States in the Hilbert space formulation and in the phase space formulation of quantum mechanics
International Nuclear Information System (INIS)
Tosiek, J.; Brzykcy, P.
2013-01-01
We consider the problem of testing whether a given matrix in the Hilbert space formulation of quantum mechanics or a function considered in the phase space formulation of quantum theory represents a quantum state. We propose several practical criteria for recognising states in these two versions of quantum physics. After minor modifications, they can be applied to check positivity of any operators acting in a Hilbert space or positivity of any functions from an algebra with a ∗-product of Weyl type. -- Highlights: ► Methods of testing whether a given matrix represents a quantum state. ► The Stratonovich–Weyl correspondence on an arbitrary symplectic manifold. ► Criteria for checking whether a function on a symplectic space is a Wigner function
Nonrelativistic multichannel quantum scattering theory in a two Hilbert space formulation
International Nuclear Information System (INIS)
Chandler, C.
1977-08-01
A two-Hilbert-space form of an abstract scattering theory specifically applicable to multichannel quantum scattering problems is outlined. General physical foundations of the theory are reviewed. Further topics discussed include the invariance principle, asymptotic completeness of the wave operators, representations of the scattering operator in terms of transition operators and fundamental equations that these transition operators satisfy. Outstanding problems, including the difficulties of including Coulomb interactions in the theory, are pointed out. (D.P.)
Plymen, Roger; Robinson, Paul
1995-01-01
Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum mechanical study of electrons. In this book, the authors give a definitive account of the various Clifford algebras over a real Hilbert space and of their Fock representations. A careful consideration of the latter's transformation properties under Bogoliubov automorphisms leads to the restricted orthogonal group. From there, a study of inner Bogoliubov automorphisms enables the authors to construct infinite-dimensional spin groups. Apart from assuming a basic background in functional analysis and operator algebras, the presentation is self-contained with complete proofs, many of which offer a fresh perspective on the subject.
Open superstring field theory on the restricted Hilbert space
International Nuclear Information System (INIS)
Konopka, Sebastian; Sachs, Ivo
2016-01-01
It appears that the formulation of an action for the Ramond sector of open superstring field theory requires to either restrict the Hilbert space for the Ramond sector or to introduce auxiliary fields with picture −3/2. The purpose of this note is to clarify the relation of the restricted Hilbert space with other approaches and to formulate open superstring field theory entirely in the small Hilbert space.
Hilbert space theory of classical electrodynamics
Indian Academy of Sciences (India)
Hilbert space; Koopman–von Neumann theory; classical electrodynamics. PACS No. 03.50. ... The paper is divided into four sections. Section 2 .... construction of Sudarshan is to be contrasted with that of Koopman and von Neumann. ..... ture from KvN and [16] in this formulation is to define new momentum and coordinate.
International Nuclear Information System (INIS)
Exner, P.; Kolerov, G.I.
1980-01-01
A Hilbert space of paths, the elements of which are determined by trigonometric series, was proposed and used recently by Truman. This space is shown to consist precisely of all absolutely continuous paths ending in the origin with square-integrable derivatives
Hilbert-type inequalities for Hilbert space operators | Krnic ...
African Journals Online (AJOL)
In this paper we establish a general form of the Hilbert inequality for positive invertible operators on a Hilbert space. Special emphasis is given to such inequalities with homogeneous kernels. In some general cases the best possible constant factors are also derived. Finally, we obtain the improvement of previously deduced ...
Teleportation schemes in infinite dimensional Hilbert spaces
International Nuclear Information System (INIS)
Fichtner, Karl-Heinz; Freudenberg, Wolfgang; Ohya, Masanori
2005-01-01
The success of quantum mechanics is due to the discovery that nature is described in infinite dimension Hilbert spaces, so that it is desirable to demonstrate the quantum teleportation process in a certain infinite dimensional Hilbert space. We describe the teleportation process in an infinite dimensional Hilbert space by giving simple examples
Weaving Hilbert space fusion frames
Neyshaburi, Fahimeh Arabyani; Arefijamaal, Ali Akbar
2018-01-01
A new notion in frame theory, so called weaving frames has been recently introduced to deal with some problems in signal processing and wireless sensor networks. Also, fusion frames are an important extension of frames, used in many areas especially for wireless sensor networks. In this paper, we survey the notion of weaving Hilbert space fusion frames. This concept can be had potential applications in wireless sensor networks which require distributed processing using different fusion frames...
Frames and bases in tensor products of Hilbert spaces and Hilbert C ...
Indian Academy of Sciences (India)
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 ⊗ B -module E ⊗ F , and we get more results. For Hilbert ...
Means of Hilbert space operators
Hiai, Fumio
2003-01-01
The monograph is devoted to a systematic study of means of Hilbert space operators by a unified method based on the theory of double integral transformations and Peller's characterization of Schur multipliers. General properties on means of operators such as comparison results, norm estimates and convergence criteria are established. After some general theory, special investigations are focused on three one-parameter families of A-L-G (arithmetic-logarithmic-geometric) interpolation means, Heinz-type means and binomial means. In particular, norm continuity in the parameter is examined for such means. Some necessary technical results are collected as appendices.
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
Quantum holonomy theory and Hilbert space representations
Energy Technology Data Exchange (ETDEWEB)
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)
Rigged Hilbert spaces for chaotic dynamical systems
International Nuclear Information System (INIS)
Suchanecki, Z.; Antoniou, I.; Bandtlow, O.F.
1996-01-01
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 1996 American Institute of Physics
Quantum theory in complex Hilbert space
International Nuclear Information System (INIS)
Sharma, C.S.
1988-01-01
The theory of complexification of a real Hilbert space as developed by the author is scrutinized with the aim of explaining why quantum theory should be done in a complex Hilbert space in preference to real Hilbert space. It is suggested that, in order to describe periodic motions in stationary states of a quantum system, the mathematical object modelling a state of a system should have enough points in it to be able to describe explicit time dependence of a periodic motion without affecting the probability distributions of observables. Heuristic evidence for such an assumption comes from Dirac's theory of interaction between radiation and matter. If the assumption is adopted as a requirement on the mathematical model for a quantum system, then a real Hilbert space is ruled out in favour of a complex Hilbert space for a possible model for such a system
A constructive presentation of rigged Hilbert spaces
International Nuclear Information System (INIS)
Celeghini, Enrico
2015-01-01
We construct a rigged Hilbert space for the square integrable functions on the line L2(R) adding to the generators of the Weyl-Heisenberg algebra a new discrete operator, related to the degree of the Hermite polynomials. All together, continuous and discrete operators, constitute the generators of the projective algebra io(2). L 2 (R) and the vector space of the line R are shown to be isomorphic representations of such an algebra and, as both these representations are irreducible, all operators defined on the rigged Hilbert spaces L 2 (R) or R are shown to belong to the universal enveloping algebra of io(2). The procedure can be extended to orthogonal and pseudo-orthogonal spaces of arbitrary dimension by tensorialization.Circumventing all formal problems the paper proposes a kind of toy model, well defined from a mathematical point of view, of rigged Hilbert spaces where, in contrast with the Hilbert spaces, operators with different cardinality are allowed. (paper)
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.
Transverse entanglement migration in Hilbert space
International Nuclear Information System (INIS)
Chan, K. W.; Torres, J. P.; Eberly, J. H.
2007-01-01
We show that, although the amount of mutual entanglement of photons propagating in free space is fixed, the type of correlations between the photons that determine the entanglement can dramatically change during propagation. We show that this amounts to a migration of entanglement in Hilbert space, rather than real space. For the case of spontaneous parametric down-conversion, the migration of entanglement in transverse coordinates takes place from modulus to phase of the biphoton state and back again. We propose an experiment to observe this migration in Hilbert space and to determine the full entanglement
κ-Minkowski representations on Hilbert spaces
International Nuclear Information System (INIS)
Agostini, Alessandra
2007-01-01
The algebra of functions on κ-Minkowski noncommutative space-time is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction of integration in κ-Minkowski space-time in terms of the usual trace of operators
Spectral Theory of Operators on Hilbert Spaces
Kubrusly, Carlos S
2012-01-01
This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated. Spectral Theory of Operators on Hilbert Space is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will also be useful to working mathemat
The role of the rigged Hilbert space in quantum mechanics
International Nuclear Information System (INIS)
Madrid, Rafael de la
2005-01-01
There is compelling evidence that, when a continuous spectrum is present, the natural mathematical setting for quantum mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's braket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in quantum mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space
Reproducing kernel Hilbert spaces of Gaussian priors
Vaart, van der A.W.; Zanten, van J.H.; Clarke, B.; Ghosal, S.
2008-01-01
We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of posterior distributions based on Gaussian priors can be described
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
Vertical integration from the large Hilbert space
Erler, Theodore; Konopka, Sebastian
2017-12-01
We develop an alternative description of the procedure of vertical integration based on the observation that amplitudes can be written in BRST exact form in the large Hilbert space. We relate this approach to the description of vertical integration given by Sen and Witten.
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...
Convexity Of Inversion For Positive Operators On A Hilbert Space
International Nuclear Information System (INIS)
Sangadji
2001-01-01
This paper discusses and proves three theorems for positive invertible operators on a Hilbert space. The first theorem gives a comparison of the generalized arithmetic mean, generalized geometric mean, and generalized harmonic mean for positive invertible operators on a Hilbert space. For the second and third theorems each gives three inequalities for positive invertible operators on a Hilbert space that are mutually equivalent
Resonances, scattering theory and rigged Hilbert spaces
International Nuclear Information System (INIS)
Parravicini, G.; Gorini, V.; Sudarshan, E.C.G.
1979-01-01
The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free, in, and out eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian; the singularities of the out eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of complete sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the out eigenvectors. The free, in and out eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee-Friedrichs model. 48 references
Semiclassical propagation: Hilbert space vs. Wigner representation
Gottwald, Fabian; Ivanov, Sergei D.
2018-03-01
A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. Based on this viewpoint, the Wigner Herman-Kluk propagator is conceptually the most general one. Nonetheless, the respective semiclassical expressions for expectation values in terms of the density matrix and the Wigner function are mathematically proven here to coincide. The only remaining difference is a mere technical flexibility of the Wigner version in choosing the Gaussians' width for the underlying coherent states beyond minimal uncertainty. This flexibility is investigated numerically on prototypical potentials and it turns out to provide neither qualitative nor quantitative improvements. Given the aforementioned generality, utilizing the Wigner representation for semiclassical propagation thus leads to the same performance as employing the respective most-developed (Hilbert-space) methods for the density matrix.
Moretti, Valter; Oppio, Marco
As earlier conjectured by several authors and much later established by Solèr (relying on partial results by Piron, Maeda-Maeda and other authors), from the lattice theory point of view, Quantum Mechanics may be formulated in real, complex or quaternionic Hilbert spaces only. Stückelberg provided some physical, but not mathematically rigorous, reasons for ruling out the real Hilbert space formulation, assuming that any formulation should encompass a statement of Heisenberg principle. Focusing on this issue from another — in our opinion, deeper — viewpoint, we argue that there is a general fundamental reason why elementary quantum systems are not described in real Hilbert spaces. It is their basic symmetry group. In the first part of the paper, we consider an elementary relativistic system within Wigner’s approach defined as a locally-faithful irreducible strongly-continuous unitary representation of the Poincaré group in a real Hilbert space. We prove that, if the squared-mass operator is non-negative, the system admits a natural, Poincaré invariant and unique up to sign, complex structure which commutes with the whole algebra of observables generated by the representation itself. This complex structure leads to a physically equivalent reformulation of the theory in a complex Hilbert space. Within this complex formulation, differently from what happens in the real one, all selfadjoint operators represent observables in accordance with Solèr’s thesis, and the standard quantum version of Noether theorem may be formulated. In the second part of this work, we focus on the physical hypotheses adopted to define a quantum elementary relativistic system relaxing them on the one hand, and making our model physically more general on the other hand. We use a physically more accurate notion of irreducibility regarding the algebra of observables only, we describe the symmetries in terms of automorphisms of the restricted lattice of elementary propositions of the
Frames and bases in tensor products of Hilbert spaces and Hilbert C ...
Indian Academy of Sciences (India)
[14] Heil C E and Walnut D F, Continuous and discrete wavelet transforms, SIAM Review 31. (1989) 628–666. [15] Khosravi A and Asgari M S, Frames and bases in tensor product of Hilbert spaces, Int. J. Math. 4(6) (2003) 527–538. [16] Lance E C, Hilbert C. ∗. -modules – a toolkit for operator algebraists, London Math. Soc.
Unstable quantum states and rigged Hilbert spaces
International Nuclear Information System (INIS)
Gorini, V.; Parravicini, G.
1978-10-01
Rigged Hilbert space techniques are applied to the quantum mechanical treatment of unstable states in nonrelativistic scattering theory. A method is discussed which is based on representations of decay amplitudes in terms of expansions over complete sets of generalized eigenvectors of the interacting Hamiltonian, corresponding to complex eigenvalues. These expansions contain both a discrete and a continuum contribution. The former corresponds to eigenvalues located at the second sheet poles of the S matrix, and yields the exponential terms in the survival amplitude. The latter arises from generalized eigenvectors associated to complex eigenvalues on background contours in the complex plane, and gives the corrections to the exponential law. 27 references
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.
Eigenfunction expansions and scattering theory in rigged Hilbert spaces
Energy Technology Data Exchange (ETDEWEB)
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.
Multipliers for continuous frames in Hilbert spaces
International Nuclear Information System (INIS)
Balazs, P; Bayer, D; Rahimi, A
2012-01-01
In this paper, we examine the general theory of continuous frame multipliers in Hilbert space. These operators are a generalization of the widely used notion of (discrete) frame multipliers. Well-known examples include anti-Wick operators, STFT multipliers or Calderón–Toeplitz operators. Due to the possible peculiarities of the underlying measure spaces, continuous frames do not behave quite as their discrete counterparts. Nonetheless, many results similar to the discrete case are proven for continuous frame multipliers as well, for instance compactness and Schatten-class properties. Furthermore, the concepts of controlled and weighted frames are transferred to the continuous setting. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)
A note on tensor fields in Hilbert spaces
Directory of Open Access Journals (Sweden)
LEONARDO BILIOTTI
2002-06-01
Full Text Available We discuss and extend to infinite dimensional Hilbert spaces a well-known tensoriality criterion for linear endomorphisms of the space of smooth vector fields in n.Discutimos e estendemos para espaços de Hilbert um critério de tensorialidade para endomorfismos do espaço dos campos vetoriais em Rpot(n.
ON STRONG AND WEAK CONVERGENCE IN n-HILBERT SPACES
Directory of Open Access Journals (Sweden)
Agus L. Soenjaya
2014-03-01
Full Text Available We discuss the concepts of strong and weak convergence in n-Hilbert spaces and study their properties. Some examples are given to illustrate the concepts. In particular, we prove an analogue of Banach-Saks-Mazur theorem and Radon-Riesz property in the case of n-Hilbert space.
Hilbert space, Poincare dodecahedron and golden mean transfiniteness
International Nuclear Information System (INIS)
El Naschie, M.S.
2007-01-01
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
Isometric Reflection Vectors and Characterizations of Hilbert Spaces
Directory of Open Access Journals (Sweden)
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.
Introduction to Hilbert space and the theory of spectral multiplicity
Halmos, Paul R
2017-01-01
Concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. 1957 edition.
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
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 $\\mathbb{S}^2$.
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...
Hilbert space representation of the SOq(N)-covariant Heisenberg algebra
International Nuclear Information System (INIS)
Hebecker, A.; Weich, W.
1993-01-01
The differential calculus on SO q (N)-covariant quantum planes is rewritten in polar co-ordinates. Thus a Hilbert space formulation of q-deformed quantum mechanics can be developed particularly suitable for spherically symmetric potentials. The simplest case of a free particle is solved showing a discrete energy spectrum. (orig.)
Diagonalization of Bounded Linear Operators on Separable Quaternionic Hilbert Space
International Nuclear Information System (INIS)
Feng Youling; Cao, Yang; Wang Haijun
2012-01-01
By using the representation of its complex-conjugate pairs, we have investigated the diagonalization of a bounded linear operator on separable infinite-dimensional right quaternionic Hilbert space. The sufficient condition for diagonalizability of quaternionic operators is derived. The result is applied to anti-Hermitian operators, which is essential for solving Schroedinger equation in quaternionic quantum mechanics.
On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space
Directory of Open Access Journals (Sweden)
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.
Ad Hoc Physical Hilbert Spaces in Quantum Mechanics
Czech Academy of Sciences Publication Activity Database
Fernandez, F. M.; Garcia, J.; Semorádová, Iveta; Znojil, Miloslav
2015-01-01
Roč. 54, č. 12 (2015), s. 4187-4203 ISSN 0020-7748 Institutional support: RVO:61389005 Keywords : quantum mechanics * physical Hilbert spaces * ad hoc inner product * singular potentials regularized * low lying energies Subject RIV: BE - Theoretical Physics Impact factor: 1.041, year: 2015
Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment
International Nuclear Information System (INIS)
El Naschie, M.S.
2006-01-01
On the one hand, a rigorous mathematical formulation of quantum mechanics requires the introduction of a Hilbert space and as we move to the second quantization, a Fock space. On the other hand, the Cantorian E-infinity approach to quantum physics was developed largely without any direct reference to the afore mentioned mathematical spaces. In the present work we utilize some novel reinterpretations of basic E (∞) Cantorian spacetime relations in terms of the Hilbert space of quantum mechanics. Proceeding in this way, we gain a better understanding of the physico-mathematical structure of quantum spacetime which is at the heart of the paradoxical and non-intuitive outcome of the famous quantum two-slit gedanken experiment
A Hilbert space structure on Banach algebras
International Nuclear Information System (INIS)
Mohammad, N.; Thaheem, A.B.
1988-08-01
In this note we define an inner product on ''reduced'' Banach *-algebras via a measure on the set of positive functionals. It is shown here that the resultant inner product space is a topological algebra and also a completeness condition is obtained. (author). 9 refs
The Hilbert Series of the One Instanton Moduli Space
Benvenuti, Sergio; Mekareeya, Noppadol; 10.1007
2010-01-01
The moduli space of k G-instantons on R^4 for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1) dimensional gauge theories have N = 2 supersymmetry and can be represented by quiver diagrams. The F and D term equations coincide with the ADHM construction. The Hilbert series of the moduli spaces of one instanton for classical gauge groups is easy to compute and turns out to take a particularly simple form which is previously unknown. This allows for a G invariant character expansion and hence easily generalisable for exceptional gauge groups, where an ADHM construction is not known. The conjectures for exceptional groups are further checked using some new techniques like sewing relations in Hilbert Series. This is applied to Argyres-Seiberg dualities.
The method of moments and nested Hilbert spaces in quantum mechanics
International Nuclear Information System (INIS)
Adeniyi Bangudu, E.
1980-08-01
It is shown how the structures of a nested Hilbert space Hsub(I), associated with a given Hilbert space Hsub(O), may be used to simplify our understanding of the effects of parameters, whose values have to be chosen rather than determined variationally, in the method of moments. The result, as applied to non-relativistic quartic oscillator and helium atom, is to associate the parameters with sequences of Hilbert spaces, while the error of the method of moments relative to the variational method corresponds to a nesting operator of the nested Hilbert space. Difficulties hindering similar interpretations in terms of rigged Hilbert space structures are highlighted. (author)
Adaptive Learning in Cartesian Product of Reproducing Kernel Hilbert Spaces
Yukawa, Masahiro
2014-01-01
We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed to contain multiple components such as (i) linear and nonlinear components, (ii) high- and low- frequency components etc. In this case, the use of multiple RKHSs permits a compact representation of multicomponent functions. The proposed algorithm is where t...
Classical and quantum contents of solvable game theory on Hilbert space
International Nuclear Information System (INIS)
Cheon, Taksu; Tsutsui, Izumi
2006-01-01
A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be equivalent to a family of classical games supplemented by quantum interference. Our formulation gives a clear perspective to understand why and how quantum strategies outmaneuver classical strategies. It also reveals novel aspects of quantum games such as the stone-scissor-paper phase sub-game and the fluctuation-induced moderation
Aveiro method in reproducing kernel Hilbert spaces under complete dictionary
Mai, Weixiong; Qian, Tao
2017-12-01
Aveiro Method is a sparse representation method in reproducing kernel Hilbert spaces (RKHS) that gives orthogonal projections in linear combinations of reproducing kernels over uniqueness sets. It, however, suffers from determination of uniqueness sets in the underlying RKHS. In fact, in general spaces, uniqueness sets are not easy to be identified, let alone the convergence speed aspect with Aveiro Method. To avoid those difficulties we propose an anew Aveiro Method based on a dictionary and the matching pursuit idea. What we do, in fact, are more: The new Aveiro method will be in relation to the recently proposed, the so called Pre-Orthogonal Greedy Algorithm (P-OGA) involving completion of a given dictionary. The new method is called Aveiro Method Under Complete Dictionary (AMUCD). The complete dictionary consists of all directional derivatives of the underlying reproducing kernels. We show that, under the boundary vanishing condition, bring available for the classical Hardy and Paley-Wiener spaces, the complete dictionary enables an efficient expansion of any given element in the Hilbert space. The proposed method reveals new and advanced aspects in both the Aveiro Method and the greedy algorithm.
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
Geometry of quantum dynamics in infinite-dimensional Hilbert space
Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana
2018-04-01
We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.
On convergence of nuclear and correlation operators in Hilbert space
International Nuclear Information System (INIS)
Kubrusly, C.S.
1985-01-01
The convergence of sequences of nuclear operators on a separable Hilbert space is studied. Emphasis is given to trace-norm convergence, which is a basic property in stochastic systems theory. Obviously trace-norm convergence implies uniform convergence. The central theme of the paper focus the opposite way, by investigating when convergence in a weaker topology turns out to imply convergence in a stronger topology. The analysis carried out here is exhaustive in the following sense. All possible implications within a selected set of asymptotic properties for sequences of nuclear operators are established. The special case of correlation operators is also considered in detail. (Author) [pt
Perturbation for Frames for a Subspace of a Hilbert Space
DEFF Research Database (Denmark)
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...... similarresult for frames in the case where the gap between the subspaces$\\overline{span} \\{f_i \\}$ and $\\overline{span} \\{ g_i \\}$ is small enough. We give a geometric interpretation of the result....
Explicit signal to noise ratio in reproducing kernel Hilbert spaces
DEFF Research Database (Denmark)
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...
Directory of Open Access Journals (Sweden)
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.
An Hilbert space approach for a class of arbitrage free implied volatilities models
Brace, A.; Fabbri, G.; Goldys, B.
2007-01-01
We present an Hilbert space formulation for a set of implied volatility models introduced in \\cite{BraceGoldys01} in which the authors studied conditions for a family of European call options, varying the maturing time and the strike price $T$ an $K$, to be arbitrage free. The arbitrage free conditions give a system of stochastic PDEs for the evolution of the implied volatility surface ${\\hat\\sigma}_t(T,K)$. We will focus on the family obtained fixing a strike $K$ and varying $T$. In order to...
Friedrichs systems in a Hilbert space framework: Solvability and multiplicity
Antonić, N.; Erceg, M.; Michelangeli, A.
2017-12-01
The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antonić and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide sufficient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.
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...
Hamiltonian and physical Hilbert space in polymer quantum mechanics
International Nuclear Information System (INIS)
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A
2007-01-01
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 (HW) 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
International Nuclear Information System (INIS)
Luks, A.; Perinova, V.
1993-01-01
A suitable ordering of phase exponential operators has been compared with the antinormal ordering of the annihilation and creation operators of a single mode optical field. The extended Wigner function for number and phase in the enlarged Hilbert space has been used for the derivation of the Wigner function for number and phase in the original Hilbert space. (orig.)
International Nuclear Information System (INIS)
Bach, A.
1981-01-01
A representation of quantum mechanics in terms of classical probability theory by means of integration in Hilbert space is discussed. This formal hidden-variables representation is analysed in the context of impossibility proofs concerning hidden-variables theories. The structural analogy of this formulation of quantum theory with classical statistical mechanics is used to elucidate the difference between classical mechanics and quantum mechanics. (author)
The physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
International Nuclear Information System (INIS)
Ding You; Rovelli, Carlo
2010-01-01
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit). We also generalize the definition of the volume operator in the spin-foam model to the Lorentzian signature and show that it matches the one of loop quantum gravity, as in the Euclidean case.
Continuous Slice Functional Calculus in Quaternionic Hilbert Spaces
Ghiloni, Riccardo; Moretti, Valter; Perotti, Alessandro
2013-04-01
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic C*-algebras and to define, on each of these C*-algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.
Characterizing sequential isomorphisms on Hilbert-space effect algebras
International Nuclear Information System (INIS)
Hou Jinchuan; He Kan; Qi Xiaofei
2010-01-01
Let * be any sequential product on the Hilbert-space effect algebra E(H) with dim H≥2, and Φ:E(H)→E(H) be a bijective map. We show that if Φ satisfies Φ(A*B) = Φ(A)*Φ(B) for A,B element of E(H), then there is either a unitary or an anti-unitary operator U such that Φ(A) = UAU† for every A element of E(H). Let g:[0,1]→{λ|λ element of C, |λ|=0 or 1} be a Borel function satisfying g(0) = 0, g(1) = 1 and let us define a binary operation lozenge g on E(H) by A lozenge g B = A 1/2 g(A)Bg(A)†A 1/2 , where T† denotes the conjugate of the operator T. We also show that a bijective map Φ:E(H)→E(H) satisfies Φ(A lozenge g B) = Φ(A) lozenge g Φ(B) for A,B element of E(H) if and only if there is either a unitary or an anti-unitary operator U such that Φ(A) = UAU† for every A element of E(H).
Wiener-Hopf operators on spaces of functions on R+ with values in a Hilbert space
Petkova, Violeta
2006-01-01
A Wiener-Hopf operator on a Banach space of functions on R+ is a bounded operator T such that P^+S_{-a}TS_a=T, for every positive a, where S_a is the operator of translation by a. We obtain a representation theorem for the Wiener-Hopf operators on a large class of functions on R+ with values in a separable Hilbert space.
Hilbert spaces contractively included in the Hardy space of the bidisk
Alpay, D.; Bolotnikov, V.; Dijksma, A.; Sadosky, C.
We study the reproducing kernel Hilbert spaces h(D-2,S) with kernels of the form I-S(z(1),z(2)>)S(w(1),w(2))*/(1-z(1)w(1)*) (1-z(2)w(2)*) where S(z(1),z(2)) is a Schur function of two variables z(1),z(2)is an element of D. They are analogs of the spaces h(D,S) with reproducing kernel
Generalized Polar Decompositions for Closed Operators in Hilbert Spaces and Some Applications
Gesztesy, Fritz; Malamud, Mark; Mitrea, Marius; Naboko, Serguei
2008-01-01
We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and m-sectorial operators.
Positive-definite functions and unitary representations of locally compact groups in a Hilbert space
International Nuclear Information System (INIS)
Gali, I.M.; Okb el-Bab, A.S.; Hassan, H.M.
1977-08-01
It is proved that the necessary and sufficient condition for the existence of an integral representation of a group of unitary operators in a Hilbert space is that it is positive-definite and continuous in some topology
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.
On the minimizers of calculus of variations problems in Hilbert spaces
Gomes, Diogo A.; Nurbekyan, Levon
2014-01-01
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.
An introduction of gauge field by the Lie-isotopic lifting of the Hilbert space
International Nuclear Information System (INIS)
Nishioka, M.
1984-01-01
It is introduced the gauge field by the Lie-isotopic lifting of the Hilbert space. Our method is different from other's in that the commutator between the isotropic element and the generators of the Lie algebra does not vanish in our case, but vanishes in other cases. Our method uses the Lie-isotopic lifting of the Hilbert space, but others do not use it
Oscillatory integrals on Hilbert spaces and Schroedinger equation with magnetic fields
International Nuclear Information System (INIS)
Albeverio, S.; Brzezniak, Z.
1994-01-01
We extend the theory of oscillatory integrals on Hilbert spaces (the mathematical version of ''Feynman path integrals'') to cover more general integrable functions, preserving the property of the integrals to have converging finite dimensional approximations. We give an application to the representation of solutions of the time dependent Schroedinger equation with a scalar and a magnetic potential by oscillatory integrals on Hilbert spaces. A relation with Ramer's functional in the corresponding probabilistic setting is found. (orig.)
Soft and hard classification by reproducing kernel Hilbert space methods.
Wahba, Grace
2002-12-24
Reproducing kernel Hilbert space (RKHS) methods provide a unified context for solving a wide variety of statistical modelling and function estimation problems. We consider two such problems: We are given a training set [yi, ti, i = 1, em leader, n], where yi is the response for the ith subject, and ti is a vector of attributes for this subject. The value of y(i) is a label that indicates which category it came from. For the first problem, we wish to build a model from the training set that assigns to each t in an attribute domain of interest an estimate of the probability pj(t) that a (future) subject with attribute vector t is in category j. The second problem is in some sense less ambitious; it is to build a model that assigns to each t a label, which classifies a future subject with that t into one of the categories or possibly "none of the above." The approach to the first of these two problems discussed here is a special case of what is known as penalized likelihood estimation. The approach to the second problem is known as the support vector machine. We also note some alternate but closely related approaches to the second problem. These approaches are all obtained as solutions to optimization problems in RKHS. Many other problems, in particular the solution of ill-posed inverse problems, can be obtained as solutions to optimization problems in RKHS and are mentioned in passing. We caution the reader that although a large literature exists in all of these topics, in this inaugural article we are selectively highlighting work of the author, former students, and other collaborators.
Parallel magnetic resonance imaging as approximation in a reproducing kernel Hilbert space
International Nuclear Information System (INIS)
Athalye, Vivek; Lustig, Michael; Martin Uecker
2015-01-01
In magnetic resonance imaging 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. To understand and design k-space sampling patterns, a theoretical framework is needed to analyze how well arbitrary sampling patterns reconstruct unsampled k-space using receive coil information. 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 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 image-domain g-factor noise analysis to both noise amplification and approximation errors in k-space. This is demonstrated with numerical examples. (paper)
Alpay, Daniel
2015-01-01
This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.
Some means inequalities for positive operators in Hilbert spaces
Directory of Open Access Journals (Sweden)
Jin Liang
2017-01-01
Full Text Available Abstract In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate geometric mean and show that the weighted multivariate operator geometric mean possess several attractive properties and means inequalities.
Yuji, NAKAWAKI; Azuma, TANAKA; Kazuhiko, OZAKI; Division of Physics and Mathematics, Faculty of Engineering Setsunan University; Junior College of Osaka Institute of Technology; Faculty of General Education, Osaka Institute of Technology
1994-01-01
Gauge Equivalence of the A_3=0 (axial) gauge to the Coulomb gauge is directly verified in QED. For that purpose a pair of conjugate zero-norm fields are introduced. This enables us to construct a canonical formulation in the axial gauge embedded in the indefinite metric Hilbert space in such a way that the Feynman rules are not altered. In the indefinite metric Hilbert space we can implement a gauge transformation, which otherwise has to be carried out only by hand, as main parts of a canonic...
Space Inside a Liquid Sphere Transforms into De Sitter Space by Hilbert Radius
Rabounski, Dmitri; Borissova, Larissa
2010-04-01
Consider space inside a sphere of incompressible liquid, and space surrounding a mass-point. Metrics of the spaces were deduced in 1916 by Karl Schwarzschild. 1) Our calculation shows that a liquid sphere can be in the state of gravitational collapse (g00 = 0) only if its mass and radius are close to those of the Universe (M = 8.7x10^55 g, a = 1.3x10^28 cm). However if the same mass is presented as a mass-point, the radius of collapse rg (Hilbert radius) is many orders lesser: g00 = 0 realizes in a mass-point's space by other conditions. 2) We considered a liquid sphere whose radius meets, formally, the Hilbert radius of a mass-point bearing the same mass: a = rg, however the liquid sphere is not a collapser (see above). We show that in this case the metric of the liquid sphere's internal space can be represented as de Sitter's space metric, wherein λ = 3/a^2 > 0: physical vacuum (due to the λ-term) is the same as the field of an ideal liquid where ρ0 0 (the mirror world liquid). The gravitational redshift inside the sphere is produced by the non-Newtonian force of repulsion (which is due to the λ-term, λ = 3/a^2 > 0); it is also calculated.
Asymptotic behaviour of unbounded trajectories for some non-autonomous systems in a Hilbert space
International Nuclear Information System (INIS)
Djafari Rouhani, B.
1990-07-01
The asymptotic behaviour of unbounded trajectories for non expansive mappings in a real Hilbert space and the extension to more general Banach spaces and to nonlinear contraction semi-group have been studied by many authors. In this paper we study the asymptotic behaviour of unbounded trajectories for a quasi non-autonomous dissipative systems. 26 refs
Frames in super Hilbert modules
Directory of Open Access Journals (Sweden)
Mehdi Rashidi-Kouchi
2018-01-01
Full Text Available In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.
A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces
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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.
Two New Iterative Methods for a Countable Family of Nonexpansive Mappings in Hilbert Spaces
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Hu Changsong
2010-01-01
Full Text Available We consider two new iterative methods for a countable family of nonexpansive mappings in Hilbert spaces. We proved that the proposed algorithms strongly converge to a common fixed point of a countable family of nonexpansive mappings which solves the corresponding variational inequality. Our results improve and extend the corresponding ones announced by many others.
Weighted Traffic Equilibrium Problem in Non Pivot Hilbert Spaces with Long Term Memory
International Nuclear Information System (INIS)
Giuffre, Sofia; Pia, Stephane
2010-01-01
In the paper we consider a weighted traffic equilibrium problem in a non-pivot Hilbert space and prove the equivalence between a weighted Wardrop condition and a variational inequality with long term memory. As an application we show, using recent results of the Senseable Laboratory at MIT, how wireless devices can be used to optimize the traffic equilibrium problem.
Tensor algebra over Hilbert space: Field theory in classical phase space
International Nuclear Information System (INIS)
Matos Neto, A.; Vianna, J.D.M.
1984-01-01
It is shown using tensor algebras, namely Symmetric and Grassmann algebras over Hilbert Space that it is possible to introduce field operators, associated to the Liouville equation of classical statistical mechanics, which are characterized by commutation (for Symmetric) and anticommutation (for Grassmann) rules. The procedure here presented shows by construction that many-particle classical systems admit an algebraic structure similar to that of quantum field theory. It is considered explicitly the case of n-particle systems interacting with an external potential. A new derivation of Schoenberg's result about the equivalence between his field theory in classical phase space and the usual classical statistical mechanics is obtained as a consequence of the algebraic structure of the theory as introduced by our method. (Author) [pt
A simple proof to an extension of a theorem of A. Pazy in Hilbert space
International Nuclear Information System (INIS)
Djafari Rouhani, B.
1990-08-01
We prove that if (x n ) n≥0 is a non expansive sequence in a Hilbert space H, the sequence ( n x n ) n≥1 converges strongly in H to the element of minimum norm in the closed convex hull of the sequence (x n+1 -x n ) n≥0 . This result was previously proved; the proof we give here is even much simpler and can be extended to a Banach space. 29 refs
Estimates of solutions of certain classes of second-order differential equations in a Hilbert space
International Nuclear Information System (INIS)
Artamonov, N V
2003-01-01
Linear second-order differential equations of the form u''(t)+(B+iD)u'(t)+(T+iS)u(t)=0 in a Hilbert space are studied. Under certain conditions on the (generally speaking, unbounded) operators T, S, B and D the correct solubility of the equation in the 'energy' space is proved and best possible (in the general case) estimates of the solutions on the half-axis are obtained
Relativistic resonances as non-orthogonal states in Hilbert space
Blum, W
2003-01-01
We analyze the energy-momentum properties of relativistic short-lived particles with the result that they are characterized by two 4-vectors: in addition to the familiar energy-momentum vector (timelike) there is an energy-momentum 'spread vector' (spacelike). The wave functions in space and time for unstable particles are constructed. For the relativistic properties of unstable states we refer to Wigner's method of Poincare group representations that are induced by representations of the space-time translation and rotation groups. If stable particles, unstable particles and resonances are treated as elementary objects that are not fundamentally different one has to take into account that they will not generally be orthogonal to each other in their state space. The scalar product between a stable and an unstable state with otherwise identical properties is calculated in a particular Lorentz frame. The spin of an unstable particle is not infinitely sharp but has a 'spin spread' giving rise to 'spin neighbors'....
Alternative structures and bi-Hamiltonian systems on a Hilbert space
International Nuclear Information System (INIS)
Marmo, G; Scolarici, G; Simoni, A; Ventriglia, F
2005-01-01
We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian structures in generic relative position. We provide a few necessary and sufficient conditions for two Hermitian structures to be in generic relative position to better illustrate the relevance of this notion. The group of bi-unitary transformations is considered in both the generic and the non-generic case. Finally, we generalize the analysis to real Hilbert spaces and extend to infinite dimensions results already available in the framework of finite-dimensional linear bi-Hamiltonian systems
Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space
Cao, ChunJun; Carroll, Sean M.
2018-04-01
We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.
Controlled G-Frames and Their G-Multipliers in Hilbert spaces
Rahimi, Asghar; Fereydooni, Abolhassan
2012-01-01
Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are operators that combine (frame-like) analysis, a multiplication with a fixed sequence (called the symbol) and synthesis. Weighted and controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator Also g-frames are the most popular generalization of frames that include almost all of the frame extens...
Response to the Comment by G. Emch on projective group representations in quaternionic Hilbert space
International Nuclear Information System (INIS)
Adler, S.L.
1996-01-01
We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embeddings, and leads to a detailed theory of quaternionic, as well as complex, projective group representations. copyright 1996 American Institute of Physics
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 constructed via perturbation theory. An alternative bound is derived for the rich class of Gabor frames, by using the Walnut representation of the frame operator to estimate the deviation from equality in...
Limit distribution function of inhomogeneities in regions with random boundary in the Hilbert space
International Nuclear Information System (INIS)
Rasulova, M.Yu.; Tashpulatov, S.M.
2004-10-01
The interaction of charged particle systems with a membrane consisting of nonhomogeneities which are randomly distributed by the same law in the vicinity of appropriate sites of a planax crystal lattice is studied. A system of equations for the self-consistent potential U 1 (x,ξ 0 ,..., ξ N ,...) and the density of induced charges σ(x,ξ 0 ,...,ξ N ,...) is solved on Hilbert space. (author)
INFORMATIVE ENERGY METRIC FOR SIMILARITY MEASURE IN REPRODUCING KERNEL HILBERT SPACES
Directory of Open Access Journals (Sweden)
Songhua Liu
2012-02-01
Full Text Available In this paper, information energy metric (IEM is obtained by similarity computing for high-dimensional samples in a reproducing kernel Hilbert space (RKHS. Firstly, similar/dissimilar subsets and their corresponding informative energy functions are defined. Secondly, IEM is proposed for similarity measure of those subsets, which converts the non-metric distances into metric ones. Finally, applications of this metric is introduced, such as classification problems. Experimental results validate the effectiveness of the proposed method.
