators on Hilbert Lattices
邓春源; 杜鸿科
2007-01-01
Some spectral characterizations of positive operators on Hilbert lattices are presented. The application of these results can yield some equivalent relations of an irreducible positive operator. Some related results for positive operators on Hilbert lattice are also obtained.
Hilbert series and operator bases with derivatives in effective field theories
Henning, Brian; Lu, Xiaochuan; Melia, Tom; Murayama, Hitoshi
2016-10-01
We introduce a systematic framework for counting and finding independent operators in effective field theories, taking into account the redundancies associated with use of the classical equations of motion and integration by parts. By working in momentum space, we show that the enumeration problem can be mapped onto that of understanding a polynomial ring in the field momenta. All-order information about the number of independent operators in an effective field theory is encoded in a geometrical object of the ring known as the Hilbert series. We obtain the Hilbert series for the theory of N real scalar fields in (0+1) dimensions—an example, free of space-time and internal symmetries, where aspects of our framework are most transparent. Although this is as simple a theory involving derivatives as one could imagine, it provides fruitful lessons to be carried into studies of more complicated theories: we find surprising and rich structure from an interplay between integration by parts and equations of motion and a connection with SL(2,C) representation theory, which controls the structure of the operator basis.
A DISTRIBUTION-THEORETICAL APPROACH TO CERTAIN LEBESGUE AND SOBOLEV SPACES.
FUNCTIONAL ANALYSIS, * DISTRIBUTION THEORY ), PARTIAL DIFFERENTIAL EQUATIONS, OPERATORS(MATHEMATICS), FOURIER ANALYSIS, HILBERT SPACE, INTEGRAL TRANSFORMS, NUMERICAL INTEGRATION, TOPOLOGY, SERIES(MATHEMATICS), THEOREMS
A new extension of Hilbert's inequality for multifunctions with best constant factors
H. A. Agwo
2009-08-01
Full Text Available The aim of this paper is to establish a new extension of Hilbert's inequality and Hardy-Hilbert's inequality for multifunctions with best constants factors. Also, we present some applications for Hilbert's inequality which give new integral inequalities.
Riemann-Hilbert problems from Donaldson-Thomas theory
Bridgeland, Tom
2016-01-01
We study a class of Riemann-Hilbert problems arising naturally in Donaldson-Thomas theory. In certain special cases we show that these problems have unique solutions which can be written explicitly as products of gamma functions. We briefly explain connections with Gromov-Witten theory and exact WKB analysis.
Some New Inverse-type Hilbert-Pachpatte Integral Inequalities
Young Ho KIM
2004-01-01
In this paper, some new generalizations of inverse type Hilbert-Pachpatte integral inequalities are proved. The results of this paper reduce to those of Pachpatte (1998, J. Math. Anal. Appl.226, 166-179) and Zhao and Debnath (2001, J. Math. Anal. Appl. 262, 411-418).
AN EFFICIENT HILBERT AND INTEGER WAVELET TRANSFORM BASED VIDEO WATERMARKING
AGILANDEESWARI L.
2016-03-01
Full Text Available In this paper, an efficient, highly imperceptible, robust, and secure digital video watermarking technique for content authentication based on Hilbert transform in the Integer Wavelet Transform (IWT domain has been introduced. The Hilbert coefficients of gray watermark image are embedded into the cover video frames Hilbert coefficients on the 2-level IWT decomposed selected block on sub-bands using Principal Component Analysis (PCA technique. The authentication is achieved by using the digital signature mechanism. This mechanism is used to generate and embed a digital signature after embedding the watermarks. Since, the embedding process is done in Hilbert transform domain, the imperceptibility and the robustness of the watermark is greatly improved. At the receiver end, prior to the extraction of watermark, the originality of the content is verified through the authentication test. If the generated and received signature matches, it proves that the received content is original and performs the extraction process, otherwise deny the extraction process due to unauthenticated received content. The proposed method avoids typical degradations in the imperceptibility level of watermarked video in terms of Average Peak Signal – to – Noise Ratio (PSNR value of about 48db, while it is still providing better robustness against common video distortions such as frame dropping, averaging, and various image processing attacks such as noise addition, median filtering, contrast adjustment, and geometrical attacks such as, rotation and cropping in terms of Normalized Correlation Coefficient (NCC value of about nearly 1.
Application of Hilbert's Projective Metric on Symmetric Cones
Khalid KOUFANY
2006-01-01
Let Ω be a symmetric cone. In this note, we introduce Hilbert's projective metric on Ω in terms of Jordan algebras and we apply it to prove that, given a linear invertible transformation g such that g(Ω) = Ω and a real number p, |p| ＞ 1, there exists a unique element x ∈Ω satisfying g(x) = xp.
Generalized noncommutative Hardy and Hardy-Hilbert type inequalities
Hansen, Frank; Krulic, Kristina; Pecaric, Josip
2010-01-01
We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1...
Convexity and the "Pythagorean" metric of space(-time)
Kalogeropoulos, Nikos
2016-01-01
We address the question about the reasons why the "Wick-rotated", positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces providing the kinematic framework for the statistical or quantum treatments of gravity. We rely on particular moduli of convexity and smoothness which are extremized by Hilbert spaces. In the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a functional integral approach. The "Pythagorean" metric of space(-time) is then induced by such Hilbert spaces.
Santhosh George
2003-01-01
Full Text Available Recently, Tautenhahn and Hämarik (1999 have considered a monotone rule as a parameter choice strategy for choosing the regularization parameter while considering approximate solution of an ill-posed operator equation Tx=y, where T is a bounded linear operator between Hilbert spaces. Motivated by this, we propose a new discrepancy principle for the simplified regularization, in the setting of Hilbert scales, when T is a positive and selfadjoint operator. When the data y is known only approximately, our method provides optimal order under certain natural assumptions on the ill-posedness of the equation and smoothness of the solution. The result, in fact, improves an earlier work of the authors (1997.
Endurance test for mini-plate fuel rig
Chung, Heung June; Yang, Sun Kyu; Park, Jong Man; Kim, Chang Kyu; Ryu, Jeong Soo
1999-07-01
This report presents the pressure drop, vibration and endurance test results for mini-plate fuel rig which were designed by KAERI and fabricated by Daewoo Precision Co. From the pressure drop test results, it is noted that the flow velocity across the fuel rig corresponding to the pressure drop of 200 kPa is measured to be about 6.78 kg/sec. Vibration frequency for the fuel rig ranges from 14 to 19 Hz. RMZ (Root Mean Square) displacement for the fuel rig is less than 7 {mu}m, and the maximum displacement is less than 20 {mu}m. Based on the endurance rest results, the appreciable fretting wear for the fuel rig is not observed but the small amount of wear was observed at the interface region between the mini-plates and upper housing cap as well as at the slot regions of a bottom endplate interfacing with the bottom guide arms. (author). 4 refs., 10 tabs., 33 figs.
Design and Characterization of a Centrifugal Compressor Surge Test Rig
Kin Tien Lim
2011-01-01
Full Text Available A detailed description of a new centrifugal compressor surge test rig is presented. The objective of the design and development of the rig is to study the surge phenomenon in centrifugal compression systems and to investigate a novel method of surge control by active magnetic bearing servo actuation of the impeller axial tip clearance. In this paper, we focus on the design, initial setup, and testing of the rig. The latter two include the commissioning of the rig and the experimental characterization of the compressor performance. The behavior of the compressor during surge is analyzed by driving the experimental setup into surge. Two fundamental frequencies, 21 Hz and 7 Hz, connected to the surge oscillation in the test rig are identified, and the observed instability is categorized according to the intensity of pressure fluctuations. Based on the test results, the excited pressure waves are clearly the result of surge and not stall. Also, they exhibit the characteristics of mild and classic surge instead of deep surge. Finally, the change in the compressor performance due to variation in the impeller tip clearance is experimentally examined, and the results support the potential of the tip clearance modulation for the control of compressor surge. This is the first such demonstration of the feasibility of surge control of a compressor using active magnetic bearings.
RIG-I and dsRNA-induced IFNbeta activation.
Stéphane Hausmann
Full Text Available Except for viruses that initiate RNA synthesis with a protein primer (e.g., picornaviruses, most RNA viruses initiate RNA synthesis with an NTP, and at least some of their viral (pppRNAs remain unblocked during the infection. Consistent with this, most viruses require RIG-I to mount an innate immune response, whereas picornaviruses require mda-5. We have examined a SeV infection whose ability to induce interferon depends on the generation of capped dsRNA (without free 5' tri-phosphate ends, and found that this infection as well requires RIG-I and not mda-5. We also provide evidence that RIG-I interacts with poly-I/C in vivo, and that heteropolymeric dsRNA and poly-I/C interact directly with RIG-I in vitro, but in different ways; i.e., poly-I/C has the unique ability to stimulate the helicase ATPase of RIG-I variants which lack the C-terminal regulatory domain.
