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.

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

CERN Document Server

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

Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincaré symmetry

Science.gov (United States)

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

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

Aveiro method in reproducing kernel Hilbert spaces under complete dictionary

Science.gov (United States)

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.

Elements of Hilbert spaces and operator theory

CERN Document Server

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...

Projective loop quantum gravity. I. State space

Science.gov (United States)

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.

Adaptive Learning in Cartesian Product of Reproducing Kernel Hilbert Spaces

OpenAIRE

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...

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.

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

Hilbert space methods in partial differential equations

CERN Document Server

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.

Invariant Hilbert spaces of holomorphic functions

NARCIS (Netherlands)

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

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.

Semiclassical propagation: Hilbert space vs. Wigner representation

Science.gov (United States)

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.

Reproducing kernel Hilbert spaces of Gaussian priors

NARCIS (Netherlands)

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

Vertical integration from the large Hilbert space

Science.gov (United States)

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.

Weaving Hilbert space fusion frames

OpenAIRE

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 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.

An advanced complex analysis problem book topological vector spaces, functional analysis, and Hilbert spaces of analytic functions

CERN Document Server

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.

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.)

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.

Spinors in Hilbert Space

Science.gov (United States)

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.

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

Structure of Hilbert space operators

CERN Document Server

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

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

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

Hilbert spaces contractively included in the Hardy space of the bidisk

NARCIS (Netherlands)

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

Quantum mechanics in an evolving Hilbert space

Science.gov (United States)

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.

Means of Hilbert space operators

CERN Document Server

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.

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

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

Introduction to Hilbert space and the theory of spectral multiplicity

CERN Document Server

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.

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.

The Hilbert Series of the One Instanton Moduli Space

CERN Document Server

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.

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.

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)

Space Inside a Liquid Sphere Transforms into De Sitter Space by Hilbert Radius

Science.gov (United States)

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.

On the minimizers of calculus of variations problems in Hilbert spaces

KAUST Repository

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

KAUST Repository

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.

Ordering of ''ladder'' operators, the Wigner function for number and phase, and the enlarged Hilbert space

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.)

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)

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.)

Wiener-Hopf operators on spaces of functions on R+ with values in a Hilbert space

OpenAIRE

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.

Generalized Polar Decompositions for Closed Operators in Hilbert Spaces and Some Applications

OpenAIRE

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.

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.

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

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

Rosette of rosettes of Hilbert spaces in the indefinite metric state space of the quantized Maxwell field

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

Real analysis measure theory, integration, and Hilbert spaces

CERN Document Server

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

Controlled G-Frames and Their G-Multipliers in Hilbert spaces

OpenAIRE

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...

Projective limits of state spaces II. Quantum formalism

Science.gov (United States)

Lanéry, Suzanne; Thiemann, Thomas

2017-06-01

In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013), which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanéry (2016). After discussing the formalism at the classical level in a first paper (Lanéry, 2017), the present second paper is devoted to the quantum theory. In particular, we inspect in detail how such quantum projective state spaces relate to inductive limit Hilbert spaces and to infinite tensor product constructions (Lanéry, 2016, subsection 3.1) [1]. Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okołów (2013), that were set up in the context of linear configuration spaces, to configuration spaces given by simply-connected Lie groups, and to holomorphic quantization of complex phase spaces (Lanéry, 2016, subsection 2.2) [1].

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.

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

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

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

Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

Science.gov (United States)

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.

Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space.

Science.gov (United States)

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.

Geometry of quantum dynamics in infinite-dimensional Hilbert space

Science.gov (United States)

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.

Exponential Hilbert series of equivariant embeddings

OpenAIRE

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...

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....

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

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.)

Approximately dual frames in Hilbert spaces and applications to Gabor frames

OpenAIRE

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...

Lectures on Hilbert modular varieties and modular forms

CERN Document Server

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...

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...

Friedrichs systems in a Hilbert space framework: Solvability and multiplicity

Science.gov (United States)

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.

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

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.

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.

Recipes for stable linear embeddings from Hilbert spaces to R^m

OpenAIRE

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

OpenAIRE

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...

Projective limits of state spaces IV. Fractal label sets

Science.gov (United States)

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.

Convex analysis and monotone operator theory in Hilbert spaces

CERN Document Server

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...