Quantum limits to information about states for finite dimensional Hilbert space
International Nuclear Information System (INIS)
Jones, K.R.W.
1990-01-01
A refined bound for the correlation information of an N-trial apparatus is developed via an heuristic argument for Hilbert spaces of arbitrary finite dimensionality. Conditional upon the proof of an easily motivated inequality it was possible to find the optimal apparatus for large ensemble quantum Inference, thereby solving the asymptotic optimal state determination problem. In this way an alternative inferential uncertainty principle, is defined which is then contrasted with the usual Heisenberg uncertainty principle. 6 refs
Covariant loops and strings in a positive definite Hilbert space
International Nuclear Information System (INIS)
Rohrlich, F.
1977-01-01
Relativistic loops and strings are defined in the conventional way as solutions of a one-dimensional wave equation with certain boundary conditions and satisfying the orthogonal gauge conditions. Conventional pseudo-Cartesian co-ordinates (rather than null-plane co-ordinates) are used. The creation and annihilation operator four-vector αsub(μ)sup(+) and αsub(m) are required to be spacelike (orthogonal to the total momentum Psup(μ), so that the resulting Fock space is positive definite. This requirements is shown to be mathematically consistent with Poincare' invariance and to impose no additional physical constraints on the system. It can be implemented in a canonical realization of the Poincare' algebra as a condition on a state vectors, or in a noncanonical realization as an operator equation, as is done here. The space is further restricted by the Virasoro conditions to a physical subspace PHI which is of course also positive definite. In this way there arises no critical-dimension problem and Poincare' invariance holds also in 3+1 dimensions. The energy and spin spectra are the same as usual, leading to linear Regge trajectories, except that there are no tachyons and no zero mass states. The leading Regge trajectory has negative intercept
Directory of Open Access Journals (Sweden)
George Isac
2004-01-01
Full Text Available In the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical systems in infinite dimensional Hilbert space. We show that this development is possible if we use the viable solutions of differential inclusions. We use also pseudomonotone operators.
Effective realistic interactions for low momentum Hilbert spaces
International Nuclear Information System (INIS)
Weber, Dennis
2012-01-01
Realistic nucleon-nucleon potentials are an essential ingredient of modern microscopic many-body calculations. These potentials can be represented in two different ways: operator representation or matrix element representation. In operator representation the potential is represented by a set of quantum mechanical operators while in matrix element representation it is defined by the matrix elements in a given basis. Many modern potentials are constructed directly in matrix element representation. While the matrix element representation can be calculated from the operator representation, the determination of the operator representation from the matrix elements is more difficult. Some methods to solve the nuclear many-body problem, such as Fermionic Molecular Dynamics (FMD) or the Green's Function Monte Carlo (GFMC) method, however require explicitly the operator representation of the potential, as they do not work in a fixed many-body basis. It is therefore desirable to derive an operator representation also for the interactions given by matrix elements. In this work a method is presented which allows the derivation of an approximate operator representation starting from the momentum space partial wave matrix elements of the interaction. For that purpose an ansatz for the operator representation is chosen. The parameters in the ansatz are determined by a fit to the partial wave matrix elements. Since a perfect reproduction of the matrix elements in general cannot be achieved with a finite number of operators and the quality of the results depends on the choice of the ansatz, the obtained operator representation is tested in nuclear many-body calculations and the results are compared with those from the initial interaction matrix elements. For the calculation of the nucleon-nucleon scattering phase shifts and the deuteron properties a computer code written within this work is used. For larger nuclei the No Core Shell Model (NCSM) and FMD are applied. The described
The kinematical Hilbert space of loop quantum gravity from BF theories
International Nuclear Information System (INIS)
Cianfrani, Francesco
2011-01-01
In this work, it is demonstrated how the kinematical Hilbert space of loop quantum gravity (LQG) can be inferred from the configuration space of BF theories via the imposition of the Hamiltonian constraints. In particular, it is outlined how the projection to the representations associated with Ashtekar-Barbero connections provides the correct procedure to implement second-class constraints and the corresponding nontrivial induced symplectic structure. Then, the reduction to SU(2) invariant intertwiners is analyzed and the properties of LQG states under Lorentz transformations are discussed.
Quantum computation via local control theory: Direct sum vs. direct product Hilbert spaces
International Nuclear Information System (INIS)
Sklarz, Shlomo E.; Tannor, David J.
2006-01-01
The central objective in any quantum computation is the creation of a desired unitary transformation; the mapping that this unitary transformation produces between the input and output states is identified with the computation. In [S.E. Sklarz, D.J. Tannor, arXiv:quant-ph/0404081 (submitted to PRA) (2004)] it was shown that local control theory can be used to calculate fields that will produce such a desired unitary transformation. In contrast with previous strategies for quantum computing based on optimal control theory, the local control scheme maintains the system within the computational subspace at intermediate times, thereby avoiding unwanted decay processes. In [S.E. Sklarz et al.], the structure of the Hilbert space had a direct sum structure with respect to the computational register and the mediating states. In this paper, we extend the formalism to the important case of a direct product Hilbert space. The final equations for the control algorithm for the two cases are remarkably similar in structure, despite the fact that the derivations are completely different and that in one case the dynamics is in a Hilbert space and in the other case the dynamics is in a Liouville space. As shown in [S.E. Sklarz et al.], the direct sum implementation leads to a computational mechanism based on virtual transitions, and can be viewed as an extension of the principles of Stimulated Raman Adiabatic Passage from state manipulation to evolution operator manipulation. The direct product implementation developed here leads to the intriguing concept of virtual entanglement - computation that exploits second-order transitions that pass through entangled states but that leaves the subsystems nearly separable at all intermediate times. Finally, we speculate on a connection between the algorithm developed here and the concept of decoherence free subspaces
A Riemann-Hilbert formulation for the finite temperature Hubbard model
Energy Technology Data Exchange (ETDEWEB)
Cavaglià, Andrea [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); Cornagliotto, Martina [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); DESY Hamburg, Theory Group,Notkestrasse 85, D-22607 Hamburg (Germany); Mattelliano, Massimo; Tateo, Roberto [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy)
2015-06-03
Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by Jüttner, Klümper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.
Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space.
Stępień, Grzegorz
2018-03-17
The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems-interior and exterior orientation of sensors-to a common, known in both systems, point. Each of the systems is translated along its axis (the systems have common origins) and at the same time the angular relative orientation of both coordinate systems is constant. The translation of both coordinate systems is defined by the spatial norm determining the length of vectors in the new Hilbert type space. As such, the displacement of two relative oblique orthogonal systems is reduced to zero. This makes it possible to directly calculate the rotation matrix of the sensor. The next and final step is the return translation of the system along an already known track. The method can be used for big rotation angles. The method was verified in laboratory conditions for the test data set and measurement data (field data). The accuracy of the results in the laboratory test is on the level of 10 -6 of the input data. This confirmed the correctness of the assumed calculation method. The method is a further development of the author's 2017 Total Free Station (TFS) transformation to several centroids in Hilbert type space. This is the reason why the method is called Multi-Centroid Isometric Transformation-MCIT. MCIT is very fast and enables, by reducing to zero the translation of two relative oblique orthogonal coordinate systems, direct calculation of the exterior orientation of the sensors.
Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space
Directory of Open Access Journals (Sweden)
Grzegorz Stępień
2018-03-01
Full Text Available The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems—interior and exterior orientation of sensors—to a common, known in both systems, point. Each of the systems is translated along its axis (the systems have common origins and at the same time the angular relative orientation of both coordinate systems is constant. The translation of both coordinate systems is defined by the spatial norm determining the length of vectors in the new Hilbert type space. As such, the displacement of two relative oblique orthogonal systems is reduced to zero. This makes it possible to directly calculate the rotation matrix of the sensor. The next and final step is the return translation of the system along an already known track. The method can be used for big rotation angles. The method was verified in laboratory conditions for the test data set and measurement data (field data. The accuracy of the results in the laboratory test is on the level of 10−6 of the input data. This confirmed the correctness of the assumed calculation method. The method is a further development of the author’s 2017 Total Free Station (TFS transformation to several centroids in Hilbert type space. This is the reason why the method is called Multi-Centroid Isometric Transformation—MCIT. MCIT is very fast and enables, by reducing to zero the translation of two relative oblique orthogonal coordinate systems, direct calculation of the exterior orientation of the sensors.
Construction of rigged Hilbert spaces to describe resonances and virtual states
International Nuclear Information System (INIS)
Gadella, M.
1983-01-01
In the present communication we present a mathematical formalism for the description of resonances and virtual states. We start by constructing rigged Hilbert spaces of Hardy class functions restricted to the positive half of the real line. Then resonances and virtual states can be written as generalized eigenvectors of the total Hamiltonian. We also define time evolution on functionals. We see that the time evolution group U(t) splits into two semigroups, one for t > 0 and the other for t < 0, hence showing the irreversibility of the decaying process
Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces
Directory of Open Access Journals (Sweden)
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.
Construction of rigged Hilbert spaces to describe resonances and virtual states
International Nuclear Information System (INIS)
Gadella, M.
1984-01-01
In the present communication we present a mathematical formalism for the description of resonances and virtual states. We start by constructing rigged Hilbert spaces of Hardy class functions restricted to the positive half of the real line. Then resonances and virtual states can be written as generalized eigenvectors of the total Hamiltonian. We also define time evolution on functionals. We see that the time evolution group U(t) splits into two semigroups, one for t>0 and the other for t<0, hence showing the irreversibility of the decaying process. (orig.)
On knottings in the physical Hilbert space of LQG as given by the EPRL model
International Nuclear Information System (INIS)
Bahr, Benjamin
2011-01-01
We consider the EPRL spin foam amplitude for arbitrary embedded two-complexes. Choosing a definition of the face- and edge amplitudes which lead to spin foam amplitudes invariant under trivial subdivisions, we investigate invariance properties of the amplitude under consistent deformations, which are deformations of the embedded two-complex where faces are allowed to pass through each other in a controlled way. Using this surprising invariance, we are able to show that the physical Hilbert space, as defined by the sum over all spin foams, contains no information about knotting classes of graphs anymore.
Recipes for stable linear embeddings from Hilbert spaces to R^m
Puy, Gilles; Davies, Michael; Gribonval, Remi
2017-01-01
We consider the problem of constructing a linear map from a Hilbert space H (possibly infinite dimensional) to Rm that satisfies a restricted isometry property (RIP) on an arbitrary signal model, i.e., a subset of H. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map satisfies a general RIP with high probability. We also describe a generic technique ...
Recipes for stable linear embeddings from Hilbert spaces to R^m
Puy, Gilles; Davies, Mike; Gribonval, Rémi
2015-01-01
We consider the problem of constructing a linear map from a Hilbert space $\\mathcal{H}$ (possibly infinite dimensional) to $\\mathbb{R}^m$ that satisfies a restricted isometry property (RIP) on an arbitrary signal model $\\mathcal{S} \\subset \\mathcal{H}$. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map satisfies a general RIP on $\\mathcal{S}$ with h...
International Nuclear Information System (INIS)
Schroer, Bert; FU-Berlin
2012-02-01
Massive quantum matter of prescribed spin permits infinitely many possibilities of covariantization in terms of spinorial (undotted/dotted) pointlike fields, whereas massless nite helicity representations lead to large gap in this spinorial spectrum which for s=1 excludes vector potentials. Since the nonexistence of such pointlike generators is the result of a deep structural clash between modular localization and the Hilbert space setting of QT, there are two ways out: gauge theory which sacrifices the Hilbert space and keeps the pointlike formalism and the use of string like potentials which allows to preserve the Hilbert space. The latter setting contains also string-localized charge-carrying operators whereas the gauge theoretic formulation is limited to point-like generated observables. This description also gives a much better insight into the Higgs mechanism which leads to a revival of the more physical 'Schwinger-Higgs' screening idea. The new formalism is not limited to m=0, s=1, it leads to renormalizable inter- actions in the sense of power-counting for all s in massless representations. The existence of string like vector potentials is preempted by the Aharonov-Bohm effect in QFT; it is well-known that the use of pointlike vector potentials in Stokes theorem would with lead to wrong results. Their use in Maxwell's equations is known to lead to zero Maxwell charge. The role of string-localization in the problem behind the observed invisibility and confinement of gluons and quarks leads to new questions and problems. (author)
The Schrödinger–Robinson inequality from stochastic analysis on a complex Hilbert space
International Nuclear Information System (INIS)
Khrennikov, Andrei
2013-01-01
We explored the stochastic analysis on a complex Hilbert space to show that one of the cornerstones of quantum mechanics (QM), namely Heisenberg's uncertainty relation, can be derived in the classical probabilistic framework. We created a new mathematical representation of quantum averages: as averages with respect to classical random fields. The existence of a classical stochastic model matching with Heisenberg's uncertainty relation makes the connection between classical and quantum probabilistic models essentially closer. In real physical situations, random fields are valued in the L 2 -space. Hence, although we model QM and not QFT, the classical systems under consideration have an infinite number of degrees of freedom. And in our modeling, infinite-dimensional stochastic analysis is the basic mathematical tool. (comment)
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...
International Nuclear Information System (INIS)
Khrennikov, A.
2005-01-01
We constructed the representation of contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function can be considered as Hilbert space projection of realistic dynamics in a pre space. The basic condition for representing the pre space-dynamics is the law of statistical conservation of energy-conservation of probabilities. The construction of the dynamical representation is an important step in the development of contextual statistical viewpoint of quantum processes. But the contextual statistical model is essentially more general than the quantum one. Therefore in general the Hilbert space projection of the pre space dynamics can be nonlinear and even irreversible (but it is always unitary). There were found conditions of linearity and reversibility of the Hilbert space dynamical projection. We also found conditions for the conventional Schrodinger dynamics (including time-dependent Hamiltonians). We remark that in general even the Schrodinger dynamics is based just on the statistical conservation of energy; for individual systems the law of conservation of energy can be violated (at least in our theoretical model)
3D Hilbert Space Filling Curves in 3D City Modeling for Faster Spatial Queries
DEFF Research Database (Denmark)
Ujang, Uznir; Antón Castro, Francesc/François; Azri, Suhaibah
2014-01-01
The advantages of three dimensional (3D) city models can be seen in various applications including photogrammetry, urban and regional planning, computer games, etc. They expand the visualization and analysis capabilities of Geographic Information Systems on cities, and they can be developed using...... 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...... objects. In this research, the authors propose an opponent data constellation technique of space-filling curves (3D Hilbert curves) for 3D city model data representation. Unlike previous methods, that try to project 3D or n-dimensional data down to 2D or 3D using Principal Component Analysis (PCA...
Ito, Kazufumi
1987-01-01
The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.
Regularization in Hilbert space under unbounded operators and general source conditions
International Nuclear Information System (INIS)
Hofmann, Bernd; Mathé, Peter; Von Weizsäcker, Heinrich
2009-01-01
The authors study ill-posed equations with unbounded operators in Hilbert space. This setup has important applications, but only a few theoretical studies are available. First, the question is addressed and answered whether every element satisfies some general source condition with respect to a given self-adjoint unbounded operator. This generalizes a previous result from Mathé and Hofmann (2008 Inverse Problems 24 015009). The analysis then proceeds to error bounds for regularization, emphasizing some specific points for regularization under unbounded operators. The study finally reviews two examples within the light of the present study, as these are fractional differentiation and some Cauchy problems for the Helmholtz equation, both studied previously and in more detail by U Tautenhahn and co-authors
Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces
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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.
A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces
Energy Technology Data Exchange (ETDEWEB)
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.
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...
International Nuclear Information System (INIS)
Gessner, W.; Ernst, V.
1980-01-01
The indefinite metric space O/sub M/ of the covariant form of the quantized Maxwell field M is analyzed in some detail. S/sub M/ contains not only the pre-Hilbert space X 0 of states of transverse photons which occurs in the Gupta--Bleuler formalism of the free M, but a whole rosette of continuously many, isomorphic, complete, pre-Hilbert spaces L/sup q/ disjunct up to the zero element o of S/sub M/. The L/sup q/ are the maximal subspaces of S/sub M/ which allow the usual statistical interpretation. Each L/sup q/ corresponds uniquely to one square integrable, spatial distribution j/sup o/(x) of the total charge Q=0. If M is in any state from L/sup q/, the bare charge j 0 (x) appears to be inseparably dressed by the quantum equivalent of its proper, classical Coulomb field E(x). The vacuum occurs only in the state space L 0 of the free Maxwell field. Each L/sup q/ contains a secondary rosette of continuously many, up to o disjunct, isomorphic Hilbert spaces H/sub g//sup q/ related to different electromagnetic gauges. The space H/sub o//sup q/, which corresponds to the Coulomb gauge within the Lorentz gauge, plays a physically distinguished role in that only it leads to the usual concept of energy. If M is in any state from H/sub g//sup q/, the bare 4-current j 0 (x), j(x), where j(x) is any square integrable, transverse current density in space, is endowed with its proper 4-potential which depends on the chosen gauge, and with its proper, gauge independent, Coulomb--Oersted field E(x), B(x). However, these fields exist only in the sense of quantum mechanical expectation values equipped with the corresponding field fluctuations. So they are basically different from classical electromagnetic fields
Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces
International Nuclear Information System (INIS)
Höhn, Philipp A.
2014-01-01
A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in the quantum theory, an according formalism for constrained variational discrete systems is constructed. While this paper focuses on global evolution moves and, for simplicity, restricts to flat configuration spaces R N , a Paper II [P. A. Höhn, “Quantization of systems with temporally varying discretization. II. Local evolution moves,” J. Math. Phys., e-print http://arxiv.org/abs/arXiv:1401.7731 [gr-qc].] discusses local evolution moves. In order to link the covariant and canonical picture, the dynamics of the quantum states is generated by propagators which satisfy the canonical constraints and are constructed using the action and group averaging projectors. This projector formalism offers a systematic method for tracing and regularizing divergences in the resulting state sums. Non-trivial coarse graining evolution moves lead to non-unitary, and thus irreversible, projections of physical Hilbert spaces and Dirac observables such that these concepts become evolution move dependent on temporally varying discretizations. The formalism is illustrated in a toy model mimicking a “creation from nothing.” Subtleties arising when applying such a formalism to quantum gravity models are discussed
A differential equation for Lerch's transcendent and associated symmetric operators in Hilbert space
International Nuclear Information System (INIS)
Kaplitskii, V M
2014-01-01
The function Ψ(x,y,s)=e iy Φ(−e 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 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
State-Space Formulation for Circuit Analysis
Martinez-Marin, T.
2010-01-01
This paper presents a new state-space approach for temporal analysis of electrical circuits. The method systematically obtains the state-space formulation of nondegenerate linear networks without using concepts of topology. It employs nodal/mesh systematic analysis to reduce the number of undesired variables. This approach helps students to…
Directory of Open Access Journals (Sweden)
Zhou Yinying
2014-01-01
Full Text Available We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009, Min and Chang (2012, Plubtieng and Punpaeng (2007, S. Takahashi and W. Takahashi (2007, Tada and Takahashi (2007, Gang and Changsong (2009, Ying (2013, Y. Yao and J. C. Yao (2007, and Yong-Cho and Kang (2012.
International Nuclear Information System (INIS)
Gallego-Castillo, Cristobal; Bessa, Ricardo; Cavalcante, Laura; Lopez-Garcia, Oscar
2016-01-01
Wind power probabilistic forecast is being used as input in several decision-making problems, such as stochastic unit commitment, operating reserve setting and electricity market bidding. This work introduces a new on-line quantile regression model based on the Reproducing Kernel Hilbert Space (RKHS) framework. Its application to the field of wind power forecasting involves a discussion on the choice of the bias term of the quantile models, and the consideration of the operational framework in order to mimic real conditions. Benchmark against linear and splines quantile regression models was performed for a real case study during a 18 months period. Model parameter selection was based on k-fold crossvalidation. Results showed a noticeable improvement in terms of calibration, a key criterion for the wind power industry. Modest improvements in terms of Continuous Ranked Probability Score (CRPS) were also observed for prediction horizons between 6 and 20 h ahead. - Highlights: • New online quantile regression model based on the Reproducing Kernel Hilbert Space. • First application to operational probabilistic wind power forecasting. • Modest improvements of CRPS for prediction horizons between 6 and 20 h ahead. • Noticeable improvements in terms of Calibration due to online learning.
International Nuclear Information System (INIS)
Arik, M.
1991-01-01
It is shown that the differential calculus of Wess and Zumino for the quantum hyperplane is intimately related to the q-difference operator acting on the n-dimensional complex space C n . An explicit transformation relates the variables and the q-difference operators on C n to the variables and the quantum derivatives on the quantum hyperplane. For real values of the quantum parameter q, the consideration of the variables and the derivatives as hermitean conjugates yields a quantum deformation of the Bargmann-Segal Hilbert space of analytic functions on C n . Physically such a system can be interpreted as the quantum deformation of the n dimensional harmonic oscillator invariant under the unitary quantum group U q (n) with energy eigenvalues proportional to the basic integers. Finally, a construction of the variables and quantum derivatives on the quantum hyperplane in terms of variables and ordinary derivatives on C n is presented. (orig.)
Directory of Open Access Journals (Sweden)
Kan Li
2018-04-01
Full Text Available This paper presents a novel real-time dynamic framework for quantifying time-series structure in spoken words using spikes. Audio signals are converted into multi-channel spike trains using a biologically-inspired leaky integrate-and-fire (LIF spike generator. These spike trains are mapped into a function space of infinite dimension, i.e., a Reproducing Kernel Hilbert Space (RKHS using point-process kernels, where a state-space model learns the dynamics of the multidimensional spike input using gradient descent learning. This kernelized recurrent system is very parsimonious and achieves the necessary memory depth via feedback of its internal states when trained discriminatively, utilizing the full context of the phoneme sequence. A main advantage of modeling nonlinear dynamics using state-space trajectories in the RKHS is that it imposes no restriction on the relationship between the exogenous input and its internal state. We are free to choose the input representation with an appropriate kernel, and changing the kernel does not impact the system nor the learning algorithm. Moreover, we show that this novel framework can outperform both traditional hidden Markov model (HMM speech processing as well as neuromorphic implementations based on spiking neural network (SNN, yielding accurate and ultra-low power word spotters. As a proof of concept, we demonstrate its capabilities using the benchmark TI-46 digit corpus for isolated-word automatic speech recognition (ASR or keyword spotting. Compared to HMM using Mel-frequency cepstral coefficient (MFCC front-end without time-derivatives, our MFCC-KAARMA offered improved performance. For spike-train front-end, spike-KAARMA also outperformed state-of-the-art SNN solutions. Furthermore, compared to MFCCs, spike trains provided enhanced noise robustness in certain low signal-to-noise ratio (SNR regime.
Li, Kan; Príncipe, José C
2018-01-01
This paper presents a novel real-time dynamic framework for quantifying time-series structure in spoken words using spikes. Audio signals are converted into multi-channel spike trains using a biologically-inspired leaky integrate-and-fire (LIF) spike generator. These spike trains are mapped into a function space of infinite dimension, i.e., a Reproducing Kernel Hilbert Space (RKHS) using point-process kernels, where a state-space model learns the dynamics of the multidimensional spike input using gradient descent learning. This kernelized recurrent system is very parsimonious and achieves the necessary memory depth via feedback of its internal states when trained discriminatively, utilizing the full context of the phoneme sequence. A main advantage of modeling nonlinear dynamics using state-space trajectories in the RKHS is that it imposes no restriction on the relationship between the exogenous input and its internal state. We are free to choose the input representation with an appropriate kernel, and changing the kernel does not impact the system nor the learning algorithm. Moreover, we show that this novel framework can outperform both traditional hidden Markov model (HMM) speech processing as well as neuromorphic implementations based on spiking neural network (SNN), yielding accurate and ultra-low power word spotters. As a proof of concept, we demonstrate its capabilities using the benchmark TI-46 digit corpus for isolated-word automatic speech recognition (ASR) or keyword spotting. Compared to HMM using Mel-frequency cepstral coefficient (MFCC) front-end without time-derivatives, our MFCC-KAARMA offered improved performance. For spike-train front-end, spike-KAARMA also outperformed state-of-the-art SNN solutions. Furthermore, compared to MFCCs, spike trains provided enhanced noise robustness in certain low signal-to-noise ratio (SNR) regime.
Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces
International Nuclear Information System (INIS)
Khrennikov, Andrei
2010-01-01
One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical random fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.
Coherent states on Hilbert modules
International Nuclear Information System (INIS)
Ali, S Twareque; Bhattacharyya, T; Roy, S S
2011-01-01
We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.
International Nuclear Information System (INIS)
Hermann, M.R.; Langhoff, P.W.
1983-01-01
Explicit Hilbert-space techniques are reported for construction of the discrete and continuum Schroedinger states required in atomic and molecular photoexcitation and/or photoionization studies. These developments extend and clarify previously described moment-theory methods for determinations of photoabsorption cross sections from discrete basis-set calculations to include explicit construction of underlying wave functions. The appropriate Stieltjes-Tchebycheff excitation and ionization functions of nth order are defined as Radau-type eigenstates of an appropriate operator in an n-term Cauchy-Lanczos basis. The energies of these states are the Radau quadrature points of the photoabsorption cross section, and their (reciprocal) norms provide the corresponding quadrature weights. Although finite-order Stieltjes-Tchebycheff functions are L 2 integrable, and do not have asymptotic spatial tails in the continuous spectrum, the Radau quadrature weights nevertheless provide information for normalization in the conventional Dirac delta-function sense. Since one Radau point can be placed anywhere in the spectrum, appropriately normalized convergent approximations to any of the discrete or continuum Schroedinger states are obtained from the development. Connections with matrix partitioning methods are established, demonstrating that nth-order Stieltjes-Tchebycheff functions are optical-potential solutions of the matrix Schroedinger equation in the full Cauchy-Lanczos basis
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.
Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems
International Nuclear Information System (INIS)
Barbu, Viorel; Marinelli, Carlo
2008-01-01
We study the existence theory for parabolic variational inequalities in weighted L 2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L 2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coefficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs
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...
N-body quantum scattering theory in two Hilbert spaces. VII. Real-energy limits
International Nuclear Information System (INIS)
Chandler, C.; Gibson, A.G.
1994-01-01
A study is made of the real-energy limits of approximate solutions of the Chandler--Gibson equations, as well as the real-energy limits of the approximate equations themselves. It is proved that (1) the approximate time-independent transition operator T π (z) and an auxiliary operator M π (z), when restricted to finite energy intervals, are trace class operators and have limits in trace norm for almost all values of the real energy; (2) the basic dynamical equation that determines the operator M π (z), when restricted to the space of trace class operators, has a real-energy limit in trace norm for almost all values of the real energy; (3) the real-energy limit of M π (z) is a solution of the real-energy limit equation; (4) the diagonal (on-shell) elements of the kernels of the real-energy limit of T π (z) and of all solutions of the real-energy limit equation exactly equal the on-shell transition operator, implying that the real-energy limit equation uniquely determines the physical transition amplitude; and (5) a sequence of approximate on-shell transition operators converges strongly to the exact on-shell transition operator. These mathematically rigorous results are believed to be the most general of their type for nonrelativistic N-body quantum scattering theories
Directory of Open Access Journals (Sweden)
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
International Nuclear Information System (INIS)
Loubenets, Elena R.
2015-01-01
We prove the existence for each Hilbert space of the two new quasi hidden variable (qHV) models, statistically noncontextual and context-invariant, reproducing all the von Neumann joint probabilities via non-negative values of real-valued measures and all the quantum product expectations—via the qHV (classical-like) average of the product of the corresponding random variables. In a context-invariant model, a quantum observable X can be represented by a variety of random variables satisfying the functional condition required in quantum foundations but each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. The proved existence of this model negates the general opinion that, in terms of random variables, the Hilbert space description of all the joint von Neumann measurements for dimH≥3 can be reproduced only contextually. The existence of a statistically noncontextual qHV model, in particular, implies that every N-partite quantum state admits a local quasi hidden variable model introduced in Loubenets [J. Math. Phys. 53, 022201 (2012)]. The new results of the present paper point also to the generality of the quasi-classical probability model proposed in Loubenets [J. Phys. A: Math. Theor. 45, 185306 (2012)
Compact Hilbert Curve Index Algorithm Based on Gray Code
Directory of Open Access Journals (Sweden)
CAO Xuefeng
2016-12-01
Full Text Available Hilbert curve has best clustering in various kinds of space filling curves, and has been used as an important tools in discrete global grid spatial index design field. But there are lots of redundancies in the standard Hilbert curve index when the data set has large differences between dimensions. In this paper, the construction features of Hilbert curve is analyzed based on Gray code, and then the compact Hilbert curve index algorithm is put forward, in which the redundancy problem has been avoided while Hilbert curve clustering preserved. Finally, experiment results shows that the compact Hilbert curve index outperforms the standard Hilbert index, their 1 computational complexity is nearly equivalent, but the real data set test shows the coding time and storage space decrease 40%, the speedup ratio of sorting speed is nearly 4.3.
Direct formulation of the supersonic acoustic intensity in space domain
DEFF Research Database (Denmark)
Fernandez Grande, Efren; Jacobsen, Finn; Leclre, Quentin
2012-01-01
into the far field. To date, its calculation has been formulated in the wave number domain, filtering out the evanescent waves outside the radiation circle and reconstructing the acoustic field with only the propagating waves. In this study, the supersonic intensity is calculated directly in space domain......This paper proposes and examines a direct formulation in space domain of the so-called supersonic acoustic intensity. This quantity differs from the usual (active) intensity by excluding the circulating energy in the near-field of the source, providing a map of the acoustic energy that is radiated...... by means of a two-dimensional convolution between the acoustic field and a spatial filter mask that corresponds to the space domain representation of the radiation circle. Therefore, the acoustic field that propagates effectively to the far field is calculated via direct filtering in space domain...
Remarks on the formulation of quantum mechanics on noncommutative phase spaces
International Nuclear Information System (INIS)
Muthukumar, Balasundaram
2007-01-01
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry
Manifestly T-dual formulation of AdS space
International Nuclear Information System (INIS)
Hatsuda, Machiko; Kamimura, Kiyoshi; Siegel, Warren
2017-01-01
We present a manifestly T-dual formulation of curved spaces such as an AdS space. For group manifolds related by the orthogonal vielbein fields the three form H=dB in the doubled space is universal at least locally. We construct an affine nondegenerate doubled bosonic AdS algebra to define the AdS space with the Ramond-Ramond flux. The non-zero commutator of the left and right momenta leads to that the left momentum is in an AdS space while the right momentum is in a dS space. Dimensional reduction constraints and the physical AdS algebra are shown to preserve all the doubled coordinates.
Manifestly T-dual formulation of AdS space
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Machiko [Physics Division, Faculty of Medicine, Juntendo University,Chiba 270-1695 (Japan); KEK Theory Center, High Energy Accelerator Research Organization,Tsukuba, Ibaraki 305-0801 (Japan); Kamimura, Kiyoshi [Physics Division, Faculty of Medicine, Juntendo University,Chiba 270-1695 (Japan); Siegel, Warren [C.N. Yang Institute for Theoretical Physics, Stony Brook University,Stony Brook, NY 11794-3840 (United States)
2017-05-12
We present a manifestly T-dual formulation of curved spaces such as an AdS space. For group manifolds related by the orthogonal vielbein fields the three form H=dB in the doubled space is universal at least locally. We construct an affine nondegenerate doubled bosonic AdS algebra to define the AdS space with the Ramond-Ramond flux. The non-zero commutator of the left and right momenta leads to that the left momentum is in an AdS space while the right momentum is in a dS space. Dimensional reduction constraints and the physical AdS algebra are shown to preserve all the doubled coordinates.
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.
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Guenaydin, M.
1979-05-01
Quadratic Jordan formulation of quantum mechanics in terms of Jordan triple product is presented. This formulation extends to the case of octonionic quantum mechanics for which no Hilbert space formulation exists. Using ternary algebraic techniques we then five the constructions of the derivation, structure and Tits-Koecher (Moebius) algebras of Jordan superalgebras. (orig.) [de
A General State-Space Formulation for Online Scheduling
Directory of Open Access Journals (Sweden)
Dhruv Gupta
2017-11-01
Full Text Available We present a generalized state-space model formulation particularly motivated by an online scheduling perspective, which allows modeling (1 task-delays and unit breakdowns; (2 fractional delays and unit downtimes, when using discrete-time grid; (3 variable batch-sizes; (4 robust scheduling through the use of conservative yield estimates and processing times; (5 feedback on task-yield estimates before the task finishes; (6 task termination during its execution; (7 post-production storage of material in unit; and (8 unit capacity degradation and maintenance. Through these proposed generalizations, we enable a natural way to handle routinely encountered disturbances and a rich set of corresponding counter-decisions. Thereby, greatly simplifying and extending the possible application of mathematical programming based online scheduling solutions to diverse application settings. Finally, we demonstrate the effectiveness of this model on a case study from the field of bio-manufacturing.
Quantum mechanics in Hilbert space
Prugovecki, Eduard
1981-01-01
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
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...
Functional Analysis: Entering Hilbert Space
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
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...
Hilbert schemes of points on some classes surface singularities
Gyenge, Ádám
2016-01-01
We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C^2/G], respectively the singular quotient surface C^2/G, where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition of the (equivariant) Hilbert scheme of the orbifold into affine space strata indexed by a certain combinatorial set, the set of Young walls. The generating series of Euler characteristics of Hilbert schemes of points of the singular surface of type A or D is computed in...
Lectures on Hilbert schemes of points on surfaces
Nakajima, Hiraku
1999-01-01
This beautifully written book deals with one shining example: the Hilbert schemes of points on algebraic surfaces ... The topics are carefully and tastefully chosen ... The young person will profit from reading this book. --Mathematical Reviews The Hilbert scheme of a surface X describes collections of n (not necessarily distinct) points on X. More precisely, it is the moduli space for 0-dimensional subschemes of X of length n. Recently it was realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory--even theoretical physics. The discussion in the book reflects this feature of Hilbert schemes. One example of the modern, broader interest in the subject is a construction of the representation of the infinite-dimensional Heisenberg algebra, i.e., Fock space. This representation has been studied extensively in the literature in connection with affine Lie algebras, conformal field...
A SIMPLIFIED FORMULATION OF SPACE-ENERGY CELL THEORY
Energy Technology Data Exchange (ETDEWEB)
Cady, K. B.; MacVean, C. R.
1963-11-15
A simple formulation of polyenergetic thermal utilization theory for heterogeneous lattices is proposed. The main ideas are those of Leslie, who postulated an infinite moderator region with a fictitious, energy dependent absorption which includes all heterogeneous properties of the lattice, and those of Amouyal, Benoist, and Horowitz who postulated absorption rates in terms of fuel and moderator escape probabilities. Simple approximations to energy dependent escape probabilities are discussed and lattice spectra are calculated for several light water lattices. (auth)
Foundations of phase-space quantum mechanics
International Nuclear Information System (INIS)
Guz, W.
1984-01-01
In the present paper a general concept of a phase-space representation of the ordinary Hilbert-space quantum theory is formulated, and then, by using some elementary facts of functional analysis, several equivalent forms of that concept are analyzed. Several important physical examples are presented in Section 3 of the paper. (author)
Hydrogen atom in the phase-space formulation of quantum mechanics
International Nuclear Information System (INIS)
Gracia-Bondia, J.M.
1984-01-01
Using a coordinate transformation which regularizes the classical Kepler problem, we show that the hydrogen-atom case may be analytically solved via the phase-space formulation of nonrelativistic quantum mechanics. The problem is essentially reduced to that of a four-dimensional oscillator whose treatment in the phase-space formulation is developed. Furthermore, the method allows us to calculate the Green's function for the H atom in a surprisingly simple way
Formulating state space models in R with focus on longitudinal regression models
DEFF Research Database (Denmark)
Dethlefsen, Claus; Lundbye-Christensen, Søren
We provide a language for formulating a range of state space models. The described methodology is implemented in the R -package sspir available from cran.r-project.org . A state space model is specified similarly to a generalized linear model in R , by marking the time-varying terms in the form...... We provide a language for formulating a range of state space models. The described methodology is implemented in the R -package sspir available from cran.r-project.org . A state space model is specified similarly to a generalized linear model in R , by marking the time-varying terms...
Loop-space quantum formulation of free electromagnetism
International Nuclear Information System (INIS)
Di Bartolo, C.; Nori, F.; Gambini, R.; Trias, A.
1983-01-01
A procedure for direct quantization of free electromagnetism in the loop-space is proposed. Explicit solutions for the loop-dependent vacuum and the Wilson loop-average are given. It is shown that elementary lines of magnetic field appear as extremals in the vacuum state as a result of the regularization procedure
Formulating state space models in R with focus on longitudinal regression models
DEFF Research Database (Denmark)
Dethlefsen, Claus; Lundbye-Christensen, Søren
2006-01-01
We provide a language for formulating a range of state space models with response densities within the exponential family. The described methodology is implemented in the R-package sspir. A state space model is specified similarly to a generalized linear model in R, and then the time-varying terms...
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.
Hilbert W*-modules and coherent states
International Nuclear Information System (INIS)
Bhattacharyya, T; Roy, S Shyam
2012-01-01
Hilbert C*-module valued coherent states was introduced earlier by Ali, Bhattacharyya and Shyam Roy. We consider the case when the underlying C*-algebra is a W*-algebra. The construction is similar with a substantial gain. The associated reproducing kernel is now algebra valued, rather than taking values in the space of bounded linear operators between two C*-algebras. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)
Quaternionic formulation of tachyons, superluminal transformations and a complex space-time
Energy Technology Data Exchange (ETDEWEB)
Imaeda, K [Dublin Inst. for Advanced Studies (Ireland)
1979-04-11
A theory of tachyons and superluminal transformations is developed on the basis of the quaternionic formulation. A complex space-time adn a complex transformation group which contains both Lorentz transformations and superluminal transformations are introduced. The complex space-time '' the biquaternion space'' which is closed under the superluminal transformations is introduced. The principle of special relativity, such as the conservation of the quadratic form of the metric of the space-time, and the principle of duality are extended to the complex space-time and to bradyons, luxons and tachyons under the complex transformations. SeVeral characteristic features of the superluminal transformations and of tachyons are derived.