Advanced jack up rig breaking U.S. construction drought
Kelly, P. [Rowan Companies Inc., Houston, TX (United States)
1997-03-10
A new heavy duty jack up, due in mid-1998, will be able to simultaneously drill and produce wells in harsher environments and deeper water than current jack ups in the worldwide fleet. Rowan Cos. Inc.`s Gorilla V is the only mobile offshore drilling unit (MODU) currently under construction in the US. Two more enhanced Gorilla design rigs are planned before the year 2000. The enhanced Gorilla class jack up represents the most technologically advanced jack up unit constructed to date. The rigs are structurally designed to meet year-round weather challenges in the harshest geographical environments. Rising demand for drilling rigs, coupled with a dwindling fleet, is generating supply shortages around the world, particularly at the high-specification end of the market. Even increasing the historical retirement age from 20 to 25 years, rig attrition continues at a level of about 18 rigs per year. Apart from the jack up market per se, however, Rowan`s strategy in designing and building enhanced Gorillas is to improve existing jack up drilling technology and offer the versatility to operate as a drilling unit, a mobile production unit, or both simultaneously in either open water locations or alongside existing platforms. The paper discusses the market for these heavy jack-ups, the use of one on the Cohasset project in Nova Scotia, the Gorilla V and enhanced Gorillas, geographical range of use, and MOPU economics.
Heat-and-pull rig for fiber taper fabrication
Ward, Jonathan M.; O'Shea, Danny G.; Shortt, Brian J.; Morrissey, Michael J.; Deasy, Kieran; Nic Chormaic, Síle G.
2006-08-01
We describe a reproducible method of fabricating adiabatic tapers with 3-4μm diameter. The method is based on a heat-and-pull rig, whereby a CO2 laser is continuously scanned across a length of fiber that is being pulled synchronously. Our system relies on a CO2 mirror mounted on a geared stepper motor in order to scan the laser beam across the taper region. We show that this system offers a reliable alternative to more traditional rigs incorporating galvanometer scanners. We have routinely obtained transmission losses between 0.1 and 0.3dB indicating the satisfactory production of adiabatic tapers. The operation of the rig is described in detail and an analysis on the produced tapers is provided. The flexibility of the rig is demonstrated by fabricating prolate dielectric microresonators using a microtapering technique. Such a rig is of interest to a range of fields that require tapered fiber fabrication such as microcavity-taper coupling, atom guiding along a tapered fiber, optical fiber sensing, and the fabrication of fused biconical tapered couplers.
The Hilbert series of 3d N=2 Yang-Mills theories with vectorlike matter
Cremonesi, Stefano
2015-01-01
This paper presents a formula for the Hilbert series that counts gauge invariant chiral operators in 3d N=2 Yang-Mills theories with vectorlike matter and no Chern-Simons interactions. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background, which is determined by the Higgs mechanism. The sum over magnetic charges is restricted due to instanton effects that partially lift the classical Coulomb branch. The formalism is applied to unitary and symplectic gauge theories with fundamental matter, reproducing old results for the moduli space of vacua and the chiral ring, without resorting to any further effective superpotential on the moduli space.
Espiro, J Lorca
2014-01-01
In this work we consider the effects of coupling characteristic classes to gravity by introducing appropriate operators in the Einstein--Hilbert action. As it is well known, this approach strays from the framework of General Relativity since it results in theories in which torsion can be present. An important point of our approach is that the solutions obtained explicitly carry topological information of the considered space-time manifold. We consider here all the characteristic classes that are consistent with a space-time manifold leading to the definition of an 'effective Cosmological Constant' that inherits topological information. We present analytical solutions for the contortion $1$-form that can be obtained under general conditions in various cases of interest. We show how to use these solutions to study cosmological scenarios that are obtained mainly by selecting a metric and an ideal fluid. We also discuss some of the consequences of these cosmological models over the topological and differential st...
COSL Signs Rig Equipment Contract with US Company
无
2004-01-01
@@ China Oilfield Services Limited (COSL), the leading integrated oilfield services provider in China for the offshore oil market, has recently signed an equipment purchase contract with the US-based National Oilwell L.P. Under the US$30-million contract, National Oilwell provide four sets of equipment for COSL's new 400-feet jack-up drilling rig under construction, consisting of a drilling system, a mud mixing and solid controlling system,a BOP handling system and a rig jacking system.National Oilwell will provide the drilling system on EPC basis, including its design, construction,equipment supply and commissioning.
SOAR - Stereo Obstacle Avoidance Rig Project
National Aeronautics and Space Administration — The ultimate goal of the SOAR program is to develop robust hardware and algorithms for low light, passive terrain sensing. The SOAR system will provide NASA with a...
T^{\\sigma}_{\\rho}(G) Theories and Their Hilbert Series
Cremonesi, Stefano; Mekareeya, Noppadol; Zaffaroni, Alberto
2015-01-01
We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3d N=4 superconformal gauge theories T^{\\sigma}_{\\rho}(G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, \\sigma is a partition of G and \\rho a partition of the dual group G^\\vee. In deriving such a formula we make use of the recently discovered formula for the Hilbert series of the quantum Coulomb branch of N=4 superconformal theories. The result can be expressed in terms of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials, and can be interpreted in mathematical language in terms of localization. We mainly consider the case G=SU(N) but some interesting results are also given for orthogonal and symplectic groups.
A Riemann-Hilbert approach to rotating attractors
Câmara, M. C.; Cardoso, G. L.; Mohaupt, T.; Nampuri, S.
2017-06-01
We construct rotating extremal black hole and attractor solutions in gravity theories by solving a Riemann-Hilbert problem associated with the Breitenlohner-Maison linear system. By employing a vectorial Riemann-Hilbert factorization method we explicitly factorize the corresponding monodromy matrices, which have second order poles in the spectral parameter. In the underrotating case we identify elements of the Geroch group which implement Harrison-type transformations which map the attractor geometries to interpolating rotating black hole solutions. The factorization method we use yields an explicit solution to the linear system, from which we do not only obtain the spacetime solution, but also an explicit expression for the master potential encoding the potentials of the infinitely many conserved currents which make this sector of gravity integrable.
A Photonic Bandgap Filter Using Metallic Hilbert Curves
LI Hong-Qiang; WEI Ze-Yong; CHEN Hong; ZHANG Ye-Wen
2005-01-01
@@ We theoretically suggest that a metallic plate with Hilbert curves can possesses multiple resonances in a linear scale, leading to multiple stop bands and pass bands for electromagnetic waves over a wide frequency range.The forward transmission from a line source nearby a small plate covered by four cells with Hilbert curves is checked by a probe at the far field, the results agree well with the multiple resonance frequencies calculated by the plane wave incidence under a periodic boundary condition, the return loss spectra show that radiations of a line antenna working at 4.5 GHz can be greatly enhanced, which results from the interaction of the antenna and the subwavelength metallic plate. This kind of metallic pattern is very practical in multi-frequency functioned wave devices with sub-wavelength sizes.
Liu, Jin; Wang, Chuan-Bing; Liu, Lu; Sun, Wei-Huai
2016-04-01
The Hilbert-Huang transform (HHT) is an adaptive data analysis method that can accommodate the variety of data generated by nonlinear and nonstationary processes in nature. In this paper, we focus on the small geomagnetically induced current (GIC) at the local substations in low-latitude power grid of China, responding to a moderate storm on 14-18 July 2012. The HHT is applied to analyze the neutral point currents (NPCs) of transformers measured at different substations, and the GIC indices converted from local geomagnetic field measurements. The original data are decomposed into intrinsic mode functions (IMFs) using the ensemble empirical mode decomposition. After removal of the quasi-diurnal components related with the solar quiet variation, the IMFs representing storm disturbances are transformed into Hilbert energy spectra. The results show that some transformers have more or less responses to the moderate storm in the form of Hilbert energy spectra with the frequency around 2-3 mHz. A comparison on the amplitude changes of the spectra total energy of NPCs' perturbation during storm time intervals at different sites suggests that a shell type of three-phase single transformer group seems to be more vulnerable in the storm. Although the low-latitude power grids usually show very small GIC, these can be used to investigate the potential risk of space weather to the system.
Extension groups of tautological sheaves on Hilbert schemes
Krug, Andreas
2011-01-01
We give formulas for the extension groups between tautological sheaves and more general between tautological objects twisted by a determinant line bundle on the Hilbert scheme of points on a smooth quasi-projective surface. We do this using L. Scala's results about the image of tautological sheaves under the Bridgeland-King-Reid equivalence. We also compute the Yoneda products in terms of these formulas.
Improved Hilbert phase contrast for transmission electron microscopy
Koeck, Philip J.B.
2015-07-15
Hilbert phase contrast has been recognized as a means of recording high resolution images with high contrast using a transmission electron microscope. This imaging mode could be used to image typical phase objects such as unstained biological molecules or cryo sections of biological tissue. According to the original proposal by (Danev et al., 2002) the Hilbert phase plate applies a phase shift of π to approximately half the focal plane (for example the right half excluding the central beam) and an image is recorded at Gaussian focus. After correction for the inbuilt asymmetry of differential phase contrast this image will have an almost perfect contrast transfer function (close to 1) from the lowest spatial frequency up to a maximum resolution determined by the wave length and spherical aberration of the microscope. In this paper I present theory and simulations showing that this maximum spatial frequency can be increased considerably almost without loss of contrast by using a Hilbert phase plate of half the thickness, leading to a phase shift of π/2, and recording images at Scherzer defocus. The maximum resolution can be improved even more by imaging at extended Scherzer defocus, though at the cost of contrast loss at lower spatial frequencies. - Highlights: • In this paper I present theory and simulations for a Hilbert phase plate that phase shifts the electron wave by π/2 instead of π while images are recorded close to Scherzer defocus instead of Gaussian focus. • I show that the point resolution for this new imaging mode is considerably higher without loss of contrast. • An additional advantage lies in the reduced thickness of the phase plate which leads to reduced inelastic scattering in the phase plate and less noise.