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

Projective flatness in the quantisation of bosons and fermions

Science.gov (United States)

Wu, Siye

2015-07-01

We compare the quantisation of linear systems of bosons and fermions. We recall the appearance of projectively flat connection and results on parallel transport in the quantisation of bosons. We then discuss pre-quantisation and quantisation of fermions using the calculus of fermionic variables. We define a natural connection on the bundle of Hilbert spaces and show that it is projectively flat. This identifies, up to a phase, equivalent spinor representations constructed by various polarisations. We introduce the concept of metaplectic correction for fermions and show that the bundle of corrected Hilbert spaces is naturally flat. We then show that the parallel transport in the bundle of Hilbert spaces along a geodesic is a rescaled projection provided that the geodesic lies within the complement of a cut locus. Finally, we study the bundle of Hilbert spaces when there is a symmetry.

Two New Iterative Methods for a Countable Family of Nonexpansive Mappings in Hilbert Spaces

Directory of Open Access Journals (Sweden)

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.

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

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.)

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

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

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

Lectures on Hilbert schemes of points on surfaces

CERN Document Server

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 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

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...

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)

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.

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)

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...

Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces

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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.

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.

An Hilbert space approach for a class of arbitrage free implied volatilities models

OpenAIRE

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...

Hilbert schemes of points on some classes surface singularities

OpenAIRE

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...

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)

Quantum Hilbert Hotel.

Science.gov (United States)

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.

Continuous Slice Functional Calculus in Quaternionic Hilbert Spaces

Science.gov (United States)

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.

Verification of Equivalence of the Axial Gauge to the Coulomb Gauge in QED by Embedding in the Indefinite Metric Hilbert Space : Particles and Fields

OpenAIRE

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...

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

Hilbert schemes of points and infinite dimensional Lie algebras

CERN Document Server

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...

Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

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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.

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).

Galerkin approximations of nonlinear optimal control problems in Hilbert spaces

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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 $\\mathbb{S}^2$.

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)

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...

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...

Unexplored regions in QFT: an alternative resolution of the gauge-theoretic clash between localization and the Hilbert space of quantum theory

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)

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)

Image decomposition model Shearlet-Hilbert-L2 with better performance for denoising in ESPI fringe patterns.

Science.gov (United States)

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 .

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

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.

On-line quantile regression in the RKHS (Reproducing Kernel Hilbert Space) for operational probabilistic forecasting of wind power

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.

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

H-SLAM: Rao-Blackwellized Particle Filter SLAM Using Hilbert Maps

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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.

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)

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.

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

Twenty-first century quantum mechanics Hilbert space to quantum computers mathematical methods and conceptual foundations

CERN Document Server

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...

Aspects of a representation of quantum theory in terms of classical probability theory by means of integration in Hilbert space

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)

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.

Monopole operators and Hilbert series of Coulomb branches of 3 d = 4 gauge theories

Science.gov (United States)

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.

Hilbert's programs and beyond

CERN Document Server

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.

Context-invariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space

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)

Some means inequalities for positive operators in Hilbert spaces

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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.

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.

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

The q-difference operator, the quantum hyperplane, Hilbert spaces of analytic functions and q-oscillators

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.)

A product of three projections

Czech Academy of Sciences Publication Activity Database

Kopecká, E.; Müller, Vladimír

2014-01-01

Roč. 223, č. 2 (2014), s. 175-186 ISSN 0039-3223 R&D Projects: GA ČR(CZ) GA14-07880S Institutional support: RVO:67985840 Keywords : Hilbert space * projection * extension Subject RIV: BA - General Mathematics Impact factor: 0.610, year: 2014 http://journals.impan.pl/cgi-bin/doi?sm223-2-4

Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

Science.gov (United States)

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.

Computing Instantaneous Frequency by normalizing Hilbert Transform

Science.gov (United States)

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.

Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space

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.

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)

A note on the von Neumann alternating projections algorithm

Czech Academy of Sciences Publication Activity Database

Kopecká, Eva; Reich, S.

2004-01-01

Roč. 5, č. 3 (2004), s. 379-386 ISSN 1345-4773 Institutional research plan: CEZ:AV0Z1019905 Keywords : alternating orthogonal projections * Hilbert space * nearest point mapping Subject RIV: BA - General Mathematics

Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics

Science.gov (United States)

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'.

Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics.

Science.gov (United States)

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).

Power Spectral Density and Hilbert Transform

Science.gov (United States)

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

Theory and experiments on Peano and Hilbert curve RFID tags

Science.gov (United States)

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].

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)

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.

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 ...