Real-space formulation of the electrostatic potential and total energy of solids
International Nuclear Information System (INIS)
Pask, J E; Sterne, P A
2004-01-01
We develop expressions for the electrostatic potential and total energy of crystalline solids which are amenable to direct evaluation in real space. Unlike conventional reciprocal space formulations, no Fourier transforms or reciprocal lattice summations are required, and the formulation is well suited for large-scale, parallel computations. The need for reciprocal space expressions is eliminated by replacing long-range potentials by equivalent localized charge distributions and incorporating long-range interactions into boundary conditions on the unit cell. In so doing, a simplification of the conventional reciprocal space formalism is obtained. The equivalence of the real- and reciprocal space formalisms is demonstrated by direct comparison in self-consistent density-functional calculations
Topological freeness for Hilbert bimodules
DEFF Research Database (Denmark)
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...
Four-dimensional hilbert curves for R-trees
DEFF Research Database (Denmark)
Haverkort, Herman; Walderveen, Freek van
2011-01-01
Two-dimensional R-trees are a class of spatial index structures in which objects are arranged to enable fast window queries: report all objects that intersect a given query window. One of the most successful methods of arranging the objects in the index structure is based on sorting the objects...... according to the positions of their centers along a two-dimensional Hilbert space-filling curve. Alternatively, one may use the coordinates of the objects' bounding boxes to represent each object by a four-dimensional point, and sort these points along a four-dimensional Hilbert-type curve. In experiments...
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...
Computing Instantaneous Frequency by normalizing Hilbert Transform
Huang, Norden E.
2005-05-31
This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.
A Convex Formulation for Magnetic Particle Imaging X-Space Reconstruction.
Konkle, Justin J; Goodwill, Patrick W; Hensley, Daniel W; Orendorff, Ryan D; Lustig, Michael; Conolly, Steven M
2015-01-01
Magnetic Particle Imaging (mpi) is an emerging imaging modality with exceptional promise for clinical applications in rapid angiography, cell therapy tracking, cancer imaging, and inflammation imaging. Recent publications have demonstrated quantitative mpi across rat sized fields of view with x-space reconstruction methods. Critical to any medical imaging technology is the reliability and accuracy of image reconstruction. Because the average value of the mpi signal is lost during direct-feedthrough signal filtering, mpi reconstruction algorithms must recover this zero-frequency value. Prior x-space mpi recovery techniques were limited to 1d approaches which could introduce artifacts when reconstructing a 3d image. In this paper, we formulate x-space reconstruction as a 3d convex optimization problem and apply robust a priori knowledge of image smoothness and non-negativity to reduce non-physical banding and haze artifacts. We conclude with a discussion of the powerful extensibility of the presented formulation for future applications.
Liquid identification by Hilbert spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Lyatti, M; Divin, Y; Poppe, U; Urban, K, E-mail: M.Lyatti@fz-juelich.d, E-mail: Y.Divin@fz-juelich.d [Forschungszentrum Juelich, 52425 Juelich (Germany)
2009-11-15
Fast and reliable identification of liquids is of great importance in, for example, security, biology and the beverage industry. An unambiguous identification of liquids can be made by electromagnetic measurements of their dielectric functions in the frequency range of their main dispersions, but this frequency range, from a few GHz to a few THz, is not covered by any conventional spectroscopy. We have developed a concept of liquid identification based on our new Hilbert spectroscopy and high- T{sub c} Josephson junctions, which can operate at the intermediate range from microwaves to THz frequencies. A demonstration setup has been developed consisting of a polychromatic radiation source and a compact Hilbert spectrometer integrated in a Stirling cryocooler. Reflection polychromatic spectra of various bottled liquids have been measured at the spectral range of 15-300 GHz with total scanning time down to 0.2 s and identification of liquids has been demonstrated.
Liquid identification by Hilbert spectroscopy
Lyatti, M.; Divin, Y.; Poppe, U.; Urban, K.
2009-11-01
Fast and reliable identification of liquids is of great importance in, for example, security, biology and the beverage industry. An unambiguous identification of liquids can be made by electromagnetic measurements of their dielectric functions in the frequency range of their main dispersions, but this frequency range, from a few GHz to a few THz, is not covered by any conventional spectroscopy. We have developed a concept of liquid identification based on our new Hilbert spectroscopy and high- Tc Josephson junctions, which can operate at the intermediate range from microwaves to THz frequencies. A demonstration setup has been developed consisting of a polychromatic radiation source and a compact Hilbert spectrometer integrated in a Stirling cryocooler. Reflection polychromatic spectra of various bottled liquids have been measured at the spectral range of 15-300 GHz with total scanning time down to 0.2 s and identification of liquids has been demonstrated.
Liquid identification by Hilbert spectroscopy
International Nuclear Information System (INIS)
Lyatti, M; Divin, Y; Poppe, U; Urban, K
2009-01-01
Fast and reliable identification of liquids is of great importance in, for example, security, biology and the beverage industry. An unambiguous identification of liquids can be made by electromagnetic measurements of their dielectric functions in the frequency range of their main dispersions, but this frequency range, from a few GHz to a few THz, is not covered by any conventional spectroscopy. We have developed a concept of liquid identification based on our new Hilbert spectroscopy and high- T c Josephson junctions, which can operate at the intermediate range from microwaves to THz frequencies. A demonstration setup has been developed consisting of a polychromatic radiation source and a compact Hilbert spectrometer integrated in a Stirling cryocooler. Reflection polychromatic spectra of various bottled liquids have been measured at the spectral range of 15-300 GHz with total scanning time down to 0.2 s and identification of liquids has been demonstrated.
Frame transforms, star products and quantum mechanics on phase space
International Nuclear Information System (INIS)
Aniello, P; Marmo, G; Man'ko, V I
2008-01-01
Using the notions of frame transform and of square integrable projective representation of a locally compact group G, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group G x G. These transforms have remarkable properties. In particular, their ranges are reproducing kernel Hilbert spaces endowed with a suitable 'star product' which mimics, at the level of functions, the original product of operators. A 'phase space formulation' of quantum mechanics relying on the frame transforms introduced in the present paper, and the link of these maps with both the Wigner transform and the wavelet transform are discussed
What is Quantum Mechanics? A Minimal Formulation
Friedberg, R.; Hohenberg, P. C.
2018-03-01
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called "microscopic theory", applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen-Specker-Bell theorem and Gleason's theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantum mechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory.
Euclidean and Minkowski space formulations of linearized gravitational potential in various gauges
International Nuclear Information System (INIS)
Lim, S.C.
1979-01-01
We show that there exists a unitary map connecting linearized theories of gravitational potential in vacuum, formulated in various covariant gauges and noncovariant radiation gauge. The free Euclidean gravitational potentials in covariant gauges satisfy the Markov property of Nelson, but are nonreflexive. For the noncovariant radiation gauge, the corresponding Euclidean field is reflexive but it only satisfies the Markov property with respect to special half spaces. The Feynman--Kac--Nelson formula is established for the Euclidean gravitational potential in radiation gauge
On integral formulation of the Mach principle in a conformally flat space
International Nuclear Information System (INIS)
Mal'tsev, V.K.
1976-01-01
The integral formulation of the Mach principle represents a rather complicated mathematical formalism in which many aspects of the physical content of theory are not clear. Below an attempt is made to consider the integral representation for the most simple case of conformally flat spaces. The fact that this formalism there is only one scalar function makes it possible to analyse in more detail many physical peculiarities of this representation of the Mach principle: the absence of asymptotically flat spaces, problems of inertia and gravity, constraints on state equations, etc
Exponential Hilbert series of equivariant embeddings
Johnson, Wayne A.
2018-01-01
In this article, we study properties of the exponential Hilbert series of a $G$-equivariant projective variety, where $G$ is a semisimple, simply-connected complex linear algebraic group. We prove a relationship between the exponential Hilbert series and the degree and dimension of the variety. We then prove a combinatorial identity for the coefficients of the polynomial representing the exponential Hilbert series. This formula is used in examples to prove further combinatorial identities inv...
Clustering in Hilbert simplex geometry
Nielsen, Frank
2017-04-03
Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.
Harvey, James A.; Butler, John M.; Chartoff, Richard P.
1988-01-01
Four commercially available polyisocyanurate polyurethane spray-foam insulation formulations are used to coat the external tank of the space shuttle. There are several problems associated with these formulations. For example, some do not perform well as pourable closeout/repair systems. Some do not perform well at cryogenic temperatures (poor adhesion to aluminum at liquid nitrogen temperatures). Their thermal stability at elevated temperatures is not adequate. A major defect in all the systems is the lack of detailed chemical information. The formulations are simply supplied to NASA and Martin Marietta, the primary contractor, as components; Part A (isocyanate) and Part B (poly(s) and additives). Because of the lack of chemical information the performance behavior data for the current system, NASA sought the development of a non-proprietary room temperature curable foam insulation. Requirements for the developed system were that it should exhibit equal or better thermal stability both at elevated and cryogenic temperatures with better adhesion to aluminum as compared to the current system. Several formulations were developed that met these requirements, i.e., thermal stability, good pourability, and good bonding to aluminum.
Regularization methods for ill-posed problems in multiple Hilbert scales
International Nuclear Information System (INIS)
Mazzieri, Gisela L; Spies, Ruben D
2012-01-01
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a multiple Hilbert scale on a product space is introduced, and regularization methods on these scales are defined, both for the case of a single observation and for the case of multiple observations. In the latter case, it is shown how vector-valued regularization functions in these multiple Hilbert scales can be used. In all cases, convergence is proved and orders and optimal orders of convergence are shown. Finally, some potential applications and open problems are discussed. (paper)
Fast estimation of space-robots inertia parameters: A modular mathematical formulation
Nabavi Chashmi, Seyed Yaser; Malaek, Seyed Mohammad-Bagher
2016-10-01
This work aims to propose a new technique that considerably helps enhance time and precision needed to identify ;Inertia Parameters (IPs); of a typical Autonomous Space-Robot (ASR). Operations might include, capturing an unknown Target Space-Object (TSO), ;active space-debris removal; or ;automated in-orbit assemblies;. In these operations generating precise successive commands are essential to the success of the mission. We show how a generalized, repeatable estimation-process could play an effective role to manage the operation. With the help of the well-known Force-Based approach, a new ;modular formulation; has been developed to simultaneously identify IPs of an ASR while it captures a TSO. The idea is to reorganize the equations with associated IPs with a ;Modular Set; of matrices instead of a single matrix representing the overall system dynamics. The devised Modular Matrix Set will then facilitate the estimation process. It provides a conjugate linear model in mass and inertia terms. The new formulation is, therefore, well-suited for ;simultaneous estimation processes; using recursive algorithms like RLS. Further enhancements would be needed for cases the effect of center of mass location becomes important. Extensive case studies reveal that estimation time is drastically reduced which in-turn paves the way to acquire better results.
6th Hilbert's problem and S.Lie's infinite groups
International Nuclear Information System (INIS)
Konopleva, N.P.
1999-01-01
The progress in Hilbert's sixth problem solving is demonstrated. That became possible thanks to the gauge field theory in physics and to the geometrical treatment of the gauge fields. It is shown that the fibre bundle spaces geometry is the best basis for solution of the problem being discussed. This talk has been reported at the International Seminar '100 Years after Sophus Lie' (Leipzig, Germany)
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 theory of classical electrodynamics
Indian Academy of Sciences (India)
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.
Quantum mechanics: why complex Hilbert space?
Cassinelli, G.; Lahti, P.
2017-10-01
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'.
On using the Hilbert transform for blind identification of complex modes: A practical approach
Antunes, Jose; Debut, Vincent; Piteau, Pilippe; Delaune, Xavier; Borsoi, Laurent
2018-01-01
The modal identification of dynamical systems under operational conditions, when subjected to wide-band unmeasured excitations, is today a viable alternative to more traditional modal identification approaches based on processing sets of measured FRFs or impulse responses. Among current techniques for performing operational modal identification, the so-called blind identification methods are the subject of considerable investigation. In particular, the SOBI (Second-Order Blind Identification) method was found to be quite efficient. SOBI was originally developed for systems with normal modes. To address systems with complex modes, various extension approaches have been proposed, in particular: (a) Using a first-order state-space formulation for the system dynamics; (b) Building complex analytic signals from the measured responses using the Hilbert transform. In this paper we further explore the latter option, which is conceptually interesting while preserving the model order and size. Focus is on applicability of the SOBI technique for extracting the modal responses from analytic signals built from a set of vibratory responses. The novelty of this work is to propose a straightforward computational procedure for obtaining the complex cross-correlation response matrix to be used for the modal identification procedure. After clarifying subtle aspects of the general theoretical framework, we demonstrate that the correlation matrix of the analytic responses can be computed through a Hilbert transform of the real correlation matrix, so that the actual time-domain responses are no longer required for modal identification purposes. The numerical validation of the proposed technique is presented based on time-domain simulations of a conceptual physical multi-modal system, designed to display modes ranging from normal to highly complex, while keeping modal damping low and nearly independent of the modal complexity, and which can prove very interesting in test bench
Gauge invariant Lagrangian formulation of massive higher spin fields in (A)dS3 space
International Nuclear Information System (INIS)
Buchbinder, I.L.; Snegirev, T.V.; Zinoviev, Yu.M.
2012-01-01
We develop the frame-like formulation of massive bosonic higher spin fields in the case of three-dimensional (A)dS space with the arbitrary cosmological constant. The formulation is based on gauge invariant description by involving the Stueckelberg auxiliary fields. The explicit form of the Lagrangians and the gauge transformation laws are found. The theory can be written in terms of gauge invariant objects similar to the massless theories, thus allowing us to hope to use the same methods for investigation of interactions. In the massive spin 3 field example we are able to rewrite the Lagrangian using the new the so-called separated variables, so that the study of Lagrangian formulation reduces to finding the Lagrangian containing only half of the fields. The same construction takes places for arbitrary integer spin field as well. Further working in terms of separated variables, we build Lagrangian for arbitrary integer spin and write it in terms of gauge invariant objects. Also, we demonstrate how to restore the full set of variables, thus receiving Lagrangian for the massive fields of arbitrary spin in the terms of initial fields.
Power Spectral Density and Hilbert Transform
2016-12-01
there is 1.3 W of power. How much bandwidth does a pure sine wave require? The bandwidth of an ideal sine wave is 0 Hz. How do you represent a 1-W...the Hilbert transform. 2.3 Hilbert Transform The Hilbert transform is a math function used to convert a real function into an analytic signal...The math operation minus 2 means to move 2 steps back on the number line. For minus –2, we move 2 steps backwards from –2, which is the same as
Chiang, Bryce; Venugopal, Nitin; Grossniklaus, Hans E; Jung, Jae Hwan; Edelhauser, Henry F; Prausnitz, Mark R
2017-01-01
To determine the effect of injection volume and formulation of a microneedle injection into the suprachoroidal space (SCS) on SCS thickness and closure kinetics. Microneedle injections containing 25 to 150 μL Hanks' balanced salt solution (HBSS) were performed in the rabbit SCS ex vivo. Distribution of SCS thickness was measured by ultrasonography and three-dimensional (3D) cryo-reconstruction. Microneedle injections were performed in the rabbit SCS in vivo using HBSS, Discovisc, and 1% to 5% carboxymethyl cellulose (CMC) in HBSS. Ultrasonography was used to track SCS thickness over time. Increasing HBSS injection volume increased the area of expanded SCS, but did not increase SCS thickness ex vivo. With SCS injections in vivo, the SCS initially expanded to thicknesses of 0.43 ± 0.06 mm with HBSS, 1.5 ± 0.4 mm with Discovisc, and 0.69 to 2.1 mm with 1% to 5% CMC. After injection with HBSS, Discovisc, and 1% CMC solution, the SCS collapsed to baseline with time constants of 19 minutes, 6 hours, and 2.4 days, respectively. In contrast, injections with 3% to 5% CMC solution resulted in SCS expansion to 2.3 to 2.8 mm over the course of 2.8 to 9.1 hours, after which the SCS collapsed to baseline with time constants of 4.5 to 9.2 days. With low-viscosity formulations, SCS expands to a thickness that remains roughly constant, independent of the volume of fluid injected. Increasing injection fluid viscosity significantly increased SCS thickness. Expansion of the SCS is hypothesized to be controlled by a balance between the viscous forces of the liquid formulation and the resistive biomechanical forces of the tissue.
A Beddoes-Leishman type dynamic stall model in state-space and indicial formulations
DEFF Research Database (Denmark)
Hansen, M.H.; Gaunaa, Mac; Aagaard Madsen, Helge
2004-01-01
This report contains a description of a Beddoes-Leishman type dynamic stall model in both a state-space and an indicial function formulation. The model predicts the unsteady aerodynamic forces and moment on an airfoil section undergoing arbitrary motionin heave, lead-lag, and pitch. The model...... features, such as overshoot of the lift, in the stall region. The linearized model is shown to give identicalresults to the full model for small amplitude oscillations. Furthermore, it is shown that the response of finite thichkness airfoils can be reproduced to a high accuracy by the use of specific...... is carried out by comparing the response of the model with inviscid solutions and observing the general behavior of the model using known airfoil data as input. Theproposed dynamic model gives results identical to inviscid solutions within the attached-flow region; and it exhibits the expected dynamic...
Guimarães, José Maria Ximenes; Jorge, Maria Salete Bessa; Maia, Regina Claudia Furtado; de Oliveira, Lucia Conde; Morais, Ana Patrícia Pereira; Lima, Marcos Paulo de Oliveira; Assis, Marluce Maria Araújo; dos Santos, Adriano Maia
2010-07-01
The article approaches the comprehension of professionals that act in the mental health area about the movement of construction of social participation in the health system of Fortaleza, Ceará State. The methodology adopted is based upon qualitative approach. The study was developed with semi-structured interviews with 17 mental health professionals of the city above mentioned. The empirical data was analyzed through the technique of thematic content analysis, where it was identified three cores of analysis: social participation as space of citizenship and policy formulation; oriented to attention of collective needs; and decision taking. The study reveals that social participation represents a possibility of amplifying X the relations between the Civil Society and the State, which makes possible the social intervention in proposals of the health policies. It is highlighted the right to health linked to the consolidation of democracy in the attention to the needs and collective edification.
International Nuclear Information System (INIS)
Pontaza, J.P.; Reddy, J.N.
2004-01-01
We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least
A nonrecursive order N preconditioned conjugate gradient: Range space formulation of MDOF dynamics
Kurdila, Andrew J.
1990-01-01
While excellent progress has been made in deriving algorithms that are efficient for certain combinations of system topologies and concurrent multiprocessing hardware, several issues must be resolved to incorporate transient simulation in the control design process for large space structures. Specifically, strategies must be developed that are applicable to systems with numerous degrees of freedom. In addition, the algorithms must have a growth potential in that they must also be amenable to implementation on forthcoming parallel system architectures. For mechanical system simulation, this fact implies that algorithms are required that induce parallelism on a fine scale, suitable for the emerging class of highly parallel processors; and transient simulation methods must be automatically load balancing for a wider collection of system topologies and hardware configurations. These problems are addressed by employing a combination range space/preconditioned conjugate gradient formulation of multi-degree-of-freedom dynamics. The method described has several advantages. In a sequential computing environment, the method has the features that: by employing regular ordering of the system connectivity graph, an extremely efficient preconditioner can be derived from the 'range space metric', as opposed to the system coefficient matrix; because of the effectiveness of the preconditioner, preliminary studies indicate that the method can achieve performance rates that depend linearly upon the number of substructures, hence the title 'Order N'; and the method is non-assembling. Furthermore, the approach is promising as a potential parallel processing algorithm in that the method exhibits a fine parallel granularity suitable for a wide collection of combinations of physical system topologies/computer architectures; and the method is easily load balanced among processors, and does not rely upon system topology to induce parallelism.
Quantum mechanics in phase space
DEFF Research Database (Denmark)
Hansen, Frank
1984-01-01
A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...
Effects of different peracetic acid formulations on post space radicular dentin.
Belizário, Lauriê Garcia; Kuga, Milton Carlos; Castro-Núñez, Gabriela Mariana; Escalante-Otárola, Wilfredo Gustavo; Só, Marcus Vinicius Reis; Pereira, Jefferson Ricardo
2018-01-05
The optimal irrigating solution with antimicrobial and dentin cleansing properties for post space preparation for fiber posts is unclear. Peracetic acid is one option but is available in various chemical formulations that require evaluation. The purpose of this in vitro study was to evaluate dentin surface cleanliness based on the presence of a smear layer and the number of open dentin tubules. It also investigates the chemical composition of residues after canal irrigation with a 1% peracetic acid solution (PA) at low or high concentration of hydrogen peroxide during the preparation of intracanal fiber posts. After filling the root canals of 40 mandibular incisors, a rotary instrument was used for intracanal preparation to place fiber posts. The teeth were divided into 4 groups (n=10) according to the post space irrigation protocol as follows: CG (control): distilled water; NA (NaOCl): 2.5% sodium hypochlorite; LH: PA with low concentration of hydrogen peroxide; and HH: PA with high concentrations of hydrogen peroxide. After irrigation, the teeth were sectioned, and the intracanal dentin surface was subjected to analysis using energy dispersive spectroscopy to evaluate chemical composition and to scanning electron microscopy (×500) to evaluate the presence of the smear layer. The number of open dentin tubules was measured by scanning electron microscopy analysis (×2000) using photo-editing software. ANOVA and the Tukey test (α=.05) were used to evaluate the data, except for the presence of a smear layer, for which the Kruskal-Wallis and Dunn tests were used (α=.05). The highest concentrations of oxygen in the dentin residues were detected in LH and HH (P.05). NA had a higher concentration of chlorine (P.05), except for HH, which also had a larger number of open dentin tubules than CG and NA (P<.05). PA 1% with a low concentration of hydrogen peroxide yielded a lower amount of smear layer and a larger number of open dentin tubules in the dentin of the post
Hilbert schemes of points and Heisenberg algebras
International Nuclear Information System (INIS)
Ellingsrud, G.; Goettsche, L.
2000-01-01
Let X [n] be the Hilbert scheme of n points on a smooth projective surface X over the complex numbers. In these lectures we describe the action of the Heisenberg algebra on the direct sum of the cohomologies of all the X [n] , which has been constructed by Nakajima. In the second half of the lectures we study the relation of the Heisenberg algebra action and the ring structures of the cohomologies of the X [n] , following recent work of Lehn. In particular we study the Chern and Segre classes of tautological vector bundles on the Hilbert schemes X [n] . (author)
Multisymplectic unified formalism for Einstein-Hilbert gravity
Gaset, Jordi; Román-Roy, Narciso
2018-03-01
We present a covariant multisymplectic formulation for the Einstein-Hilbert model of general relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified Lagrangian-Hamiltonian formalism is particularly interesting when it is applied to these kinds of theories, since it simplifies the treatment of them, in particular, the implementation of the constraint algorithm, the retrieval of the Lagrangian description, and the construction of the covariant Hamiltonian formalism. In order to apply this algorithm to the covariant field equations, they must be written in a suitable geometrical way, which consists of using integrable distributions, represented by multivector fields of a certain type. We apply all these tools to the Einstein-Hilbert model without and with energy-matter sources. We obtain and explain the geometrical and physical meaning of the Lagrangian constraints and we construct the multimomentum (covariant) Hamiltonian formalisms in both cases. As a consequence of the gauge freedom and the constraint algorithm, we see how this model is equivalent to a first-order regular theory, without gauge freedom. In the case of the presence of energy-matter sources, we show how some relevant geometrical and physical characteristics of the theory depend on the type of source. In all the cases, we obtain explicitly multivector fields which are solutions to the gravitational field equations. Finally, a brief study of symmetries and conservation laws is done in this context.
Quantum Hilbert matrices and orthogonal polynomials
DEFF Research Database (Denmark)
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|<1 , and for the special value they are closely related to Hankel matrice...
Hilbert's Grand Hotel with a series twist
Wijeratne, Chanakya; Mamolo, Ami; Zazkis, Rina
2014-08-01
This paper presents a new twist on a familiar paradox, linking seemingly disparate ideas under one roof. Hilbert's Grand Hotel, a paradox which addresses infinite set comparisons is adapted and extended to incorporate ideas from calculus - namely infinite series. We present and resolve several variations, and invite the reader to explore his or her own variations.
Notes on Hilbert and Cauchy Matrices
Czech Academy of Sciences Publication Activity Database
Fiedler, Miroslav
2010-01-01
Roč. 432, č. 1 (2010), s. 351-356 ISSN 0024-3795 Institutional research plan: CEZ:AV0Z10300504 Keywords : Hilbert matrix * Cauchy matrix * combined matrix * AT-property Subject RIV: BA - General Mathematics Impact factor: 1.005, year: 2010
Noise properties of Hilbert transform evaluation
Czech Academy of Sciences Publication Activity Database
Pavlíček, Pavel; Svak, V.
2015-01-01
Roč. 26, č. 8 (2015), s. 085207 ISSN 0957-0233 R&D Projects: GA ČR GA13-12301S Institutional support: RVO:68378271 Keywords : Hilbert transform * noise * measurement uncertainty * white -light interferometry * fringe-pattern analysis Subject RIV: BH - Optics, Masers, Lasers Impact factor: 1.492, year: 2015
A relative Hilbert-Mumford criterion
DEFF Research Database (Denmark)
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...
Theory and experiments on Peano and Hilbert curve RFID tags
McVay, John; Hoorfar, Ahmad; Engheta, Nader
2006-05-01
Recently, there has been considerable interest in the area of Radio Frequency Identification (RFID) and Radio Frequency Tagging (RFTAG). This emerging area of interest can be applied for inventory control (commercial) as well as friend/foe identification (military) to name but a few. The current technology can be broken down into two main groups, namely passive and active RFID tags. Utilization of Space-Filling Curve (SFC) geometries, such as the Peano and Hilbert curves, has been recently investigated for use in completely passive RFID applications [1, 2]. In this work, we give an overview of our work on the space-filling curves and the potential for utilizing the electrically small, resonant characteristics of these curves for use in RFID technologies with an emphasis on the challenging issues involved when attempting to tag conductive objects. In particular, we investigate the possible use of these tags in conjunction with high impedance ground-planes made of Hilbert or Peano curve inclusions [3, 4] to develop electrically small RFID tags that may also radiate efficiently, within close proximity of large conductive objects [5].
Commentaries on Hilbert's Basis Theorem | Apine | Science World ...
African Journals Online (AJOL)
The famous basis theorem of David Hilbert is an important theorem in commutative algebra. In particular the Hilbert's basis theorem is the most important source of Noetherian rings which are by far the most important class of rings in commutative algebra. In this paper we have used Hilbert's theorem to examine their unique ...
nth roots with Hilbert-Schmidt defect operator of normal contractions
International Nuclear Information System (INIS)
Duggal, B.P.
1992-08-01
Let T be a normal contraction (on a complex separable Hilbert space H into itself) with an nth root A such that the defect operator D A =(1-A*A) 1/2 is of the Hilbert-Schmidt class C 2 . Then either A is normal or A is similar to a normal contraction. In the case in which T is hyponormal, A n =T and D A is an element of C 2 , A is a ''coupling'' of a contraction similar to a normal contraction and a contraction which is the quasi-affine transform of a unilateral shift. These results are applied to prove a (Putnam-Fuglede type) commutatively theorem for operator valued roots of commutative analytic functions and hyponormal contractions T which have an nth root with Hilbert-Schmidt defect operator. 23 refs
Experimental Investigation of a Direct Methanol Fuel Cell with Hilbert Fractal Current Collectors
Directory of Open Access Journals (Sweden)
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.
H-SLAM: Rao-Blackwellized Particle Filter SLAM Using Hilbert Maps
Directory of Open Access Journals (Sweden)
Guillem Vallicrosa
2018-05-01
Full Text Available Occupancy Grid maps provide a probabilistic representation of space which is important for a variety of robotic applications like path planning and autonomous manipulation. In this paper, a SLAM (Simultaneous Localization and Mapping framework capable of obtaining this representation online is presented. The H-SLAM (Hilbert Maps SLAM is based on Hilbert Map representation and uses a Particle Filter to represent the robot state. Hilbert Maps offer a continuous probabilistic representation with a small memory footprint. We present a series of experimental results carried both in simulation and with real AUVs (Autonomous Underwater Vehicles. These results demonstrate that our approach is able to represent the environment more consistently while capable of running online.
Goal oriented adaptivity in the IRGNM for parameter identification in PDEs: I. reduced formulation
International Nuclear Information System (INIS)
Kaltenbacher, B; Kirchner, A; Veljović, S
2014-01-01
In this paper we study adaptive discretization of the iteratively regularized Gauss–Newton method (IRGNM) with an a posteriori (discrepancy principle) choice of the regularization parameter in each Newton step and of the stopping index. We first of all prove convergence and convergence rates under some accuracy requirements formulated in terms of four quantities of interest. Then computation of error estimators for these quantities based on a weighted dual residual method is discussed, which results in an algorithm for adaptive refinement. Finally we extend the results from the Hilbert space setting with quadratic penalty to Banach spaces and general Tikhonov functionals for the regularization of each Newton step. (paper)
Nonclassical Problem for Ultraparabolic Equation in Abstract Spaces
Directory of Open Access Journals (Sweden)
Gia Avalishvili
2016-01-01
Full Text Available Nonclassical problem for ultraparabolic equation with nonlocal initial condition with respect to one time variable is studied in abstract Hilbert spaces. We define the space of square integrable vector-functions with values in Hilbert spaces corresponding to the variational formulation of the nonlocal problem for ultraparabolic equation and prove trace theorem, which allows one to interpret initial conditions of the nonlocal problem. We obtain suitable a priori estimates and prove the existence and uniqueness of solution of the nonclassical problem and continuous dependence upon the data of the solution to the nonlocal problem. We consider an application of the obtained abstract results to nonlocal problem for ultraparabolic partial differential equation with second-order elliptic operator and obtain well-posedness result in Sobolev spaces.
On quantization of free fields in stationary space-times
International Nuclear Information System (INIS)
Moreno, C.
1977-01-01
In Section 1 the structure of the infinite-dimensional Hamiltonian system described by the Klein-Gordon equation (free real scalar field) in stationary space-times with closed space sections, is analysed, an existence and uniqueness theorem is given for the Lichnerowicz distribution kernel G 1 together with its proper Fourier expansion, and the Hilbert spaces of frequency-part solutions defined by means of G 1 are constructed. In Section 2 an analysis, a theorem and a construction similar to the above are formulated for the free real field spin 1, mass m>0, in one kind of static space-times. (Auth.)
International Nuclear Information System (INIS)
Bagrov, V.G.; Evseevich, A.A.; Obukhov, V.V.; Osetrin, K.E.
1987-01-01
The authors consider the problem of the classification of the Stackel spaces of the electrovacuum with isotropic complete sets. The metrics of the spaces are represented in a form that is convenient for their investigation. We obtain necessary relations for the construction of the field equations
Xu, Wenjun; Tang, Chen; Su, Yonggang; Li, Biyuan; Lei, Zhenkun
2018-02-01
In this paper, we propose an image decomposition model Shearlet-Hilbert-L 2 with better performance for denoising in electronic speckle pattern interferometry (ESPI) fringe patterns. In our model, the low-density fringes, high-density fringes, and noise are, respectively, described by shearlet smoothness spaces, adaptive Hilbert space, and L 2 space and processed individually. Because the shearlet transform has superior directional sensitivity, our proposed Shearlet-Hilbert-L 2 model achieves commendable filtering results for various types of ESPI fringe patterns, including uniform density fringe patterns, moderately variable density fringe patterns, and greatly variable density fringe patterns. We evaluate the performance of our proposed Shearlet-Hilbert-L 2 model via application to two computer-simulated and nine experimentally obtained ESPI fringe patterns with various densities and poor quality. Furthermore, we compare our proposed model with windowed Fourier filtering and coherence-enhancing diffusion, both of which are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. We also compare our proposed model with the previous image decomposition model BL-Hilbert-L 2 .
Nested Hilbert schemes on surfaces: Virtual fundamental class
DEFF Research Database (Denmark)
Gholampour, Amin; Sheshmani, Artan; Yau, Shing-Tung
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...
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
Finite element formulation for fluid-structure interaction in three-dimensional space
International Nuclear Information System (INIS)
Kulak, R.F.
1979-01-01
A development is presented for a three-dimension hexahedral hydrodynamic finite-element. Using trilinear shape functions and assuming a constant pressure field in each element, simple relations were obtained for internal nodal forces. Because the formulation was based upon a rate approach it was applicable to problems involving large displacements. This element was incorporated into an existing plate-shell finite element code. Diagonal mass matrices were used and the resulting discrete equations of motion were solved using explicit temporal integrator. Results for several problems were presented which compare numerical predictions to closed form analytical solutions. In addition, the fluid-structure interaction problem of a fluid-filled, cylindrical vessel containing internal cylinders was studied. The internal cylinders were cantilever supported from the top cover of the vessel and were periodically located circumferentially at a fixed radius. A pressurized cylindrical cavity located at the bottom of the vessel at its centerline provided the loading
Modelling population dynamics model formulation, fitting and assessment using state-space methods
Newman, K B; Morgan, B J T; King, R; Borchers, D L; Cole, D J; Besbeas, P; Gimenez, O; Thomas, L
2014-01-01
This book gives a unifying framework for estimating the abundance of open populations: populations subject to births, deaths and movement, given imperfect measurements or samples of the populations. The focus is primarily on populations of vertebrates for which dynamics are typically modelled within the framework of an annual cycle, and for which stochastic variability in the demographic processes is usually modest. Discrete-time models are developed in which animals can be assigned to discrete states such as age class, gender, maturity, population (within a metapopulation), or species (for multi-species models). The book goes well beyond estimation of abundance, allowing inference on underlying population processes such as birth or recruitment, survival and movement. This requires the formulation and fitting of population dynamics models. The resulting fitted models yield both estimates of abundance and estimates of parameters characterizing the underlying processes.
Towards a Rigorous Formulation of the Space Mapping Technique for Engineering Design
DEFF Research Database (Denmark)
Koziel, Slawek; Bandler, John W.; Madsen, Kaj
2005-01-01
This paper deals with the Space Mapping (SM) approach to engineering design optimization. We attempt here a theoretical justification of methods that have already proven efficient in solving practical problems, especially in the RF and microwave area. A formal definition of optimization algorithm...
Creating Spaces for Children's Agency: "I Wonder…" Formulations in Teacher-Child Interactions
Houen, Sandy; Danby, Susan; Farrell, Ann; Thorpe, Karen
2016-01-01
Affording children's agency is an important pedagogical underpinning of a high-quality early childhood program. Yet little is known about how teachers' interactions create spaces for children's agency. From the perspectives of ethnomethodology and conversation analysis, this paper investigates how teachers and children navigate agency through…
International Nuclear Information System (INIS)
Marchiolli, M.A.; Ruzzi, M.
2012-01-01
We propose a self-consistent theoretical framework for a wide class of physical systems characterized by a finite space of states which allows us, within several mathematical virtues, to construct a discrete version of the Weyl–Wigner–Moyal (WWM) formalism for finite-dimensional discrete phase spaces with toroidal topology. As a first and important application from this ab initio approach, we initially investigate the Robertson–Schrödinger (RS) uncertainty principle related to the discrete coordinate and momentum operators, as well as its implications for physical systems with periodic boundary conditions. The second interesting application is associated with a particular uncertainty principle inherent to the unitary operators, which is based on the Wiener–Khinchin theorem for signal processing. Furthermore, we also establish a modified discrete version for the well-known Heisenberg–Kennard–Robertson (HKR) uncertainty principle, which exhibits additional terms (or corrections) that resemble the generalized uncertainty principle (GUP) into the context of quantum gravity. The results obtained from this new algebraic approach touch on some fundamental questions inherent to quantum mechanics and certainly represent an object of future investigations in physics. - Highlights: ► We construct a discrete version of the Weyl–Wigner–Moyal formalism. ► Coherent states for finite-dimensional discrete phase spaces are established. ► Discrete coordinate and momentum operators are properly defined. ► Uncertainty principles depend on the topology of finite physical systems. ► Corrections for the discrete Heisenberg uncertainty relation are also obtained.
Hilbert schemes of points and infinite dimensional Lie algebras
Qin, Zhenbo
2018-01-01
Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes X^{[n]} of collections of n points (zero-dimensional subschemes) in a smooth algebraic surface X. Schemes X^{[n]} turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of X^{[n]}, including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of X^{[n]} a...
International Nuclear Information System (INIS)
Burdík, C; Reshetnyak, A
2012-01-01
We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux Y(s 1 ,..., s k ) with κ ≥ 2 rows on d-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for κ = 2 Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic sp(2κ) algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin (s 1 , s 2 ) is derived.
Monopole operators and Hilbert series of Coulomb branches of 3 d = 4 gauge theories
Cremonesi, Stefano; Hanany, Amihay; Zaffaroni, Alberto
2014-01-01
This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces, with enough symmetry, or to Higgs branches of sufficiently small gauge theories. We introduce a simple formula for the Hilbert series of the Coulomb branch, which applies to any good or ugly three-dimensional = 4 gauge theory. The formula counts monopole operators which are dressed by classical operators, the Casimir invariants of the residual gauge group that is left unbroken by the magnetic flux. We apply our formula to several classes of gauge theories. Along the way we make various tests of mirror symmetry, successfully comparing the Hilbert series of the Coulomb branch with the Hilbert series of the Higgs branch of the mirror theory.
Transition probability spaces in loop quantum gravity
Guo, Xiao-Kan
2018-03-01
We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability spaces. This is exemplified by first checking such structures in covariant quantum mechanics and then identifying the transition probability spaces in spin foam models via a simplified version of general boundary formulation. The transition probability space thus defined gives a simple way to reconstruct the discrete analog of the Hilbert space of the canonical theory and the relevant quantum logical structures. Second, we show that the transition probability space and in particular the spin foam model are 2-categories. Then we discuss how to realize in spin foam models two proposals by Crane about the mathematical structures of quantum gravity, namely, the quantum topos and causal sites. We conclude that transition probability spaces provide us with an alternative framework to understand various foundational questions of loop quantum gravity.