Application of Huang-Hilbert Transforms to Geophysical Datasets
Duffy, Dean G.
2003-01-01
The Huang-Hilbert transform is a promising new method for analyzing nonstationary and nonlinear datasets. In this talk I will apply this technique to several important geophysical datasets. To understand the strengths and weaknesses of this method, multi- year, hourly datasets of the sea level heights and solar radiation will be analyzed. Then we will apply this transform to the analysis of gravity waves observed in a mesoscale observational net.
The plasma dispersion function the Hilbert transform of the Gaussian
Fried, Burton D
1961-01-01
The Plasma Dispersion Function: The Hilbert Transform of the Gaussian focuses on the reactions, transformations, and calculations involved in plasma dispersion function. The book first offers information on the properties of Z, including symmetry properties, values for special arguments, power series, asymptotic expansion, and differential equation characterization. The text then ponders on the applications to plasma physics. Numerical calculations on the function of Z are presented. The manuscript takes a look at table generation and accuracy wherein various methods are proposed in computin
Parameterized Hilbert-Type Integral Inequalities in the Whole Plane
2014-01-01
By the use of the way of real analysis, we estimate the weight functions and give some new Hilbert-type integral inequalities in the whole plane with nonhomogeneous kernels and multiparameters. The constant factors related to the hypergeometric function and the beta function are proved to be the best possible. We also consider the equivalent forms, the reverses, and some particular cases in the homogeneous kernels. PMID:25215314
How were the Hilbert-Einstein equations discovered?
Logunov, Anatolii A; Mestvirishvili, Mirian A; Petrov, Vladimir A [State Research Center ' Institute of High Energy Physics' , Protvino, Moscow Region (Russian Federation)
2004-06-30
The ways in which Albert Einstein and David Hilbert independently arrived at the gravitational field equations are traced. A critical analysis is presented of a number of papers in which the history of the derivation of the equations is viewed in a way that 'radically differs from the standard point of view'. The conclusions of these papers are shown to be totally unfounded. (from the history of physics)
Semilinear mixed problems on Hilbert complexes and their numerical approximation
Holst, Michael
2010-01-01
Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article [arXiv:1005.4455], we extended the Arnold-Falk-Winther framework by analyzing variational crimes (a la Strang) on Hilbert complexes. In particular, this gave a treatment of finite element exterior calculus on manifolds, generalizing techniques from surface finite element methods and recovering earlier a priori estimates for the Laplace-Beltrami operator on 2- and 3-surfaces, due to Dziuk [Lecture Notes in Math., vol. 1357 (1988), 142-155] and later Demlow [SIAM J. Numer. Anal., 47 (2009), 805-827], as special cases. In the present article, we extend the Hilbert complex framework in a second distinct direction: to the study of semilinear mixed problems. We do this, first, by introducing an operator-theoretic reformulatio...
The laboratory test rig with miniature jet engine to research aviation fuels combustion process
Gawron Bartosz; Białecki Tomasz
2015-01-01
This article presents laboratory test rig with a miniature turbojet engine (MiniJETRig – Miniature Jet Engine Test Rig), that was built in the Air Force Institute of Technology. The test rig has been developed for research and development works aimed at modelling and investigating processes and phenomena occurring in full scale jet engines. In the article construction of a test rig is described, with a brief discussion on the functionality of each of its main components. Additionally examples...
On Improving International Competitiveness of China-Made Drilling Rigs
Gong Huijuan
2009-01-01
@@ Current state of technology for China made drilling rigs With accelerated oil & gas exploration and development,and the implementation of "going out"strategy in recent years,the manufacturing of drilling equipment has entered a phase of rapid development in China.
Heat-and-pull rig for fiber taper fabrication
Ward, Jonathan M.; O'Shea, Danny G.; Shortt, Brian J.; Morrissey, Michael J.; Deasy, Kieran; Chormaic, Sile G. Nic
2006-01-01
We describe a reproducible method of fabricating adiabatic tapers with 3-4 mu m diameter. The method is based on a heat-and-pull rig, whereby a CO(2) laser is continuously scanned across a length of fiber that is being pulled synchronously. Our system relies on a CO(2) mirror mounted on a geared ste
Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations
Kirillov, Anatol N.; Sakamoto, Reiho
2009-07-01
There are two distinct approaches to the study of initial value problem of the periodic box-ball systems. One way is the rigged configuration approach due to Kuniba-Takagi-Takenouchi and another way is the 10-elimination approach due to Mada-Idzumi-Tokihiro. In this paper, we describe precisely interrelations between these two approaches.
DMPD: MDA5/RIG-I and virus recognition. [Dynamic Macrophage Pathway CSML Database
Full Text Available 18272355 MDA5/RIG-I and virus recognition. Takeuchi O, Akira S. Curr Opin Immunol. ...2008 Feb;20(1):17-22. Epub 2008 Feb 12. (.png) (.svg) (.html) (.csml) Show MDA5/RIG-I and virus recognition.... PubmedID 18272355 Title MDA5/RIG-I and virus recognition. Authors Takeuchi O, Akira S. Publication Curr Opi
朱从旭
1999-01-01
从一般形式上构造了有限维希尔伯特(Hilbert)空间q-畸变谐振子的偶相干态, 并讨论了其量子统计特性. 发现有限维希尔伯特空间的偶q-相干态与通常无限维空间的偶q-相干态或偶相干态有明显不同的压缩和反聚束特性. 前者的偶q-相干态不仅出现正交压缩, 而且出现反聚束效应.
Lu, Yun-Gang
1995-01-01
The present article is devoted to the explanation of the irreversible behavior of quantum systems as a limiting case (in a sense to be made precise) of usual quantum dynamics. One starts with a system, whose Hamiltonian has a continuous spectrum, interacting with a reservoir and studies the limits of quantities related to the whole compound system. A macroscopic equation is obtained for the limit of the compound system, which is a quantum stochastic differential equation of Poisson type on some Hilbert module (no longer a space) and whose coefficients are uniquely determined by the one-particle Hamiltonian of the original system and whose driving noises are the creation, annihilation, and number (or gauge) processes living on the Fock module over this module.
The Canonical Structure of the First-Order Einstein-Hilbert Action
McKeon, D. G. C.
The Dirac constraint formalism is used to analyze the first-order form of the Einstein-Hilbert action in d > 2 dimensions. Unlike previous treatments, this is done without eliminating fields at the outset by solving equations of motion that are independent of time derivatives when they correspond to first class constraints. As anticipated by the way in which the affine connection transforms under a diffeomorphism, not only primary and secondary but also tertiary first class constraints arise. These leave d(d-3) degrees of freedom in phase space. The gauge invariance of the action is discussed, with special attention being paid to the gauge generators of Henneaux, Teitelboim and Zanelli and of Castellani.
The Canonical Structure of the First Order Einstein-Hilbert Action
McKeon, D G C
2010-01-01
The Dirac constraint formalism is used to analyze the first order form of the Einstein-Hilbert action in d > 2 dimensions. Unlike previous treatments, this is done without eliminating fields at the outset by solving equations of motion that are independent of time derivatives when they correspond to first class constraints. As anticipated by the way in which the affine connection transforms under a diffeomorphism, not only primary and secondary but also tertiary first class constraints arise. These leave d(d - 3) degrees of freedom in phase space. The gauge invariance of the action is discussed, with special attention being paid to the gauge generators of Henneaux, Teitelboim and Zanelli and of Castellani.
Wilce, Alexander
2004-01-01
A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with incommensurable random quantities. In the case of quantum mechanics, the relevant test space, the set of orthonormal bases of a Hilbert space, carries significant topological structure. This paper inaugurates a general study of topological test spaces. Among ...
The Hilbert series of U/SU SQCD and Toeplitz determinants
Chen Yang, E-mail: ychen@imperial.ac.uk [Department of Mathematics, Imperial College London, 180 Queen' s Gates, London SW7 2BZ (United Kingdom); Mekareeya, Noppadol, E-mail: n.mekareeya07@imperial.ac.uk [Theoretical Physics Group, Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ (United Kingdom)
2011-09-21
We present a new technique for computing Hilbert series of N=1 supersymmetric QCD in four dimensions with unitary and special unitary gauge groups. We show that the Hilbert series of this theory can be written in terms of determinants of Toeplitz matrices. Applying related theorems from random matrix theory, we compute a number of exact Hilbert series as well as asymptotic formulae for large numbers of colours and flavours - many of which have not been derived before.
The G-Hilbert scheme for 1/r(1,a,r-a)
Kedzierski, Oskar
2010-01-01
Following Craw, Maclagan, Thomas and Nakamura work on Hilbert schemes for abelian groups we give an explicit description of the G-Hilbert scheme for G equal to a cyclic group of order r, acting on C^3 with weights 1,a,r-a. We describe how the combinatorial properties of the fan of G-Hilbert scheme relates to the Euclidean algorithm for b and r-b, where b is an inverse of a modulo r.
The laboratory test rig with miniature jet engine to research aviation fuels combustion process
Gawron Bartosz
2015-12-01
Full Text Available This article presents laboratory test rig with a miniature turbojet engine (MiniJETRig – Miniature Jet Engine Test Rig, that was built in the Air Force Institute of Technology. The test rig has been developed for research and development works aimed at modelling and investigating processes and phenomena occurring in full scale jet engines. In the article construction of a test rig is described, with a brief discussion on the functionality of each of its main components. Additionally examples of measurement results obtained during the realization of the initial tests have been included, presenting the capabilities of the test rig.