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

Mathematical methods in physics distributions, Hilbert space operators, variational methods, and applications in quantum physics

CERN Document Server

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...

The classes of the quasihomogeneous Hilbert schemes of points on the plane

NARCIS (Netherlands)

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

Soft and hard classification by reproducing kernel Hilbert space methods.

Science.gov (United States)

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.

q-deformed Minkowski space

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.)

Another note on the von Neumann alternating projections algorithm

Czech Academy of Sciences Publication Activity Database

Kopecká, Eva; Reich, S.

2010-01-01

Roč. 11, č. 3 (2010), s. 455-460 ISSN 1345-4773 Institutional research plan: CEZ:AV0Z10190503 Keywords : projection * iteration * Hilbert space Subject RIV: BA - General Mathematics Impact factor: 0.738, year: 2010 http://www.ybook.co.jp/online/jncae/vol11/p455.html

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

Convexity and the Euclidean Metric of Space-Time

Directory of Open Access Journals (Sweden)

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.

Approximation of 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

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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.

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

Hilbert-Twin – A Novel Hilbert Transform-Based Method To Compute Envelope Of Free Decaying Oscillations Embedded In Noise, And The Logarithmic Decrement In High-Resolution Mechanical Spectroscopy HRMS

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.

Biologically-Inspired Spike-Based Automatic Speech Recognition of Isolated Digits Over a Reproducing Kernel Hilbert Space

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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.

Biologically-Inspired Spike-Based Automatic Speech Recognition of Isolated Digits Over a Reproducing Kernel Hilbert Space.

Science.gov (United States)

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.

Improved specimen reconstruction by Hilbert phase contrast tomography.

Science.gov (United States)

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.

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

Terahertz bandwidth all-optical Hilbert transformers based on long-period gratings.

Science.gov (United States)

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.

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

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.

Regularization methods in Banach spaces

CERN Document Server

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

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)

Hilbert's 'Foundations of Physics': Gravitation and electromagnetism within the axiomatic method

Science.gov (United States)

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.

Practical interior tomography with radial Hilbert filtering and a priori knowledge in a small round area.

Science.gov (United States)

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

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

Science.gov (United States)

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.

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.

Frames and outer frames for Hilbert C^*-modules

OpenAIRE

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...

Explicit Hilbert-space representations of atomic and molecular photoabsorption spectra: Computational studies of Stieltjes-Tchebycheff functions

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

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

Independence and totalness of subspaces in phase space methods

Science.gov (United States)

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.

A generalization of the Friedrichs angle and the method of alternating projections

Czech Academy of Sciences Publication Activity Database

Badea, C.; Grivaux, S.; Müller, Vladimír

2010-01-01

Roč. 348, 1-2 (2010), s. 53-56 ISSN 1631-073X R&D Projects: GA ČR(CZ) GA201/06/0128 Institutional research plan: CEZ:AV0Z10190503 Keywords : Hilbert space * Neumann -Halperin method Subject RIV: BA - General Mathematics Impact factor: 0.399, year: 2010 http://www.sciencedirect.com/science/article/pii/S1631073X09004002

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...

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.

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

To quantum averages through asymptotic expansion of classical averages on infinite-dimensional space

International Nuclear Information System (INIS)

Khrennikov, Andrei

2007-01-01

We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of scaling of the covariation operator of a Gaussian measure and the second (Frechet) derivative of a functional. In this way we couple classical average (given by an infinite-dimensional Gaussian integral) and quantum average (given by the von Neumann trace formula). We can interpret this mathematical construction as a procedure of 'dequantization' of quantum mechanics. We represent quantum mechanics as an asymptotic projection of classical statistical mechanics with infinite-dimensional phase space. This space can be represented as the space of classical fields, so quantum mechanics is represented as a projection of 'prequantum classical statistical field theory'

Hörmander spaces, interpolation, and elliptic problems

CERN Document Server

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

Convergence rates in constrained Tikhonov regularization: equivalence of projected source conditions and variational inequalities

International Nuclear Information System (INIS)

Flemming, Jens; Hofmann, Bernd

2011-01-01

In this paper, we enlighten the role of variational inequalities for obtaining convergence rates in Tikhonov regularization of nonlinear ill-posed problems with convex penalty functionals under convexity constraints in Banach spaces. Variational inequalities are able to cover solution smoothness and the structure of nonlinearity in a uniform manner, not only for unconstrained but, as we indicate, also for constrained Tikhonov regularization. In this context, we extend the concept of projected source conditions already known in Hilbert spaces to Banach spaces, and we show in the main theorem that such projected source conditions are to some extent equivalent to certain variational inequalities. The derived variational inequalities immediately yield convergence rates measured by Bregman distances

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....