International Nuclear Information System (INIS)
Nakawaki, Yuji; McCartor, Gary
2006-01-01
We construct a new perturbative formulation of pure space-like axial gauge QED in which the inherent infrared divergences are regularized by residual gauge fields. For this purpose, we carry out our calculations in the coordinates x μ =(x + , x - , x 1 , x 2 ), where x + =x 0 sinθ + x 3 cosθ and x - = x 0 cosθ - x 3 sinθ. Here, A=A 0 cosθ + A 3 sinθ = n·A=0 is taken as the gauge fixing condition. We show in detail that, in perturbation theory, infrared divergences resulting from the residual gauge fields cancel infrared divergences resulting from the physical parts of the gauge field. As a result, we obtain the gauge field propagator proposed by Mandelstam and Leibbrandt. By taking the limit θ→π/4, we are able to construct a light-cone formulation that is free from infrared divergences. With that analysis complete, we next calculate the one-loop electron self-energy, something not previously done in the light-cone quantization and light-cone gauge. (author)
Energy Technology Data Exchange (ETDEWEB)
Fachruddin, Imam, E-mail: imam.fachruddin@sci.ui.ac.id; Salam, Agus [Departemen Fisika, Universitas Indonesia, Depok 16424 (Indonesia)
2016-03-11
A new momentum-space formulation for scattering of two spin-half particles, both either identical or unidentical, is formulated. As basis states the free linear-momentum states are not expanded into the angular-momentum states, the system’s spin states are described by the product of the spin states of the two particles, and the system’s isospin states by the total isospin states of the two particles. We evaluate the Lippmann-Schwinger equations for the T-matrix elements in these basis states. The azimuthal behavior of the potential and of the T-matrix elements leads to a set of coupled integral equations for the T-matrix elements in two variables only, which are the magnitude of the relative momentum and the scattering angle. Some symmetry relations for the potential and the T-matrix elements reduce the number of the integral equations to be solved. A set of six spin operators to express any interaction of two spin-half particles is introduced. We show the spin-averaged differential cross section as being calculated in terms of the solution of the set of the integral equations.
Matter tensor from the Hilbert variational principle
International Nuclear Information System (INIS)
Pandres, D. Jr.
1976-01-01
We consider the Hilbert variational principle which is conventionally used to derive Einstein's equations for the source-free gravitational field. We show that at least one version of the equivalence principle suggests an alternative way of performing the variation, resulting in a different set of Einstein equations with sources automatically present. This illustrates a technique which may be applied to any theory that is derived from a variational principle and that admits a gauge group. The essential point is that, if one first imposes a gauge condition and then performs the variation, one obtains field equations with source terms which do not appear if one first performs the variation and then imposes the gauge condition. A second illustration is provided by the variational principle conventionally used to derive Maxwell's equations for the source-free electromagnetic field. If one first imposes the Lorentz gauge condition and then performs the variation, one obtains Maxwell's equations with sources present
Noise properties of Hilbert transform evaluation
International Nuclear Information System (INIS)
Pavliček, Pavel; Svak, Vojtěch
2015-01-01
The Hilbert transform is a standard method for the calculation of the envelope and phase of a modulated signal in optical measurement methods. Usually, the intensity of light is converted into an electric signal at a detector. Therefore the actual spatially or temporally sampled signal is always affected by noise. Because the noise values of individual samples are independent, the noise can be considered as white. If the envelope and phase are calculated from the noised signal, they will also be affected by the noise. We calculate the variance and spectral density of both the envelope noise and the phase noise. We determine which parameters influence the variance and spectral density of both the envelope noise and the phase noise. Finally, we determine the influence of the noise on the measurement uncertainty in white-light interferometry and fringe-pattern analysis. (paper)
Haisch, B. M.
1976-01-01
A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.
Empirical mode decomposition and Hilbert transforms for analysis of oil-film interferograms
International Nuclear Information System (INIS)
Chauhan, Kapil; Ng, Henry C H; Marusic, Ivan
2010-01-01
Oil-film interferometry is rapidly becoming the preferred method for direct measurement of wall shear stress in studies of wall-bounded turbulent flows. Although being widely accepted as the most accurate technique, it does have inherent measurement uncertainties, one of which is associated with determining the fringe spacing. This is the focus of this paper. Conventional analysis methods involve a certain level of user input and thus some subjectivity. In this paper, we consider empirical mode decomposition (EMD) and the Hilbert transform as an alternative tool for analyzing oil-film interferograms. In contrast to the commonly used Fourier-based techniques, this new method is less subjective and, as it is based on the Hilbert transform, is superior for treating amplitude and frequency modulated data. This makes it particularly robust to wide differences in the quality of interferograms
Schroedinger--Dirac spaces of entire functions
International Nuclear Information System (INIS)
De Branges, L.
1977-01-01
A study is made of some Hilbert spaces of entire function which appear in the quantum mechanical theory of the hydrogen atoms. These spaces are examples in the theory of Hilbert spaces whose elements are entire functions and which have certain given properties. 1 reference
A Beddoes-Leishman type dynamic stall model in state-space and indicial formulations[Wind turbines
Energy Technology Data Exchange (ETDEWEB)
Hansen, M.H.; Gaunaa, M.; Aagaard Madsen, H.
2004-06-01
This report contains a description of a Beddoes-Leishman type dynamic stall model in both a state-space and an indicial function formulation. The m odel predicts the unsteady aerodynamic foreces and moment on an airfoil section undergoing arbitrary motion in heavy, lead-lag, and pitch. The model includes the effects of shed vorticity from the trailing edge (Theodorsen Theory), and the effects of an instationary trailing edge separation point. The governing equations of the model are nonlinear, and they are linearized about a steady state for application in stability analyzes. A validation is carried out by comparing the response of the model with inviscid solutions and observing the general behavior of the model using known airfoil data as input. The proposed dyanmic model gives results identical to inviscid solutions within the attached-flow region; and it exhibits the expected dynamic features, such as overshoot of the lift, in the stall region. The linearized model is shown to give identical results to the full model for small amplitude oscillations. furthermore, it is shown that the response of finite thickness airfoils can be reproduced to a high accuracy by the use of specific inviscid response functions. (au)
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.
On Nyman, Beurling and Baez-Duarte's Hilbert space reformulation ...
Indian Academy of Sciences (India)
an expert is usually defined to be a person who has the relevant piece of information.) Moreover, the main result in [2] is not the ... Recall that Riemann's zeta function is the analytic function defined on the half-plane {σ > 1} by the absolutely ... Our intention in this article is to point out that the entire gamut of these results is ...
Stochastic Moyal product on the Wiener space
International Nuclear Information System (INIS)
Dito, Giuseppe; Leandre, Remi
2007-01-01
We propose a stochastic extension of deformation quantization on a Hilbert space. The Moyal product is defined in this context on the space of functionals belonging to all of the Sobolev spaces of the Malliavin calculus
Improved specimen reconstruction by Hilbert phase contrast tomography.
Barton, Bastian; Joos, Friederike; Schröder, Rasmus R
2008-11-01
The low signal-to-noise ratio (SNR) in images of unstained specimens recorded with conventional defocus phase contrast makes it difficult to interpret 3D volumes obtained by electron tomography (ET). The high defocus applied for conventional tilt series generates some phase contrast but leads to an incomplete transfer of object information. For tomography of biological weak-phase objects, optimal image contrast and subsequently an optimized SNR are essential for the reconstruction of details such as macromolecular assemblies at molecular resolution. The problem of low contrast can be partially solved by applying a Hilbert phase plate positioned in the back focal plane (BFP) of the objective lens while recording images in Gaussian focus. Images recorded with the Hilbert phase plate provide optimized positive phase contrast at low spatial frequencies, and the contrast transfer in principle extends to the information limit of the microscope. The antisymmetric Hilbert phase contrast (HPC) can be numerically converted into isotropic contrast, which is equivalent to the contrast obtained by a Zernike phase plate. Thus, in-focus HPC provides optimal structure factor information without limiting effects of the transfer function. In this article, we present the first electron tomograms of biological specimens reconstructed from Hilbert phase plate image series. We outline the technical implementation of the phase plate and demonstrate that the technique is routinely applicable for tomography. A comparison between conventional defocus tomograms and in-focus HPC volumes shows an enhanced SNR and an improved specimen visibility for in-focus Hilbert tomography.
Diagonalization of a self-adjoint operator acting on a Hilbert module
Directory of Open Access Journals (Sweden)
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.
Frames and outer frames for Hilbert C^*-modules
Arambašić, Ljiljana; Bakić, Damir
2015-01-01
The goal of the present paper is to extend the theory of frames for countably generated Hilbert $C^*$-modules over arbitrary $C^*$-algebras. In investigating the non-unital case we introduce the concept of outer frame as a sequence in the multiplier module $M(X)$ that has the standard frame property when applied to elements of the ambient module $X$. Given a Hilbert $\\A$-module $X$, we prove that there is a bijective correspondence of the set of all adjointable surjections from the generalize...
Measurement of vibration mode shape by using Hilbert transform
International Nuclear Information System (INIS)
Kang, Min Sig
2001-01-01
This paper concerns on modal analysis of mechanical structures by using a continuous scanning laser Doppler vibrometer. In modal analysis the Hilbert transform based approach is superior to the Fourier transform based approach because of its fine accuracy and its flexible experimental settings. In this paper the Hilbert transform based approach is extended to measure area mode shape data of a structure by simply modifying the scanning pattern ranging the entire surface of the structure. The effectiveness of this proposed method is illustrated along with results of numerical simulation for a rectangular plate
Some Remarks on Space-Time Decompositions, and Degenerate Metrics, in General Relativity
Bengtsson, Ingemar
Space-time decomposition of the Hilbert-Palatini action, written in a form which admits degenerate metrics, is considered. Simple numerology shows why D = 3 and 4 are singled out as admitting a simple phase space. The canonical structure of the degenerate sector turns out to be awkward. However, the real degenerate metrics obtained as solutions are the same as those that occur in Ashtekar's formulation of complex general relativity. An exact solution of Ashtekar's equations, with degenerate metric, shows that the manifestly four-dimensional form of the action, and its 3 + 1 form, are not quite equivalent.
Generalized noncommutative Hardy and Hardy-Hilbert type inequalities
DEFF Research Database (Denmark)
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, it ...
Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira
2014-06-01
Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.
Study on a phase space representation of quantum theory
International Nuclear Information System (INIS)
Ranaivoson, R.T.R; Raoelina Andriambololona; Hanitriarivo, R.; Raboanary, R.
2013-01-01
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current formulation of quantum mechanics which is based on the use of Hilbert space and linear operators theory. Phase space representation of quantum states and wave functions in phase space are introduced using properties of a set of functions called harmonic Gaussian functions. Then, new operators called dispersion operators are defined and identified as the operators which admit as eigenstates the basis states of the phase space representation. Generalization of the approach for multidimensional cases is shown. Examples of applications are given.
Functional equations in matrix normed spaces
Indian Academy of Sciences (India)
The abstract characterization given for linear spaces of bounded Hilbert space operators in terms of ... effect on operator algebra theory (see [12]). .... of functional equations for the proof of new fixed point theorems with applications. By.
on differential operators on w 1,2 space and fredholm operators
African Journals Online (AJOL)
A selfadjoint differential operator defined over a closed and bounded interval on Sobolev space which is a dense linear subspace of a Hilbert space over the same interval is considered and shown to be a Fredholm operator with index zero. KEY WORDS: Sobolev space, Hilbert space, dense subspace, Fredholm operator
A concise treatise on quantum mechanics in phase space
Curtright, Thomas L; Zachos, Cosmas K
2014-01-01
This is a text on quantum mechanics formulated simultaneously in terms of position and momentum, i.e. in phase space. It is written at an introductory level, drawing on the remarkable history of the subject for inspiration and motivation. Wigner functions density -- matrices in a special Weyl representation -- and star products are the cornerstones of the formalism. The resulting framework is a rich source of physical intuition. It has been used to describe transport in quantum optics, structure and dynamics in nuclear physics, chaos, and decoherence in quantum computing. It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative way to formulate and understand quantum mechanics, independent of the conventional Hilbert space or path integral approaches to the subject. In this logically complete and self-standing formula...
International Nuclear Information System (INIS)
Ogievetsky, O.; Pillin, M.; Schmidke, W.B.; Wess, J.; Zumino, B.
1993-01-01
In this lecture I discuss the algebraic structure of a q-deformed four-vector space. It serves as a good example of quantizing Minkowski space. To give a physical interpretation of such a quantized Minkowski space we construct the Hilbert space representation and find that the relevant time and space operators have a discrete spectrum. Thus the q-deformed Minkowski space has a lattice structure. Nevertheless this lattice structure is compatible with the operation of q-deformed Lorentz transformations. The generators of the q-deformed Lorentz group can be represented as linear operators in the same Hilbert space. (orig.)
Lim, Hongki; Dewaraja, Yuni K.; Fessler, Jeffrey A.
2018-02-01
Most existing PET image reconstruction methods impose a nonnegativity constraint in the image domain that is natural physically, but can lead to biased reconstructions. This bias is particularly problematic for Y-90 PET because of the low probability positron production and high random coincidence fraction. This paper investigates a new PET reconstruction formulation that enforces nonnegativity of the projections instead of the voxel values. This formulation allows some negative voxel values, thereby potentially reducing bias. Unlike the previously reported NEG-ML approach that modifies the Poisson log-likelihood to allow negative values, the new formulation retains the classical Poisson statistical model. To relax the non-negativity constraint embedded in the standard methods for PET reconstruction, we used an alternating direction method of multipliers (ADMM). Because choice of ADMM parameters can greatly influence convergence rate, we applied an automatic parameter selection method to improve the convergence speed. We investigated the methods using lung to liver slices of XCAT phantom. We simulated low true coincidence count-rates with high random fractions corresponding to the typical values from patient imaging in Y-90 microsphere radioembolization. We compared our new methods with standard reconstruction algorithms and NEG-ML and a regularized version thereof. Both our new method and NEG-ML allow more accurate quantification in all volumes of interest while yielding lower noise than the standard method. The performance of NEG-ML can degrade when its user-defined parameter is tuned poorly, while the proposed algorithm is robust to any count level without requiring parameter tuning.
National Aeronautics and Space Administration — Development of a candidate bi-propellant system consisting of a gelled hydrocarbon fuel coupled with a highly energetic gelled oxidizer suitable for outer planetary...
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.
The Hilbert-Schmidt method for nucleon-deuteron scattering
International Nuclear Information System (INIS)
Moeller, K.; Narodetskii, I.M.
1984-01-01
The Hilbert-Schmidt technique is used for computing the divergent multiple-scattering series for scattering of nucleons by deuterons at energies above the deuteron breakup. We have found that for each partial amplitude a series of s-channel resonances diverges because of the logarithmic singularities which reflect the t-channel singularities of the total amplitude. However, the convergence of the Hilbert-Schmidt series may be improved by iterating the Faddeev equations thereby extracting the most strong logarithmic singularities. We show that the series for the amplitudes with the first two iteration subtracted converges rapidly. Our final results are in excellent agreement with exact results obtained by a direct matrix technique. (orig.)
Hilbert-Schmidt method for nucleon-deuteron scattering
International Nuclear Information System (INIS)
Moeller, K.; Narodetskij, I.M.
1983-01-01
The Hilbert-Schmidt technique is used for computing the divergent multiple-scattering series for scattering of nucleons by deuterons at energies above the deuteron breakup. It is found that for each partial amplitude a series of s-channel resonances diverges because of the logarithmic singularities which reflect the t-channel singularities of the total amplitude. However, the convergence of the Hilbert-Schmidt series may be improved by iterating the Faddeev equations thereby extracting the most strong logarithmic singularities. It is shown that the series for the amplitudes with first two iterations subtracted converges rapidly. Final results are in excellent agreement with exact results obtained by a direct matrix technique
Geometry and experience: Einstein's 1921 paper and Hilbert's axiomatic system
International Nuclear Information System (INIS)
De Gandt, Francois
2006-01-01
In his 1921 paper Geometrie und Erfahrung, Einstein decribes the new epistemological status of geometry, divorced from any intuitive or a priori content. He calls that 'axiomatics', following Hilbert's theoretical developments on axiomatic systems, which started with the stimulus given by a talk by Hermann Wiener in 1891 and progressed until the Foundations of geometry in 1899. Difficult questions arise: how is a theoretical system related to an intuitive empirical content?
How were the Hilbert-Einstein equations discovered?
International Nuclear Information System (INIS)
Logunov, Anatolii A; Mestvirishvili, Mirian A; Petrov, Vladimir A
2004-01-01
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)
Von Neuman representations on self-dual Hilbert W* moduli
International Nuclear Information System (INIS)
Frank, M.
1987-01-01
Von Neumann algebras M of bounded operators on self-dual Hilbert W* moduli H possessing a cyclic-separating element x-bar in H are considered. The close relation of them to certain real subspaces of H is established. Under the supposition that the underlying W*-algebra is commutative, a Tomita-Takesaki type theorem is stated. The natural cone in H arising from the pair (M, x-bar) is investigated and its properties are obtained
The Einstein-Hilbert gravitation with minimum length
Louzada, H. L. C.
2018-05-01
We study the Einstein-Hilbert gravitation with the deformed Heisenberg algebra leading to the minimum length, with the intention to find and estimate the corrections in this theory, clarifying whether or not it is possible to obtain, by means of the minimum length, a theory, in D=4, which is causal, unitary and provides a massive graviton. Therefore, we will calculate and analyze the dispersion relationships of the considered theory.
Liu, Jian; Miller, William H
2011-03-14
We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.
Diffeomorphism invariance in the Hamiltonian formulation of General Relativity
International Nuclear Information System (INIS)
Kiriushcheva, N.; Kuzmin, S.V.; Racknor, C.; Valluri, S.R.
2008-01-01
It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity
Fewster, Christopher J
2015-08-06
The framework of locally covariant quantum field theory is discussed, motivated in part using 'ignorance principles'. It is shown how theories can be represented by suitable functors, so that physical equivalence of theories may be expressed via natural isomorphisms between the corresponding functors. The inhomogeneous scalar field is used to illustrate the ideas. It is argued that there are two reasonable definitions of the local physical content associated with a locally covariant theory; when these coincide, the theory is said to be dynamically local. The status of the dynamical locality condition is reviewed, as are its applications in relation to (i) the foundational question of what it means for a theory to represent the same physics in different space-times and (ii) a no-go result on the existence of natural states. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Uniform sparse bounds for discrete quadratic phase Hilbert transforms
Kesler, Robert; Arias, Darío Mena
2017-09-01
For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.
A Proof of the Hilbert-Smith Conjecture
McAuley, Louis F.
2001-01-01
The Hilbert-Smith Conjecture states that if G is a locally compact group which acts effectively on a connected manifold as a topological transformation group, then G is a Lie group. A rather straightforward proof of this conjecture is given. The motivation is work of Cernavskii (``Finite-to-one mappings of manifolds'', Trans. of Math. Sk. 65 (107), 1964.) His work is generalized to the orbit map of an effective action of a p-adic group on compact connected n-manifolds with the aid of some new...
Time average vibration fringe analysis using Hilbert transformation
International Nuclear Information System (INIS)
Kumar, Upputuri Paul; Mohan, Nandigana Krishna; Kothiyal, Mahendra Prasad
2010-01-01
Quantitative phase information from a single interferogram can be obtained using the Hilbert transform (HT). We have applied the HT method for quantitative evaluation of Bessel fringes obtained in time average TV holography. The method requires only one fringe pattern for the extraction of vibration amplitude and reduces the complexity in quantifying the data experienced in the time average reference bias modulation method, which uses multiple fringe frames. The technique is demonstrated for the measurement of out-of-plane vibration amplitude on a small scale specimen using a time average microscopic TV holography system.
International Nuclear Information System (INIS)
Oliveira, F.R.; Bodmann, B.E.J.; Vilhena, M.T.; Carvalho, F.
2017-01-01
Highlights: • The present work presents an exact solution to neutron spatial kinetic equation. • It is an exact solution in a heterogeneous cylinder with temporal dependence. • The solution was constructed through the separation of variables method. - Abstract: In the present work we discuss a system of partial differential equations that model neutron space-kinetics in cylindrical geometry and are defined by two sectionally homogeneous cylinder cells, mono-energetic neutrons and one group of delayed neutron precursors. The solution is determined using the technique of variable separation. The associated complete spectra with respect to each variable separation are analysed and truncated such as to allow a parameterized global solution. For the obtained solution we present some numerical results for the scalar neutron flux and its time dependence and projection on the cylinder axis z and the radial and cylinder axis projection. As a case study we consider an insertion of an absorbing medium in the upper cylinder cell. Continuity of the scalar flux at the interface between the two cylinder elements and conserved current density is explained and related to scale invariance of the partial differential equation system together with the initial and boundary conditions. Some numerical results for the scalar angular neutron flux and associated current densities are shown.
Applications of Hilbert Spectral Analysis for Speech and Sound Signals
Huang, Norden E.
2003-01-01
A new method for analyzing nonlinear and nonstationary data has been developed, and the natural applications are to speech and sound signals. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF 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, which give sharp identifications of imbedded structures. This method invention can be used to process all acoustic signals. Specifically, it can process the speech signals for Speech synthesis, Speaker identification and verification, Speech recognition, and Sound signal enhancement and filtering. Additionally, as the acoustical signals from machinery are essentially the way the machines are talking to us. Therefore, the acoustical signals, from the machines, either from sound through air or vibration on the machines, can tell us the operating conditions of the machines. Thus, we can use the acoustic signal to diagnosis the problems of machines.
International Roughness Index (IRI) measurement using Hilbert-Huang transform
Zhang, Wenjin; Wang, Ming L.
2018-03-01
International Roughness Index (IRI) is an important metric to measure condition of roadways. This index is usually used to justify the maintenance priority and scheduling for roadways. Various inspection methods and algorithms are used to assess this index through the use of road profiles. This study proposes to calculate IRI values using Hilbert-Huang Transform (HHT) algorithm. In particular, road profile data is provided using surface radar attached to a vehicle driving at highway speed. Hilbert-Huang transform (HHT) is used in this study because of its superior properties for nonstationary and nonlinear data. Empirical mode decomposition (EMD) processes the raw data into a set of intrinsic mode functions (IMFs), representing various dominating frequencies. These various frequencies represent noises from the body of the vehicle, sensor location, and the excitation induced by nature frequency of the vehicle, etc. IRI calculation can be achieved by eliminating noises that are not associated with the road profile including vehicle inertia effect. The resulting IRI values are compared favorably to the field IRI values, where the filtered IMFs captures the most characteristics of road profile while eliminating noises from the vehicle and the vehicle inertia effect. Therefore, HHT is an effect method for road profile analysis and for IRI measurement. Furthermore, the application of HHT method has the potential to eliminate the use of accelerometers attached to the vehicle as part of the displacement measurement used to offset the inertia effect.
Hilbert-Schmidt quantum coherence in multi-qudit systems
Maziero, Jonas
2017-11-01
Using Bloch's parametrization for qudits ( d-level quantum systems), we write the Hilbert-Schmidt distance (HSD) between two generic n-qudit states as an Euclidean distance between two vectors of observables mean values in R^{Π_{s=1}nds2-1}, where ds is the dimension for qudit s. Then, applying the generalized Gell-Mann's matrices to generate SU(ds), we use that result to obtain the Hilbert-Schmidt quantum coherence (HSC) of n-qudit systems. As examples, we consider in detail one-qubit, one-qutrit, two-qubit, and two copies of one-qubit states. In this last case, the possibility for controlling local and non-local coherences by tuning local populations is studied, and the contrasting behaviors of HSC, l1-norm coherence, and relative entropy of coherence in this regard are noticed. We also investigate the decoherent dynamics of these coherence functions under the action of qutrit dephasing and dissipation channels. At last, we analyze the non-monotonicity of HSD under tensor products and report the first instance of a consequence (for coherence quantification) of this kind of property of a quantum distance measure.
Bayne, Michael G; Scher, Jeremy A; Ellis, Benjamin H; Chakraborty, Arindam
2018-05-21
Electron-hole or quasiparticle representation plays a central role in describing electronic excitations in many-electron systems. For charge-neutral excitation, the electron-hole interaction kernel is the quantity of interest for calculating important excitation properties such as optical gap, optical spectra, electron-hole recombination and electron-hole binding energies. The electron-hole interaction kernel can be formally derived from the density-density correlation function using both Green's function and TDDFT formalism. The accurate determination of the electron-hole interaction kernel remains a significant challenge for precise calculations of optical properties in the GW+BSE formalism. From the TDDFT perspective, the electron-hole interaction kernel has been viewed as a path to systematic development of frequency-dependent exchange-correlation functionals. Traditional approaches, such as MBPT formalism, use unoccupied states (which are defined with respect to Fermi vacuum) to construct the electron-hole interaction kernel. However, the inclusion of unoccupied states has long been recognized as the leading computational bottleneck that limits the application of this approach for larger finite systems. In this work, an alternative derivation that avoids using unoccupied states to construct the electron-hole interaction kernel is presented. The central idea of this approach is to use explicitly correlated geminal functions for treating electron-electron correlation for both ground and excited state wave functions. Using this ansatz, it is derived using both diagrammatic and algebraic techniques that the electron-hole interaction kernel can be expressed only in terms of linked closed-loop diagrams. It is proved that the cancellation of unlinked diagrams is a consequence of linked-cluster theorem in real-space representation. The electron-hole interaction kernel derived in this work was used to calculate excitation energies in many-electron systems and results
Tse, Peter W; Wang, Dong
2017-02-14
Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL). Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI) so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions.
Directory of Open Access Journals (Sweden)
Peter W. Tse
2017-02-01
Full Text Available Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL. Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions.
Differentiable absorption of Hilbert C*-modules, connections and lifts of unbounded operators
DEFF Research Database (Denmark)
Kaad, Jens
2017-01-01
. The differentiable absorption theorem is then applied to construct densely defined connections (or correpondences) on Hilbert C∗C∗-modules. These connections can in turn be used to define selfadjoint and regular "lifts" of unbounded operators which act on an auxiliary Hilbert C∗C∗-module....
Directory of Open Access Journals (Sweden)
Majewski M.
2015-06-01
Full Text Available The parametric OMI (Optimization in Multiple Intervals, the Yoshida-Magalas (YM and a novel Hilbert-twin (H-twin methods are advocated for computing the logarithmic decrement in the field of internal friction and mechanical spectroscopy of solids. It is shown that dispersion in experimental points results mainly from the selection of the computing methods, the number of oscillations, and noise. It is demonstrated that conventional Hilbert transform method suffers from high dispersion in internal friction values. It is unequivocally demonstrated that the Hilbert-twin method, which yields a ‘true envelope’ for exponentially damped harmonic oscillations is superior to conventional Hilbert transform method. The ‘true envelope’ of free decaying strain signals calculated from the Hilbert-twin method yields excellent estimation of the logarithmic decrement in metals, alloys, and solids.
Terahertz bandwidth all-optical Hilbert transformers based on long-period gratings.
Ashrafi, Reza; Azaña, José
2012-07-01
A novel, all-optical design for implementing terahertz (THz) bandwidth real-time Hilbert transformers is proposed and numerically demonstrated. An all-optical Hilbert transformer can be implemented using a uniform-period long-period grating (LPG) with a properly designed amplitude-only grating apodization profile, incorporating a single π-phase shift in the middle of the grating length. The designed LPG-based Hilbert transformers can be practically implemented using either fiber-optic or integrated-waveguide technologies. As a generalization, photonic fractional Hilbert transformers are also designed based on the same optical platform. In this general case, the resulting LPGs have multiple π-phase shifts along the grating length. Our numerical simulations confirm that all-optical Hilbert transformers capable of processing arbitrary optical signals with bandwidths well in the THz range can be implemented using feasible fiber/waveguide LPG designs.
Moretti, Valter
2017-01-01
This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing ...
Public channel cryptography: chaos synchronization and Hilbert's tenth problem.
Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang
2008-08-22
The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signals are concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-complete problems [problems that are both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP problem can be translated into this problem)]. This bridge between nonlinear dynamics and NP-complete problems opens a horizon for new types of secure public-channel protocols.
Multitask Classification Hypothesis Space With Improved Generalization Bounds.
Li, Cong; Georgiopoulos, Michael; Anagnostopoulos, Georgios C
2015-07-01
This paper presents a pair of hypothesis spaces (HSs) of vector-valued functions intended to be used in the context of multitask classification. While both are parameterized on the elements of reproducing kernel Hilbert spaces and impose a feature mapping that is common to all tasks, one of them assumes this mapping as fixed, while the more general one learns the mapping via multiple kernel learning. For these new HSs, empirical Rademacher complexity-based generalization bounds are derived, and are shown to be tighter than the bound of a particular HS, which has appeared recently in the literature, leading to improved performance. As a matter of fact, the latter HS is shown to be a special case of ours. Based on an equivalence to Group-Lasso type HSs, the proposed HSs are utilized toward corresponding support vector machine-based formulations. Finally, experimental results on multitask learning problems underline the quality of the derived bounds and validate this paper's analysis.
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
Hilbert-Schmidt expansion for the nucleon-deuteron scattering amplitude
International Nuclear Information System (INIS)
Moeller, K.; Narodetskii, I.M.
1983-01-01
The Hilbert-Schmidt method is used to sum the divergent iterative series for the partial amplitudes of nucleon-deuteron scattering in the energy region above the deuteron breakup threshold. It is observed that the Hilbert-Schmidt series for the partial amplitudes themselves diverges, which is due to the closeness of the logarithmic singularities. But if the first iterations in the series for multiple scattering are subtracted from the amplitude, the Hilbert-Schmidt series for the remainder converges rapidly. The final answer obtained in the present paper is in excellent agreement with the results obtained in exact calculations
Application of Arbitrary-Order Hilbert Spectral Analysis to Passive Scalar Turbulence
International Nuclear Information System (INIS)
Huang, Y X; Lu, Z M; Liu, Y L; Schmitt, F G; Gagne, Y
2011-01-01
In previous work [Huang et al., PRE 82, 26319, 2010], we found that the passive scalar turbulence field maybe less intermittent than what we believed before. Here we apply the same method, namely arbitrary-order Hilbert spectral analysis, to a passive scalar (temperature) time series with a Taylor's microscale Reynolds number Re λ ≅ 3000. We find that with increasing Reynolds number, the discrepancy of scaling exponents between Hilbert ξ θ (q) and Kolmogorov-Obukhov-Corrsin (KOC) theory is increasing, and consequently the discrepancy between Hilbert and structure function could disappear at infinite Reynolds number.
Phase difference estimation method based on data extension and Hilbert transform
International Nuclear Information System (INIS)
Shen, Yan-lin; Tu, Ya-qing; Chen, Lin-jun; Shen, Ting-ao
2015-01-01
To improve the precision and anti-interference performance of phase difference estimation for non-integer periods of sampling signals, a phase difference estimation method based on data extension and Hilbert transform is proposed. Estimated phase difference is obtained by means of data extension, Hilbert transform, cross-correlation, auto-correlation, and weighted phase average. Theoretical analysis shows that the proposed method suppresses the end effects of Hilbert transform effectively. The results of simulations and field experiments demonstrate that the proposed method improves the anti-interference performance of phase difference estimation and has better performance of phase difference estimation than the correlation, Hilbert transform, and data extension-based correlation methods, which contribute to improving the measurement precision of the Coriolis mass flowmeter. (paper)
Integrated reconfigurable photonic filters based on interferometric fractional Hilbert transforms.
Sima, C; Cai, B; Liu, B; Gao, Y; Yu, Y; Gates, J C; Zervas, M N; Smith, P G R; Liu, D
2017-10-01
In this paper, we present integrated reconfigurable photonic filters using fractional Hilbert transformers (FrHTs) and optical phase tuning structure within the silica-on-silicon platform. The proposed structure, including grating-based FrHTs, an X-coupler, and a pair of thermal tuning filaments, is fabricated through the direct UV grating writing technique. The thermal tuning effect is realized by the controllable microheaters located on the two arms of the X-coupler. We investigate the 200 GHz maximum bandwidth photonic FrHTs based on apodized planar Bragg gratings, and analyze the reflection spectrum responses. Through device integration and thermal modulation, the device could operate as photonic notch filters with 5 GHz linewidth and controllable single sideband suppression filters with measured 12 dB suppression ratio. A 50 GHz instantaneous frequency measuring system using this device is also schematically proposed and analyzed with potential 3 dB measurement improvement. The device could be configured with these multiple functions according to need. The reconfigurable structure has great potential in ultrafast all-optical signal processing fields.
Majewski M.; Magalas L.B.
2015-01-01
The parametric OMI (Optimization in Multiple Intervals), the Yoshida-Magalas (YM) and a novel Hilbert-twin (H-twin) methods are advocated for computing the logarithmic decrement in the field of internal friction and mechanical spectroscopy of solids. It is shown that dispersion in experimental points results mainly from the selection of the computing methods, the number of oscillations, and noise. It is demonstrated that conventional Hilbert transform method suffers from high dispersion in in...
Application of Hilbert-Huang Transform in Generating Spectrum-Compatible Earthquake Time Histories
Ni, Shun-Hao; Xie, Wei-Chau; Pandey, Mahesh
2011-01-01
Spectrum-compatible earthquake time histories have been widely used for seismic analysis and design. In this paper, a data processing method, Hilbert-Huang transform, is applied to generate earthquake time histories compatible with the target seismic design spectra based on multiple actual earthquake records. Each actual earthquake record is decomposed into several components of time-dependent amplitude and frequency by Hilbert-Huang transform. The spectrum-compatible earthquake time history ...
International Nuclear Information System (INIS)
Bonora, Loriano; Bytsenko, Andrey; Elizalde, Emilio
2012-01-01
This review paper contains a concise introduction to highest weight representations of infinite-dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera of superconformal quantum mechanics and superstring models. The common link of all these concepts and of the many examples considered in this paper is to be found in a very important feature of the theory of infinite-dimensional Lie algebras: the modular properties of the characters (generating functions) of certain representations. The characters of the highest weight modules represent the holomorphic parts of the partition functions on the torus for the corresponding conformal field theories. We discuss the role of the unimodular (and modular) groups and the (Selberg-type) Ruelle spectral functions of hyperbolic geometry in the calculation of elliptic genera and associated q-series. For mathematicians, elliptic genera are commonly associated with new mathematical invariants for spaces, while for physicists elliptic genera are one-loop string partition function. (Therefore, they are applicable, for instance, to topological Casimir effect calculations.) We show that elliptic genera can be conveniently transformed into product expressions, which can then inherit the homology properties of appropriate polygraded Lie algebras. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (review)
Hilbert's 'Foundations of Physics': Gravitation and electromagnetism within the axiomatic method
Brading, K. A.; Ryckman, T. A.
2008-01-01
In November and December 1915, Hilbert presented two communications to the Göttingen Academy of Sciences under the common title 'The Foundations of Physics'. Versions of each eventually appeared in the Nachrichten of the Academy. Hilbert's first communication has received significant reconsideration in recent years, following the discovery of printer's proofs of this paper, dated 6 December 1915. The focus has been primarily on the 'priority dispute' over the Einstein field equations. Our contention, in contrast, is that the discovery of the December proofs makes it possible to see the thematic linkage between the material that Hilbert cut from the published version of the first communication and the content of the second, as published in 1917. The latter has been largely either disregarded or misinterpreted, and our aim is to show that (a) Hilbert's two communications should be regarded as part of a wider research program within the overarching framework of 'the axiomatic method' (as Hilbert expressly stated was the case), and (b) the second communication is a fine and coherent piece of work within this framework, whose principal aim is to address an apparent tension between general invariance and causality (in the precise sense of Cauchy determination), pinpointed in Theorem I of the first communication. This is not the same problem as that found in Einstein's 'hole argument'-something that, we argue, never confused Hilbert.
Sinha, Shriprakash
2017-12-04
Ever since the accidental discovery of Wingless [Sharma R.P., Drosophila information service, 1973, 50, p 134], research in the field of Wnt signaling pathway has taken significant strides in wet lab experiments and various cancer clinical trials, augmented by recent developments in advanced computational modeling of the pathway. Information rich gene expression profiles reveal various aspects of the signaling pathway and help in studying different issues simultaneously. Hitherto, not many computational studies exist which incorporate the simultaneous study of these issues. This manuscript ∙ explores the strength of contributing factors in the signaling pathway, ∙ analyzes the existing causal relations among the inter/extracellular factors effecting the pathway based on prior biological knowledge and ∙ investigates the deviations in fold changes in the recently found prevalence of psychophysical laws working in the pathway. To achieve this goal, local and global sensitivity analysis is conducted on the (non)linear responses between the factors obtained from static and time series expression profiles using the density (Hilbert-Schmidt Information Criterion) and variance (Sobol) based sensitivity indices. The results show the advantage of using density based indices over variance based indices mainly due to the former's employment of distance measures & the kernel trick via Reproducing kernel Hilbert space (RKHS) that capture nonlinear relations among various intra/extracellular factors of the pathway in a higher dimensional space. In time series data, using these indices it is now possible to observe where in time, which factors get influenced & contribute to the pathway, as changes in concentration of the other factors are made. This synergy of prior biological knowledge, sensitivity analysis & representations in higher dimensional spaces can facilitate in time based administration of target therapeutic drugs & reveal hidden biological information within
Projective limits of state spaces IV. Fractal label sets
Lanéry, Suzanne; Thiemann, Thomas
2018-01-01
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski (1977) to represent quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces (see Lanéry (2016) [1] for a concise introduction to this formalism). One can thus bypass the need to select a vacuum state for the theory, and still be provided with an explicit and constructive description of the quantum state space, at least as long as the label set indexing the projective structure is countable. Because uncountable label sets are much less practical in this context, we develop in the present article a general procedure to trim an originally uncountable label set down to countable cardinality. In particular, we investigate how to perform this tightening of the label set in a way that preserves both the physical content of the algebra of observables and its symmetries. This work is notably motivated by applications to the holonomy-flux algebra underlying Loop Quantum Gravity. Building on earlier work by Okołów (2013), a projective state space was introduced for this algebra in Lanéry and Thiemann (2016). However, the non-trivial structure of the holonomy-flux algebra prevents the construction of satisfactory semi-classical states (Lanéry and Thiemann, 2017). Implementing the general procedure just mentioned in the case of a one-dimensional version of this algebra, we show how a discrete subalgebra can be extracted without destroying universality nor diffeomorphism invariance. On this subalgebra, quantum states can then be constructed which are more regular than was possible on the original algebra. In particular, this allows the design of semi-classical states whose semi-classicality is enforced step by step, starting from collective, macroscopic degrees of freedom and going down progressively toward smaller and smaller scales.