Visualizing long vectors of measurements by use of the Hilbert curve
Estevez-Rams, E; Fernández, B Aragón; Lora-Serrano, R
2015-01-01
The use of Hilbert curves to visualize massive vector of data is revisited following previous authors. The Hilbert curve mapping preserves locality and makes meaningful representation of the data. We call such visualization as Hilbert plots. The combination of a Hilbert plot with its Fourier transform allows to identify patterns in the underlying data sequence. The use of different granularity representation also allows to identify periodic intervals within the data. Data from different sources are presented: periodic, aperiodic, logistic map and 1/2-Ising model. A real data example from the study of heartbeat data is also discussed.
Nguyen, Thach G; Chu, Sai T; Little, Brent E; Morandotti, Roberto; Mitchell, Arnan; Moss, David J
2015-01-01
We demonstrate a photonic RF Hilbert transformer for broadband microwave in-phase and quadrature-phase generation based on an integrated frequency optical comb, generated using a nonlinear microring resonator based on a CMOS compatible, high-index contrast, doped-silica glass platform. The high quality and large frequency spacing of the comb enables filters with up to 20 taps, allowing us to demonstrate a quadrature filter with more than a 5-octave (3 dB) bandwidth and an almost uniform phase response.
Characterizing R-duality in Banach spaces
Christensen, Ole; Xiao, Xiang Chun; Zhu, Yu Can
2013-01-01
R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces.......R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces....
Distribution of cusp sections in the Hilbert modular orbifold
Arias, Samuel Estala
2011-01-01
Let K be a number field, let M be the Hilbert modular orbifold of K, and let m(q) be the probability measure uniformly supported on the cusp cross sections of M at height q. We generalize a method of Zagier and show that m(q) distributes uniformly with respect to the normalized Haar measure m on M as q tends to zero, and relate the rate by which m(q) approaches m to the Riemann hypothesis for the Dedekind zeta function of K.
Development of nanolubricant automotive air conditioning (AAC test rig
Redhwan A.A.M.
2017-01-01
Full Text Available Nanolubricant been introduced in compressor might improve the performance of automotive air conditioning system. Prior testing of the nanolubricant enhancement performance, an automotive air conditioning (AAC system test rig base on compact car has to be developed; therefore this paper presented the development process of AAC test rig. There are 15 thermocouples, 2 pressure gauges and power analyzer were assembled on the system in order to analyse its performance. The experiment was conducted with four different charged of refrigerant. The charging was based on initial weight charged. At each quantity of refrigerant charge, performance of the AAC system was evaluated by determining three important parameters which is cooling capacity, compressor work and coefficient of performance (COP. The maximum average COP is achieved at 900 RPM is 7.07. The average and maximum COP enhancement of 7.07 % and 13.34 % were achieved by applying SiO2 nanolubricant inside the compressor.
RIG-A New Management Information System for Railway Transportation
Jian-Bo Wang; Da-Ke He; Yan Xu
2009-01-01
A grid technology together with data warehouse and mediator is used to develop the railway transport management information system (TMIS), which is aiming at managing and publishing all kinds of enterprise resources among dynamic collections of such information systems with heterogeneous architectures and distributed in geography within Chinese Ministry of Railway. As one logical information integration framework and a uniform interface for accessing resources, a prototype named railway information grid (RIG) is proposed. Its main modules and the key technologies, together with its feasibility, are discussed in detail. RIG can not only provide the integral information service and the interoperability of information at the application level, but also bring us such benefits as: easy use, high efficiency, and reasonable total cost of ownership.
RESEARCH RIG FOR EXAMINATION OF PRESSURE IN HYRDODYNAMIC OIL FILM
Wojciech HORAK
2014-06-01
Full Text Available The paper presents a concept of a didactic research rig for investigation and visualization of pressure distribution in an oil film of a journal fluid friction slide bearing. The rig being presented may be used during classes on subjects associated machine design. The paper presents an idea of a specific design, using an asynchronic motor with a long shaft, on which the slide bearing assembly is fixed. The design is elastic and allows many modifications of the construction. The possible modifications are presented in the summary part of the paper. The paper also presents ideas for development of the design, either to enable measurements of additional physical values, or presentation of specific cases of slide bearings operation.
Regularization methods in Banach spaces
Schuster, Thomas; Hofmann, Bernd; Kazimierski, Kamil S
2012-01-01
Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert spaces. However, for numerous problems the reasons for using a Hilbert space setting seem to be based rather on conventions than on an approprimate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the B
Projective loop quantum gravity. I. State space
Lanéry, Suzanne; Thiemann, Thomas
2016-12-01
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In a latter work by Okolów, the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.
Nie, Li; Zhang, Ying-sheng; Dong, Wei-ren; Xiang, Li-xin; Shao, Jian-zhong
2015-01-01
The retinoic acid-inducible gene I (RIG-I) is a critical sensor for host recognition of RNA virus infection and initiation of antiviral signaling pathways in mammals. However, data on the occurrence and functions of this molecule in lower vertebrates are limited. In this study, we characterized an RIG-I homolog (DrRIG-I) from zebrafish. Structurally, this DrRIG-I shares a number of conserved functional domains/motifs with its mammalian counterparts, namely, caspase activation and recruitment domain, DExD/H box, a helicase domain, and a C-terminal domain. Functionally, stimulation with DrRIG-I CARD in zebrafish embryos significantly activated the NF-κB and IFN signaling pathways, leading to the expression of TNF-α, IL-8 and IFN-induced Mx, ISG15, and viperin. However, knockdown of TRIM25 (a pivotal activator for RIG-I receptors) significantly suppressed the induced activation of IFN signaling. Results suggested the functional conservation of RIG-I receptors in the NF-κB and IFN signaling pathways between teleosts and mammals, providing a perspective into the evolutionary history of RIG-I-mediated antiviral innate immunity.
Hilbert Statistics of Vorticity Scaling in Two-Dimensional Turbulence
Tan, H S; Meng, Jianping
2014-01-01
In this paper, the scaling property of the inverse energy cascade and forward enstrophy cascade of the vorticity filed $\\omega(x,y)$ in two-dimensional (2D) turbulence is analyzed. This is accomplished by applying a Hilbert-based technique, namely Hilbert-Huang Transform, to a vorticity field obtained from a $8192^2$ grid-points direct numerical simulation of the 2D turbulence with a forcing scale $k_f=100$ and an Ekman friction. The measured joint probability density function $p(C,k)$ of mode $C_i(x)$ of the vorticity $\\omega$ and instantaneous wavenumber $k(x)$ is separated by the forcing scale $k_f$ into two parts, which corresponding to the inverse energy cascade and the forward enstrophy cascade. It is found that all conditional pdf $p(C\\vert k)$ at given wavenumber $k$ has an exponential tail. In the inverse energy cascade, the shape of $p(C\\vert k)$ does collapse with each other, indicating a nonintermittent cascade. The measured scaling exponent $\\zeta_{\\omega}^I(q)$ is linear with the statistical ord...
Hilbert K-模上广义框架的不相交性%Disjointness of Generalized Frames in Hilbert K-Module
董芳芳
2014-01-01
The concepts of generalized frames,generalized frame transform and generalized frame opera-tor and (strong)disjointness of generalized frames in Hilbert K-modules are introduced.The necessary and sufficient conditions of disjointness of generalized frames in Hilbert K-modules are given and proven.%引入了紧算子代数模（简称Hilbert K-模）上广义框架，广义框架变换，广义框架算子，（强）不相交等概念，给出并证明了Hilbert K-模上广义框架（强）不相交的充要条件。
Intersection numbers on the relative Hilbert schemes of points on surfaces
Gholampour, Amin; Sheshmani, Artan
2015-01-01
We study certain top intersection products on the Hilbert scheme of points on a nonsingular surface relative to an effective smooth divisor. We find a formula relating these numbers to the corresponding intersection numbers on the non-relative Hilbert schemes. In particular, we obtain a relative...
A Slice Algorithm for Corners and Hilbert-Poincaré Series of Monomial Ideals
Roune, Bjarke Hammersholt
2010-01-01
We present an algorithm for computing the corners of a monomial ideal. The corners are a set of multidegrees that support the numerical information of a monomial ideal such as Betti numbers and Hilbert-Poincaré series. We show an experiment using corners to compute Hilbert-Poincaré series...
Fixed point theorems for generalized Lipschitzian semigroups in Banach spaces
Balwant Singh Thakur
1999-01-01
Full Text Available Fixed point theorems for generalized Lipschitzian semigroups are proved in p-uniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, in Lp spaces, in Hardy space Hp, and in Sobolev spaces Hk,p, for 1
Destefano, Anthony; Heerikhuisen, Jacob
2015-04-01
Fully 3D particle simulations can be a computationally and memory expensive task, especially when high resolution grid cells are required. The problem becomes further complicated when parallelization is needed. In this work we focus on computational methods to solve these difficulties. Hilbert curves are used to map the 3D particle space to the 1D contiguous memory space. This method of organization allows for minimized cache misses on the GPU as well as a sorted structure that is equivalent to an octal tree data structure. This type of sorted structure is attractive for uses in adaptive mesh implementations due to the logarithm search time. Implementations using the Message Passing Interface (MPI) library and NVIDIA's parallel computing platform CUDA will be compared, as MPI is commonly used on server nodes with many CPU's. We will also compare static grid structures with those of adaptive mesh structures. The physical test bed will be simulating heavy interstellar atoms interacting with a background plasma, the heliosphere, simulated from fully consistent coupled MHD/kinetic particle code. It is known that charge exchange is an important factor in space plasmas, specifically it modifies the structure of the heliosphere itself. We would like to thank the Alabama Supercomputer Authority for the use of their computational resources.