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.)

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

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

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...

Terahertz bandwidth photonic Hilbert transformers based on synthesized planar Bragg grating fabrication.

Science.gov (United States)

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.

Magnetomyographic recording and identification of uterine contractions using Hilbert-wavelet transforms

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

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.

Image restoration by the method of convex projections: part 1 theory.

Science.gov (United States)

Youla, D C; Webb, H

1982-01-01

A projection operator onto a closed convex set in Hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms. Moreover, it minimizes distance and is nonexpansive, and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds. In this paper, we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically. Their common conceptual basis is as follows. Every known property of an original image f is envisaged as restricting it to lie in a well-defined closed convex set. Thus, m such properties place f in the intersection E(0) = E(i) of the corresponding closed convex sets E(1),E(2),...EE(m). Given only the projection operators PE(i) onto the individual E(i)'s, i = 1 --> m, we restore f by recursive means. Clearly, in this approach, the realization of the P(i)'s in a Hilbert space setting is one of the major synthesis problems. Section I describes the geometrical significance of the three main theorems in considerable detail, and most of the underlying ideas are illustrated with the aid of simple diagrams. Section II presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal-processing applications, and the Appendix contains proofs of all the major results.

Improving 3d Spatial Queries Search: Newfangled Technique of Space Filling Curves in 3d City Modeling

Science.gov (United States)

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

Critical Assessment Of The Issues In The Application Of Hilbert Transform To Compute The Logarithmic Decrement

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.

Bundles over Quantum RealWeighted Projective Spaces

Directory of Open Access Journals (Sweden)

Tomasz Brzeziński

2012-09-01

Full Text Available The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1-bundles over quantum real weighted projective spaces are constructed. As the spaces in question fall into two separate classes, the negative or odd class that generalises quantum real projective planes and the positive or even class that generalises the quantum disc, so do the constructed principal bundles. In the negative case the principal bundle is proven to be non-trivial and associated projective modules are described. In the positive case the principal bundles turn out to be trivial, and so all the associated modules are free. It is also shown that the circle (coactions on the quantum Seifert manifold that define quantum real weighted projective spaces are almost free.

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.

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.

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.

Chinese Manned Space Utility Project

Science.gov (United States)

Gu, Y.

Since 1992 China has been carrying out a conspicuous manned space mission A utility project has been defined and created during the same period The Utility Project of the Chinese Manned Space Mission involves wide science areas such as earth observation life science micro-gravity fluid physics and material science astronomy space environment etc In the earth observation area it is focused on the changes of global environments and relevant exploration technologies A Middle Revolution Image Spectrometer and a Multi-model Micro-wave Remote Sensor have been developed The detectors for cirrostratus distribution solar constant earth emission budget earth-atmosphere ultra-violet spectrum and flux have been manufactured and tested All of above equipment was engaged in orbital experiments on-board the Shenzhou series spacecrafts Space life science biotechnologies and micro-gravity science were much concerned with the project A series of experiments has been made both in ground laboratories and spacecraft capsules The environmental effect in different biological bodies in space protein crystallization electrical cell-fusion animal cells cultural research on separation by using free-low electrophoresis a liquid drop Marangoni migration experiment under micro-gravity as well as a set of crystal growth and metal processing was successfully operated in space The Gamma-ray burst and high-energy emission from solar flares have been explored A set of particle detectors and a mass spectrometer measured

Girls InSpace project: A new space physics outreach initiative.

Science.gov (United States)

Abe Pacini, A.; Tegbaru, D.; Max, A., Sr.