Coherent states in the fermionic Fock space
International Nuclear Information System (INIS)
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. (paper)
Seizure classification in EEG signals utilizing Hilbert-Huang transform
Directory of Open Access Journals (Sweden)
Abdulhay Enas W
2011-05-01
Full Text Available Abstract Background Classification method capable of recognizing abnormal activities of the brain functionality are either brain imaging or brain signal analysis. The abnormal activity of interest in this study is characterized by a disturbance caused by changes in neuronal electrochemical activity that results in abnormal synchronous discharges. The method aims at helping physicians discriminate between healthy and seizure electroencephalographic (EEG signals. Method Discrimination in this work is achieved by analyzing EEG signals obtained from freely accessible databases. MATLAB has been used to implement and test the proposed classification algorithm. The analysis in question presents a classification of normal and ictal activities using a feature relied on Hilbert-Huang Transform. Through this method, information related to the intrinsic functions contained in the EEG signal has been extracted to track the local amplitude and the frequency of the signal. Based on this local information, weighted frequencies are calculated and a comparison between ictal and seizure-free determinant intrinsic functions is then performed. Methods of comparison used are the t-test and the Euclidean clustering. Results The t-test results in a P-value Conclusion An original tool for EEG signal processing giving physicians the possibility to diagnose brain functionality abnormalities is presented in this paper. The proposed system bears the potential of providing several credible benefits such as fast diagnosis, high accuracy, good sensitivity and specificity, time saving and user friendly. Furthermore, the classification of mode mixing can be achieved using the extracted instantaneous information of every IMF, but it would be most likely a hard task if only the average value is used. Extra benefits of this proposed system include low cost, and ease of interface. All of that indicate the usefulness of the tool and its use as an efficient diagnostic tool.
Comments on the interacting Einstein-Hilbert drop
International Nuclear Information System (INIS)
Khanal, U.
2004-12-01
The bosonic internal co-ordinates of the Einstein-Hilbert drop is complexified to include U(1) gauge interaction. The equations of motion of the gauge fields are Maxwell equations. The EOM of the internal co-ordinates are elliptic under matter domination and hyperbolic under vacuum domination. These equations take on the familiar form of the wave equation of the interacting massless scalar field in any world spacetime that has the sum of its energy-momentum and Einstein tensors proportional to the induced metric. The reparametrization invariance of the worldtime can be used to identify it with the internal time. This results in a gauge condition that relates time to the curvature, gauge potential and energy-momentum. In gaussian normal co-ordinates of a constant curvature worldspace with real time, this condition translates into vanishing pressure, allowing a solution for the time dependence of the time-component of the vector potential. This potential has a simple pole at the origin of the complex time-plane, and another at a point on the imaginary axis. The singularity at the origin occurs only in the imaginary part of the potential. This potential in turn makes it possible to solve for the time dependence of the internal co-ordinates. Real internal co-ordinates have to be linear in worldtime. The complex internal co-ordinate also has two simple poles: one is at the same point on the imaginary axis as the potential; the other at infinity occurs only in the imaginary part. The origin turns out to be a regular point. (author)
Seizure classification in EEG signals utilizing Hilbert-Huang transform.
Oweis, Rami J; Abdulhay, Enas W
2011-05-24
Classification method capable of recognizing abnormal activities of the brain functionality are either brain imaging or brain signal analysis. The abnormal activity of interest in this study is characterized by a disturbance caused by changes in neuronal electrochemical activity that results in abnormal synchronous discharges. The method aims at helping physicians discriminate between healthy and seizure electroencephalographic (EEG) signals. Discrimination in this work is achieved by analyzing EEG signals obtained from freely accessible databases. MATLAB has been used to implement and test the proposed classification algorithm. The analysis in question presents a classification of normal and ictal activities using a feature relied on Hilbert-Huang Transform. Through this method, information related to the intrinsic functions contained in the EEG signal has been extracted to track the local amplitude and the frequency of the signal. Based on this local information, weighted frequencies are calculated and a comparison between ictal and seizure-free determinant intrinsic functions is then performed. Methods of comparison used are the t-test and the Euclidean clustering. The t-test results in a P-value with respect to its fast response and ease to use. An original tool for EEG signal processing giving physicians the possibility to diagnose brain functionality abnormalities is presented in this paper. The proposed system bears the potential of providing several credible benefits such as fast diagnosis, high accuracy, good sensitivity and specificity, time saving and user friendly. Furthermore, the classification of mode mixing can be achieved using the extracted instantaneous information of every IMF, but it would be most likely a hard task if only the average value is used. Extra benefits of this proposed system include low cost, and ease of interface. All of that indicate the usefulness of the tool and its use as an efficient diagnostic tool.
Directory of Open Access Journals (Sweden)
Magalas L.B.
2015-06-01
Full Text Available In this work, we present a novel Hilbert-twin method to compute an envelope and the logarithmic decrement, δ, from exponentially damped time-invariant harmonic strain signals embedded in noise. The results obtained from five computing methods: (1 the parametric OMI (Optimization in Multiple Intervals method, two interpolated discrete Fourier transform-based (IpDFT methods: (2 the Yoshida-Magalas (YM method and (3 the classic Yoshida (Y method, (4 the novel Hilbert-twin (H-twin method based on the Hilbert transform, and (5 the conventional Hilbert transform (HT method are analyzed and compared. The fundamental feature of the Hilbert-twin method is the efficient elimination of intrinsic asymmetrical oscillations of the envelope, aHT (t, obtained from the discrete Hilbert transform of analyzed signals. Excellent performance in estimation of the logarithmic decrement from the Hilbert-twin method is comparable to that of the OMI and YM for the low- and high-damping levels. The Hilbert-twin method proved to be robust and effective in computing the logarithmic decrement and the resonant frequency of exponentially damped free decaying signals embedded in experimental noise. The Hilbert-twin method is also appropriate to detect nonlinearities in mechanical loss measurements of metals and alloys.
Einstein and Hilbert: The creation of general relativity
International Nuclear Information System (INIS)
Todorov, I.T.
1992-12-01
It took eight years after Einstein announced the basic physical ideas behind the relativistic gravity theory before the proper mathematical formulation of general-relativity was mastered. The efforts of the greatest physicist and of the greatest mathematician of the time was involved and reached a breathtaking concentration during the last month of the work. (author)
Hilbert transform and optical tomography for anisotropic edge enhancement of phase objects
International Nuclear Information System (INIS)
Montes-Perez, Areli; Meneses-Fabian, Cruz; Rodriguez-Zurita, Gustavo
2011-01-01
In phase object tomography a slice reconstruction is related to distribution of refractive index. Typically, this is obtained by applying the filtered back-projection algorithm to the set of projections (sinogram) obtained experimentally, which are sequentially obtained by calculating the phase of the wave emerging from the slice of the object at different angles. In this paper, based on optical implementation of the Hilbert-transform in a 4f Fourier operator, the Hilbert transform of the projections leaving of the object are obtained numerically. When these projection data are captured for a set of viewing angles an unconventional sinogram is eventually obtained, we have called it as an Hilbert-sinogram. The reconstruction obtained by applying the filtered back-projection algorithm is proportional to the Hilbert transform of the distribution of refractive index of the slice and the obtained image shows a typical isotropic edge enhancement. In this manuscript, the theoretical analysis and the numerical implementation of the Hilbert-transform, mathematical model of the edge enhancement reconstructed are extensively detailed.
Wavelet Based Hilbert Transform with Digital Design and Application to QCM-SS Watermarking
Directory of Open Access Journals (Sweden)
S. P. Maity
2008-04-01
Full Text Available In recent time, wavelet transforms are used extensively for efficient storage, transmission and representation of multimedia signals. Hilbert transform pairs of wavelets is the basic unit of many wavelet theories such as complex filter banks, complex wavelet and phaselet etc. Moreover, Hilbert transform finds various applications in communications and signal processing such as generation of single sideband (SSB modulation, quadrature carrier multiplexing (QCM and bandpass representation of a signal. Thus wavelet based discrete Hilbert transform design draws much attention of researchers for couple of years. This paper proposes an (i algorithm for generation of low computation cost Hilbert transform pairs of symmetric filter coefficients using biorthogonal wavelets, (ii approximation to its rational coefficients form for its efficient hardware realization and without much loss in signal representation, and finally (iii development of QCM-SS (spread spectrum image watermarking scheme for doubling the payload capacity. Simulation results show novelty of the proposed Hilbert transform design and its application to watermarking compared to existing algorithms.
International Nuclear Information System (INIS)
Furdea, A; Wilson, J D; Eswaran, H; Lowery, C L; Govindan, R B; Preissl, H
2009-01-01
We propose a multi-stage approach using Wavelet and Hilbert transforms to identify uterine contraction bursts in magnetomyogram (MMG) signals measured using a 151 magnetic sensor array. In the first stage, we decompose the MMG signals by wavelet analysis into multilevel approximate and detail coefficients. In each level, the signals are reconstructed using the detail coefficients followed by the computation of the Hilbert transform. The Hilbert amplitude of the reconstructed signals from different frequency bands (0.1–1 Hz) is summed up over all the sensors to increase the signal-to-noise ratio. Using a novel clustering technique, affinity propagation, the contractile bursts are distinguished from the noise level. The method is applied on simulated MMG data, using a simple stochastic model to determine its robustness and to seven MMG datasets
Sima, Chaotan; Gates, J C; Holmes, C; Mennea, P L; Zervas, M N; Smith, P G R
2013-09-01
Terahertz bandwidth photonic Hilbert transformers are proposed and experimentally demonstrated. The integrated device is fabricated via a direct UV grating writing technique in a silica-on-silicon platform. The photonic Hilbert transformer operates at bandwidths of up to 2 THz (~16 nm) in the telecom band, a 10-fold greater bandwidth than any previously reported experimental approaches. Achieving this performance requires detailed knowledge of the system transfer function of the direct UV grating writing technique; this allows improved linearity and yields terahertz bandwidth Bragg gratings with improved spectral quality. By incorporating a flat-top reflector and Hilbert grating with a waveguide coupler, an ultrawideband all-optical single-sideband filter is demonstrated.
Casazza, Peter G
1989-01-01
This monograph provides a structure theory for the increasingly important Banach space discovered by B.S. Tsirelson. The basic construction should be accessible to graduate students of functional analysis with a knowledge of the theory of Schauder bases, while topics of a more advanced nature are presented for the specialist. Bounded linear operators are studied through the use of finite-dimensional decompositions, and complemented subspaces are studied at length. A myriad of variant constructions are presented and explored, while open questions are broached in almost every chapter. Two appendices are attached: one dealing with a computer program which computes norms of finitely-supported vectors, while the other surveys recent work on weak Hilbert spaces (where a Tsirelson-type space provides an example).
Cutting force response in milling of Inconel: analysis by wavelet and Hilbert-Huang Transforms
Directory of Open Access Journals (Sweden)
Grzegorz Litak
Full Text Available We study the milling process of Inconel. By continuously increasing the cutting depth we follow the system response and appearance of oscillations of larger amplitude. The cutting force amplitude and frequency analysis has been done by means of wavelets and Hilbert-Huang transform. We report that in our system the force oscillations are closely related to the rotational motion of the tool and advocate for a regenerative mechanism of chatter vibrations. To identify vibrations amplitudes occurrence in time scale we apply wavelet and Hilbert-Huang transforms.
Methods for detection and characterization of signals in noisy data with the Hilbert-Huang transform
International Nuclear Information System (INIS)
Stroeer, Alexander; Cannizzo, John K.; Camp, Jordan B.; Gagarin, Nicolas
2009-01-01
The Hilbert-Huang transform is a novel, adaptive approach to time series analysis that does not make assumptions about the data form. Its adaptive, local character allows the decomposition of nonstationary signals with high time-frequency resolution but also renders it susceptible to degradation from noise. We show that complementing the Hilbert-Huang transform with techniques such as zero-phase filtering, kernel density estimation and Fourier analysis allows it to be used effectively to detect and characterize signals with low signal-to-noise ratios.
On the discovery of the gravitational field equations by Einstein and Hilbert: new materials
International Nuclear Information System (INIS)
Vizgin, Vladimir P
2001-01-01
This article describes the history of discovery of the equations of gravitational field by Albert Einstein and David Hilbert in November 1915. The proof sheet of Hilbert's lecture report, made on 20 November 1915 and published in March 1916, rediscovered in 1997 in the archive of the university of Goettingen, throws new light on the history of this discovery. We also discuss the early history of the general theory of relativity that led to the expression of the general covariant equations of gravitational field. (from the history of physics)
Zhuang, L.; Khan, M.R.H.; Beeker, Willem; Beeker, W.P.; Leinse, Arne; Heideman, Rene; Roeloffzen, C.G.H.
2012-01-01
We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonatorbased optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance
Convexity and the Euclidean Metric of Space-Time
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Nikolaos Kalogeropoulos
2017-02-01
Full Text Available We address 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 purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces.
Barbagallo, Annamaria; Di Meglio, Guglielmo; Mauro, Paolo
2017-07-01
The aim of the paper is to study, in a Hilbert space setting, a general random oligopolistic market equilibrium problem in presence of both production and demand excesses and to characterize the random Cournot-Nash equilibrium principle by means of a stochastic variational inequality. Some existence results are presented.
Hilbert scheme of points on cyclic quotient singularities of type (p,1)
Gyenge, Ádám
2016-01-01
In this note we investigate the generating series of the Euler characteristics of Hilbert scheme of points on cyclic quotient singularities of type (p,1). We link the appearing combinatorics to p-fountains, a generalization of the notion of fountain of coins. We obtain a representation of the generating series as coefficient of a two variable generating series.
Experimental validation of a structural damage detection method based on marginal Hilbert spectrum
Banerji, Srishti; Roy, Timir B.; Sabamehr, Ardalan; Bagchi, Ashutosh
2017-04-01
Structural Health Monitoring (SHM) using dynamic characteristics of structures is crucial for early damage detection. Damage detection can be performed by capturing and assessing structural responses. Instrumented structures are monitored by analyzing the responses recorded by deployed sensors in the form of signals. Signal processing is an important tool for the processing of the collected data to diagnose anomalies in structural behavior. The vibration signature of the structure varies with damage. In order to attain effective damage detection, preservation of non-linear and non-stationary features of real structural responses is important. Decomposition of the signals into Intrinsic Mode Functions (IMF) by Empirical Mode Decomposition (EMD) and application of Hilbert-Huang Transform (HHT) addresses the time-varying instantaneous properties of the structural response. The energy distribution among different vibration modes of the intact and damaged structure depicted by Marginal Hilbert Spectrum (MHS) detects location and severity of the damage. The present work investigates damage detection analytically and experimentally by employing MHS. The testing of this methodology for different damage scenarios of a frame structure resulted in its accurate damage identification. The sensitivity of Hilbert Spectral Analysis (HSA) is assessed with varying frequencies and damage locations by means of calculating Damage Indices (DI) from the Hilbert spectrum curves of the undamaged and damaged structures.
Analysis of the Cofrentes instability with the Hilbert-Huang transform
International Nuclear Information System (INIS)
Blazquez, J.; Galindo, A.
2010-01-01
The most obvious application of the Hilbert-Huang transform is the denoising (signal isolation). In this article, the dynamic system is the power of a BWR reactor that undergoes instability. The signal and the dynamic systems are described, which in this case corresponds to a current incident in a commercial BWR reactor (Cofrentes). Finally, empirical modes are calculated and the results are analyzed.
Pairs of dual Gabor frames generated by functions of Hilbert-Schmidt type
DEFF Research Database (Denmark)
Christiansen, Lasse Hjuler
2015-01-01
where each member may be written as a linear combination of integer translates of any B-spline. We introduce functions of Hilbert-Schmidt type along with a new method which allows us to associate to certain such functions finite families of recursively defined dual windows of arbitrary smoothness...
Heterotic reduction of Courant algebroid connections and Einstein–Hilbert actions
Energy Technology Data Exchange (ETDEWEB)
Jurčo, Branislav, E-mail: jurco@karlin.mff.cuni.cz [Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Prague 186 75 (Czech Republic); Vysoký, Jan, E-mail: vysoky@math.cas.cz [Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, Prague 115 67 (Czech Republic); Mathematical Sciences Institute, Australian National University, Acton ACT 2601 (Australia)
2016-08-15
We discuss Levi-Civita connections on Courant algebroids. We define an appropriate generalization of the curvature tensor and compute the corresponding scalar curvatures in the exact and heterotic case, leading to generalized (bosonic) Einstein–Hilbert type of actions known from supergravity. In particular, we carefully analyze the process of the reduction for the generalized metric, connection, curvature tensor and the scalar curvature.
Heterotic reduction of Courant algebroid connections and Einstein–Hilbert actions
International Nuclear Information System (INIS)
Jurčo, Branislav; Vysoký, Jan
2016-01-01
We discuss Levi-Civita connections on Courant algebroids. We define an appropriate generalization of the curvature tensor and compute the corresponding scalar curvatures in the exact and heterotic case, leading to generalized (bosonic) Einstein–Hilbert type of actions known from supergravity. In particular, we carefully analyze the process of the reduction for the generalized metric, connection, curvature tensor and the scalar curvature.
Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics.
Corry, Leo
2018-04-28
The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).
Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics
Corry, Leo
2018-04-01
The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932. This article is part of the theme issue `Hilbert's sixth problem'.
The classes of the quasihomogeneous Hilbert schemes of points on the plane
Buryak, A.
2012-01-01
Abstract: In this paper we give a formula for the classes (in the Grothendieck ring of complex quasi-projective varieties) of irreducible components of -quasi-homogeneous Hilbert schemes of points on the plane. We find a new simple geometric interpretation of the -Catalan numbers. Finally, we
Infinite conformal symmetries and Riemann-Hilbert transformation in super principal chiral model
International Nuclear Information System (INIS)
Hao Sanru; Li Wei
1989-01-01
This paper shows a new symmetric transformation - C transformation in super principal chiral model and discover an infinite dimensional Lie algebra related to the Virasoro algebra without central extension. By using the Riemann-Hilbert transformation, the physical origination of C transformation is discussed
A more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function.
Wang, Aizhen; Yang, Bicheng
2017-01-01
By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.
A more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function
Directory of Open Access Journals (Sweden)
Aizhen Wang
2017-06-01
Full Text Available Abstract By means of the weight functions, the technique of real analysis and Hermite-Hadamard’s inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.
International Nuclear Information System (INIS)
Chau Ling-Lie; Ge Mo-Lin; Teh, Rosy.
1984-09-01
The Baecklund Transformations and the hidden symmetry algebra for Self-Dual Yang-Mills Equations, Landau-Lifshitz equations and the Extended Super Yang-Mills fields (N>2) are discussed on the base of the Regular Riemann-Hilbert Transform and the linearization equations. (author)
DEFF Research Database (Denmark)
Miyagi, Haruhide; Madsen, Lars Bojer
We have developed a new theoretical framework for time-dependent many-electron problems named time-dependent restricted-active-space self-consistent field (TD-RASSCF) theory. The theory generalizes the multicongurational time-dependent Hartree-Fock (MCTDHF) theory by truncating the expansion...
The canonical quantization of local scalar fields over quantum space-time
International Nuclear Information System (INIS)
Banai, M.
1983-05-01
Canonical quantization of a classical local field theory (CLFT) consisting of N real scalar fields is formulated in the Hilbert space over the sup(*)-algebra A of linear operators of L 2 (R 3 ). The canonical commutation relations (CCR) have an irreducible solution, unique up to A-unitary equivalence. The canonical equations as operator equations are equivalent to the classical (c) field equations. The interaction picture can be introduced in a well-defined manner. The main adventage of this treatment is that the corresponding S-matrix is free of divergences. The Feynman's graph technique is adaptable in a straightforward manner. This approach is a natural extension of the conventional canonical quantization method of quantum mechanics. (author)
Crystallization Formulation Lab
Federal Laboratory Consortium — The Crystallization Formulation Lab fills a critical need in the process development and optimization of current and new explosives and energetic formulations. The...
Asghari, Mohammad H; Azaña, José
2009-02-01
A simple all-fiber design for implementing an all-optical temporal Hilbert transformer is proposed and numerically demonstrated. We show that an all-optical Hilbert transformer can be implemented using a uniform-period fiber Bragg grating (FBG) with a properly designed amplitude-only grating apodization profile incorporating a single pi phase shift in the middle of the grating length. All-optical Hilbert transformers capable of processing arbitrary optical waveforms with bandwidths up to a few hundreds of gigahertz can be implemented using feasible FBGs.
The fiber bundle formalism for the quantization in curved spaces
International Nuclear Information System (INIS)
Wyrozumski, T.
1989-01-01
We set up a geometrical formulation of the canonical quantization of free Klein-Gordon field on a gravitational background. We introduce the notion of the Bogolubov bundle as the principal fiber bundle over the space of all Cauchy surfaces belonging to some fixed foliation of space-time, with the Bogolubov group as the structure group, as a tool in considering local Bogolubov transformations. Sections of the associated complex structure bundle have the meaning of attaching Hilbert spaces to Cauchy surfaces. We single out, as physical, sections defined by the equation of parallel transport on the Bogolubov bundle. The connection is then subjected to a certain nonlinear differential equation. We find a particular solution, which happens to coincide with a formula given by L.Parker for Robertson-Walker space-times. Finally, we adopt the adiabatic hypothesis as the physical input to the formalism and fix in this way a free parameter in the connection. Concluding, we comment on a possible geometrical interpretation of the regularization of stress-energy tensor and on generalizations of the formalism toward quantum gravity. 14 refs. (Author)
International Nuclear Information System (INIS)
Reznik, Benni; Groisman, Berry; Aharonov, Yakir
2002-01-01
We present a systematic simple method for constructing deterministic remote operations on single and multiple systems of arbitrary discrete dimensionality. These operations include remote rotations, remote interactions, and measurements. The resources needed for an operation on a two-level system are one ebit and a bidirectional communication of two cbits, and for an n-level system, a pair of entangled n-level particles and two classical 'nits'. In the latter case, there are n-1 possible distinct operations per n-level entangled pair. Similar results apply for generating interaction between a pair of remote systems, while for remote measurements only one-directional classical communication is needed. We further consider remote operations on N spatially distributed systems, and show that the number of possible distinct operations increases here exponentially, with the available number of entangled pairs that are initially distributed between the systems. Our results follow from the properties of a hybrid state-operator object (stator), which describes quantum correlations between states and operations
Approximately dual frames in Hilbert spaces and applications to Gabor frames
DEFF Research Database (Denmark)
Christensen, Ole; Laugesen, Richard S.
2011-01-01
constructed via perturbation theory. An alternative bound is derived for the rich class of Gabor frames, by using the Walnut representation of the frame operator to estimate the deviation from equality in the duality conditions. To illustrate these results, we construct explicit approximate duals of Gabor...
Hilbert Space Inner Products for PJ-symmetric Su-Schrieffer-Heeger Models
Czech Academy of Sciences Publication Activity Database
Růžička, František
2015-01-01
Roč. 54, č. 11 (2015), s. 4154-4163 ISSN 0020-7748 Institutional support: RVO:61389005 Keywords : Su-Schrieffer-Heeger model * physical inner products * complete set of pseudometrics * exceptional points Subject RIV: BE - Theoretical Physics Impact factor: 1.041, year: 2015
A new look at the harmonic oscillator problem in a finite-dimensional Hilbert space
International Nuclear Information System (INIS)
Bagchi, B.
1995-01-01
In this Letter some basic properties of a truncated oscillator are studied. By using finite-dimensional representation matrices of the truncated oscillator we construct new parasupersymmetric schemes and remark on their relevance to the transition operators of the non-interacting N-level system endowed with bosonic modes. ((orig.))
Moment problems in Hilbert space with applications to magnetic resonance imaging
International Nuclear Information System (INIS)
Zwaan, Marcel.
1991-01-01
This thesis is concerned with the mathematical and computational aspects of reconstruction techniques by means of magnetic resonance imaging, in particular for the time-dependent case, referred to as dynamic MRI. The main subjects are: a mathematical framework for dynamic MRI reconstruction; analytic solutions, numerical algorithms and development of reconstruction techniques; stability analysis of the reconstruction algorithms; comparison between these algorithms. (author). 63 refs.; 38 figs.; 5 tabs
Applications of automata and graphs: Labeling operators in Hilbert space. II
International Nuclear Information System (INIS)
Cho, Ilwoo; Jorgensen, Palle E. T.
2009-01-01
We introduced a family of infinite graphs directly associated with a class of von Neumann automaton model A G . These are finite state models used in symbolic dynamics: stimuli models and in control theory. In the context of groupoid von Neumann algebras, and an associated fractal group, we prove a classification theorem for representations of automata.
A Hilbert Space Geometric Representation of Shared Awareness and Joint Decision Making
Canan, Mustafa
2017-01-01
Two people in the same situation may ascribe very different meanings to their experiences. They will form different awareness, reacting differently to shared information. Various factors can give rise to this behavior. These factors include, but are not limited to, prior knowledge, training, biases, cultural factors, social factors, team vs.…
Macroscopicity of quantum superpositions on a one-parameter unitary path in Hilbert space
Volkoff, T. J.; Whaley, K. B.
2014-12-01
We analyze quantum states formed as superpositions of an initial pure product state and its image under local unitary evolution, using two measurement-based measures of superposition size: one based on the optimal quantum binary distinguishability of the branches of the superposition and another based on the ratio of the maximal quantum Fisher information of the superposition to that of its branches, i.e., the relative metrological usefulness of the superposition. A general formula for the effective sizes of these states according to the branch-distinguishability measure is obtained and applied to superposition states of N quantum harmonic oscillators composed of Gaussian branches. Considering optimal distinguishability of pure states on a time-evolution path leads naturally to a notion of distinguishability time that generalizes the well-known orthogonalization times of Mandelstam and Tamm and Margolus and Levitin. We further show that the distinguishability time provides a compact operational expression for the superposition size measure based on the relative quantum Fisher information. By restricting the maximization procedure in the definition of this measure to an appropriate algebra of observables, we show that the superposition size of, e.g., NOON states and hierarchical cat states, can scale linearly with the number of elementary particles comprising the superposition state, implying precision scaling inversely with the total number of photons when these states are employed as probes in quantum parameter estimation of a 1-local Hamiltonian in this algebra.
Alam, Md. Ashad; Fukumizu, Kenji; Wang, Yu-Ping
2016-01-01
To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). They are sensitive to contaminated data, even when using bounded positive definite kernels. First, we propose robust kernel covariance operator (robust kernel CO) and robust kernel crosscovariance operator (robust kern...
Dirac-like operators on the Hilbert space of differential forms on manifolds with boundaries
Pérez-Pardo, Juan Manuel
The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analyzed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like potentials, in manifolds of dimension higher than one. Self-adjoint boundary conditions for the case of dimension 2 are obtained explicitly.
Independence and totalness of subspaces in phase space methods
Vourdas, A.
2018-04-01
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the non-distributivity of the lattice of subspaces, there are various levels of independence, from pairwise independence up to (full) independence. Pairwise totalness, totalness and other intermediate concepts are also introduced, which roughly express that the subspaces overlap strongly among themselves, and they cover the full Hilbert space. A duality between independence and totalness, that involves orthocomplementation (logical NOT operation), is discussed. Another approach to independence is also studied, using Rota's formalism on independent partitions of the Hilbert space. This is used to define informational independence, which is proved to be equivalent to independence. As an application, the pentagram (used in discussions on contextuality) is analysed using these concepts.
Ether formulations of relativity
International Nuclear Information System (INIS)
Duffy, M.C.
1980-01-01
Contemporary ether theories are surveyed and criticised, especially those formally identical to orthodox Relativity. The historical development of Relativity, Special and General, in terms of an ether, is briefly indicated. Classical interpretations of Generalized Relativity using ether are compared to Euclidean formulations using a background space. The history of a sub-group of theories, formulating a 'new' Relativity involving modified transforms, is outlined. According to the theory with which they agree, recent supposed detections of drift are classified and criticised. Cosmological evidence suggesting an ether is mentioned. Only ether theories formally identical to Relativity have been published in depth. They stand criticised as being contrary to the positivist spirit. The history of mechanical analogues is traced, from Hartley's representing gravitating matter as spherical standing waves, to recent suggestions that vortex-sponge might model electromagnetic, quantum, uncertainty and faster-than-light phenomena. Contemporary theories are particular physical theories, themselves 'second interpretations' of a primary mathematical model. Mechanical analogues are auxiliary, not necessary, to other theory, disclosing relationships between classical and non-classical descriptions of assemblies charging state. The ether-relativity polemic, part of a broader dispute about relativity, is founded on mistaken conceptions of the roles of mathematical and physical models, mechanical analogues; and a distored view of history, which indicates that ether theories have become relativistic. (author)
Hörmander spaces, interpolation, and elliptic problems
Mikhailets, Vladimir A; Malyshev, Peter V
2014-01-01
The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hörmander function spaces. This theory was constructed by the authors in a number of papers published in 2005-2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature. The monograph is written in detail and in a
Martins, Luis Gustavo Nogueira; Stefanello, Michel Baptistella; Degrazia, Gervásio Annes; Acevedo, Otávio Costa; Puhales, Franciano Scremin; Demarco, Giuliano; Mortarini, Luca; Anfossi, Domenico; Roberti, Débora Regina; Costa, Felipe Denardin; Maldaner, Silvana
2016-11-01
In this study we analyze natural complex signals employing the Hilbert-Huang spectral analysis. Specifically, low wind meandering meteorological data are decomposed into turbulent and non turbulent components. These non turbulent movements, responsible for the absence of a preferential direction of the horizontal wind, provoke negative lobes in the meandering autocorrelation functions. The meandering characteristic time scales (meandering periods) are determined from the spectral peak provided by the Hilbert-Huang marginal spectrum. The magnitudes of the temperature and horizontal wind meandering period obtained agree with the results found from the best fit of the heuristic meandering autocorrelation functions. Therefore, the new method represents a new procedure to evaluate meandering periods that does not employ mathematical expressions to represent observed meandering autocorrelation functions.
Hilbert Series and Mixed Branches of T[SU(N)] theories
Energy Technology Data Exchange (ETDEWEB)
Carta, Federico [Departamento de Física Teórica and Instituto de Física Teórica UAM-CSIC,Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Hayashi, Hirotaka [Departamento de Física Teórica and Instituto de Física Teórica UAM-CSIC,Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Tokai University,4-1-1 Kitakaname, Hiratsuka, Kanagawa 259-1292 (Japan)
2017-02-07
We consider mixed branches of 3dN=4T[SU(N)] theory. We compute the Hilbert series of the Coulomb branch part of the mixed branch from a restriction rule acting on the Hilbert series of the full Coulomb branch that will truncate the magnetic charge summation only to the subset of BPS dressed monopole operators that arise in the Coulomb branch sublocus where the mixed branch stems. This restriction can be understood directly from the type IIB brane picture by a relation between the magnetic charges of the monopoles and brane position moduli. We also apply the restriction rule to the Higgs branch part of a given mixed branch by exploiting 3d mirror symmetry. Both cases show complete agreement with the results calculated by different methods.
International Nuclear Information System (INIS)
Mei Jianwei
2012-01-01
We suggest a way to study possible conformal symmetries on black hole horizons. We do this by carrying out a Kaluza-Klein-like reduction of the Einstein-Hilbert action along the ignorable coordinates of stationary and axisymmetric black holes. Rigid diffeomorphism invariance of the m-ignorable coordinates then becomes a global SL(m, R) gauge symmetry of the reduced action. Related to each non-vanishing angular velocity, there is a particular SL(2, R) subgroup, which can be extended to the Witt algebra on the black hole horizons. The classical Einstein-Hilbert action thus has k-copies of infinite-dimensional conformal symmetries on a given black hole horizon, with k being the number of non-vanishing angular velocities of the black hole. (paper)
A two-step Hilbert transform method for 2D image reconstruction
International Nuclear Information System (INIS)
Noo, Frederic; Clackdoyle, Rolf; Pack, Jed D
2004-01-01
The paper describes a new accurate two-dimensional (2D) image reconstruction method consisting of two steps. In the first step, the backprojected image is formed after taking the derivative of the parallel projection data. In the second step, a Hilbert filtering is applied along certain lines in the differentiated backprojection (DBP) image. Formulae for performing the DBP step in fan-beam geometry are also presented. The advantage of this two-step Hilbert transform approach is that in certain situations, regions of interest (ROIs) can be reconstructed from truncated projection data. Simulation results are presented that illustrate very similar reconstructed image quality using the new method compared to standard filtered backprojection, and that show the capability to correctly handle truncated projections. In particular, a simulation is presented of a wide patient whose projections are truncated laterally yet for which highly accurate ROI reconstruction is obtained
Frequency hopping signal detection based on wavelet decomposition and Hilbert-Huang transform
Zheng, Yang; Chen, Xihao; Zhu, Rui
2017-07-01
Frequency hopping (FH) signal is widely adopted by military communications as a kind of low probability interception signal. Therefore, it is very important to research the FH signal detection algorithm. The existing detection algorithm of FH signals based on the time-frequency analysis cannot satisfy the time and frequency resolution requirement at the same time due to the influence of window function. In order to solve this problem, an algorithm based on wavelet decomposition and Hilbert-Huang transform (HHT) was proposed. The proposed algorithm removes the noise of the received signals by wavelet decomposition and detects the FH signals by Hilbert-Huang transform. Simulation results show the proposed algorithm takes into account both the time resolution and the frequency resolution. Correspondingly, the accuracy of FH signals detection can be improved.
Directory of Open Access Journals (Sweden)
Isti Qomah
2017-01-01
Full Text Available Kerusakan batang rotor merupakan salah satu jenis kerusakan pada motor induksi yang dapat menyebabkan masalah serius. Kerusakan tersebut dapat mencapai 5% - 10% dari seluruh kasus gangguan motor induksi. Oleh karena itu, perlu adanya diagnosis awal yang mendeteksi adanya gangguan pada rotor motor induksi, agar dapat dilakukan perbaikan lebih cepat dan tanggap sebelum terjadi gangguan yang lebih besar. Tugas Akhir ini membahas terkait teknik deteksi kerusakan batang rotor pada motor induksi dengan menggunakan analisis arus mula. Sistem yang digunakan berbasis decomposition wavelet transform terlebih dahulu kemudian dilanjutkan dengan analisis berbasis hilbert transform sebagai perangkat pengolahan sinyal sehingga mampu mendeteksi motor dalam keadaan sehat atau mengalami kerusakan. Pengujian sistem dilakukan dalam beberapa kondisi, yaitu kondisi tanpa beban dan berbeban. Selain itu, kondisi yang diberikan adalah kecacatan mulai dai 1BRB hingga 3BRB. Hasil pengujian membuktikan bahwa decomposition wavelet transform dan Hilbert transform mampu mendeteksi perbedaan kondisi pada motor induksi normal ataupun rusak pada batang rotor.
Explicit solution of Riemann-Hilbert problems for the Ernst equation
Klein, C.; Richter, O.
1998-01-01
Riemann-Hilbert problems are an important solution technique for completely integrable differential equations. They are used to introduce a free function in the solutions which can be used at least in principle to solve initial or boundary value problems. But even if the initial or boundary data can be translated into a Riemann-Hilbert problem, it is in general impossible to obtain explicit solutions. In the case of the Ernst equation, however, this is possible for a large class because the matrix problem can be shown to be gauge equivalent to a scalar one on a hyperelliptic Riemann surface that can be solved in terms of theta functions. As an example we discuss the rigidly rotating dust disk.
International Nuclear Information System (INIS)
Liu, Yangqing; Tan, Yi; Xie, Huiqiao; Wang, Wenhao; Gao, Zhe
2014-01-01
An improved Hilbert-Huang transform method is developed to the time-frequency analysis of non-stationary signals in tokamak plasmas. Maximal overlap discrete wavelet packet transform rather than wavelet packet transform is proposed as a preprocessor to decompose a signal into various narrow-band components. Then, a correlation coefficient based selection method is utilized to eliminate the irrelevant intrinsic mode functions obtained from empirical mode decomposition of those narrow-band components. Subsequently, a time varying vector autoregressive moving average model instead of Hilbert spectral analysis is performed to compute the Hilbert spectrum, i.e., a three-dimensional time-frequency distribution of the signal. The feasibility and effectiveness of the improved Hilbert-Huang transform method is demonstrated by analyzing a non-stationary simulated signal and actual experimental signals in fusion plasmas
Apisa, Paul
2017-01-01
We show that all GL(2, R)-equivariant point markings over orbit closures of primitive genus two translation surfaces arise from marking pairs of points exchanged by the hyperelliptic involution, Weierstrass points, or the golden points in the golden eigenform locus. As corollaries, we classify the holomorphically varying families of points over orbifold covers of genus two Hilbert modular surfaces, solve the finite blocking problem on genus two translation surfaces, and show that there is at ...
Bazargani, Hamed Pishvai; Burla, Maurizio; Chrostowski, Lukas; Azaña, José
2016-11-01
We experimentally demonstrate high-performance integer and fractional-order photonic Hilbert transformers based on laterally apodized Bragg gratings in a silicon-on-insulator technology platform. The sub-millimeter-long gratings have been fabricated using single-etch electron beam lithography, and the resulting HT devices offer operation bandwidths approaching the THz range, with time-bandwidth products between 10 and 20.
DEFF Research Database (Denmark)
Truelsen, Jimi Lee
W. Luo and P. Sarnak have proved quantum unique ergodicity for Eisenstein series on $PSL(2,Z) \\backslash H$. We extend their result to Eisenstein series on $PSL(2,O) \\backslash H^n$, where $O$ is the ring of integers in a totally real field of degree $n$ over $Q$ with narrow class number one, using...... the Eisenstein series considered by I. Efrat. We also give an expository treatment of the theory of Hecke operators on non-holomorphic Hilbert modular forms....
Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
Energy Technology Data Exchange (ETDEWEB)
Agaltsov, A. D., E-mail: agalets@gmail.com [Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow (Russian Federation); Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr [CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau (France); IEPT RAS, 117997 Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation)
2014-10-15
We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.
Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
International Nuclear Information System (INIS)
Agaltsov, A. D.; Novikov, R. G.
2014-01-01
We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given
Vertex operators, non-abelian orbifolds and the Riemann-Hilbert problem
International Nuclear Information System (INIS)
Gato, B.; Massachusetts Inst. of Tech., Cambridge
1990-01-01
We show how to construct the oscillator part of vertex operators for the bosonic string moving on non-abelian orbifolds, using the conserved charges method. When the three-string vertices are twisted by non-commuting group elements, the construction of the conserved charges becomes the Riemann-Hilbert problem with monodromy matrices given by the twists. This is solvable for any given configuration and any non-abelian orbifold. (orig.)
Treatment of electrochemical noise data by the Hilbert-Huang transform
International Nuclear Information System (INIS)
Rahier, A.