ENERGY-SAVING TYPE OF HYDRAULIC WORKOVER RIG AND SIMULATION FOR LOWERING PIPESTRING
Zhang Lujun; Gu Xinyi; Chen Su
2005-01-01
Research has been done on an energy-saving type of hydraulic workover rig. This rig can recover and reuse the potential energy which is released by the pipestring when lowered, and the equipped power of this rig is only one third of an ordinary rig. The structure and theory of this rig are introduced. The mathematical model of lowering the pipestring is established and a simulation analysis is conducted. Through simulation some conclusions are obtained: The lighter the pipestring is, the less velocity of lowering the pipestring is; The smaller the throttle valve path area is, the less velocity of lowering the pipestring is; Different air vessel volumes have no evident effect on the pipestring lowering velocity. The actual measure results prove that the simulation results are right. Finally, the energy-saving effect of this rig is proved by the field test results.
The powerstroke and camshaft of the RIG-I antiviral RNA detection machine.
O'Neill, Luke A J; Bowie, Andrew G
2011-10-14
The innate immune sensor RIG-I responds to infection by binding to viral double-stranded RNA (dsRNA). In this issue of Cell, Kowalinski et al. (2011) and Luo et al. (2011) reveal the structure of RIG-I, and in combination with functional analyses, they show how RIG-I recognizes viral RNA to initiate signaling and a type I interferon response.
A p -adic algorithm to compute the Hilbert class polynomial
Broeker, Reinier
2008-12-01
Classically, the Hilbert class polynomial P_{Delta }in mathbf{Z} [X] of an imaginary quadratic discriminant Delta is computed using complex analytic techniques. In 2002, Couveignes and Henocq suggested a p -adic algorithm to compute P_{Delta } . Unlike the complex analytic method, it does not suffer from problems caused by rounding errors. In this paper we give a detailed description of the algorithm in the paper by Couveignes and Henocq, and our careful study of the complexity shows that, if the Generalized Riemann Hypothesis holds true, the expected runtime of the p -adic algorithm is O(\\vertDelta \\vert(log \\vertDelta \\vert)^{8+\\varepsilon }) instead of O(\\vertDelta \\vert^{1+\\varepsilon }) . We illustrate the algorithm by computing the polynomial P_{-639} using a 643 -adic algorithm.
Universal Polynomials for Tautological Integrals on Hilbert Schemes
Rennemo, Jørgen Vold
2012-01-01
We show that tautological integrals on Hilbert schemes of points can be written in terms of universal polynomials in Chern numbers. The results hold in all dimensions, though they strengthen known results even for surfaces by allowing integrals over arbitrary "geometric" subsets (and their Chern-Schwartz-MacPherson classes). We apply this to enumerative questions, proving a generalised G\\"ottsche Conjecture for all singularity types and in all dimensions. So if L is a sufficiently ample line bundle on a smooth variety X, in a general subsystem P^d of |L| of appropriate dimension the number of hypersurfaces with given singularity types is a polynomial in the Chern numbers of (X,L). When X is a surface, we get similar results for the locus of curves with fixed "BPS spectrum" in the sense of stable pairs theory.
Tunable, nondispersive optical filter using photonic Hilbert transformation.
Bazargani, Hamed Pishvai; Fernández-Ruiz, María del Rosario; Azaña, José
2014-09-01
We propose and numerically demonstrate a new design concept for implementing nondispersive complementary (band-pass/band-reject) optical filters with a wide range of bandwidth tunability. The device consists of two photonic Hilbert transformers (PHTs) incorporated into a Michelson interferometer (MI). By controlling the central frequency of PHTs with respect to each other, both the central frequency and the spectral width of the rejection/pass bands of the filter are proved to be tunable. Bandwidth tuning from 260 MHz to 60 GHz is numerically demonstrated using two readily feasible fiber Bragg grating-based PHTs. The designed filter offers a high extinction ratio between the pass band and rejection band (>20 dB in the narrow-band filtering case) with a very sharp transition with a slope of 170 dB/GHz from rejection to pass band.
On the Hilbert-Huang Transform Theoretical Foundation
Kizhner, Semion; Blank, Karin; Huang, Norden E.
2004-01-01
The Hilbert-Huang Transform [HHT] is a novel empirical method for spectrum analysis of non-linear and non-stationary signals. The HHT is a recent development and much remains to be done to establish the theoretical foundation of the HHT algorithms. This paper develops the theoretical foundation for the convergence of the HHT sifting algorithm and it proves that the finest spectrum scale will always be the first generated by the HHT Empirical Mode Decomposition (EMD) algorithm. The theoretical foundation for cutting an extrema data points set into two parts is also developed. This then allows parallel signal processing for the HHT computationally complex sifting algorithm and its optimization in hardware.
The Hilbert Transform in Analysis of Uterine Contraction Activity
Borowska Marta
2015-12-01
Full Text Available Prevention and early diagnosis of forthcoming preterm labor is of vital importance in preventing child mortality. To date, our understanding of the coordination of uterine contractions is incomplete. Among the many methods of recording uterine contractility, electrohysterography (EHG – the recording of changes in electrical potential associated with contraction of the uterine muscle, seems to be the most important from a diagnostic point of view. There is some controversy regarding whether EHG may identify patients with a high risk of preterm delivery. There is a need to check various digital signal processing techniques to describe the recorded signals. The study of synchronization of multivariate signals is important from both a theoretical and a practical point of view. Application of the Hilbert transformation seems very promising.
Detection of earthquake induced radon precursors by Hilbert Huang Transform
Barman, Chiranjib; Ghose, Debasis; Sinha, Bikash; Deb, Argha
2016-10-01
Continuous measurement of radon-222 concentration in soil was carried out across duration of one year at a geologically faulted area having high regional heat flow to detect anomalies caused by seismic activities. The data reveals a range of periodicities present in the radon time series. To identify seismic induced radon changes we treat the time series data through various filtering methods to remove inherent periodicities. The Ensemble Empirical Mode Decomposition (EEMD) is deployed to decompose the signal into its characteristic modes. Hilbert Huang Transform (HHT) is applied for the first time on the physically significant modes obtained by EEMD to represent time-energy-frequency of the recorded soil radon time series. After removing the periodic and quasi-periodic constituents from the original time series, the simulated result shows a forceful correlation in recorded radon-222 anomalies with regional and local seismic events.
Design and Development of High-Velocity Slurry Erosion Test Rig Using CFD
Grewal, H. S.; Agrawal, Anupam; Singh, H.
2013-01-01
Slurry erosion (SE) is commonly observed in almost all kinds of components and machineries involved in fluid (liquid) transfer and delivery. During design and development phase of these components, test rigs are usually required to evaluate their performance; however, only few detailed designs of test rigs are available for SE investigations. Among the existing designs of SE test rigs, most of them belong to rotary type. In the present study, design of a new type of SE test rig has been proposed, which is simpler in construction and working. This newly designed test rig could possibly eliminate some of the limitations (velocity-concentration interdependence and lack of acceleration distance) found in the existing set-ups. Calibration of the test rig was done for jet velocity and erodent concentration. Commissioning of the rig was undertaken by evaluating the effect of operating parameters (concentration and impingement angle) on the erosion rates of aluminum and cast iron. Results show that the rig was able to capture the traditional responses of ductile and brittle erosion behaviors being observed for these materials. Repeatability of the test rig was ensured, and the results were found to be within the acceptable error limits.
Stag rig Tibetan Village: Hair Changing and Marriage
'Brug mo skyid
2010-12-01
Full Text Available Marriage in Stag rig Village, Shar lung Township, Khri ka County, Mtsho lho Tibetan Autonomous Prefecture, Mtsho sngon Province, China is described in the context of the hair dressing ritual, rules of exclusion and inclusion, the process of marriage (spouse selection, free choice marriage, arranged marriage, engagement, drinking contract liquor, bride wealth discussion, choosing a date for the wedding ritual, wedding preparations at the bride and groom's homes, the wedding ritual and banquet, marrying a groom into the bride's home, divorce, and the atmosphere surrounding the bride's arrival.
Rig safety depends on equipment, regulations, and personnel
Bates, T.R. Jr.; Tait, S. (Sedco Forex, Aberdeen (GB)); Mumford, G. (Sedco Forex, Montrouge (FR))
1990-03-05
The authors discuss how improvements that can increase rig safety can be made in equipment, regulations, and stabilized personnel levels. With regard to equipment, exposure to material handling must be reduced through automation, and well-control technology must be improved by enhanced use of computers and better systems to handle gas. According to this analysis, regulations are needed that are global in scope and have had their costs-to-benefits fully and fairly assessed. Self regulation must be used effectively throughout the industry. Job security and wages should be made adequate to maintain an experienced, motivated, and safe work force.
Test Rig Design and Presentation for a Hydraulic Yaw System
Stubkier, Søren; Pedersen, Henrik C.; Andersen, Torben Ole
2013-01-01
dynamics under real conditions. The behavior of the system is analyzed with regard to 20 years of operation. This is for example done by applying loads from different design load cases, e.g. normal turbulence, extreme turbulence and different fault scenarios on the turbine. The paper first presents...... an introduction with the current state of the art and problem description, followed by a system description, where the system is designed and dimensioned. Based on the design, results from the test rig are presented and analyzed. Finally a conclusion summing up the design, model and test results is given....