2017-12-01

We present here the concept and state-of-art of the new space physics youth education and outreach initiative called "Girls InSpace project". The project goal is to spread quality scientific information to underrepresented groups, motivate girls in STEM and promote gender equality in the Space Physics area. Initially, the "Girls InSpace project" will be available in two languages (Portuguese and English) aiming to reach out to the youth of Brazil, United States, Nigeria, South Africa, Ethiopia and Angola. Eventually, the material will be translated to French and Spanish, focusing on French-speaking countries in Africa and Latin America. The project spans a collection of four books about a group of young girls and their adventures (always related to the sky and simultaneously introducing earth and space science concepts). Ancillary content such as a webpage, mobile applications and lesson plans are also in development. The books were written by a Space Physicist PhD woman, illustrated by a Brazilian young artist and commented by senior female scientists, creating positive role models for the next generation of girls in STEM. The story lines were drawn around the selected topics of astronomy and space physics, introducing scientific information to the target readers (girls from 8-13 years old) and enhancing their curiosity and critical thinking. The books instill the readers to explore the available extra web-content (with images, videos, interviews with scientists, real space data, coding and deeper scientific information) and game apps (with Virtual Reality components and real space images). Moreover, for teachers K-12, a collection of lesson plans will be made available, aiming to facilitate scientific content discussed in the books and inside classroom environments. Gender bias in STEM reported earlier this year in Nature and based on a study of the American Geophysical Union's member database showed a competitive disadvantage for women in the Earth and Space

Life sciences space biology project planning

Science.gov (United States)

Primeaux, G.; Newkirk, K.; Miller, L.; Lewis, G.; Michaud, R.

1988-01-01

The Life Sciences Space Biology (LSSB) research will explore the effect of microgravity on humans, including the physiological, clinical, and sociological implications of space flight and the readaptations upon return to earth. Physiological anomalies from past U.S. space flights will be used in planning the LSSB project.The planning effort integrates science and engineering. Other goals of the LSSB project include the provision of macroscopic view of the earth's biosphere, and the development of spinoff technology for application on earth.

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)

Time-frequency analysis of non-stationary fusion plasma signals using an improved Hilbert-Huang transform

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

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).

Application of Hilbert-Huang Transform in Generating Spectrum-Compatible Earthquake Time Histories

OpenAIRE

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 ...

Multivariate prediction, de Branges spaces, and related extension and inverse problems

CERN Document Server

Arov, Damir Z

2018-01-01

This monograph deals primarily with the prediction of vector valued stochastic processes that are either weakly stationary, or have weakly stationary increments, from finite segments of their past. The main focus is on the analytic counterpart of these problems, which amounts to computing projections onto subspaces of a Hilbert space of p x 1 vector valued functions with an inner product that is defined in terms of the p x p matrix valued spectral density of the process. The strategy is to identify these subspaces as vector valued de Branges spaces and then to express projections in terms of the reproducing kernels of these spaces and/or in terms of a generalized Fourier transform that is obtained from the solution of an associated inverse spectral problem. Subsequently, the projection of the past onto the future and the future onto the past is interpreted in terms of the range of appropriately defined Hankel operators and their adjoints, and, in the last chapter, assorted computations are carried out for rat...

Projected quasiparticle theory for molecular electronic structure

Science.gov (United States)

Scuseria, Gustavo E.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Samanta, Kousik; Ellis, Jason K.

2011-09-01

We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a self-consistent variation-after-projection approach. We show that the resulting method yields a comprehensive black-box treatment of static correlations with effective one-electron (mean-field) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proof-of-principle examples demonstrating the compelling power of projected quasiparticle theory for quantum chemistry.

Novel microwave photonic fractional hilbert transformer using a ring resonator-based optical all-pass filter

NARCIS (Netherlands)

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

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

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

An algorithm for the split-feasibility problems with application to the split-equality problem.

Science.gov (United States)

Chuang, Chih-Sheng; Chen, Chi-Ming

2017-01-01

In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

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 ...

Hilbert's Grand Hotel with a series twist

Science.gov (United States)

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.

All-optical Hilbert transformer based on a single phase-shifted fiber Bragg grating: design and analysis.

Science.gov (United States)

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.

Explicit solution of Riemann-Hilbert problems for the Ernst equation

Science.gov (United States)

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.

Analyticity spaces of self-adjoint operators subjected to perturbations with applications to Hankel invariant distribution spaces

NARCIS (Netherlands)

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

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

Experimental validation of a structural damage detection method based on marginal Hilbert spectrum

Science.gov (United States)

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.

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.

Density operators in quantum mechanics

International Nuclear Information System (INIS)

Burzynski, A.