2009-01-01
Most of the classical approaches for treating electro-chemical noise (ECN) data suffer from the non-linear and non steady-state character of the delivered signal. Very often, the link between time and the local corrosion events supposedly responsible for ECN data signatures is lost during treatment, as is obvious when using the classical Fourier Transform (FT), followed by an analysis of the response in the frequency domain. In this particular case, the information directly related to the corrosion events is distributed into the full spectra, thereby preventing the operator to derive clear and precise conclusions. In 2005, we suggested an alternative data treatment based on the Hilbert-Huang transform (HHT). The latter keeps track of the time variable and copes with non-linear and non steady-state behaviours of the system under examination. In 2006, we demonstrated the applicability of the newly proposed data treatment in the case of ECN data collected under BWR (Boiling Water Reactor) conditions. In 2007, we collected additional ECN data and started a preliminary investigation of two mathematical restrictions that are susceptible to impair the interpretation of the results. We discovered a possible modification of the Hilbert transform allowing generating controlled phase shifts that are different from pi/2 as is always the case for the Hilbert transform
Li, Xiangyu; Huang, Zhanhua; Zhu, Meng; He, Jin; Zhang, Hao
2014-12-01
Hilbert transform (HT) is widely used in temporal speckle pattern interferometry, but errors from low modulations might propagate and corrupt the calculated phase. A spatio-temporal method for phase retrieval using temporal HT and spatial phase unwrapping is presented. In time domain, the wrapped phase difference between the initial and current states is directly determined by using HT. To avoid the influence of the low modulation intensity, the phase information between the two states is ignored. As a result, the phase unwrapping is shifted from time domain to space domain. A phase unwrapping algorithm based on discrete cosine transform is adopted by taking advantage of the information in adjacent pixels. An experiment is carried out with a Michelson-type interferometer to study the out-of-plane deformation field. High quality whole-field phase distribution maps with different fringe densities are obtained. Under the experimental conditions, the maximum number of fringes resolvable in a 416×416 frame is 30, which indicates a 15λ deformation along the direction of loading.
Mukharya, Amit; Patel, Paresh U; Shenoy, Dinesh; Chaudhary, Shivang
2013-01-01
Lacidipine (LCDP) is a very low soluble and highly biovariable calcium channel blocker used in the treatment of hypertension. To increase its apparent solubility and to reduce its biovariability, solid dispersion fluid bed processing technology was explored, as it produces highly dispersible granules with a characteristic porous structure that enhances dispersibility, wettability, blend uniformity (by dissolving and spraying a solution of actives), flow ability and compressibility of granules for tableting and reducing variability by uniform drug-binder solution distribution on carrier molecules. Main object of this quality risk management (QRM) study is to provide a sophisticated "robust and rugged" Fluidized Bed Process (FBP) for the preparation of LCDP tablets with desired quality (stability) and performance (dissolution) by quality by design (QbD) concept. THIS STUDY IS PRINCIPALLY FOCUSING ON THOROUGH MECHANISTIC UNDERSTANDING OF THE FBP BY WHICH IT IS DEVELOPED AND SCALED UP WITH A KNOWLEDGE OF THE CRITICAL RISKS INVOLVED IN MANUFACTURING PROCESS ANALYZED BY RISK ASSESSMENT TOOLS LIKE: Qualitative Initial Risk-based Matrix Analysis (IRMA) and Quantitative Failure Mode Effective Analysis (FMEA) to identify and rank parameters with potential to have an impact on In Process/Finished Product Critical Quality Attributes (IP/FP CQAs). These Critical Process Parameters (CPPs) were further refined by DoE and MVDA to develop design space with Real Time Release Testing (RTRT) that leads to implementation of a control strategy to achieve consistent finished product quality at lab scale itself to prevent possible product failure at larger manufacturing scale.
Polynomial approximation of functions in Sobolev spaces
International Nuclear Information System (INIS)
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces
Geometric approach to evolution problems in metric spaces
Stojković, Igor
2011-01-01
This PhD thesis contains four chapters where research material is presented. In the second chapter the extension of the product formulas for semigroups induced by convex functionals, from the classical Hilbert space setting to the setting of general CAT(0) spaces. In the third chapter, the
A theoretical formulation of the electrophysiological inverse problem on the sphere.
Riera, Jorge J; Valdés, Pedro A; Tanabe, Kunio; Kawashima, Ryuta
2006-04-07
The construction of three-dimensional images of the primary current density (PCD) produced by neuronal activity is a problem of great current interest in the neuroimaging community, though being initially formulated in the 1970s. There exist even now enthusiastic debates about the authenticity of most of the inverse solutions proposed in the literature, in which low resolution electrical tomography (LORETA) is a focus of attention. However, in our opinion, the capabilities and limitations of the electro and magneto encephalographic techniques to determine PCD configurations have not been extensively explored from a theoretical framework, even for simple volume conductor models of the head. In this paper, the electrophysiological inverse problem for the spherical head model is cast in terms of reproducing kernel Hilbert spaces (RKHS) formalism, which allows us to identify the null spaces of the implicated linear integral operators and also to define their representers. The PCD are described in terms of a continuous basis for the RKHS, which explicitly separates the harmonic and non-harmonic components. The RKHS concept permits us to bring LORETA into the scope of the general smoothing splines theory. A particular way of calculating the general smoothing splines is illustrated, avoiding a brute force discretization prematurely. The Bayes information criterion is used to handle dissimilarities in the signal/noise ratios and physical dimensions of the measurement modalities, which could affect the estimation of the amount of smoothness required for that class of inverse solution to be well specified. In order to validate the proposed method, we have estimated the 3D spherical smoothing splines from two data sets: electric potentials obtained from a skull phantom and magnetic fields recorded from subjects performing an experiment of human faces recognition.
Eijndhoven, van S.J.L.; Graaf, de J.
1986-01-01
A new theory of generalized functions has been developed by one of the authors (de Graaf). In this theory the analyticity domain of each positive self-adjoint unbounded operator $\\mathcal{A}$ in a Hilbert space $X$ is regarded as a test space denoted by $\\mathcal{S}_{x,\\mathcal{A}} $. In the first
Schuster, Thomas; Hofmann, Bernd; Kaltenbacher, Barbara
2012-10-01
Inverse problems can usually be modelled as operator equations in infinite-dimensional spaces with a forward operator acting between Hilbert or Banach spaces—a formulation which quite often also serves as the basis for defining and analyzing solution methods. The additional amount of structure and geometric interpretability provided by the concept of an inner product has rendered these methods amenable to a convergence analysis, a fact which has led to a rigorous and comprehensive study of regularization methods in Hilbert spaces over the last three decades. However, for numerous problems such as x-ray diffractometry, certain inverse scattering problems and a number of parameter identification problems in PDEs, the reasons for using a Hilbert space setting seem to be based on conventions rather than an appropriate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, non-Hilbertian regularization and data fidelity terms incorporating a priori information on solution and noise, such as general Lp-norms, TV-type norms, or the Kullback-Leibler divergence, have recently become very popular. These facts have motivated intensive investigations on regularization methods in Banach spaces, a topic which has emerged as a highly active research field within the area of inverse problems. Meanwhile some of the most well-known regularization approaches, such as Tikhonov-type methods requiring the solution of extremal problems, and iterative ones like the Landweber method, the Gauss-Newton method, as well as the approximate inverse method, have been investigated for linear and nonlinear operator equations in Banach spaces. Convergence with rates has been proven and conditions on the solution smoothness and on the structure of nonlinearity have been formulated. Still, beyond the existing results a large number of challenging open questions have arisen, due to the more involved handling of general Banach spaces and the larger variety
Directory of Open Access Journals (Sweden)
Juan Ospina
2006-12-01
Full Text Available Hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. An adaptation of Tien D. Kieu¿s quantum hypercomputational algorithm is carried out for the dynamical algebra su(1, 1 of the Poschl-Teller potentials. The classically incomputable problem that is resolved with this hypercomputational algorithm is Hilbert¿s tenth problem. We indicated that an essential mathematical condition of these algorithms is the existence of infinitedimensional unitary irreducible representations of low dimensional dynamical algebras that allow the construction of coherent states of the Barut-Girardello type. In addition, we presented as a particular case of our hypercomputational algorithm on Poschl-Teller potentials, the hypercomputational algorithm on an infinite square well presented previously by the authors.Los hipercomputadores computan funciones o números, o en general solucionan problemas que no pueden ser computados o solucionados por una máquina de Turing. Se presenta una adaptación del algoritmo cuántico hipercomputacional propuesto por Tien D. Kieu, al álgebra dinámica su(1, 1 realizada en los potenciales Pöschl-Teller. El problema clásicamente incomputable que se resuelve con este algoritmo hipercomputacional es el d´ecimo problema de Hilbert. Se señala que una condición matemática fundamental para estos algoritmos es la existencia de una representación unitaria infinito dimensional irreducible de álgebras de baja dimensión que admitan la construcción de estados coherentes del tipo Barut-Girardello. Adicionalmente se presenta como caso límite del algoritmo propuesto sobre los potenciales Pöschl-Teller, el algoritmo hipercomputacional sobre la caja de potencial infinita construido previamente por los autores.
DEFF Research Database (Denmark)
Vincent, Claire Louise; Giebel, Gregor; Pinson, Pierre
2010-01-01
a 4-yr time series of 10-min wind speed observations. An adaptive spectral analysis method called the Hilbert–Huang transform is chosen for the analysis, because the nonstationarity of time series of wind speed observations means that they are not well described by a global spectral analysis method...... such as the Fourier transform. The Hilbert–Huang transform is a local method based on a nonparametric and empirical decomposition of the data followed by calculation of instantaneous amplitudes and frequencies using the Hilbert transform. The Hilbert–Huang transformed 4-yr time series is averaged and summarized...
Tang, Shaojie; Yang, Yi; Tang, Xiangyang
2012-01-01
Interior tomography problem can be solved using the so-called differentiated backprojection-projection onto convex sets (DBP-POCS) method, which requires a priori knowledge within a small area interior to the region of interest (ROI) to be imaged. In theory, the small area wherein the a priori knowledge is required can be in any shape, but most of the existing implementations carry out the Hilbert filtering either horizontally or vertically, leading to a vertical or horizontal strip that may be across a large area in the object. In this work, we implement a practical DBP-POCS method with radial Hilbert filtering and thus the small area with the a priori knowledge can be roughly round (e.g., a sinus or ventricles among other anatomic cavities in human or animal body). We also conduct an experimental evaluation to verify the performance of this practical implementation. We specifically re-derive the reconstruction formula in the DBP-POCS fashion with radial Hilbert filtering to assure that only a small round area with the a priori knowledge be needed (namely radial DBP-POCS method henceforth). The performance of the practical DBP-POCS method with radial Hilbert filtering and a priori knowledge in a small round area is evaluated with projection data of the standard and modified Shepp-Logan phantoms simulated by computer, followed by a verification using real projection data acquired by a computed tomography (CT) scanner. The preliminary performance study shows that, if a priori knowledge in a small round area is available, the radial DBP-POCS method can solve the interior tomography problem in a more practical way at high accuracy. In comparison to the implementations of DBP-POCS method demanding the a priori knowledge in horizontal or vertical strip, the radial DBP-POCS method requires the a priori knowledge within a small round area only. Such a relaxed requirement on the availability of a priori knowledge can be readily met in practice, because a variety of small
An explicit formula for the Hilbert symbol for Honda groups in a multidimensional local field
International Nuclear Information System (INIS)
Vostokov, S V; Lorenz, F
2003-01-01
Based on the pairing on Cartier curves explicitly constructed in the previous paper of the authors, an explicit formula for the Hilbert symbol is constructed in a multidimensional local field of characteristic zero with residue field of positive characteristic on the formal module of a one-dimensional Honda formal group. In the proof a Shafarevich basis on the formal module is constructed, and so-called integer μ-modules in two-dimensional local rings of a special form ( μ-rings) are studied
Vogt, Dominik Walter; Leonhardt, Rainer
2017-07-10
We report on data processing for continuous wave (CW) terahertz (THz) spectroscopy measurements based on a Hilbert spectral analysis to achieve MHz resolution. As an example we investigate the spectral properties of a whispering gallery mode (WGM) THz bubble resonator at critical coupling. The experimental verification clearly demonstrates the significant advantages in relative frequency resolution and required acquisition time of the proposed method over the traditional data analysis. An effective frequency resolution, only limited by the precision and stability of the laser beat signal, can be achieved without complex extensions to a standard commercially available CW THz spectrometer.
DEFF Research Database (Denmark)
Truelsen, Jimi Lee
2011-01-01
W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on PSL(2, )\\. Their result is quantitative in the sense that they find the precise asymptotics of the measure considered. We extend their result to Eisenstein series on , where is the ring of integers...... in a totally real field of degree n over with narrow class number one, using the Eisenstein series considered by I. Efrat. We also give an expository treatment of the theory of Hecke operators on non-holomorphic Hilbert modular forms....
Hilbert and Blaschke phases in the temporal coherence function of stationary broadband light.
Fernández-Pousa, Carlos R; Maestre, Haroldo; Torregrosa, Adrián J; Capmany, Juan
2008-10-27
We show that the minimal phase of the temporal coherence function gamma (tau) of stationary light having a partially-coherent symmetric spectral peak can be computed as a relative logarithmic Hilbert transform of its amplitude with respect to its asymptotic behavior. The procedure is applied to experimental data from amplified spontaneous emission broadband sources in the 1.55 microm band with subpicosecond coherence times, providing examples of degrees of coherence with both minimal and non-minimal phase. In the latter case, the Blaschke phase is retrieved and the position of the Blaschke zeros determined.
A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line
Its, A.; Sukhanov, V.
2016-05-01
The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.
Four-nucleon problem in terms of scattering of Hilbert-Schmidt resonances
International Nuclear Information System (INIS)
Narodetsky, I.M.
1974-01-01
The four-body integral equations are written in terms of the scattering amplitudes for the Hilbert-Schmidt resonances corresponding to the 3*1 and 2*2 subsystems. As a result, the four-body problem is reduced to the many channel two-body problem. A simple diagram technique is introduced which is the generalization of the usual time-ordered nonrelativistic one. The connection between the amplitudes of the two-body reactions and the scattering amplitudes for the resonances is obtained
Riemann-Hilbert approach to the time-dependent generalized sine kernel
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2010-12-15
We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann-Hilbert based analysis. (orig.)
Notes on qubit phase space and discrete symplectic structures
International Nuclear Information System (INIS)
Livine, Etera R
2010-01-01
We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite-dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the Moyal product and the differential calculus on these discrete phase spaces. In particular, the qubit phase space provides the simplest example of a four-point non-commutative phase space. We give an explicit expression of the Moyal bracket as a differential operator. We then compare the quantum dynamics encoded by the Moyal bracket to the classical dynamics: we show that the classical Poisson bracket does not satisfy the Jacobi identity thus leaving the Moyal bracket as the only consistent symplectic structure. We finally generalize our analysis to Hilbert spaces of prime dimensions d and their associated d x d phase spaces.
The de Finetti theorem for test spaces
International Nuclear Information System (INIS)
Barrett, Jonathan; Leifer, Matthew
2009-01-01
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
Method of solving conformal models in D-dimensional space I
International Nuclear Information System (INIS)
Fradkin, E.S.; Palchik, M.Y.
1996-01-01
We study the Hilbert space of conformal field theory in D-dimensional space. The latter is shown to have model-independent structure. The states of matter fields and gauge fields form orthogonal subspaces. The dynamical principle fixing the choice of model may be formulated either in each of these subspaces or in their direct sum. In the latter case, gauge interactions are necessarily present in the model. We formulate the conditions specifying the class of models where gauge interactions are being neglected. The anomalous Ward identities are derived. Different values of anomalous parameters (D-dimensional analogs of a central charge, including operator ones) correspond to different models. The structure of these models is analogous to that of 2-dimensional conformal theories. Each model is specified by D-dimensional analog of null vector. The exact solutions of the simplest models of this type are examined. It is shown that these models are equivalent to Lagrangian models of scalar fields with a triple interaction. The values of dimensions of such fields are calculated, and the closed sets of differential equations for higher Green functions are derived. Copyright copyright 1996 Academic Press, Inc
Moduli Spaces for Linear Differential Equations and the Painlevé Equations
Put, Marius van der; Saito, Masa-Hiko
2009-01-01
A systematic construction of isomonodromic families of connections of rank two on the Riemarm sphere is obtained by considering the analytic Riemann-Hilbert map RH : M -> R, where M is a moduli space of connections and 72, the monodromy space, is a moduli space for analytic data (i.e., ordinary
Second order evolution inclusions governed by sweeping process in Banach spaces
Directory of Open Access Journals (Sweden)
A. G. Ibrahim
2009-11-01
Full Text Available In this paper we prove two existence theorems concerning the existence of solutions for second order evolution inclusions governed by sweeping process with closed convex sets depending on time and state in Banach spaces. This work extends some recent existence theorems cncerning sweeping process from Hilbert spaces to Banach spaces.
Matter Loops Corrected Modified Gravity in Palatini Formulation
International Nuclear Information System (INIS)
Meng Xinhe; Wang Peng
2008-01-01
Recently, corrections to the standard Einstein-Hilbert action were proposed to explain the current cosmic acceleration in stead of introducing dark energy. In the Palatini formulation of those modified gravity models, there is an important observation due to Arkani-Hamed: matter loops will give rise to a correction to the modified gravity action proportional to the Ricci scalar of the metric. In the presence of such a term, we show that the current forms of modified gravity models in Palatini formulation, specifically, the 1/R gravity and ln R gravity, will have phantoms. Then we study the possible instabilities due to the presence of phantom fields. We show that the strong instability in the metric formulation of 1/R gravity indicated by Dolgov and Kawasaki will not appear and the decay timescales for the phantom fields may be long enough for the theories to make sense as effective field theory. On the other hand, if we change the sign of the modification terms to eliminate the phantoms, some other inconsistencies will arise for the various versions of the modified gravity models. Finally, we comment on the universal property of the Palatini formulation of the matter loops corrected modified gravity models and its implications
The solution of the sixth Hilbert problem: the ultimate Galilean revolution
D'Ariano, Giacomo Mauro
2018-04-01
I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: `physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as `clock', `rigid rod', `force', `inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory. This article is part of the theme issue `Hilbert's sixth problem'.
Energy Technology Data Exchange (ETDEWEB)
Huang, Xianjun, E-mail: xianjun.huang@manchester.ac.uk [School of Electrical and Electronic Engineering, University of Manchester, Manchester M13 9PL (United Kingdom); College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073 (China); Hu, Zhirun [School of Electrical and Electronic Engineering, University of Manchester, Manchester M13 9PL (United Kingdom); Liu, Peiguo [College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073 (China)
2014-11-15
This paper proposes a new type of graphene based tunable radar absorbing screen. The absorbing screen consists of Hilbert curve metal strip array and chemical vapour deposition (CVD) graphene sheet. The graphene based screen is not only tunable when the chemical potential of the graphene changes, but also has broadband effective absorption. The absorption bandwidth is from 8.9GHz to 18.1GHz, ie., relative bandwidth of more than 68%, at chemical potential of 0eV, which is significantly wider than that if the graphene sheet had not been employed. As the chemical potential varies from 0 to 0.4eV, the central frequency of the screen can be tuned from 13.5GHz to 19.0GHz. In the proposed structure, Hilbert curve metal strip array was designed to provide multiple narrow band resonances, whereas the graphene sheet directly underneath the metal strip array provides tunability and averagely required surface resistance so to significantly extend the screen operation bandwidth by providing broadband impedance matching and absorption. In addition, the thickness of the screen has been optimized to achieve nearly the minimum thickness limitation for a nonmagnetic absorber. The working principle of this absorbing screen is studied in details, and performance under various incident angles is presented. This work extends applications of graphene into tunable microwave radar cross section (RCS) reduction applications.
Bearing fault detection utilizing group delay and the Hilbert-Huang transform
International Nuclear Information System (INIS)
Jin, Shuai; Lee, Sang-Kwon
2017-01-01
Vibration signals measured from a mechanical system are useful to detect system faults. Signal processing has been used to extract fault information in bearing systems. However, a wide vibration signal frequency band often affects the ability to obtain the effective fault features. In addition, a few oscillation components are not useful at the entire frequency band in a vibration signal. By contrast, useful fatigue information can be embedded in the noise oscillation components. Thus, a method to estimate which frequency band contains fault information utilizing group delay was proposed in this paper. Group delay as a measure of phase distortion can indicate the phase structure relationship in the frequency domain between original (with noise) and denoising signals. We used the empirical mode decomposition of a Hilbert-Huang transform to sift the useful intrinsic mode functions based on the results of group delay after determining the valuable frequency band. Finally, envelope analysis and the energy distribution after the Hilbert transform were used to complete the fault diagnosis. The practical bearing fault data, which were divided into inner and outer race faults, were used to verify the efficiency and quality of the proposed method
Directory of Open Access Journals (Sweden)
Yaqeen S Mezaal
Full Text Available This paper presents new Wide Bandpass Filter (WBPF and Narrow Bandstop Filter (NBSF incorporating two microstrip resonators, each resonator is based on 2nd iteration of Hilbert fractal geometry. The type of filter as pass or reject band has been adjusted by coupling gap parameter (d between Hilbert resonators using a substrate with a dielectric constant of 10.8 and a thickness of 1.27 mm. Numerical simulation results as well as a parametric study of d parameter on filter type and frequency responses are presented and studied. WBPF has designed at resonant frequencies of 2 and 2.2 GHz with a bandwidth of 0.52 GHz, -28 dB return loss and -0.125 dB insertion loss while NBSF has designed for electrical specifications of 2.37 GHz center frequency, 20 MHz rejection bandwidth, -0.1873 dB return loss and 13.746 dB insertion loss. The proposed technique offers a new alternative to construct low-cost high-performance filter devices, suitable for a wide range of wireless communication systems.
Discrete Hilbert transformation and its application to estimate the wind speed in Hong Kong
Energy Technology Data Exchange (ETDEWEB)
Zhu, Zuojin [Department of Thermal Science and Energy Engineering, Institute of Engineering Science, University of Science and Technology of China, Hefei, Anhui (China); Yang, Hongxing [Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong (Hong Kong)
2002-01-01
Discrete Hilbert Transform (DHT) has been applied to estimate the wind speed with the sample data sequence selected from the data record observed by the observatory in Hong Kong in June 1989, during which the data pertain to deep valleys and sharp crests due to manifold weather conditions in this region. To confirm the performance of the discrete Hilbert transformer, two harmonic input sequences were used to inspect the output signals, whether good agreement with the theoretical results is obtained. It was found that the energy spectrum and the outputs for the two different harmonic discrete waves are certainly correct. After the inspection of the DHT filter, the sample data for wind speed in Hong Kong were used for wind speed forecasting. For zero mean input sequence, the variance of the output is the same as that of the input signals, and so is the energy spectrum. The DHT of an individual input sample can really reflect the local variation performance, since it is the convolution with the reciprocal of time and the input data sequence, but there exists phase shift. For harmonic signals, the output signal holds a 90 phase delay.
International Nuclear Information System (INIS)
Huang, Xianjun; Hu, Zhirun; Liu, Peiguo
2014-01-01
This paper proposes a new type of graphene based tunable radar absorbing screen. The absorbing screen consists of Hilbert curve metal strip array and chemical vapour deposition (CVD) graphene sheet. The graphene based screen is not only tunable when the chemical potential of the graphene changes, but also has broadband effective absorption. The absorption bandwidth is from 8.9GHz to 18.1GHz, ie., relative bandwidth of more than 68%, at chemical potential of 0eV, which is significantly wider than that if the graphene sheet had not been employed. As the chemical potential varies from 0 to 0.4eV, the central frequency of the screen can be tuned from 13.5GHz to 19.0GHz. In the proposed structure, Hilbert curve metal strip array was designed to provide multiple narrow band resonances, whereas the graphene sheet directly underneath the metal strip array provides tunability and averagely required surface resistance so to significantly extend the screen operation bandwidth by providing broadband impedance matching and absorption. In addition, the thickness of the screen has been optimized to achieve nearly the minimum thickness limitation for a nonmagnetic absorber. The working principle of this absorbing screen is studied in details, and performance under various incident angles is presented. This work extends applications of graphene into tunable microwave radar cross section (RCS) reduction applications
The solution of the sixth Hilbert problem: the ultimate Galilean revolution.
D'Ariano, Giacomo Mauro
2018-04-28
I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: 'physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as 'clock', 'rigid rod', 'force', 'inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).
International Nuclear Information System (INIS)
Wang, Zuo-Cai; Ren, Wei-Xin; Chen, Gen-Da
2012-01-01
This paper presents a recursive Hilbert transform method for the time-varying property identification of large-scale shear-type buildings with limited sensor deployments. An observer technique is introduced to estimate the building responses from limited available measurements. For an n-story shear-type building with l measurements (l ≤ n), the responses of other stories without measurements can be estimated based on the first r mode shapes (r ≤ l) as-built conditions and l measurements. Both the measured responses and evaluated responses and their Hilbert transforms are then used to track any variation of structural parameters of a multi-story building over time. Given floor masses, both the stiffness and damping coefficients of the building are identified one-by-one from the top to the bottom story. When variations of parameters are detected, a new developed branch-and-bound technique can be used to update the first r mode shapes with the identified parameters. A 60-story shear building with abruptly varying stiffness at different floors is simulated as an example. The numerical results indicate that the proposed method can detect variations of the parameters of large-scale shear-type buildings with limited sensor deployments at appropriate locations. (paper)
Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert Lagrangian
International Nuclear Information System (INIS)
Edelstein, Jose D.; Hassaine, Mokhtar; Troncoso, Ricardo; Zanelli, Jorge
2006-01-01
Starting from gravity as a Chern-Simons action for the AdS algebra in five dimensions, it is possible to modify the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein-Hilbert action plus non-minimally coupled matter. The modified system is gauge invariant under the Poincare group enlarged by an Abelian ideal. Although the resulting action naively looks like general relativity plus corrections due to matter sources, it is shown that the non-minimal couplings produce a radical departure from GR. Indeed, the dynamics is not continuously connected to the one obtained from Einstein-Hilbert action. In a matter-free configuration and in the torsionless sector, the field equations are too strong a restriction on the geometry as the metric must satisfy both the Einstein and pure Gauss-Bonnet equations. In particular, the five-dimensional Schwarzschild geometry fails to be a solution; however, configurations corresponding to a brane-world with positive cosmological constant on the worldsheet are admissible when one of the matter fields is switched on. These results can be extended to higher odd dimensions
From Kant to Hilbert a source book in the foundations of mathematics
Ewald, William Bragg
1996-01-01
This two-volume work brings together a comprehensive selection of mathematical works from the period 1707-1930. During this time the foundations of modern mathematics were laid, and From Kant to Hilbert provides an overview of the foundational work in each of the main branches of mathmeatics with narratives showing how they were linked. Now available as a separate volume. - ;Immanuel Kant''s Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics--algebra, geometry, number. theory, analysis, logic and set theory--with narratives to show how they are linked. Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are repro...
Arbitrary-order Hilbert Spectral Analysis and Intermittency in Solar Wind Density Fluctuations
Carbone, Francesco; Sorriso-Valvo, Luca; Alberti, Tommaso; Lepreti, Fabio; Chen, Christopher H. K.; Němeček, Zdenek; Šafránková, Jana
2018-05-01
The properties of inertial- and kinetic-range solar wind turbulence have been investigated with the arbitrary-order Hilbert spectral analysis method, applied to high-resolution density measurements. Due to the small sample size and to the presence of strong nonstationary behavior and large-scale structures, the classical analysis in terms of structure functions may prove to be unsuccessful in detecting the power-law behavior in the inertial range, and may underestimate the scaling exponents. However, the Hilbert spectral method provides an optimal estimation of the scaling exponents, which have been found to be close to those for velocity fluctuations in fully developed hydrodynamic turbulence. At smaller scales, below the proton gyroscale, the system loses its intermittent multiscaling properties and converges to a monofractal process. The resulting scaling exponents, obtained at small scales, are in good agreement with those of classical fractional Brownian motion, indicating a long-term memory in the process, and the absence of correlations around the spectral-break scale. These results provide important constraints on models of kinetic-range turbulence in the solar wind.
Prediction of unknown deep foundation lengths using the Hilbert Huang Transform (HHT
Directory of Open Access Journals (Sweden)
Ahmed T.M. Farid
2012-08-01
Full Text Available Prediction of unknown deep foundation embedment depth is a great deal nowadays, especially in case of upgrading or rehabilitation of old structures. Many old bridges and marine or pier structures in the United States are established using deep foundations system of timber piles and their foundation records do not exist. Non-Destructive Testing (NDT or Non-Destructive Evaluation (NDE method for a great variety of materials and structures has become an integral part of many tests. However, the process of testing long piles, deeply embedded in the ground, is more complex than (NDT of the other structural materials. This paper summarizes some of the most common non-destructive test methods for deep foundations and presents a new method called the Hilbert Huang Transform (HHT. This Hilbert Huang Transform (HHT method is used now by a wide range in a different health monitoring of many systems. In this paper, some field tests on the timber Piles of one bridge at North Carolina was performed to verify the using the (HHT method for predicting the embedded depth of the unknown piles. Percentage of the accuracy achieved using HHT method for pile length compared to the actual pile length data was performed. Finally, a recommendation is presented for the limitation of using this new method as a new non-destructive method for deep foundations.
Bearing fault detection utilizing group delay and the Hilbert-Huang transform
Energy Technology Data Exchange (ETDEWEB)
Jin, Shuai; Lee, Sang-Kwon [Inha University, Incheon (Korea, Republic of)
2017-03-15
Vibration signals measured from a mechanical system are useful to detect system faults. Signal processing has been used to extract fault information in bearing systems. However, a wide vibration signal frequency band often affects the ability to obtain the effective fault features. In addition, a few oscillation components are not useful at the entire frequency band in a vibration signal. By contrast, useful fatigue information can be embedded in the noise oscillation components. Thus, a method to estimate which frequency band contains fault information utilizing group delay was proposed in this paper. Group delay as a measure of phase distortion can indicate the phase structure relationship in the frequency domain between original (with noise) and denoising signals. We used the empirical mode decomposition of a Hilbert-Huang transform to sift the useful intrinsic mode functions based on the results of group delay after determining the valuable frequency band. Finally, envelope analysis and the energy distribution after the Hilbert transform were used to complete the fault diagnosis. The practical bearing fault data, which were divided into inner and outer race faults, were used to verify the efficiency and quality of the proposed method.
Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform.
Huang, Yongxiang; Biferale, Luca; Calzavarini, Enrico; Sun, Chao; Toschi, Federico
2013-04-01
The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions C(i)(t) and of their instantaneous frequency ω(i)(t). On the basis of this decomposition we define the ω-conditioned statistical moments of the C(i) modes, named q-order Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present clear empirical evidence that the energylike quantity, i.e., the second-order HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure high-order moment scaling exponents in a direct way, without resorting to the extended self-similarity procedure. This leads to an estimate of the Lagrangian structure function exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed by Biferale et al. [Phys. Rev. Lett. 93, 064502 (2004)].
Hytönen, Tuomas; Veraar, Mark; Weis, Lutz
The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional an...
Greedy Algorithms for Reduced Bases in Banach Spaces
DeVore, Ronald; Petrova, Guergana; Wojtaszczyk, Przemyslaw
2013-01-01
family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) in the case X=H is a Hilbert space. The results of Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) were
Audits of radiopharmaceutical formulations
International Nuclear Information System (INIS)
Castronovo, F.P. Jr.
1992-01-01
A procedure for auditing radiopharmaceutical formulations is described. To meet FDA guidelines regarding the quality of radiopharmaceuticals, institutional radioactive drug research committees perform audits when such drugs are formulated away from an institutional pharmacy. All principal investigators who formulate drugs outside institutional pharmacies must pass these audits before they can obtain a radiopharmaceutical investigation permit. The audit team meets with the individual who performs the formulation at the site of drug preparation to verify that drug formulations meet identity, strength, quality, and purity standards; are uniform and reproducible; and are sterile and pyrogen free. This team must contain an expert knowledgeable in the preparation of radioactive drugs; a radiopharmacist is the most qualified person for this role. Problems that have been identified by audits include lack of sterility and apyrogenicity testing, formulations that are open to the laboratory environment, failure to use pharmaceutical-grade chemicals, inadequate quality control methods or records, inadequate training of the person preparing the drug, and improper unit dose preparation. Investigational radiopharmaceutical formulations, including nonradiolabeled drugs, must be audited before they are administered to humans. A properly trained pharmacist should be a member of the audit team
Zhuang, Leimeng; Khan, Muhammad Rezaul; Beeker, Willem; Leinse, Arne; Heideman, René; Roeloffzen, Chris
2012-11-19
We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonator-based optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance analysis in both frequency and time domain validates that the proposed implementation provides a good approximation to an ideal fractional Hilbert transformer. This is also experimentally verified by an electrical S21 response characterization performed on a waveguide realization of a ring resonator. The waveguide-based structure allows the proposed Hilbert transformer to be integrated together with other building blocks on a photonic integrated circuit to create various system-level functionalities for on-chip microwave photonic signal processors. As an example, a circuit consisting of a splitter and a ring resonator has been realized which can perform on-chip phase control of microwave signals generated by means of optical heterodyning, and simultaneous generation of in-phase and quadrature microwave signals for a wide frequency range. For these functionalities, this simple and on-chip solution is considered to be practical, particularly when operating together with a dual-frequency laser. To our best knowledge, this is the first-time on-chip demonstration where ring resonators are employed to perform phase control functionalities for optical generation of microwave signals by means of optical heterodyning.
Differential Galois theory through Riemann-Hilbert correspondence an elementary introduction
Sauloy, Jacques
2017-01-01
Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equat...
Directory of Open Access Journals (Sweden)
Lajmert Paweł
2018-01-01
Full Text Available In the paper a cutting stability in the milling process of nickel based alloy Inconel 625 is analysed. This problem is often considered theoretically, but the theoretical finding do not always agree with experimental results. For this reason, the paper presents different methods for instability identification during real machining process. A stability lobe diagram is created based on data obtained in impact test of an end mill. Next, the cutting tests were conducted in which the axial cutting depth of cut was gradually increased in order to find a stability limit. Finally, based on the cutting force measurements the stability estimation problem is investigated using the recurrence plot technique and Hilbert vibration decomposition method.
Live Cell Refractometry Using Hilbert Phase Microscopy and Confocal Reflectance Microscopy†
Lue, Niyom; Choi, Wonshik; Popescu, Gabriel; Yaqoob, Zahid; Badizadegan, Kamran; Dasari, Ramachandra R.; Feld, Michael S.
2010-01-01
Quantitative chemical analysis has served as a useful tool for understanding cellular metabolisms in biology. Among many physical properties used in chemical analysis, refractive index in particular has provided molecular concentration that is an important indicator for biological activities. In this report, we present a method of extracting full-field refractive index maps of live cells in their native states. We first record full-field optical thickness maps of living cells by Hilbert phase microscopy and then acquire physical thickness maps of the same cells using a custom-built confocal reflectance microscope. Full-field and axially averaged refractive index maps are acquired from the ratio of optical thickness to physical thickness. The accuracy of the axially averaged index measurement is 0.002. This approach can provide novel biological assays of label-free living cells in situ. PMID:19803506
Live cell refractometry using Hilbert phase microscopy and confocal reflectance microscopy.
Lue, Niyom; Choi, Wonshik; Popescu, Gabriel; Yaqoob, Zahid; Badizadegan, Kamran; Dasari, Ramachandra R; Feld, Michael S
2009-11-26
Quantitative chemical analysis has served as a useful tool for understanding cellular metabolisms in biology. Among many physical properties used in chemical analysis, refractive index in particular has provided molecular concentration that is an important indicator for biological activities. In this report, we present a method of extracting full-field refractive index maps of live cells in their native states. We first record full-field optical thickness maps of living cells by Hilbert phase microscopy and then acquire physical thickness maps of the same cells using a custom-built confocal reflectance microscope. Full-field and axially averaged refractive index maps are acquired from the ratio of optical thickness to physical thickness. The accuracy of the axially averaged index measurement is 0.002. This approach can provide novel biological assays of label-free living cells in situ.
Li, Xuelong; Li, Zhonghui; Wang, Enyuan; Feng, Junjun; Chen, Liang; Li, Nan; Kong, Xiangguo
2016-09-01
This study provides a new research idea concerning rock burst prediction. The characteristics of microseismic (MS) waveforms prior to and during the rock burst were studied through the Hilbert-Huang transform (HHT). In order to demonstrate the advantage of the MS features extraction based on HHT, the conventional analysis method (Fourier transform) was also used to make a comparison. The results show that HHT is simple and reliable, and could extract in-depth information about the characteristics of MS waveforms. About 10 days prior to the rock burst, the main frequency of MS waveforms transforms from the high-frequency to low-frequency. What's more, the waveforms energy also presents accumulation characteristic. Based on our study results, it can be concluded that the MS signals analysis through HHT could provide valuable information about the coal or rock deformation and fracture.
Noether Current of the Surface Term of Einstein-Hilbert Action, Virasoro Algebra, and Entropy
Directory of Open Access Journals (Sweden)
Bibhas Ranjan Majhi
2013-01-01
Full Text Available A derivation of Noether current from the surface term of Einstein-Hilbert action is given. We show that the corresponding charge, calculated on the horizon, is related to the Bekenstein-Hawking entropy. Also using the charge, the same entropy is found based on the Virasoro algebra and Cardy formula approach. In this approach, the relevant diffeomorphisms are found by imposing a very simple physical argument: diffeomorphisms keep the horizon structure invariant. This complements similar earlier results (Majhi and Padmanabhan (2012 (arXiv:1204.1422 obtained from York-Gibbons-Hawking surface term. Finally we discuss the technical simplicities and improvements over the earlier attempts and also various important physical implications.
Multichannel photonic Hilbert transformers based on complex modulated integrated Bragg gratings.
Cheng, Rui; Chrostowski, Lukas
2018-03-01
Multichannel photonic Hilbert transformers (MPHTs) are reported. The devices are based on single compact spiral integrated Bragg gratings on silicon with coupling coefficients precisely modulated by the phase of each grating period. MPHTs with up to nine wavelength channels and a single-channel bandwidth of up to ∼625 GHz are achieved. The potential of the devices for multichannel single-sideband signal generation is suggested. The work offers a new possibility of utilizing wavelength as an extra degree of freedom in designing radio-frequency photonic signal processors. Such multichannel processors are expected to possess improved capacities and a potential to greatly benefit current widespread wavelength division multiplexed systems.
THz-bandwidth photonic Hilbert transformers based on fiber Bragg gratings in transmission.