Match Rigging and the Career Concerns of Referees
Severgnini, Battista; Boeri, Tito
2011-01-01
This paper contributes to the literature on career concerns and corruption by drawing on extensive information on the performance of referees and records from Calciopoli, a judicial inquiry carried out in 2006 on corruption in the Italian football league. Unlike previous studies, we can analyse...... in detail the assignment of the referees to the most important matches, which is an important step in their career. Moreover, we can relate this choice to the performance of referees in previous matches and the evaluations they received in this context. We find that referees involved in match rigging were...
Fuel consumption of the Autark hybrid in test rig
Hoehn, B.R. [VDI (Germany); Pflaum, H.; Guttenberg, P.
2002-07-01
The Autark Hybrid of the Technical University Munich is a parallel hybrid concept for passenger cars with the aims of saving fuel and reducing exhaust gas emissions. The drive line consists of an electric engine supplied by a 120V-Ni/MH-battery and a diesel engine. Both engines use the same gearbox, a specially developed i{sup 2}-gearbox with continuously variable transmission and wide spreading. In the meantime the concept has been realised and fuel consumption is investigated in a drive line test rig. The paper presents the actual state of fuel measurements along with energetic analysis of drive line operation. (orig.)
Coherent states in the fermionic Fock space
Oeckl, Robert
2015-01-01
We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing kernel Hilbert space of continuous holomorphic functions.
Huttrer, G.W. [Geothermal Management Company, Inc., Frisco, CO (United States)
1997-11-01
This report summarizes the investigation and evaluation of several {open_quotes}compact{close_quotes} drill rigs which could be used for drilling geothermal production wells. Use of these smaller rigs would save money by reducing mobilization costs, fuel consumption, crew sizes, and environmental impact. Advantages and disadvantages of currently-manufactured rigs are identified, and desirable characteristics for the {open_quotes}ideal{close_quotes} compact rig are defined. The report includes a detailed cost estimate of a specific rig, and an evaluation of the cost/benefit ratio of using this rig. Industry contacts for further information are given.
ISAC G.; LI Jin-lu
2005-01-01
The notion of"exceptional family of elements (EFE)" plays a very important role in solving complementarity problems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this paper, by using the generalized projection defined by Alber, we extend this notion from Hilbert spaces to uniformly smooth and uniformly convex Banach spaces,and apply this extension to the study of nonlinear complementarity problems in Banach spaces.
Calibration of stereo rigs based on the backward projection process
Gu, Feifei; Zhao, Hong; Ma, Yueyang; Bu, Penghui; Zhao, Zixin
2016-08-01
High-accuracy 3D measurement based on binocular vision system is heavily dependent on the accurate calibration of two rigidly-fixed cameras. In most traditional calibration methods, stereo parameters are iteratively optimized through the forward imaging process (FIP). However, the results can only guarantee the minimal 2D pixel errors, but not the minimal 3D reconstruction errors. To address this problem, a simple method to calibrate a stereo rig based on the backward projection process (BPP) is proposed. The position of a spatial point can be determined separately from each camera by planar constraints provided by the planar pattern target. Then combined with pre-defined spatial points, intrinsic and extrinsic parameters of the stereo-rig can be optimized by minimizing the total 3D errors of both left and right cameras. An extensive performance study for the method in the presence of image noise and lens distortions is implemented. Experiments conducted on synthetic and real data demonstrate the accuracy and robustness of the proposed method.
Wei, W.; Zhang, H. S.; Schmitt, F. G.; Huang, Y. X.; Cai, X. H.; Song, Y.; Huang, X.; Zhang, H.
2017-01-01
The CASES-99 experimental data are used to analyze turbulence behaviour under a range of stable conditions using an adaptive method based on Hilbert spectral analysis. The characteristic scales of intrinsic mode functions vary between different stratifications. The second-order Hilbert marginal spectra display clear separation between fine-scale turbulence and large-scale motions. After removing the large-scale motions, the statistical characteristics of the reconstructed signals confirm the distinction of different stratifications in the fine-scale range. The correlation coefficient analyses reveal that the Hilbert spectral analysis method separates turbulence from large-scale motions in the stable boundary layer.
Yang, Ting; Liu, Li; Liao, Shasha; Tan, Sisi; Shi, Lei; Gao, Dingshan; Zhang, Xinliang
2013-01-01
Optical differentiation and optical Hilbert transformation play important roles in communications, computing, information processing and signal analysis in optical domain which offering huge bandwidth. Meanwhile, silicon-based photonic integrated circuits are preferable in all-optical signal processing due to their intrinsic advantages of low power consumption, compact footprint and ultra-high speed. In this study, we analyze the interrelation between first-order optical differentiation and optical Hilbert transformation and then experimentally demonstrate a feasible integrated scheme which can simultaneously function as first-order optical differentiation and optical Hilbert transformation based on a single microdisk resonator. This finding may motivate the development of integrated optical signal processors.
Logarithmic space and permutations
Aubert, Clément; Seiller, Thomas
2013-01-01
In a recent work, Girard proposed a new and innovative approach to computational complexity based on the proofs-as-programs correspondence. In a previous paper, the authors showed how Girard's proposal succeeds in obtaining a new characterization of co-NL languages as a set of operators acting on...... on a Hilbert Space. In this paper, we extend this work by showing that it is also possible to define a set of operators characterizing the class L of logarithmic space languages....
Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type III. The Heun Case
Ruijsenaars, Simon N M
2009-01-01
The Heun equation can be rewritten as an eigenvalue equation for an ordinary differential operator of the form $-d^2/dx^2+V(g;x)$, where the potential is an elliptic function depending on a coupling vector $g\\in{\\mathbb R}^4$. Alternatively, this operator arises from the $BC_1$ specialization of the $BC_N$ elliptic nonrelativistic Calogero-Moser system (a.k.a. the Inozemtsev system). Under suitable restrictions on the elliptic periods and on $g$, we associate to this operator a self-adjoint operator $H(g)$ on the Hilbert space ${\\mathcal H}=L^2([0,\\omega_1],dx)$, where $2\\omega_1$ is the real period of $V(g;x)$. For this association and a further analysis of $H(g)$, a certain Hilbert-Schmidt operator ${\\mathcal I}(g)$ on ${\\mathcal H}$ plays a critical role. In particular, using the intimate relation of $H(g)$ and ${\\mathcal I}(g)$, we obtain a remarkable spectral invariance: In terms of a coupling vector $c\\in{\\mathbb R}^4$ that depends linearly on $g$, the spectrum of $H(g(c))$ is invariant under arbitrary ...
Negative regulation of RIG-I-mediated antiviral signaling by TRK-fused gene (TFG) protein
Lee, Na-Rae; Shin, Han-Bo; Kim, Hye-In; Choi, Myung-Soo; Inn, Kyung-Soo, E-mail: innks@khu.ac.kr
2013-07-19
Highlights: •TRK-fused gene product (TFG) interacts with TRIM25 upon viral infection. •TFG negatively regulates RIG-I mediated antiviral signaling. •TFG depletion leads to enhanced viral replication. •TFG act downstream of MAVS. -- Abstract: RIG-I (retinoic acid inducible gene I)-mediated antiviral signaling serves as the first line of defense against viral infection. Upon detection of viral RNA, RIG-I undergoes TRIM25 (tripartite motif protein 25)-mediated K63-linked ubiquitination, leading to type I interferon (IFN) production. In this study, we demonstrate that TRK-fused gene (TFG) protein, previously identified as a TRIM25-interacting protein, binds TRIM25 upon virus infection and negatively regulates RIG-I-mediated type-I IFN signaling. RIG-I-mediated IFN production and nuclear factor (NF)-κB signaling pathways were upregulated by the suppression of TFG expression. Furthermore, vesicular stomatitis virus (VSV) replication was significantly inhibited by small inhibitory hairpin RNA (shRNA)-mediated knockdown of TFG, supporting the suppressive role of TFG in RIG-I-mediated antiviral signaling. Interestingly, suppression of TFG expression increased not only RIG-I-mediated signaling but also MAVS (mitochondrial antiviral signaling protein)-induced signaling, suggesting that TFG plays a pivotal role in negative regulation of RNA-sensing, RIG-I-like receptor (RLR) family signaling pathways.
Scherpen, J.M.A.; Kerk, B. van der; Klaassens, J.B.; Lazeroms, M.; Kan, S.Y.
1998-01-01
In this paper three control schemes for a test set-up of a magnetic bearing system for deployment rigs of solar arrays are described. The air gap of the magnet has to be controlled to a constant value independent of the deployment of the solar array. The deployment of the rig has been modeled as a
A Universal Rig for Supporting Large Hammer Drills: Reduced Injury Risk and Improved Productivity.
Rempel, David; Barr, Alan
2015-10-01
Drilling holes into concrete with heavy hammer and rock drills is one of the most physically demanding tasks performed in commercial construction and poses risks for musculoskeletal disorders, noise induced hearing loss, hand arm vibration syndrome and silicosis. The aim of this study was to (1) use a participatory process to develop a rig to support pneumatic rock drills or large electric hammer drills in order to reduce the health risks and (2) evaluate the usability of the rig. Seven prototype rigs for supporting large hammer drills were developed and modified with feedback from commercial contractors and construction workers. The final design was evaluated by laborers and electricians (N=29) who performed their usual concrete drilling with the usual method and the new rig. Subjective regional fatigue was significantly less in the neck, shoulders, hands and arms, and lower back) when using the universal rig compared to the usual manual method. Usability ratings for the rig were significantly better than the usual method on stability, control, drilling, accuracy, and vibration. Drilling time was reduced by approximately 50% with the rig. Commercial construction contractors, laborers and electricians who use large hammer drills for drilling many holes should consider using such a rig to prevent musculoskeletal disorders, fatigue, and silicosis.