1979-01-01

A brief discussion and resume of density operator formalism in the way it occurs in modern physics (in quantum optics, quantum statistical physics, quantum theory of radiation) is presented. Particularly we emphasize the projection operator method, application of spectral theorems and superoperators formalism in operator Hilbert spaces (Hilbert-Schmidt type). The paper includes an appendix on direct sums and direct products of spaces and operators, and problems of reducibility for operator class by using the projection operators. (author)

Space Projects: Improvements Needed in Selecting Future Projects for Private Financing

Science.gov (United States)

1990-01-01

The Office of Management and Budget (OMB) and NASA jointly selected seven projects for commercialization to reduce NASA's fiscal year 1990 budget request and to help achieve the goal of increasing private sector involvement in space. However, the efforts to privately finance these seven projects did not increase the commercial sector's involvement in space to the extent desired. The General Accounting Office (GAO) determined that the projects selected were not a fair test of the potential of increasing commercial investment in space at an acceptable cost to the government, primarily because the projects were not properly screened. That is, neither their suitability for commercialization nor the economic consequences of seeking private financing for them were adequately evaluated before selection. Evaluations and market tests done after selection showed that most of the projects were not viable candidates for private financing. GAO concluded that projects should not be removed from NASA's budget for commercial development until after careful screening has been done to determine whether adequate commercial demand exists, development risks are commercially acceptable and private financing is found or judged to be highly likely, and the cost effectiveness of such a decision is acceptable. Premature removal of projects from NASA's budget ultimately can cause project delays and increased costs when unsuccessful commercialization candidates must be returned to the budget. NASA also needs to ensure appropriate comparisons of government and private financing options for future commercialization projects.

Almost sharp quantum effects

International Nuclear Information System (INIS)

Arias, Alvaro; Gudder, Stan

2004-01-01

Quantum effects are represented by operators on a Hilbert space satisfying 0≤A≤I, and sharp quantum effects are represented by projection operators. We say that an effect A is almost sharp if A=PQP for projections P and Q. We give simple characterizations of almost sharp effects. We also characterize effects that can be written as longer products of projections. For generality we first work in the formalism of von Neumann algebras. We then specialize to the full operator algebra B(H) and to finite dimensional Hilbert spaces

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)

City project and public space

CERN Document Server

2013-01-01

The book aims at nurturing theoretic reflection on the city and the territory and working out and applying methods and techniques for improving our physical and social landscapes. The main issue is developed around the projectual dimension, with the objective of visualising both the city and the territory from a particular viewpoint, which singles out the territorial dimension as the city’s space of communication and negotiation. Issues that characterise the dynamics of city development will be faced, such as the new, fresh relations between urban societies and physical space, the right to the city, urban equity, the project for the physical city as a means to reveal civitas, signs of new social cohesiveness, the sense of contemporary public space and the sustainability of urban development. Authors have been invited to explore topics that feature a pluralism of disciplinary contributions studying formal and informal practices on the project for the city and seeking conceptual and operative categories capab...

Projective invariants in a conformal finsler space - I

International Nuclear Information System (INIS)

Mishra, C.K.; Singh, M.P.

1989-12-01

The projective invariants in a conformal Finsler space have been studied in regard to certain tensor and scalar which are invariant under projective transformation in a Finsler space. They have been the subject of further investigation by the present authors. (author). 8 refs

T^{\\sigma}_{\\rho}(G) Theories and Their Hilbert Series

CERN Document Server

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.

Geometric approach to evolution problems in metric spaces

NARCIS (Netherlands)

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

The moduli space of instantons on an ALE space from 3d $\\mathcal{N}=4$ field theories

CERN Document Server

Mekareeya, Noppadol

2015-01-01

The moduli space of instantons on an ALE space is studied using the moduli space of $\\mathcal{N}=4$ field theories in three dimensions. For instantons in a simple gauge group $G$ on $\\mathbb{C}^2/\\mathbb{Z}_n$, the Hilbert series of such an instanton moduli space is computed from the Coulomb branch of the quiver given by the affine Dynkin diagram of $G$ with flavour nodes of unitary groups attached to various nodes of the Dynkin diagram. We provide a simple prescription to determine the ranks and the positions of these flavour nodes from the order of the orbifold $n$ and from the residual subgroup of $G$ that is left unbroken by the monodromy of the gauge field at infinity. For $G$ a simply laced group of type $A$, $D$ or $E$, the Higgs branch of such a quiver describes the moduli space of instantons in projective unitary group $PU(n) \\cong U(n)/U(1)$ on orbifold $\\mathbb{C}^2/\\hat{G}$, where $\\hat{G}$ is the discrete group that is in McKay correspondence to $G$. Moreover, we present the quiver whose Coulomb ...

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)

The Einstein-Hilbert gravitation with minimum length

Science.gov (United States)

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.