Fernández-Ruiz, María R; Wang, Lixian; Carballar, Alejandro; Burla, Maurizio; Azaña, José; LaRochelle, Sophie
2015-01-01
THz-bandwidth photonic Hilbert transformers (PHTs) are implemented for the first time, to the best of our knowledge, based on fiber Bragg grating (FBG) technology. To increase the practical bandwidth limitation of FBGs (typically <200 GHz), a superstructure based on two superimposed linearly-chirped FBGs operating in transmission has been employed. The use of a transmission FBG involves first a conversion of the non-minimum phase response of the PHT into a minimum-phase response by adding an anticipated instantaneous component to the desired system temporal impulse response. Using this methodology, a 3-THz-bandwidth integer PHT and a fractional (order 0.81) PHT are designed, fabricated, and successfully characterized.
Trusiak, Maciej; Patorski, Krzysztof; Wielgus, Maciej
2012-10-08
Presented method for fringe pattern enhancement has been designed for processing and analyzing low quality fringe patterns. It uses a modified fast and adaptive bidimensional empirical mode decomposition (FABEMD) for the extraction of bidimensional intrinsic mode functions (BIMFs) from an interferogram. Fringe pattern is then selectively reconstructed (SR) taking the regions of selected BIMFs with high modulation values only. Amplitude demodulation and normalization of the reconstructed image is conducted using the spiral phase Hilbert transform (HS). It has been tested using computer generated interferograms and real data. The performance of the presented SR-FABEMD-HS method is compared with other normalization techniques. Its superiority, potential and robustness to high fringe density variations and the presence of noise, modulation and background illumination defects in analyzed fringe patterns has been corroborated.
Scattering analysis of asymmetric metamaterial resonators by the Riemann-Hilbert approach
DEFF Research Database (Denmark)
Kaminski, Piotr Marek; Ziolkowski, Richard W.; Arslanagic, Samel
2016-01-01
This work presents an analytical treatment of an asymmetric metamaterial-based resonator excited by an electric line source, and explores its beam shaping capabilities. The resonator consists of two concentric cylindrical material layers covered with an infinitely thin conducting shell with an ap......This work presents an analytical treatment of an asymmetric metamaterial-based resonator excited by an electric line source, and explores its beam shaping capabilities. The resonator consists of two concentric cylindrical material layers covered with an infinitely thin conducting shell...... with an aperture. Exact analytical solution of the problem is derived; it is based on the n-series approach which is casted into the equivalent Riemann-Hilbert problem. The examined configuration leads to large enhancements of the radiated field and to steerable Huygens-like directivity patterns. Particularly...
Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering
Pelinovsky, Dmitry E.; Sulem, Catherine
A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.
Reactive decontamination formulation
Giletto, Anthony [College Station, TX; White, William [College Station, TX; Cisar, Alan J [Cypress, TX; Hitchens, G Duncan [Bryan, TX; Fyffe, James [Bryan, TX
2003-05-27
The present invention provides a universal decontamination formulation and method for detoxifying chemical warfare agents (CWA's) and biological warfare agents (BWA's) without producing any toxic by-products, as well as, decontaminating surfaces that have come into contact with these agents. The formulation includes a sorbent material or gel, a peroxide source, a peroxide activator, and a compound containing a mixture of KHSO.sub.5, KHSO.sub.4 and K.sub.2 SO.sub.4. The formulation is self-decontaminating and once dried can easily be wiped from the surface being decontaminated. A method for decontaminating a surface exposed to chemical or biological agents is also disclosed.
Indian Academy of Sciences (India)
void hilbert(int r, int d, int t, int u, int i, int h, int &x, int &y). { if(i >0). { i- -; hilbert ( d,r, u,e ,i,h,x,y); move(r ,h,x,y); hilbert(r,d,t,u,i,h,x,y); move ( d,h,x,y); hilbert(r,d,e,u,i ...
Self-Adjointness Criterion for Operators in Fock Spaces
International Nuclear Information System (INIS)
Falconi, Marco
2015-01-01
In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves the number of Fock space particles and a non-diagonal part that is at most quadratic with respect to the creation and annihilation operators. The hypotheses of the criterion are satisfied in several interesting applications
Preparation of radiopharmaceutical formulations
International Nuclear Information System (INIS)
Simon, J.; Garlich, J.R.; Frank, R.K.; McMillan, K.
1998-01-01
Radiopharmaceutical formulations for complexes comprising at least one radionuclide complexed with a ligand, or its physiologically-acceptable salts thereof, especially 153 samarium-ethylenediaminetetramethylenephosphonic acid, which optionally contains a divalent metal ion, e.g. calcium, and is frozen, thawed, and then administered by injection. Alternatively, the radiopharmaceutical formulations must contain the divalent metal and are frozen only if the time before administration is sufficiently long to cause concern for radiolysis of the ligand. 2 figs., 9 tabs
Tariff formulation and equalization
International Nuclear Information System (INIS)
Svartsund, Trond
2003-01-01
The primary goal of the transmission tariff is to provide for socioeconomic use of the transmission grid. The present tariff structure is basically right. The responsibility for the formulation of the tariff resides with the local grid owner. This must take place in agreement with the current regulations which are passed by the authorities. The formulation must be adaptable to the local requirements. EBL (Norwegian Electricity Industry Association) is content with the current regulations
Symmetry-adapted Liouville space. Pt. 7
International Nuclear Information System (INIS)
Temme, F.P.
1990-01-01
In examining nuclear spin dynamics of NMR spin clusters in density operator/generalized torque formalisms over vertical strokekqv>> operator bases of Liouville space, it is necessary to consider the symmetry mappings and carrier spaces under a specialized group for such (k i = 1) nuclear spin clusters. The SU2 X S n group provides the essential mappings and the form of H carrier space, which allows one to: (a) draw comparisons with Hilbert space duality, and (b) outline the form of the Coleman-Kotani genealogical hierarchy under induced S n -symmetry. (orig.)
Quantum de Finetti theorem in phase-space representation
International Nuclear Information System (INIS)
Leverrier, Anthony; Cerf, Nicolas J.
2009-01-01
The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
On Λ-Type Duality of Frames in Banach Spaces
Directory of Open Access Journals (Sweden)
Renu Chugh
2013-11-01
Full Text Available Frames are redundant system which are useful in the reconstruction of certain classes of spaces. The dual of a frame (Hilbert always exists and can be obtained in a natural way. Due to the presence of three Banach spaces in the definition of retro Banach frames (or Banach frames duality of frames in Banach spaces is not similar to frames for Hilbert spaces. In this paper we introduce the notion of Λ-type duality of retro Banach frames. This can be generalized to Banach frames in Banach spaces. Necessary and sufficient conditions for the existence of the dual of retro Banach frames are obtained. A special class of retro Banach frames which always admit a dual frame is discussed.
On fictitious domain formulations for Maxwell's equations
DEFF Research Database (Denmark)
Dahmen, W.; Jensen, Torben Klint; Urban, K.
2003-01-01
We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl: Omega) derived from Maxwell's equations. Boundary conditions and the divergence constraint are imposed weakly by using Lagrange multipliers. Both the time dependent and time harmonic formu...
An unconventional canonical quantization of local scalar fields over quantum space-time
International Nuclear Information System (INIS)
Banai, M.
1985-12-01
An unconventional extension of the canonical quantization method is presented for a classical local field theory. The proposed canonical commutation relations have a solution in the A-valued Hilbert space where A is the algebra of the bounded operators of the Hilbert space Lsup(2) (IRsup(3)). The canonical equations as operator equations are equivalent formally with the classical field equations, and are well defined for interacting systems, too. This model of quantized field lacks some of the difficulties of the conventional approach. Examples satisfying the asymptotic condition provide examples for Haag-Kastler's axioms, however, they satisfy Wightman's axioms only partially. (author)
Granulated decontamination formulations
Tucker, Mark D.
2007-10-02
A decontamination formulation and method of making that neutralizes the adverse health effects of both chemical and biological compounds, especially chemical warfare (CW) and biological warfare (BW) agents, and toxic industrial chemicals. The formulation provides solubilizing compounds that serve to effectively render the chemical and biological compounds, particularly CW and BW compounds, susceptible to attack, and at least one reactive compound that serves to attack (and detoxify or kill) the compound. The formulation includes at least one solubilizing agent, a reactive compound, a sorbent additive, and water. A highly adsorbent sorbent additive (e.g., amorphous silica, sorbitol, mannitol, etc.) is used to "dry out" one or more liquid ingredients into a dry, free-flowing powder that has an extended shelf life, and is more convenient to handle and mix in the field.
Trembach, Vera
2014-01-01
Space is an introduction to the mysteries of the Universe. Included are Task Cards for independent learning, Journal Word Cards for creative writing, and Hands-On Activities for reinforcing skills in Math and Language Arts. Space is a perfect introduction to further research of the Solar System.
The coevent formulation of quantum theory
International Nuclear Information System (INIS)
Wallden, Petros
2013-01-01
Understanding quantum theory has been a subject of debate from its birth. Many different formulations and interpretations have been proposed. Here we examine a recent novel formulation, namely the coevents formulation. It is a histories formulation and has as starting point the Feynman path integral and the decoherence functional. The new ontology turns out to be that of a coarse-grained history. We start with a quantum measure defined on the space of histories, and the existence of zero covers rules out single-history as potential reality (the Kochen Specker theorem casted in histories form is a special case of a zero cover). We see that allowing coarse-grained histories as potential realities avoids the previous paradoxes, maintains deductive non-contextual logic (alas non-Boolean) and gives rise to a unique classical domain. Moreover, we can recover the probabilistic predictions of quantum theory with the use of the Cournot's principle. This formulation, being both a realist formulation and based on histories, is well suited conceptually for the purposes of quantum gravity and cosmology.
Huang, Norden E.; Hu, Kun; Yang, Albert C. C.; Chang, Hsing-Chih; Jia, Deng; Liang, Wei-Kuang; Yeh, Jia Rong; Kao, Chu-Lan; Juan, Chi-Hung; Peng, Chung Kang; Meijer, Johanna H.; Wang, Yung-Hung; Long, Steven R.; Wu, Zhauhua
2016-01-01
The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through c...
SUR UNE CERTAINE CLASSE D’OPERATEURS A SPECTRE CONCENTRE EN UN POINT DANS UN ESPACE DE HILBERT
Directory of Open Access Journals (Sweden)
B BENDOUKHA
2000-12-01
Full Text Available Le présent travail est consacré à l'étude de certaines classes d’opérateurs qui sont parfaitement définis par leur spectre. Pour ces opérateurs (définis dans des espaces de Hilbert abstraits, on donnera une représentation explicite et uniquement à l’aide du spectre dans l’espace des fonctions à carrés intégrables.
Directory of Open Access Journals (Sweden)
Roque A. Osornio-Rios
2013-04-01
Full Text Available Power quality disturbance (PQD monitoring has become an important issue due to the growing number of disturbing loads connected to the power line and to the susceptibility of certain loads to their presence. In any real power system, there are multiple sources of several disturbances which can have different magnitudes and appear at different times. In order to avoid equipment damage and estimate the damage severity, they have to be detected, classified, and quantified. In this work, a smart sensor for detection, classification, and quantification of PQD is proposed. First, the Hilbert transform (HT is used as detection technique; then, the classification of the envelope of a PQD obtained through HT is carried out by a feed forward neural network (FFNN. Finally, the root mean square voltage (Vrms, peak voltage (Vpeak, crest factor (CF, and total harmonic distortion (THD indices calculated through HT and Parseval’s theorem as well as an instantaneous exponential time constant quantify the PQD according to the disturbance presented. The aforementioned methodology is processed online using digital hardware signal processing based on field programmable gate array (FPGA. Besides, the proposed smart sensor performance is validated and tested through synthetic signals and under real operating conditions, respectively.
Searching the beginning of BWR power instability events with the Hilbert Huang transform
International Nuclear Information System (INIS)
Blázquez, Juan; Montalvo, Cristina; García-Berrocal, Agustín; Balbás, Miguel
2013-01-01
Highlights: ► The report of the instability is enriched by including its beginning and its end. ► The Hilbert Huang transform (HHT) is used for indentifying both. ► The first Intrinsic Mode Function (IMF) detects both. ► The methodology is applied to neutron detector signals from two plants. ► The Decay Ratio of IMF 1 is calculated. - Abstract: When a BWR instability takes place, the Regulator usually demands a report which must include many aspects such as the initial time of the instability and also the measurements adopted by the operator at that time. This initial time normally is difficult to know from the available data. In this work, a methodology is proposed to determine accurately when the instability began based on the Hilbert–Huang transform. The Empirical Mode Decomposition is applied to neutron detector signals coming from two plants which have recorded them during real instability events. The first intrinsic mode function shows sharply the beginning and the end of the incident. Besides, through the instantaneous amplitude and frequency of the first mode a kind of Decay Ratio can be assigned allowing us to obtain a sharper description of the instability
Hilbert-Huang transform analysis of long-term solar magnetic activity
Deng, Linhua
2018-04-01
Astronomical time series analysis is one of the hottest and most important problems, and becomes the suitable way to deal with the underlying dynamical behavior of the considered nonlinear systems. The quasi-periodic analysis of solar magnetic activity has been carried out by various authors during the past fifty years. In this work, the novel Hilbert-Huang transform approach is applied to investigate the yearly numbers of polar faculae in the time interval from 1705 to 1999. The detected periodicities can be allocated to three components: the first one is the short-term variations with periods smaller than 11 years, the second one is the mid- term variations with classical periods from 11 years to 50 years, and the last one is the long-term variations with periods larger than 50 years. The analysis results improve our knowledge on the quasi-periodic variations of solar magnetic activity and could be provided valuable constraints for solar dynamo theory. Furthermore, our analysis results could be useful for understanding the long-term variations of solar magnetic activity, providing crucial information to describe and forecast solar magnetic activity indicators.
Multiple Harmonics Fitting Algorithms Applied to Periodic Signals Based on Hilbert-Huang Transform
Directory of Open Access Journals (Sweden)
Hui Wang
2013-01-01
Full Text Available A new generation of multipurpose measurement equipment is transforming the role of computers in instrumentation. The new features involve mixed devices, such as kinds of sensors, analog-to-digital and digital-to-analog converters, and digital signal processing techniques, that are able to substitute typical discrete instruments like multimeters and analyzers. Signal-processing applications frequently use least-squares (LS sine-fitting algorithms. Periodic signals may be interpreted as a sum of sine waves with multiple frequencies: the Fourier series. This paper describes a new sine fitting algorithm that is able to fit a multiharmonic acquired periodic signal. By means of a “sinusoidal wave” whose amplitude and phase are both transient, the “triangular wave” can be reconstructed on the basis of Hilbert-Huang transform (HHT. This method can be used to test effective number of bits (ENOBs of analog-to-digital converter (ADC, avoiding the trouble of selecting initial value of the parameters and working out the nonlinear equations. The simulation results show that the algorithm is precise and efficient. In the case of enough sampling points, even under the circumstances of low-resolution signal with the harmonic distortion existing, the root mean square (RMS error between the sampling data of original “triangular wave” and the corresponding points of fitting “sinusoidal wave” is marvelously small. That maybe means, under the circumstances of any periodic signal, that ENOBs of high-resolution ADC can be tested accurately.
Low-derivative operators of the Standard Model effective field theory via Hilbert series methods
Energy Technology Data Exchange (ETDEWEB)
Lehman, Landon; Martin, Adam [Department of Physics, University of Notre Dame,Nieuwland Science Hall, Notre Dame, IN 46556 (United States)
2016-02-12
In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we conjecture an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts. Specifically, the conjectured technique can be applied whenever there is only one Lorentz invariant for a given partitioning of derivatives among the fields. At higher numbers of derivatives, equation of motion redundancies can be removed, but the increased number of Lorentz contractions spoils the subtraction of integration by parts redundancies. While restricted, this technique is sufficient to automatically recreate the complete set of invariant operators of the Standard Model effective field theory for dimensions 6 and 7 (for arbitrary numbers of flavors). At dimension 8, the algorithm does not automatically generate the complete operator set; however, it suffices for all but five classes of operators. For these remaining classes, there is a well defined procedure to manually determine the number of invariants. Assuming our method is correct, we derive a set of 535 dimension-8 N{sub f}=1 operators.
NINJA data analysis with a detection pipeline based on the Hilbert-Huang transform
International Nuclear Information System (INIS)
Stroeer, Alexander; Camp, Jordan
2009-01-01
The NINJA data analysis challenge allowed the study of the sensitivity of data analysis pipelines to binary black hole numerical relativity waveforms in simulated Gaussian noise at the design level of the LIGO observatory and the VIRGO observatory. We analyzed NINJA data with a pipeline based on the Hilbert-Huang transform, utilizing a detection stage and a characterization stage: detection is performed by triggering on excess instantaneous power, characterization is performed by displaying the kernel density enhanced (KD) time-frequency trace of the signal. Using the simulated data based on the two LIGO detectors, we were able to detect 77 signals out of 126 above signal-to-noise ratio, SNR 5 in coincidence, with 43 missed events characterized by SNR < 10. Characterization of the detected signals revealed the merger part of the waveform in high time and frequency resolution, free from time-frequency uncertainty. We estimated the timelag of the signals between the detectors based on the optimal overlap of the individual KD time-frequency maps, yielding estimates accurate within a fraction of a millisecond for half of the events. A coherent addition of the data sets according to the estimated timelag eventually was used in a final characterization of the event.
Low-derivative operators of the Standard Model effective field theory via Hilbert series methods
International Nuclear Information System (INIS)
Lehman, Landon; Martin, Adam
2016-01-01
In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we conjecture an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts. Specifically, the conjectured technique can be applied whenever there is only one Lorentz invariant for a given partitioning of derivatives among the fields. At higher numbers of derivatives, equation of motion redundancies can be removed, but the increased number of Lorentz contractions spoils the subtraction of integration by parts redundancies. While restricted, this technique is sufficient to automatically recreate the complete set of invariant operators of the Standard Model effective field theory for dimensions 6 and 7 (for arbitrary numbers of flavors). At dimension 8, the algorithm does not automatically generate the complete operator set; however, it suffices for all but five classes of operators. For these remaining classes, there is a well defined procedure to manually determine the number of invariants. Assuming our method is correct, we derive a set of 535 dimension-8 N_f=1 operators.
International Nuclear Information System (INIS)
Antonino-Daviu, J.; Rodriguez, P. Jover; Riera-Guasp, M.; Arkkio, A.; Roger-Folch, J.; Perez, R.B.
2009-01-01
The identification and extraction of characteristic patterns are proposed in this work for the diagnosis and evaluation of mixed eccentricities in induction electrical machines with parallel stator branches. Whereas the classical diagnosis approaches, deeply spread in the industrial environment, are based on the Fourier analysis of the steady-state current, the basis of the proposed methodology consist of analysing the current demanded by the machine during the connection process (startup transient); the objective is to extract the characteristic evolution during the transient of some harmonic components created by the fault; this evolution is caused by the dependence of these components on the slip (s), a quantity varying during the startup transient from 1 to almost 0. For this feature extraction, the Hilbert-Huang Transform (HHT) is proposed. An analysis of the behaviour of this transform in comparison with another time-frequency approach used in other works, the Discrete Wavelet Transform (DWT), is also presented in the paper. The results show the usefulness of the methodology for the reliable diagnosis of the mixed eccentricity fault and for the correct discrimination against other types of failures.
Neural network Hilbert transform based filtered backprojection for fast inline x-ray inspection
Janssens, Eline; De Beenhouwer, Jan; Van Dael, Mattias; De Schryver, Thomas; Van Hoorebeke, Luc; Verboven, Pieter; Nicolai, Bart; Sijbers, Jan
2018-03-01
X-ray imaging is an important tool for quality control since it allows to inspect the interior of products in a non-destructive way. Conventional x-ray imaging, however, is slow and expensive. Inline x-ray inspection, on the other hand, can pave the way towards fast and individual quality control, provided that a sufficiently high throughput can be achieved at a minimal cost. To meet these criteria, an inline inspection acquisition geometry is proposed where the object moves and rotates on a conveyor belt while it passes a fixed source and detector. Moreover, for this acquisition geometry, a new neural-network-based reconstruction algorithm is introduced: the neural network Hilbert transform based filtered backprojection. The proposed algorithm is evaluated both on simulated and real inline x-ray data and has shown to generate high quality reconstructions of 400 × 400 reconstruction pixels within 200 ms, thereby meeting the high throughput criteria.
On Scalar Energy: Mathematical Formulation
International Nuclear Information System (INIS)
Hathout, A.M.
2011-01-01
A new kind of electromagnetic waves (EMW), which exists only in vacuum of the empty space, will be discussed and mathematically formulated in this paper. The mathematical existence of this energy was first proposed in a series of groundbreaking equations by Scottish Mathematician, James Clerk Maxwell, in the mid of 1800 and 39;s. This energy is called scalar energy. It is characterized by both particle and wave like. The waves of this energy are called longitudinal EMW to distinguish them from transverse EM, the kind we are familiar with in our daily life. Teslas name of this energy is scalar energy or zero point energy. It is aimed at this paper to explain more details and to verify the scalar EM concept in vacuum.
Directory of Open Access Journals (Sweden)
P Bhattacharya
2016-09-01
Full Text Available The wind resource varies with of the day and the season of the year and even some extent from year to year. Wind energy has inherent variances and hence it has been expressed by distribution functions. In this paper, we present some methods for estimating Weibull parameters in case of a low wind speed characterization, namely, shape parameter (k, scale parameter (c and characterize the discrete wind data sample by the discrete Hilbert transform. We know that the Weibull distribution is an important distribution especially for reliability and maintainability analysis. The suitable values for both shape parameter and scale parameters of Weibull distribution are important for selecting locations of installing wind turbine generators. The scale parameter of Weibull distribution also important to determine whether a wind farm is good or not. Thereafter the use of discrete Hilbert transform (DHT for wind speed characterization provides a new era of using DHT besides its application in digital signal processing. Basically in this paper, discrete Hilbert transform has been applied to characterize the wind sample data measured on College of Engineering and Management, Kolaghat, East Midnapore, India in January 2011.
A New Method for Non-linear and Non-stationary Time Series Analysis:
The Hilbert Spectral Analysis
CERN. Geneva
2000-01-01
A new method for analysing non-linear and non-stationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero crossing and extreme, and also having symmetric envelopes defined by the local maximal 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 non-linear and non-stationary 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. Classical non-l...
International Nuclear Information System (INIS)
Connes, A.; Kreimer, D.
2000-01-01
This paper gives a complete selfcontained proof of our result (1999) showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra H which is commutative asan algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra G whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of H. We show then that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop γ(z) element of G, z element of C, where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ + of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. (orig.)
A Nanodroplet Processor for Advanced Microencapsulated Drug Formulations, Phase II
National Aeronautics and Space Administration — During this Phase II program we propose to build on the key aspects of the nanodroplet encapsulation technology to demonstrate optimized formulation and...
Interpolation of quasi-Banach spaces
International Nuclear Information System (INIS)
Tabacco Vignati, A.M.
1986-01-01
This dissertation presents a method of complex interpolation for familities of quasi-Banach spaces. This method generalizes the theory for families of Banach spaces, introduced by others. Intermediate spaces in several particular cases are characterized using different approaches. The situation when all the spaces have finite dimensions is studied first. The second chapter contains the definitions and main properties of the new interpolation spaces, and an example concerning the Schatten ideals associated with a separable Hilbert space. The case of L/sup P/ spaces follows from the maximal operator theory contained in Chapter III. Also introduced is a different method of interpolation for quasi-Banach lattices of functions, and conditions are given to guarantee that the two techniques yield the same result. Finally, the last chapter contains a different, and more direct, approach to the case of Hardy spaces
Nobile, F.
2015-10-30
In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods” (Beck et al., Math Models Methods Appl Sci 22(09), 2012). The construction of a sparse grid is recast into a knapsack problem: a profit is assigned to each hierarchical surplus and only the most profitable ones are added to the sparse grid. The convergence rate of the sparse grid approximation error with respect to the number of points in the grid is then shown to depend on weighted summability properties of the sequence of profits. This is a very general argument that can be applied to sparse grids built with any uni-variate family of points, both nested and non-nested. As an example, we apply such quasi-optimal sparse grids to the solution of a particular elliptic PDE with stochastic diffusion coefficients, namely the “inclusions problem”: we detail the convergence estimates obtained in this case using polynomial interpolation on either nested (Clenshaw–Curtis) or non-nested (Gauss–Legendre) abscissas, verify their sharpness numerically, and compare the performance of the resulting quasi-optimal grids with a few alternative sparse-grid construction schemes recently proposed in the literature.
Nobile, F.; Tamellini, L.; Tempone, Raul
2015-01-01
In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods” (Beck et al., Math Models Methods Appl Sci 22(09), 2012). The construction of a sparse grid is recast into a knapsack problem: a profit is assigned to each hierarchical surplus and only the most profitable ones are added to the sparse grid. The convergence rate of the sparse grid approximation error with respect to the number of points in the grid is then shown to depend on weighted summability properties of the sequence of profits. This is a very general argument that can be applied to sparse grids built with any uni-variate family of points, both nested and non-nested. As an example, we apply such quasi-optimal sparse grids to the solution of a particular elliptic PDE with stochastic diffusion coefficients, namely the “inclusions problem”: we detail the convergence estimates obtained in this case using polynomial interpolation on either nested (Clenshaw–Curtis) or non-nested (Gauss–Legendre) abscissas, verify their sharpness numerically, and compare the performance of the resulting quasi-optimal grids with a few alternative sparse-grid construction schemes recently proposed in the literature.
Lax-Phillips scattering theory with two Hilbert spaces V(x)=0((1)/|x|β), β>1
International Nuclear Information System (INIS)
Brambila Paz, F.
1988-10-01
A scattering theory for the wave equation with a perturbation with compact support was developed by Lax and Phillips in 1967. Using Enss approach Phillips developed a Lax-Phillips scattering theory for perturbations V such that V(x)=0((1)/|x| β ), β>2. In this paper we develop a scattering theory for more general perturbations V, i.e. for V(x)=0((1)/|x| β ), β>1. (author). 8 refs
Systematic Equation Formulation
DEFF Research Database (Denmark)
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
International Nuclear Information System (INIS)
Moreno, C.
1977-01-01
In stationary space--times V/sub n/ x R with compact space-section manifold without boundary V/sub n/, the Klein--Gordon equation is solved by the one-parameter group of unitary operators generated by the energy operator i -1 T -1 in the Sobolev spaces H/sup l/(V/sub n/) x H/sup l/(V/sub n/). The canonical symplectic and complex structures of the associated dynamical system are calculated. The existence and the uniqueness of the Lichnerowicz kernel are established. The Hilbert spaces of positive and negative frequency-part solutions defined by means of this kernel are constructed
Moduli spaces for linear differential equations and the Painlev'e equations
Put, Marius van der; Saito, Masa-Hiko
2009-01-01
In this paper, we give a systematic construction of ten isomonodromic families of connections of rank two on P1 inducing Painlev´e equations. The classification of ten families is given by considering the Riemann-Hilbert morphism from a moduli space of connections with certain type of regular and
Divergence identities in curved space-time. A resolution of the stress-energy problem
International Nuclear Information System (INIS)
Yilmaz, H.; Tufts Univ., Medford, MA
1989-01-01
It is noted that the joint use of two basic differential identities in curved space-time, namely. 1) the Einstein-Hilbert identity (1915), and 2) the identity of P. Freud (1939), permits a viable alternative to general relativity and a resolution of the field stress-energy' problem of the gravitational theory. (orig.)
Drug delivery and formulations.
Breitkreutz, Jörg; Boos, Joachim
2011-01-01
Paediatric drug delivery is a major challenge in drug development. Because of the heterogeneous nature of the patient group, ranging from newborns to adolescents, there is a need to use appropriate excipients, drug dosage forms and delivery devices for different age groups. So far, there is a lack of suitable and safe drug formulations for children, especially for the very young and seriously ill patients. The new EU legislation will enforce paediatric clinical trials and drug development. Current advances in paediatric drug delivery include interesting new concepts such as fast-dissolving drug formulations, including orodispersible tablets and oral thin strips (buccal wafers), and multiparticulate dosage forms based on mini-tabletting or pelletization technologies. Parenteral administration is likely to remain the first choice for children in the neonatal period and for emergency cases. Alternative routes of administration include transdermal, pulmonary and nasal drug delivery systems. A few products are already available on the market, but others still need further investigations and clinical proof of concept.
Tensor harmonic analysis on homogenous space
International Nuclear Information System (INIS)
Wrobel, G.
1997-01-01
The Hilbert space of tensor functions on a homogenous space with the compact stability group is considered. The functions are decomposed onto a sum of tensor plane waves (defined in the text), components of which are transformed by irreducible representations of the appropriate transformation group. The orthogonality relation and the completeness relation for tensor plane waves are found. The decomposition constitutes a unitary transformation, which allows to obtain the Parseval equality. The Fourier components can be calculated by means of the Fourier transformation, the form of which is given explicitly. (author)
Trusiak, Maciej; Służewski, Łukasz; Patorski, Krzysztof
2016-02-22
Hybrid single shot algorithm for accurate phase demodulation of complex fringe patterns is proposed. It employs empirical mode decomposition based adaptive fringe pattern enhancement (i.e., denoising, background removal and amplitude normalization) and subsequent boosted phase demodulation using 2D Hilbert spiral transform aided by the Principal Component Analysis method for novel, correct and accurate local fringe direction map calculation. Robustness to fringe pattern significant noise, uneven background and amplitude modulation as well as local fringe period and shape variations is corroborated by numerical simulations and experiments. Proposed automatic, adaptive, fast and comprehensive fringe analysis solution compares favorably with other previously reported techniques.
Directory of Open Access Journals (Sweden)
Dang-Oh Kim
2012-01-01
Full Text Available A triple-band flexible loop antenna is proposed for WLAN/WiMAX applications in this paper. The proposed antenna is formed by the third-order Hilbert-curve and bending type structure which provides flexible characteristics. Even though the radius of the curvature for bending antennas is changed, a triple-band feature still remains in the proposed antenna. Moreover, the antenna exhibits the characteristics of omnidirectional radiation pattern and circular polarization. To verify the receiving performance of antenna, a simulation on the antenna factor was conducted by an EM simulator. Based on these results, the suggested antenna makes a noteworthy performance over typical loop antennas.
Hilbert-Huang transform based instrumental assessment of intention tremor in multiple sclerosis
Carpinella, Ilaria; Cattaneo, Davide; Ferrarin, Maurizio
2015-08-01
Objective. This paper describes a method to extract upper limb intention tremor from gyroscope data, through the Hilbert-Huang transform (HHT), a technique suitable for the study of nonlinear and non-stationary processes. The aims of the study were to: (i) evaluate the method’s ability to discriminate between healthy controls and MS subjects; (ii) validate the proposed procedure against clinical tremor scores assigned using Fahn’s tremor rating scale (FTRS); and (iii) compare the performance of the HHT-based method with that of linear band-pass filters. Approach. HHT was applied on gyroscope data collected on 20 MS subjects and 13 healthy controls (CO) during finger-to-nose tests (FNTs) instrumented with an inertial sensor placed on the hand. The results were compared to those obtained after traditional linear filtering. The tremor amplitude was quantified with instrumental indexes (TIs) and clinical FTRS ratings. Main results. The TIs computed after HHT-based filtering discriminated between CO and MS subjects with clinically-detected intention tremor (MS_T). In particular, TIs were significantly higher in the final part of the movement (TI2) with respect to the first part (TI1), and, for all components (X, Y, Z), MST showed a TI2 significantly higher than in CO subjects. Moreover, the HHT detected subtle alterations not visible from clinical ratings, as TI2 (Z-component) was significantly increased in MS subjects without clinically-detected tremor (MS_NT). The method’s validity was demonstrated by significant correlations between clinical FTRS scores and TI2 related to X (rs = 0.587, p = 0.006) and Y (rs = 0.682, p < 0.001) components. Contrarily, fewer differences among the groups and no correlation between instrumental and clinical indexes emerged after traditional filtering. Significance. The present results supported the use of the HHT-based procedure for a fully-automated quantitative and objective measure of intention tremor in MS, which can overcome
Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems
International Nuclear Information System (INIS)
Slater, Paul B
2010-01-01
We seek to derive the probability-expressed in terms of the Hilbert-Schmidt (Euclidean or flat) metric-that a generic (nine-dimensional) real two-qubit system is separable, by implementing the well-known Peres-Horodecki test on the partial transposes (PTs) of the associated 4 x 4 density matrices (ρ). But the full implementation of the test-requiring that the determinant of the PT be nonnegative for separability to hold-appears to be, at least presently, computationally intractable. So, we have previously implemented-using the auxiliary concept of a diagonal-entry-parameterized separability function (DESF)-the weaker implied test of nonnegativity of the six 2 x 2 principal minors of the PT. This yielded an exact upper bound on the separability probability of 1024/135π 2 ∼0.76854. Here, we piece together (reflection-symmetric) results obtained by requiring that each of the four 3 x 3 principal minors of the PT, in turn, be nonnegative, giving an improved/reduced upper bound of 22/35∼0.628571. Then, we conclude that a still further improved upper bound of 1129/2100∼0.537619 can be found by similarly piecing together the (reflection-symmetric) results of enforcing the simultaneous nonnegativity of certain pairs of the four 3 x 3 principal minors. Numerical simulations-as opposed to exact symbolic calculations-indicate, on the other hand, that the true probability is certainly less than 1/2 . Our analyses lead us to suggest a possible form for the true DESF, yielding a separability probability of 29/64∼0.453125, while the absolute separability probability of (6928-2205π)/(2 9/2 )∼0.0348338 provides the best exact lower bound established so far. In deriving our improved upper bounds, we rely repeatedly upon the use of certain integrals over cubes that arise. Finally, we apply an independence assumption to a pair of DESFs that comes close to reproducing our numerical estimate of the true separability function.
Zbožínek, Adam
2009-01-01
Tato práce uvádí základní pravidla a předpoklady pro konstrukci a použití vozů formule 1. Hlavní zaměření je na aerodynamiku, která je nejdůležitější disciplínou v tomto motoristickém sportu, dále je tato práce zaměřena na základní faktory týkající se motoru vozu, kol, nové technologie KERS a provedení volantu. This work shows basic rules and conditions for construction and use of cars formula 1. The main part of this work focus on the aerodynamics which is the most important discipline of...
Assessment of strategy formulation
DEFF Research Database (Denmark)
Acur, Nuran; Englyst, Linda
2006-01-01
of the success criteria through face-to-face interviews with 46 managers, workshops involving 40 managers, and two in-depth case studies. The success criteria have been slightly modified due to the empirical results, to yield the assessment tool. Findings – The resulting assessment tool integrates three generic...... approaches to strategy assessment, namely the goal-centred, comparative and improvement approaches, as found in the literature. Furthermore, it encompasses three phases of strategy formulation processes: strategic thinking, strategic planning and embedding of strategy. The tool reflects that the different......, but cases and managerial perceptions indicate that the need for accurate and detailed plans might be overrated in the literature, as implementation relies heavily on continuous improvement and empowerment. Concerning embedding, key aspects relate both to the goal-centred and improvement approaches, while...
Elements of mathematics topological vector spaces
Bourbaki, Nicolas
2003-01-01
This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981). This second edition is a brand new book and completely supersedes the original version of nearly 30 years ago. But a lot of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, all reflecting the progress made in the field during the last three decades. Table of Contents. Chapter I: Topological vector spaces over a valued field. Chapter II: Convex sets and locally convex spaces. Chapter III: Spaces of continuous linear mappings. Chapter IV: Duality in topological vector spaces. Chapter V: Hilbert spaces (elementary theory). Finally, there are the usual "historical note", bibliography, index of notation, index of terminology, and a list of some important properties of Banach spaces. (Based on Math Reviews, 1983).
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...
DEFF Research Database (Denmark)
Israelsen, Niels Møller; Maria, Michael; Feuchter, Thomas
2018-01-01
-linearities lead together to an unknown chirp of the detected interferogram. One method to compensate for the chirp is to perform a pixel-wavenumber calibration versus phase that requires numerical extraction of the phase. Typically a Hilbert transform algorithm is employed to extract the optical phase versus...... wavenumber for calibration and dispersion compensation. In this work we demonstrate UHR-OCT at 1300 nm using a Super continuum source and highlight the resolution constraints in using the Hilbert transform algorithm when extracting the optical phase for calibration and dispersion compensation. We demonstrate...... that the constraints cannot be explained purely by the numerical errors in the data processing module utilizing the Hilbert transform but must be dictated by broadening mechanisms originating from the experimentally obtained interferograms....
The Hilbert-Huang Transform-Based Denoising Method for the TEM Response of a PRBS Source Signal
Hai, Li; Guo-qiang, Xue; Pan, Zhao; Hua-sen, Zhong; Khan, Muhammad Younis
2016-08-01
The denoising process is critical in processing transient electromagnetic (TEM) sounding data. For the full waveform pseudo-random binary sequences (PRBS) response, an inadequate noise estimation may result in an erroneous interpretation. We consider the Hilbert-Huang transform (HHT) and its application to suppress the noise in the PRBS response. The focus is on the thresholding scheme to suppress the noise and the analysis of the signal based on its Hilbert time-frequency representation. The method first decomposes the signal into the intrinsic mode function, and then, inspired by the thresholding scheme in wavelet analysis; an adaptive and interval thresholding is conducted to set to zero all the components in intrinsic mode function which are lower than a threshold related to the noise level. The algorithm is based on the characteristic of the PRBS response. The HHT-based denoising scheme is tested on the synthetic and field data with the different noise levels. The result shows that the proposed method has a good capability in denoising and detail preservation.
Directory of Open Access Journals (Sweden)
Lili Chen
2017-01-01
Full Text Available Preterm birth (PTB is the leading cause of perinatal mortality and long-term morbidity, which results in significant health and economic problems. The early detection of PTB has great significance for its prevention. The electrohysterogram (EHG related to uterine contraction is a noninvasive, real-time, and automatic novel technology which can be used to detect, diagnose, or predict PTB. This paper presents a method for feature extraction and classification of EHG between pregnancy and labour group, based on Hilbert-Huang transform (HHT and extreme learning machine (ELM. For each sample, each channel was decomposed into a set of intrinsic mode functions (IMFs using empirical mode decomposition (EMD. Then, the Hilbert transform was applied to IMF to obtain analytic function. The maximum amplitude of analytic function was extracted as feature. The identification model was constructed based on ELM. Experimental results reveal that the best classification performance of the proposed method can reach an accuracy of 88.00%, a sensitivity of 91.30%, and a specificity of 85.19%. The area under receiver operating characteristic (ROC curve is 0.88. Finally, experimental results indicate that the method developed in this work could be effective in the classification of EHG between pregnancy and labour group.