An Insight into Spreadsheet User Behaviour through an Analysis of EuSpRIG Website Statistics
Croll, Grenville J
2011-01-01
The European Spreadsheet Risks Interest Group (EuSpRIG) has maintained a website almost since its inception in 2000. We present here longitudinal and cross-sectional statistics from the website log in order to shed some light upon end-user activity in the EuSpRIG domain.
Scherpen, J.M.A.; Kerk, B. van der; Klaassens, J.B.; Lazeroms, M.; Kan, S.Y.
1998-01-01
In this paper three control schemes for a test set-up of a magnetic bearing system for deployment rigs of solar arrays are described. The air gap of the magnet has to be controlled to a constant value independent of the deployment of the solar array. The deployment of the rig has been modeled as a v
A Universal Rig for Supporting Large Hammer Drills: Reduced Injury Risk and Improved Productivity
Rempel, David; Barr, Alan
2015-01-01
Drilling holes into concrete with heavy hammer and rock drills is one of the most physically demanding tasks performed in commercial construction and poses risks for musculoskeletal disorders, noise induced hearing loss, hand arm vibration syndrome and silicosis. The aim of this study was to (1) use a participatory process to develop a rig to support pneumatic rock drills or large electric hammer drills in order to reduce the health risks and (2) evaluate the usability of the rig. Seven prototype rigs for supporting large hammer drills were developed and modified with feedback from commercial contractors and construction workers. The final design was evaluated by laborers and electricians (N=29) who performed their usual concrete drilling with the usual method and the new rig. Subjective regional fatigue was significantly less in the neck, shoulders, hands and arms, and lower back) when using the universal rig compared to the usual manual method. Usability ratings for the rig were significantly better than the usual method on stability, control, drilling, accuracy, and vibration. Drilling time was reduced by approximately 50% with the rig. Commercial construction contractors, laborers and electricians who use large hammer drills for drilling many holes should consider using such a rig to prevent musculoskeletal disorders, fatigue, and silicosis. PMID:26005290
A reciprocating pin-on-plate test-rig for studying friction materials for holding brakes
Poulios, Konstantinos; Drago, Nicola; Klit, Peder
2014-01-01
-on-plate test-rig for studying the evolution of wear by monitoring the pin height reduction using Eddy-current proximity sensors is presented. Moreover, a new mechanism for recording the friction force is suggested. Apart from the design of the test-rig, friction force and wear rate measurements for two...
Matheswaran Kandasamy
2016-07-01
Full Text Available Retinoic acid inducible gene-I (RIG-I is an innate RNA sensor that recognizes the influenza A virus (IAV RNA genome and activates antiviral host responses. Here, we demonstrate that RIG-I signaling plays a crucial role in restricting IAV tropism and regulating host immune responses. Mice deficient in the RIG-I-MAVS pathway show defects in migratory dendritic cell (DC activation, viral antigen presentation, and priming of CD8+ and CD4+ T cell responses during IAV infection. These defects result in decreased frequency of polyfunctional effector T cells and lowered protection against heterologous IAV challenge. In addition, our data show that RIG-I activation is essential for protecting epithelial cells and hematopoietic cells from IAV infection. These diverse effects of RIG-I signaling are likely imparted by the actions of type I interferon (IFN, as addition of exogenous type I IFN is sufficient to overcome the defects in antigen presentation by RIG-I deficient BMDC. Moreover, the in vivo T cell defects in RIG-I deficient mice can be overcome by the activation of MDA5 -MAVS via poly I:C treatment. Taken together, these findings demonstrate that RIG-I signaling through MAVS is critical for determining the quality of polyfunctional T cell responses against IAV and for providing protection against subsequent infection from heterologous or novel pandemic IAV strains.
Kandasamy, Matheswaran; Suryawanshi, Amol; Tundup, Smanla; Perez, Jasmine T.; Schmolke, Mirco; Manicassamy, Santhakumar; Manicassamy, Balaji
2016-01-01
Retinoic acid inducible gene-I (RIG-I) is an innate RNA sensor that recognizes the influenza A virus (IAV) RNA genome and activates antiviral host responses. Here, we demonstrate that RIG-I signaling plays a crucial role in restricting IAV tropism and regulating host immune responses. Mice deficient in the RIG-I-MAVS pathway show defects in migratory dendritic cell (DC) activation, viral antigen presentation, and priming of CD8+ and CD4+ T cell responses during IAV infection. These defects result in decreased frequency of polyfunctional effector T cells and lowered protection against heterologous IAV challenge. In addition, our data show that RIG-I activation is essential for protecting epithelial cells and hematopoietic cells from IAV infection. These diverse effects of RIG-I signaling are likely imparted by the actions of type I interferon (IFN), as addition of exogenous type I IFN is sufficient to overcome the defects in antigen presentation by RIG-I deficient BMDC. Moreover, the in vivo T cell defects in RIG-I deficient mice can be overcome by the activation of MDA5 –MAVS via poly I:C treatment. Taken together, these findings demonstrate that RIG-I signaling through MAVS is critical for determining the quality of polyfunctional T cell responses against IAV and for providing protection against subsequent infection from heterologous or novel pandemic IAV strains. PMID:27438481
Scherpen, J.M.A.; Kerk, B. van der; Klaassens, J.B.; Lazeroms, M.; Kan, S.Y.
1998-01-01
In this paper three control schemes for a test set-up of a magnetic bearing system for deployment rigs of solar arrays are described. The air gap of the magnet has to be controlled to a constant value independent of the deployment of the solar array. The deployment of the rig has been modeled as a v
Design and Analysis of Tooth Impact Test Rig for Spur Gear
Ghazali, Wafiuddin Bin Md; Aziz, Ismail Ali Bin Abdul; Daing Idris, Daing Mohamad Nafiz Bin; Ismail, Nurazima Binti; Sofian, Azizul Helmi Bin
2016-02-01
This paper is about the design and analysis of a prototype of tooth impact test rig for spur gear. The test rig was fabricated and analysis was conducted to study its’ limitation and capabilities. The design of the rig is analysed to ensure that there will be no problem occurring during the test and reliable data can be obtained. From the result of the analysis, the maximum amount of load that can be applied, the factor of safety of the machine, the stresses on the test rig parts were determined. This is important in the design consideration of the test rig. The materials used for the fabrication of the test rig were also discussed and analysed. MSC Nastran Patran software was used to analyse the model, which was designed by using SolidWorks 2014 software. Based from the results, there were limitations found from the initial design and the test rig design needs to be improved in order for the test rig to operate properly.
Hilbert C*-模中g-框架的一些性质%Some Properties of g-Frames in Hilbert C*-Modules
姚喜妍
2011-01-01
本文运用算子理论方法,给出Hilbert C*-模中g-框架的一些性质并讨论g-框架的扰动性,得到g-框架的和的一些刻画.所得结果推广和改进了已有的结果.%In this paper, utilizing the method of operator theory, some properties and perturbation of g-franes in Hilbert C*-modules are discussed. some characterizations of sums of g-frames in Hilbert C*-modules are obtained. Moreover, it is shown that these results extend and improve the existing results.
Khovanskii, A G [Institute for System Analysis , Russian Academy of Sciences, Moscow (Russian Federation); Chulkov, S P [Independent University of Moscow, Moscow (Russian Federation)
2006-02-28
We consider systems of linear partial differential equations with analytic coefficients and discuss existence and uniqueness theorems for their formal and analytic solutions. Using elementary methods, we define and describe an analogue of the Hilbert polynomial for such systems.
Homborg, A.M.; Westing, E.P.M. van; Tinga, T.; Ferrari, G.M.; Zhang, X.; Wit, J.H.W. de; Mol, J.M.C.
2014-01-01
This study validates the ability of Hilbert spectra to investigate transients in an electrochemical noise signal for an aqueous corrosion inhibition process. The proposed analysis procedure involves the identification and analysis of transients in the electrochemical current noise signal. Their
Rodé's theorem on common fixed points of semigroup of nonexpansive mappings in CAT(0 spaces
Anakkamatee Watcharapong
2011-01-01
Full Text Available Abstract We extend Rodé's theorem on common fixed points of semigroups of nonexpansive mappings in Hilbert spaces to the CAT(0 space setting. 2000 Mathematics Subject Classification: 47H09; 47H10.
两参数Hardy-Hilbert不等式%Hardy-Hilbert's Inequalities With Two Parameters
徐景实
2007-01-01
In this paper, the author discusses Hardy-Hilbert's inequalities with two parameters and their variants. These are generalizations of Hardy-Hilbert's inequalities with one parameter in recent literatures.%讨论了两参数Hardy-Hilbert不等式和它们的一些变形.这些不等式推广了近年文献中的单参数Hardy-Hilbert不等式.
The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
Oblomkov, Alexei; Shende, Vivek
2012-01-01
The intersection of a complex plane curve with a small three-sphere surrounding one of its singularities is a nontrivial link. The refined punctual Hilbert schemes of the singularity parameterize subschemes supported at the singular point of fixed length and whose defining ideals have a fixed number of generators. We conjecture that the generating function of Euler characteristics of refined punctual Hilbert schemes is the HOMFLY polynomial of the link. The conjecture is verified for irreduci...
Hirzebruch χy genera of the Hilbert schemes of surfaces by localization formula
LIU; Kefeng(刘克锋); Catherine; YAN; ZHOU; Jian(周坚)
2002-01-01
We use the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula to calculate the Hirzebruch χy genus χy(S[n]), where S[n] is the Hilbert scheme of points of length n of a surface S. Combinatorial interpretation of the weights of the fixed points of the natural torus action on (C2)[n] is used. This is the first step to prove a conjectural formula about the elliptic genus of the Hilbert schemes.
Anastasi, Robert F.; Madaras, Eric I.
2005-01-01
Terahertz NDE is being examined as a method to inspect the adhesive bond-line of Space Shuttle tiles for defects. Terahertz signals are generated and detected, using optical excitation of biased semiconductors with femtosecond laser pulses. Shuttle tile samples were manufactured with defects that included repair regions unbond regions, and other conditions that occur in Shuttle structures. These samples were inspected with a commercial terahertz NDE system that scanned a tile and generated a data set of RF signals. The signals were post processed to generate C-scan type images that are typically seen in ultrasonic NDE. To improve defect visualization the Hilbert-Huang Transform, a transform that decomposes a signal into oscillating components called intrinsic mode functions, was applied to test signals identified as being in and out of the defect regions and then on a complete data set. As expected with this transform, the results showed that the decomposed low-order modes correspond to signal noise while the high-order modes correspond to low frequency oscillations in the signal and mid-order modes correspond to local signal oscillations. The local oscillations compare well with various reflection interfaces and the defect locations in the original signal.
Dynamic Investigation Test-rig on hAptics (DITA)
Cannella, F.; Scalise, L.; Olivieri, E.; Memeo, M.; Caldwell, D. G.
2013-09-01
Research on tactile sensitivity has been conducted since the last century and many devices have been proposed to study in detail this sense through experimental tests. The sense of touch is essential in every-day life of human beings, but it can also play a fundamental role for the assessment of some neurological disabilities and pathologies. In fact, the level of tactile perception can provide information on the health state of the nervous system. In this paper, authors propose the design and development of a novel test apparatus, named DITA (Dynamic Investigation Test-rig on hAptics), aiming to provide the measurement of the tactile sensitivity trough the determination of the Just Noticeable Difference (JND) curve of a subject. The paper reports the solution adopted for the system design and the results obtained on the set of experiments carried out on volunteers.
A Riemann-Hilbert Approach for the Novikov Equation
Boutet de Monvel, Anne; Shepelsky, Dmitry; Zielinski, Lech
2016-09-01
We develop the inverse scattering transform method for the Novikov equation u_t-u_{txx}+4u^2u_x=3u u_xu_{xx}+u^2u_{xxx} considered on the line xin(-∞,∞) in the case of non-zero constant background. The approach is based on the analysis of an associated Riemann-Hilbert (RH) problem, which in this case is a 3× 3 matrix problem. The structure of this RH problem shares many common features with the case of the Degasperis-Procesi (DP) equation having quadratic nonlinear terms (see [Boutet de Monvel A., Shepelsky D., Nonlinearity 26 (2013), 2081-2107, arXiv:1107.5995]) and thus the Novikov equation can be viewed as a ''modified DP equation'', in analogy with the relationship between the Korteweg-de Vries (KdV) equation and the modified Korteweg-de Vries (mKdV) equation. We present parametric formulas giving the solution of the Cauchy problem for the Novikov equation in terms of the solution of the RH problem and discuss the possibilities to use the developed formalism for further studying of the Novikov equation.
Hilbert transform based analyses on ship-rocking signals
Huang, Wei; Kang, Deyong; Chen, Zhi
2015-01-01
The ship-rocking is a crucial factor which affects the accuracy of the ocean-based flight vehicle measurement. Here we have analyzed four groups of ship-rocking time series in horizontal and vertical directions utilizing a Hilbert based method from statistical physics. Our method gives a way to construct an analytic signal on the two-dimensional plane from a one-dimensional time series. The analytic signal share the complete property of the original time series. From the analytic signal of a time series, we have found some information of the original time series which are often hidden from the view of the conventional methods. The analytic signals of interest usually evolve very smoothly on the complex plane. In addition, the phase of the analytic signal is usually moves linearly in time. From the auto-correlation and cross-correlation functions of the original signals as well as the instantaneous amplitudes and phase increments of the analytic signals we have found that the ship-rocking in horizontal directi...
2D Hilbert transform for phase retrieval of speckle fields
Gorsky, M. P.; Ryabyi, P. A.; Ivanskyi, D. I.
2016-09-01
The paper presents principal approaches to diagnosing the structure forming skeleton of the complex optical field. An analysis of optical field singularity algorithms depending on intensity discretization and image resolution has been carried out. An optimal approach is chosen, which allows to bring much closer the solution of the phase problem of localization speckle-field special points. The use of a "window" 2D Hilbert transform for reconstruction of the phase distribution of the intensity of a speckle field is proposed. It is shown that the advantage of this approach consists in the invariance of a phase map to a change of the position of the kernel of transformation and in a possibility to reconstruct the structure-forming elements of the skeleton of an optical field, including singular points and saddle points. We demonstrate the possibility to reconstruct the equi-phase lines within a narrow confidence interval, and introduce an additional algorithm for solving the phase problem for random 2D intensity distributions.
Hilbert-Curve Fractal Antenna With Radiation- Pattern Diversity
Nessel, James A.; Miranda, Felix A.; Zaman, Afroz
2007-01-01
A printed, folded, Hilbert-curve fractal microwave antenna has been designed and built to offer advantages of compactness and low mass, relative to other antennas designed for the same operating frequencies. The primary feature of the antenna is that it offers the advantage of radiation-pattern diversity without need for electrical or mechanical switching: it can radiate simultaneously in an end-fire pattern at a frequency of 2.3 GHz (which is in the S-band) and in a broadside pattern at a frequency of 16.8 GHz (which is in the Ku-band). This radiation-pattern diversity could be utilized, for example, in applications in which there were requirements for both S-band ground-to-ground communications and Ku-band ground-to-aircraft or ground-to-spacecraft communications. The lack of switching mechanisms or circuitry makes this antenna more reliable, easier, and less expensive to fabricate than it otherwise would be.
Practical implementation of Hilbert-Huang Transform algorithm
黄大吉; 赵进平; 苏纪兰
2003-01-01
Hilbert-Huang Transform (HHT) is a newly developed powerful method for nonlinearand non-stationary time series analysis. The empirical mode decomposition is the key part of HHT,while its algorithm was protected by NASA as a US patent, which limits the wide application among thescientific community. Two approaches, mirror periodic and extrema extending methods, have been de-veloped for handling the end effects of empirical mode decomposition. The implementation of the HHT isrealized in detail to widen the application. The detailed comparison of the results from two methods withthat from Huang et al. (1998, 1999), and the comparison between two methods are presented. Gener-ally, both methods reproduce faithful results as those of Huang et al. For mirror periodic method(MPM), the data are extended once forever. Ideally, it is a way for handling the end effects of theHHT, especially for the signal that has symmetric waveform. The extrema extending method (EEM)behaves as good as MPM, and it is better than MPM for the signal that has strong asymmetric wave-form. However, it has to perform extrema envelope extending in every shifting process.
Determination of fundamental asteroseismic parameters using the Hilbert transform
Kiefer, René; Herzberg, Wiebke; Roth, Markus
2015-01-01
Context. Solar-like oscillations exhibit a regular pattern of frequencies. This pattern is dominated by the small and large frequency separations between modes. The accurate determination of these parameters is of great interest, because they give information about e.g. the evolutionary state and the mass of a star. Aims. We want to develop a robust method to determine the large and small frequency separations for time series with low signal-tonoise ratio. For this purpose, we analyse a time series of the Sun from the GOLF instrument aboard SOHO and a time series of the star KIC 5184732 from the NASA Kepler satellite by employing a combination of Fourier and Hilbert transform. Methods. We use the analytic signal of filtered stellar oscillation time series to compute the signal envelope. Spectral analysis of the signal envelope then reveals frequency differences of dominant modes in the periodogram of the stellar time series. Results. With the described method the large frequency separation $\\Delta\
Pomeron Interactions from the Einstein-Hilbert Action
Iatrakis, Ioannis; Shuryak, Edward
2016-01-01
Holographic models of QCD, collectively known as AdS/QCD, have been proven useful in deriving several properties of hadrons. One particular feature well reproduced by such models is the Regge trajectories, both for mesons and glueballs. We focus on scalar and tensor glueballs, and derive an effective theory for the Pomeron by analytic continuation along the leading trajectory from the tensor glueball. It then follows that the Pomeron, as the tensor glueball itself, should possess a two-index polarization tensor, inherited from the graviton. The three-graviton interaction is deduced from the Einstein-Hilbert action. Using this structure in the cross section of double-Pomeron production of the tensor glueball, we calculate certain angular distributions of production and compare them with those from the CERN WA102 experiment. We find that the agreement is very good for the $f_2(2300)$ tensor glueball candidate. At the same time, other tensor states -- such as $f_2(1270)$ and $f'_2(1520)$ -- have completely diffe...