Shahoei, Hiva; Dumais, Patrick; Yao, Jianping
2014-05-01
We propose and experimentally demonstrate a continuously tunable fractional Hilbert transformer (FHT) based on a high-contrast germanium-doped silica-on-silicon (SOS) microring resonator (MRR). The propagation loss of a high-contrast germanium-doped SOS waveguide can be very small (0.02 dB/cm) while the lossless bend radius can be less than 1 mm. These characteristics lead to the fabrication of an MRR with a high Q-factor and a large free-spectral range (FSR), which is needed to implement a Hilbert transformer (HT). The SOS MRR is strongly polarization dependent. By changing the polarization direction of the input signal, the phase shift introduced at the center of the resonance spectrum is changed. The tunable phase shift at the resonance wavelength can be used to implement a tunable FHT. A germanium-doped SOS MRR with a high-index contrast of 3.8% is fabricated. The use of the fabricated MRR for the implementation of a tunable FHT with tunable orders at 1, 0.85, 0.95, 1.05, and 1.13 for a Gaussian pulse with the temporal full width at half-maximum of 80 ps is experimentally demonstrated.
Chen, Lili; Hao, Yaru
2017-01-01
Preterm birth (PTB) is the leading cause of perinatal mortality and long-term morbidity, which results in significant health and economic problems. The early detection of PTB has great significance for its prevention. The electrohysterogram (EHG) related to uterine contraction is a noninvasive, real-time, and automatic novel technology which can be used to detect, diagnose, or predict PTB. This paper presents a method for feature extraction and classification of EHG between pregnancy and labour group, based on Hilbert-Huang transform (HHT) and extreme learning machine (ELM). For each sample, each channel was decomposed into a set of intrinsic mode functions (IMFs) using empirical mode decomposition (EMD). Then, the Hilbert transform was applied to IMF to obtain analytic function. The maximum amplitude of analytic function was extracted as feature. The identification model was constructed based on ELM. Experimental results reveal that the best classification performance of the proposed method can reach an accuracy of 88.00%, a sensitivity of 91.30%, and a specificity of 85.19%. The area under receiver operating characteristic (ROC) curve is 0.88. Finally, experimental results indicate that the method developed in this work could be effective in the classification of EHG between pregnancy and labour group.
Product numerical range in a space with tensor product structure
Puchała, Zbigniew; Gawron, Piotr; Miszczak, Jarosław Adam; Skowronek, Łukasz; Choi, Man-Duen; Życzkowski, Karol
2010-01-01
We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product ...
On a Hilbert-Type Operator with a Symmetric Homogeneous Kernel of Ã¢ÂˆÂ’1-Order and Applications
Directory of Open Access Journals (Sweden)
Bicheng Yang
2007-10-01
Full Text Available Some character of the symmetric homogenous kernel of Ã¢ÂˆÂ’1-order in Hilbert-type operator T:lrÃ¢Â†Â’lrÃ‚Â (r>1 is obtained. Two equivalent inequalities with the symmetric homogenous kernel of Ã¢ÂˆÂ’ÃŽÂ»-order are given. As applications, some new Hilbert-type inequalities with the best constant factors and the equivalent forms as the particular cases are established.
Baseline LAW Glass Formulation Testing
International Nuclear Information System (INIS)
Kruger, Albert A.; Mooers, Cavin; Bazemore, Gina; Pegg, Ian L.; Hight, Kenneth; Lai, Shan Tao; Buechele, Andrew; Rielley, Elizabeth; Gan, Hao; Muller, Isabelle S.; Cecil, Richard
2013-01-01
The major objective of the baseline glass formulation work was to develop and select glass formulations that are compliant with contractual and processing requirements for each of the LAW waste streams. Other objectives of the work included preparation and characterization of glasses with respect to the properties of interest, optimization of sulfate loading in the glasses, evaluation of ability to achieve waste loading limits, testing to demonstrate compatibility of glass melts with melter materials of construction, development of glass formulations to support ILAW qualification activities, and identification of glass formulation issues with respect to contract specifications and processing requirements
Representations of locally symmetric spaces
International Nuclear Information System (INIS)
Rahman, M.S.
1995-09-01
Locally symmetric spaces in reference to globally and Hermitian symmetric Riemannian spaces are studied. Some relations between locally and globally symmetric spaces are exhibited. A lucid account of results on relevant spaces, motivated by fundamental problems, are formulated as theorems and propositions. (author). 10 refs
Topological Classification of Morse Functions and Generalisations of Hilbert's 16-th Problem
International Nuclear Information System (INIS)
Arnold, Vladimir I.
2007-01-01
The topological structures of the generic smooth functions on a smooth manifold belong to the small quantity of the most fundamental objects of study both in pure and applied mathematics. The problem of their study has been formulated by A. Cayley in 1868, who required the classification of the possible configurations of the horizontal lines on the topographical maps of mountain regions, and created the first elements of what is called today 'Morse Theory' and 'Catastrophes Theory'. In the paper we describe this problem, and in particular describe the classification of Morse functions on the 2 sphere and on the torus
Variational formulation of the Gardner's restacking algorithm
International Nuclear Information System (INIS)
Dodin, I.Y.; Fisch, N.J.
2004-01-01
The incompressibility of the phase flow of Hamiltonian wave-plasma interactions restrains the class of realizable wave-driven transformations of the particle distribution. After the interaction, the distribution remains composed of the original phase-space elements, or local densities, which are only rearranged (''restacked'') by the wave. A variational formalism is developed to study the corresponding limitations on the energy and momentum transfer. A case of particular interest is a toroidal plasma immersed in a dc magnetic field. The restacking algorithm by Gardner [Phys. Fluids 6, 839 (1963)] is formulated precisely. The minimum energy state for a plasma with a given current is determined
A geometric formulation of exceptional field theory
Energy Technology Data Exchange (ETDEWEB)
Bosque, Pascal du [Arnold Sommerfeld Center for Theoretical Physics,Department für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, Föhringer Ring 6, 80805 München (Germany); Hassler, Falk [Department of Physics and Astronomy, University of North Carolina, Phillips Hall, CB #3255, 120 E. Cameron Ave., Chapel Hill, NC 27599-3255 (United States); City University of New York, The Graduate Center, 365 Fifth Avenue, New York, NY 10016 (United States); Department of Physics, Columbia University, Pupin Hall, 550 West 120th St., New York, NY 10027 (United States); Lüst, Dieter [Arnold Sommerfeld Center for Theoretical Physics,Department für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, Föhringer Ring 6, 80805 München (Germany); Malek, Emanuel [Arnold Sommerfeld Center for Theoretical Physics,Department für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany)
2017-03-01
We formulate the full bosonic SL(5) exceptional field theory in a coordinate-invariant manner. Thereby we interpret the 10-dimensional extended space as a manifold with SL(5)×ℝ{sup +}-structure. We show that the algebra of generalised diffeomorphisms closes subject to a set of closure constraints which are reminiscent of the quadratic and linear constraints of maximal seven-dimensional gauged supergravities, as well as the section condition. We construct an action for the full bosonic SL(5) exceptional field theory, even when the SL(5)×ℝ{sup +}-structure is not locally flat.
Tan, Zhixiang; Zhang, Yi; Zeng, Deping; Wang, Hua
2015-04-01
We proposed a research of a heart sound envelope extraction system in this paper. The system was implemented on LabVIEW based on the Hilbert-Huang transform (HHT). We firstly used the sound card to collect the heart sound, and then implemented the complete system program of signal acquisition, pretreatment and envelope extraction on LabVIEW based on the theory of HHT. Finally, we used a case to prove that the system could collect heart sound, preprocess and extract the envelope easily. The system was better to retain and show the characteristics of heart sound envelope, and its program and methods were important to other researches, such as those on the vibration and voice, etc.
Directory of Open Access Journals (Sweden)
Unger Laura Anna
2015-09-01
Full Text Available This work aimed at the detection of rotor centers within the atrial cavity during atrial fibrillation on the basis of phase singularities. A voxel based method was established which employs the Hilbert transform and the phase of unipolar electrograms. The method provides a 3D overview of phase singularities at the endocardial surface and within the blood volume. Mapping those phase singularities from the inside of the atria at the endocardium yielded rotor center trajectories. We discuss the results for an unstable and a more stable rotor. The side length of the areas covered by the trajectories varied from 1.5 mm to 10 mm. These results are important for cardiologists who target rotors with RF ablation in order to cure atrial fibrillation.
Xu, Huile; Liu, Jinyi; Hu, Haibo; Zhang, Yi
2016-12-02
Wearable sensors-based human activity recognition introduces many useful applications and services in health care, rehabilitation training, elderly monitoring and many other areas of human interaction. Existing works in this field mainly focus on recognizing activities by using traditional features extracted from Fourier transform (FT) or wavelet transform (WT). However, these signal processing approaches are suitable for a linear signal but not for a nonlinear signal. In this paper, we investigate the characteristics of the Hilbert-Huang transform (HHT) for dealing with activity data with properties such as nonlinearity and non-stationarity. A multi-features extraction method based on HHT is then proposed to improve the effect of activity recognition. The extracted multi-features include instantaneous amplitude (IA) and instantaneous frequency (IF) by means of empirical mode decomposition (EMD), as well as instantaneous energy density (IE) and marginal spectrum (MS) derived from Hilbert spectral analysis. Experimental studies are performed to verify the proposed approach by using the PAMAP2 dataset from the University of California, Irvine for wearable sensors-based activity recognition. Moreover, the effect of combining multi-features vs. a single-feature are investigated and discussed in the scenario of a dependent subject. The experimental results show that multi-features combination can further improve the performance measures. Finally, we test the effect of multi-features combination in the scenario of an independent subject. Our experimental results show that we achieve four performance indexes: recall, precision, F-measure, and accuracy to 0.9337, 0.9417, 0.9353, and 0.9377 respectively, which are all better than the achievements of related works.
Directory of Open Access Journals (Sweden)
Huile Xu
2016-12-01
Full Text Available Wearable sensors-based human activity recognition introduces many useful applications and services in health care, rehabilitation training, elderly monitoring and many other areas of human interaction. Existing works in this field mainly focus on recognizing activities by using traditional features extracted from Fourier transform (FT or wavelet transform (WT. However, these signal processing approaches are suitable for a linear signal but not for a nonlinear signal. In this paper, we investigate the characteristics of the Hilbert-Huang transform (HHT for dealing with activity data with properties such as nonlinearity and non-stationarity. A multi-features extraction method based on HHT is then proposed to improve the effect of activity recognition. The extracted multi-features include instantaneous amplitude (IA and instantaneous frequency (IF by means of empirical mode decomposition (EMD, as well as instantaneous energy density (IE and marginal spectrum (MS derived from Hilbert spectral analysis. Experimental studies are performed to verify the proposed approach by using the PAMAP2 dataset from the University of California, Irvine for wearable sensors-based activity recognition. Moreover, the effect of combining multi-features vs. a single-feature are investigated and discussed in the scenario of a dependent subject. The experimental results show that multi-features combination can further improve the performance measures. Finally, we test the effect of multi-features combination in the scenario of an independent subject. Our experimental results show that we achieve four performance indexes: recall, precision, F-measure, and accuracy to 0.9337, 0.9417, 0.9353, and 0.9377 respectively, which are all better than the achievements of related works.
Novel Formulations for Antimicrobial Peptides
Directory of Open Access Journals (Sweden)
Ana Maria Carmona-Ribeiro
2014-10-01
Full Text Available Peptides in general hold much promise as a major ingredient in novel supramolecular assemblies. They may become essential in vaccine design, antimicrobial chemotherapy, cancer immunotherapy, food preservation, organs transplants, design of novel materials for dentistry, formulations against diabetes and other important strategical applications. This review discusses how novel formulations may improve the therapeutic index of antimicrobial peptides by protecting their activity and improving their bioavailability. The diversity of novel formulations using lipids, liposomes, nanoparticles, polymers, micelles, etc., within the limits of nanotechnology may also provide novel applications going beyond antimicrobial chemotherapy.
Novel Formulations for Antimicrobial Peptides
Carmona-Ribeiro, Ana Maria; Carrasco, Letícia Dias de Melo
2014-01-01
Peptides in general hold much promise as a major ingredient in novel supramolecular assemblies. They may become essential in vaccine design, antimicrobial chemotherapy, cancer immunotherapy, food preservation, organs transplants, design of novel materials for dentistry, formulations against diabetes and other important strategical applications. This review discusses how novel formulations may improve the therapeutic index of antimicrobial peptides by protecting their activity and improving their bioavailability. The diversity of novel formulations using lipids, liposomes, nanoparticles, polymers, micelles, etc., within the limits of nanotechnology may also provide novel applications going beyond antimicrobial chemotherapy. PMID:25302615
A lattice formulation of chiral gauge theories
International Nuclear Information System (INIS)
Bodwin, G.T.
1995-12-01
The authors present a method for formulating gauge theories of chiral fermions in lattice field theory. The method makes use of a Wilson mass to remove doublers. Gauge invariance is then restored by modifying the theory in two ways: the magnitude of the fermion determinant is replaced with the square root of the determinant for a fermion with vector-like couplings to the gauge field; a double limit is taken in which the lattice spacing associated with the fermion field is taken to zero before the lattice spacing associated with the gauge field. The method applies only to theories whose fermions are in an anomaly-free representation of the gauge group. They also present a related technique for computing matrix elements of operators involving fermion fields. Although the analyses of these methods are couched in weak-coupling perturbation theory, it is argued that computational prescriptions are gauge invariant in the presence of a nonperturbative gauge-field configuration
Least square regularized regression in sum space.
Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu
2013-04-01
This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.
Mathematical foundations of the projection-operator method
International Nuclear Information System (INIS)
Moore, S.M.
1979-01-01
Mathematical foundations are determined for the projection-operator method developed by Zwanzig and Mori and used in the study of cooperative phenomena in non-equilibrium processes. It is shown that the Hilbert space of operators can be taken as the Hilbert-Schmidt class. Comments are made on the possibility of a complete formulation of quantum mechanics in terms of this Hilbert space. (author)
Random path formulation of nonrelativistic quantum mechanics
International Nuclear Information System (INIS)
Roncadelli, M.
1993-01-01
Quantum amplitudes satisfy (almost) the same calculus that probabilities obey in the theory of classical stochastic diffusion processes. As a consequence of this structural analogy, a new formulation of (nonrelativistic) quantum mechanics naturally arises as the quantum counterpart of the Langevin description of (classical) stochastic diffusion processes. Quantum fluctuations are simulated here by a Fresnel white noise (FWN), which is a (real) white noise with imaginary diffusion constant, whose functional (pseudo) measure yields the amplitude distribution for its configurations. Central to this approach is the idea that classical dynamical trajectories in configuration space are perturbed by the FWN. Hence, a single (arbitrary) classical dynamical path gets replaced by a family of quantum random paths (QRPs) - one for each FWN sample - all originating from the same space-time point (x', t'). The QRPs are the basic objects of the present formulation and are given by a Langevin equation with the FWN, whose drift is controlled by a (arbitrary) solution to the classical Hamilton-Jacobi equation. So, our approach is manifestly based on classical dynamics. Now, a transition amplitude is associated with each QRP: it gives the amplitude that a particle starting from (x', t') will reach (x'', t'') by travelling just along the considered QRP. The quantum mechanical propagator (x'', t'' modul x', t') then emerges as the FWN average of the transition amplitude along a QRP. Thus, quantum mechanics looks like classical mechanics as perturbed by the FWN. The general structure of this formulation is discussed in detail, along with some practical and conceptual implications. (author). 14 refs
International Nuclear Information System (INIS)
Ageev, S M
2007-01-01
The Noebeling space N k 2k+1 , a k-dimensional analogue of the Hilbert space, is considered; this is a topologically complete separable (that is, Polish) k-dimensional absolute extensor in dimension k (that is, AE(k)) and a strongly k-universal space. The conjecture that the above-listed properties characterize the Noebeling space N k 2k+1 in an arbitrary finite dimension k is proved. In the first part of the paper a full axiom system of the Noebeling spaces is presented and the problem of the improvement of a partition connectivity is solved on its basis. Bibliography: 29 titles.
Neonates need tailored drug formulations.
Allegaert, Karel
2013-02-08
Drugs are very strong tools used to improve outcome in neonates. Despite this fact and in contrast to tailored perfusion equipment, incubators or ventilators for neonates, we still commonly use drug formulations initially developed for adults. We would like to make the point that drug formulations given to neonates need to be tailored for this age group. Besides the obvious need to search for active compounds that take the pathophysiology of the newborn into account, this includes the dosage and formulation. The dosage or concentration should facilitate the administration of low amounts and be flexible since clearance is lower in neonates with additional extensive between-individual variability. Formulations need to be tailored for dosage variability in the low ranges and also to the clinical characteristics of neonates. A specific focus of interest during neonatal drug development therefore is a need to quantify and limit excipient exposure based on the available knowledge of their safety or toxicity. Until such tailored vials and formulations become available, compounding practices for drug formulations in neonates should be evaluated to guarantee the correct dosing, product stability and safety.
Microcanonical formulation of quantum field theories
International Nuclear Information System (INIS)
Iwazaki, A.
1984-03-01
A microcanonical formulation of Euclidean quantum field theories is presented. In the formulation, correlation functions are given by a microcanonical ensemble average of fields. Furthermore, the perturbative equivalence of the formulation and the standard functional formulation is proved and the equipartition low is derived in our formulation. (author)
On a covariant 2+2 formulation of the initial value problem in general relativity
International Nuclear Information System (INIS)
Smallwood, J.
1980-03-01
The initial value problems in general relativity are considered from a geometrical standpoint with especial reference to the development of a covariant 2+2 formalism in which space-time is foliated by space-like 2-surfaces under the headings; the Cauchy problem in general relativity, the covariant 3+1 formulation of the Cauchy problem, characteristic and mixed initial value problems, on locally imbedding a family of null hypersurfaces, the 2+2 formalism, the 2+2 formulation of the Cauchy problem, the 2+2 formulation of the characteristic and mixed initial value problems, and a covariant Lagrangian 2+2 formulation. (U.K.)
Greedy Algorithms for Reduced Bases in Banach Spaces
DeVore, Ronald
2013-02-26
Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n-dimensional space X n⊂X which can be used to approximate the elements of F. The best possible error we can achieve for such an approximation is given by the Kolmogorov width dn(F)X. However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) in the case X=H is a Hilbert space. The results of Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) were significantly improved upon in Binev et al. (SIAM J. Math. Anal. 43:1457-1472, 2011). The purpose of the present paper is to give a new analysis of the performance of such greedy algorithms. Our analysis not only gives improved results for the Hilbert space case but can also be applied to the same greedy procedure in general Banach spaces. © 2013 Springer Science+Business Media New York.
Tactile friction of topical formulations.
Skedung, L; Buraczewska-Norin, I; Dawood, N; Rutland, M W; Ringstad, L
2016-02-01
The tactile perception is essential for all types of topical formulations (cosmetic, pharmaceutical, medical device) and the possibility to predict the sensorial response by using instrumental methods instead of sensory testing would save time and cost at an early stage product development. Here, we report on an instrumental evaluation method using tactile friction measurements to estimate perceptual attributes of topical formulations. Friction was measured between an index finger and an artificial skin substrate after application of formulations using a force sensor. Both model formulations of liquid crystalline phase structures with significantly different tactile properties, as well as commercial pharmaceutical moisturizing creams being more tactile-similar, were investigated. Friction coefficients were calculated as the ratio of the friction force to the applied load. The structures of the model formulations and phase transitions as a result of water evaporation were identified using optical microscopy. The friction device could distinguish friction coefficients between the phase structures, as well as the commercial creams after spreading and absorption into the substrate. In addition, phase transitions resulting in alterations in the feel of the formulations could be detected. A correlation was established between skin hydration and friction coefficient, where hydrated skin gave rise to higher friction. Also a link between skin smoothening and finger friction was established for the commercial moisturizing creams, although further investigations are needed to analyse this and correlations with other sensorial attributes in more detail. The present investigation shows that tactile friction measurements have potential as an alternative or complement in the evaluation of perception of topical formulations. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Orthogonal polynomials, Laguerre Fock space, and quasi-classical asymptotics
Engliš, Miroslav; Ali, S. Twareque
2015-07-01
Continuing our earlier investigation of the Hermite case [S. T. Ali and M. Engliš, J. Math. Phys. 55, 042102 (2014)], we study an unorthodox variant of the Berezin-Toeplitz quantization scheme associated with Laguerre polynomials. In particular, we describe a "Laguerre analogue" of the classical Fock (Segal-Bargmann) space and the relevant semi-classical asymptotics of its Toeplitz operators; the former actually turns out to coincide with the Hilbert space appearing in the construction of the well-known Barut-Girardello coherent states. Further extension to the case of Legendre polynomials is likewise discussed.
Compressing the hidden variable space of a qubit
International Nuclear Information System (INIS)
Montina, Alberto
2011-01-01
In previously exhibited hidden variable models of quantum state preparation and measurement, the number of continuous hidden variables describing the actual state of single realizations is never smaller than the quantum state manifold dimension. We introduce a simple model for a qubit whose hidden variable space is one-dimensional, i.e., smaller than the two-dimensional Bloch sphere. The hidden variable probability distributions associated with quantum states satisfy reasonable criteria of regularity. Possible generalizations of this shrinking to an N-dimensional Hilbert space are discussed.
Sun, Shuping; Jiang, Zhongwei; Wang, Haibin; Fang, Yu
2014-05-01
This paper proposes a novel automatic method for the moment segmentation and peak detection analysis of heart sound (HS) pattern, with special attention to the characteristics of the envelopes of HS and considering the properties of the Hilbert transform (HT). The moment segmentation and peak location are accomplished in two steps. First, by applying the Viola integral waveform method in the time domain, the envelope (E(T)) of the HS signal is obtained with an emphasis on the first heart sound (S1) and the second heart sound (S2). Then, based on the characteristics of the E(T) and the properties of the HT of the convex and concave functions, a novel method, the short-time modified Hilbert transform (STMHT), is proposed to automatically locate the moment segmentation and peak points for the HS by the zero crossing points of the STMHT. A fast algorithm for calculating the STMHT of E(T) can be expressed by multiplying the E(T) by an equivalent window (W(E)). According to the range of heart beats and based on the numerical experiments and the important parameters of the STMHT, a moving window width of N=1s is validated for locating the moment segmentation and peak points for HS. The proposed moment segmentation and peak location procedure method is validated by sounds from Michigan HS database and sounds from clinical heart diseases, such as a ventricular septal defect (VSD), an aortic septal defect (ASD), Tetralogy of Fallot (TOF), rheumatic heart disease (RHD), and so on. As a result, for the sounds where S2 can be separated from S1, the average accuracies achieved for the peak of S1 (AP₁), the peak of S2 (AP₂), the moment segmentation points from S1 to S2 (AT₁₂) and the cardiac cycle (ACC) are 98.53%, 98.31% and 98.36% and 97.37%, respectively. For the sounds where S1 cannot be separated from S2, the average accuracies achieved for the peak of S1 and S2 (AP₁₂) and the cardiac cycle ACC are 100% and 96.69%. Copyright © 2014 Elsevier Ireland Ltd. All
International Nuclear Information System (INIS)
Fradkin, E.S.; Palchik, M.Ya.
1996-02-01
We study a family of exactly solvable models of conformally-invariant quantum field theory in D-dimensional space. We demonstrate the existence of D-dimensional analogs of primary and secondary fields. Under the action of energy-momentum tensor and conserved currents, the primary fields creates an infinite set of (tensor) secondary fields of different generations. The commutators of secondary fields with zero components of current and energy-momentum tensor include anomalous operator terms. We show that the Hilbert space of conformal theory has a special sector which structure is solely defined by the Ward identities independently on the choice of dynamical model. The states of this sector are constructed from secondary fields. Definite self-consistent conditions on the states of the latter sector fix the choice of the field model uniquely. In particular, Lagrangian models do belong to this class of models. The above self-consistent conditions are formulated as follows. Special superpositions Q s , s = 1,2,... of secondary fields are constructed. Each superposition is determined by the requirement that the form of its commutators with energy-momentum tensor and current (i.e. transformation properties) should be identical to that of a primary field. Each equation Q s (x) = 0 is consistent, and defines an exactly solvable model for D ≥ 3. The structure of these models are analogous to that of well-known two dimensional conformal models. The states Q s (x) modul 0> are analogous to the null-vectors of two dimensional theory. In each of these models one can obtain a closed set of differential equations for all the higher Green functions, as well as algebraic equations relating the scale dimension of fundamental field to the D-dimensional analog of a central charge. As an example, we present a detailed discussion of a pair of exactly solvable models in even-dimensional space D ≥ 4. (author). 28 refs
Decontamination formulation with sorbent additive
Tucker; Mark D. , Comstock; Robert H.
2007-10-16
A decontamination formulation and method of making that neutralizes the adverse health effects of both chemical and biological compounds, especially chemical warfare (CW) and biological warfare (BW) agents, and toxic industrial chemicals. The formulation provides solubilizing compounds that serve to effectively render the chemical and biological compounds, particularly CW and BW compounds, susceptible to attack, and at least one reactive compound that serves to attack (and detoxify or kill) the compound. The formulation includes at least one solubilizing agent, a reactive compound, a bleaching activator, a sorbent additive, and water. The highly adsorbent, water-soluble sorbent additive (e.g., sorbitol or mannitol) is used to "dry out" one or more liquid ingredients, such as the liquid bleaching activator (e.g., propylene glycol diacetate or glycerol diacetate) and convert the activator into a dry, free-flowing powder that has an extended shelf life, and is more convenient to handle and mix in the field.
International Nuclear Information System (INIS)
Pereira, Luis Carlos Martins
1998-06-01
New Petrov-Galerkin formulations on the finite element methods for convection-diffusion problems with boundary layers are presented. Such formulations are based on a consistent new theory on discontinuous finite element methods. Existence and uniqueness of solutions for these problems in the new finite element spaces are demonstrated. Some numerical experiments shows how the new formulation operate and also their efficacy. (author)
Differential calculus in normed linear spaces
Mukherjea, Kalyan
2007-01-01
This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces. Not only does this lead to a simplified and transparent exposition of "difficult" results like the Inverse and Implicit Function Theorems but also permits, without any extra effort, a discussion of the Differential Calculus of functions defined on infinite dimensional Hilbert or Banach spaces.The prerequisites demanded of the reader are modest: a sound understanding of convergence of sequences and series of real numbers, the continuity and differentiability properties of functions of a real variable and a little Linear Algebra should provide adequate background for understanding the book. The first two chapters cover much of the more advanced background material on Linear Algebra (like dual spaces, multilinear functions and tensor products.) Chapter 3 gives an ab ini...
Gravity on a little warped space
International Nuclear Information System (INIS)
George, Damien P.; McDonald, Kristian L.
2011-01-01
We investigate the consistent inclusion of 4D Einstein gravity on a truncated slice of AdS 5 whose bulk-gravity and UV scales are much less than the 4D Planck scale, M * Pl . Such 'Little Warped Spaces' have found phenomenological utility and can be motivated by string realizations of the Randall-Sundrum framework. Using the interval approach to brane-world gravity, we show that the inclusion of a large UV-localized Einstein-Hilbert term allows one to consistently incorporate 4D Einstein gravity into the low-energy theory. We detail the spectrum of Kaluza-Klein metric fluctuations and, in particular, examine the coupling of the little radion to matter. Furthermore, we show that Goldberger-Wise stabilization can be successfully implemented on such spaces. Our results demonstrate that realistic low-energy effective theories can be constructed on these spaces, and have relevance for existing models in the literature.
On infinite-dimensional state spaces
International Nuclear Information System (INIS)
Fritz, Tobias
2013-01-01
It is well known that the canonical commutation relation [x, p]=i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p]=i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V −1 U 2 V=U 3 , then finite-dimensionality entails the relation UV −1 UV=V −1 UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V −1 U 2 V=U 3 holds only up to ε and then yields a lower bound on the dimension.
On infinite-dimensional state spaces
Fritz, Tobias
2013-05-01
It is well known that the canonical commutation relation [x, p] = i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p] = i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V-1U2V = U3, then finite-dimensionality entails the relation UV-1UV = V-1UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V-1U2V = U3 holds only up to ɛ and then yields a lower bound on the dimension.
International Nuclear Information System (INIS)
Manakov, S V; Santini, P M
2008-01-01
We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking
Energy Technology Data Exchange (ETDEWEB)
Manakov, S V [Landau Institute for Theoretical Physics, Moscow (Russian Federation); Santini, P M [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Piazz.le Aldo Moro 2, I-00185 Rome (Italy)
2008-02-08
We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking.
International Nuclear Information System (INIS)
Englman, R.
2016-01-01
The recent phase shift data of Takada et al. (Phys. Rev. Lett. 113 (2014) 126601) for a two level system are reconstructed from their current intensity curves by the method of Hilbert transform, for which the underlying Physics is the principle of causality. An introductory algebraic model illustrates pedagogically the working of the method and leads to newly derived relationships involving phenomenological parameters, in particular for the sign of the phase slope between the resonance peaks. While the parametrization of the experimental current intensity data in terms of a few model parameters shows only a qualitative agreement for the phase shift, due to the strong impact of small, detailed variations in the experimental intensity curve on the phase behavior, the numerical Hilbert transform yields a satisfactory reproduction of the phase.
Uznir, U.; Anton, F.; Suhaibah, A.; Rahman, A. A.; Mioc, D.
2013-09-01
The advantages of three dimensional (3D) city models can be seen in various applications including photogrammetry, urban and regional planning, computer games, etc.. They expand the visualization and analysis capabilities of Geographic Information Systems on cities, and they can be developed using web standards. However, these 3D city models consume much more storage compared to two dimensional (2D) 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 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 objects. In this research, we propose an opponent data constellation technique of space-filling curves (3D Hilbert curves) for 3D city model data representation. Unlike previous methods, that try to project 3D or n-dimensional data down to 2D or 3D using Principal Component Analysis (PCA) or Hilbert mappings, in this research, we extend the Hilbert space-filling curve to one higher dimension for 3D city model data implementations. The query performance was tested using a CityGML dataset of 1,000 building blocks and the results 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 subinterval of the [0, 1] interval to the corresponding portion of the d-dimensional Hilbert's curve, preserves the Lebesgue measure and is Lipschitz continuous. Depending on the applications, several alternatives are possible in order to cluster spatial data together in the third dimension compared to its
Cai, Jianhua
2017-05-01
The time-frequency analysis method represents signal as a function of time and frequency, and it is considered a powerful tool for handling arbitrary non-stationary time series by using instantaneous frequency and instantaneous amplitude. It also provides a possible alternative to the analysis of the non-stationary magnetotelluric (MT) signal. Based on the Hilbert-Huang transform (HHT), a time-frequency analysis method is proposed to obtain stable estimates of the magnetotelluric response function. In contrast to conventional methods, the response function estimation is performed in the time-frequency domain using instantaneous spectra rather than in the frequency domain, which allows for imaging the response parameter content as a function of time and frequency. The theory of the method is presented and the mathematical model and calculation procedure, which are used to estimate response function based on HHT time-frequency spectrum, are discussed. To evaluate the results, response function estimates are compared with estimates from a standard MT data processing method based on the Fourier transform. All results show that apparent resistivities and phases, which are calculated from the HHT time-frequency method, are generally more stable and reliable than those determined from the simple Fourier analysis. The proposed method overcomes the drawbacks of the traditional Fourier methods, and the resulting parameter minimises the estimation bias caused by the non-stationary characteristics of the MT data.
Assessment of vocal cord nodules: a case study in speech processing by using Hilbert-Huang Transform
Civera, M.; Filosi, C. M.; Pugno, N. M.; Silvestrini, M.; Surace, C.; Worden, K.
2017-05-01
Vocal cord nodules represent a pathological condition for which the growth of unnatural masses on vocal folds affects the patients. Among other effects, changes in the vocal cords’ overall mass and stiffness alter their vibratory behaviour, thus changing the vocal emission generated by them. This causes dysphonia, i.e. abnormalities in the patients’ voice, which can be analysed and inspected via audio signals. However, the evaluation of voice condition through speech processing is not a trivial task, as standard methods based on the Fourier Transform, fail to fit the non-stationary nature of vocal signals. In this study, four audio tracks, provided by a volunteer patient, whose vocal fold nodules have been surgically removed, were analysed using a relatively new technique: the Hilbert-Huang Transform (HHT) via Empirical Mode Decomposition (EMD); specifically, by using the CEEMDAN (Complete Ensemble EMD with Adaptive Noise) algorithm. This method has been applied here to speech signals, which were recorded before removal surgery and during convalescence, to investigate specific trends. Possibilities offered by the HHT are exposed, but also some limitations of decomposing the signals into so-called intrinsic mode functions (IMFs) are highlighted. The results of these preliminary studies are intended to be a basis for the development of new viable alternatives to the softwares currently used for the analysis and evaluation of pathological voice.
International Nuclear Information System (INIS)
Iwamoto, Hiroyuki; Tanaka, Nobuo; Hill, Simon G
2010-01-01
This paper concerns the active vibration control of a rectangular panel using smart sensors from the viewpoint of an active wave control theory. The objective of this paper is to present a new type of filter which enables the measurement of the wave amplitude of a rectangular panel in real time for the application of an adaptive feedforward control system which inactivates vibration modes. Firstly, a novel wave filtering method using smart PVDF sensors is proposed. It is found that the shaping function of smart sensors is a complex function. To realize the smart sensor in a practical situation, a Hilbert transformer is utilized to implement a phase shifter of 90° for broadband frequencies. Then, from the viewpoint of a numerical analysis, the characteristics of the proposed wave filter and the performance of the adaptive feedforward control system using the wave filter are discussed. Finally, experiments implementing the active wave control theory which uses the proposed wave filter are conducted, demonstrating the validity of the proposed method in suppressing the vibration of a rectangular panel
Assessment of vocal cord nodules: a case study in speech processing by using Hilbert-Huang Transform
International Nuclear Information System (INIS)
Civera, M; Surace, C; Filosi, C M; Silvestrini, M; Pugno, N M; Worden, K
2017-01-01
Vocal cord nodules represent a pathological condition for which the growth of unnatural masses on vocal folds affects the patients. Among other effects, changes in the vocal cords’ overall mass and stiffness alter their vibratory behaviour, thus changing the vocal emission generated by them. This causes dysphonia, i.e. abnormalities in the patients’ voice, which can be analysed and inspected via audio signals. However, the evaluation of voice condition through speech processing is not a trivial task, as standard methods based on the Fourier Transform, fail to fit the non-stationary nature of vocal signals. In this study, four audio tracks, provided by a volunteer patient, whose vocal fold nodules have been surgically removed, were analysed using a relatively new technique: the Hilbert-Huang Transform (HHT) via Empirical Mode Decomposition (EMD); specifically, by using the CEEMDAN (Complete Ensemble EMD with Adaptive Noise) algorithm. This method has been applied here to speech signals, which were recorded before removal surgery and during convalescence, to investigate specific trends. Possibilities offered by the HHT are exposed, but also some limitations of decomposing the signals into so-called intrinsic mode functions (IMFs) are highlighted. The results of these preliminary studies are intended to be a basis for the development of new viable alternatives to the softwares currently used for the analysis and evaluation of pathological voice. (paper)
Quantum physics of an elementary system in de Sitter space
International Nuclear Information System (INIS)
Rabeie, A.
2012-01-01
We present the coherent states of a scalar massive particle on 1+3-de Sitter space. These states are vectors in Hilbert space, and they are labeled by points in the associated phase space. To do this, we use the fact that the phase space of a scalar massive particle on 1+3-de Sitter space is a cotangent bundle T * (S 3 ) which is isomorphic with the complex sphere S C 3 . Then by using the heat kernel on '' S C 3 '' that was presented by Hall-Mitchell, we construct our coherent states. At the end, by these states we quantize the classical kinetic energy on de Sitter space. (orig.)
Curcumin nanodisks: formulation and characterization
Ghosh, Mistuni; Singh, Amareshwar T. K.; Xu, Wenwei; Sulchek, Todd; Gordon, Leo I.; Ryan, Robert O.
2010-01-01
Nanodisks (ND) are nanoscale, disk-shaped phospholipid bilayers whose edge is stabilized by apolipoproteins. In the present study, ND were formulated with the bioactive polyphenol, curcumin, at a 6:1 phospholipid:curcumin molar ratio. Atomic force microscopy revealed that curcumin-ND are particles with diameters
Covariant Formulation of Hooke's Law.
Gron, O.
1981-01-01
Introducing a four-vector strain and a four-force stress, Hooke's law is written as a four-vector equation. This formulation is shown to clarify seemingly paradoxical results in connection with uniformly accelerated motion, and rotational motion with angular acceleration. (Author/JN)
Hamiltonian formulation of the supermembrane
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Tanii, Y.
1987-06-01
The Hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence free 2-vectors are unfixed. (author). 10 refs
Statistical formulation of gravitational radiation reaction
International Nuclear Information System (INIS)
Schutz, B.F.
1980-01-01
A new formulation of the radiation-reaction problem is proposed, which is simpler than alternatives which have been used before. The new approach is based on the initial-value problem, uses approximations which need be uniformly valid only in compact regions of space-time, and makes no time-asymmetric assumptions (no a priori introduction of retarded potentials or outgoing-wave asymptotic conditions). It defines radiation reaction to be the expected evolution of a source obtained by averaging over a statistical ensemble of initial conditions. The ensemble is chosen to reflect one's complete lack of information (in real systems) about the initial data for the radiation field. The approach is applied to the simple case of a weak-field, slow-motion source in general relativity, where it yields the usual expressions for radiation reaction when the gauge is chosen properly. There is a discussion of gauge freedom, and another of the necessity of taking into account reaction corrections to the particle-conservation equation. The analogy with the second law of thermodynamics is very close, and suggests that the electromagnetic and thermodynamic arrows of time are the same. Because the formulation is based on the usual initial-value problem, it has no spurious ''runaway'' solutions
The master space of N = 1 gauge theories
International Nuclear Information System (INIS)
Forcella, Davide; Hanany, Amihay; He Yanghui; Zaffaroni, Alberto
2008-01-01
The full moduli space M of a class of N = 1 supersymmetric gauge theories is studied. For gauge theories living on a stack of D3-branes at Calabi-Yau singularities X, M is a combination of the mesonic and baryonic branches. In consonance with the mathematical literature, the single brane moduli space is called the master space F b . Illustrating with a host of explicit examples, we exhibit many algebro-geometric properties of the master space such as when F b is toric Calabi-Yau, behaviour of its Hilbert series, its irreducible components and its symmetries. In conjunction with the plethystic programme, we investigate the counting of BPS gauge invariants, baryonic and mesonic, using the geometry of F b and show how its refined Hilbert series not only engenders the generating functions for the counting but also beautifully encode 'hidden' global symmetries of the gauge theory which manifest themselves as symmetries of the complete moduli space M for N number of branes.