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.

Projection x-space magnetic particle imaging.

Science.gov (United States)

Goodwill, Patrick W; Konkle, Justin J; Zheng, Bo; Saritas, Emine U; Conolly, Steven M

2012-05-01

Projection magnetic particle imaging (MPI) can improve imaging speed by over 100-fold over traditional 3-D MPI. In this work, we derive the 2-D x-space signal equation, 2-D image equation, and introduce the concept of signal fading and resolution loss for a projection MPI imager. We then describe the design and construction of an x-space projection MPI scanner with a field gradient of 2.35 T/m across a 10 cm magnet free bore. The system has an expected resolution of 3.5 × 8.0 mm using Resovist tracer, and an experimental resolution of 3.8 × 8.4 mm resolution. The system images 2.5 cm × 5.0 cm partial field-of views (FOVs) at 10 frames/s, and acquires a full field-of-view of 10 cm × 5.0 cm in 4 s. We conclude by imaging a resolution phantom, a complex "Cal" phantom, mice injected with Resovist tracer, and experimentally confirm the theoretically predicted x-space spatial resolution.

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)

Riesz Frames and Approximation of the Frame Coefficients

DEFF Research Database (Denmark)

Christensen, Ole

1996-01-01

A frame is a familyof elements in a Hilbert space with the propertythat every element in the Hilbert space can be written as a (infinite)linear combination of the frame elements. Frame theory describes howone can choose the corresponding coefficients, which are calledframe coefficients. From...... the mathematical point of view this isgratifying, but for applications it is a problem that the calculationrequires inversion of an operator on the Hilbert space.The projection method is introduced in order to avoid this problem.The basic idea is to consider finite subfamiliesof the frame and the orthogonal...... projection onto its span. Forfin QTR H,P_nf has a representation as a linear combinationof f_i,i=1,2,..,n, and the corresponding coefficients can be calculatedusing finite dimensional methods. We find conditions implying that thosecoefficients converge to the correct frame coefficients as n goes...

Clustering in Hilbert simplex geometry

KAUST Repository

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.

Live from Space Station Learning Technologies Project

Science.gov (United States)

2001-01-01

This is the Final Report for the Live From Space Station (LFSS) project under the Learning Technologies Project FY 2001 of the MSFC Education Programs Department. AZ Technology, Inc. (AZTek) has developed and implemented science education software tools to support tasks under the LTP program. Initial audience consisted of 26 TreK in the Classroom schools and thousands of museum visitors to the International Space Station: The Earth Tour exhibit sponsored by Discovery Place museum.

Space Mission Human Reliability Analysis (HRA) Project

Data.gov (United States)

National Aeronautics and Space Administration — The purpose of this project is to extend current ground-based Human Reliability Analysis (HRA) techniques to a long-duration, space-based tool to more effectively...

On the projective curvature tensor of generalized Sasakian-space ...

African Journals Online (AJOL)

space-forms under some conditions regarding projective curvature tensor. All the results obtained in this paper are in the form of necessary and sufficient conditions. Keywords: Generalized Sasakian-space-forms; projectively flat; ...

Concerning the Hilbert 16th problem

CERN Document Server

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

TRI-Worthy Projects for the Deep Space Gateway

Science.gov (United States)

Wotring, V. E.; Strangman, G. E.; Donoviel, D.

2018-02-01

Preparations for exploration will require exposure to the actual deep space environment. The new TRI for Space Health proposes innovative projects using real space radiation to make medically-relevant measurements affecting human physiology.

Space Synthetic Biology Project

Science.gov (United States)

Howard, David; Roman, Monsi; Mansell, James (Matt)

2015-01-01

Synthetic biology is an effort to make genetic engineering more useful by standardizing sections of genetic code. By standardizing genetic components, biological engineering will become much more similar to traditional fields of engineering, in which well-defined components and subsystems are readily available in markets. Specifications of the behavior of those components and subsystems can be used to model a system which incorporates them. Then, the behavior of the novel system can be simulated and optimized. Finally, the components and subsystems can be purchased and assembled to create the optimized system, which most often will exhibit behavior similar to that indicated by the model. The Space Synthetic Biology project began in 2012 as a multi-Center effort. The purpose of this project was to harness Synthetic Biology principals to enable NASA's missions. A central target for application was to Environmental Control & Life Support (ECLS). Engineers from NASA Marshall Space Flight Center's (MSFC's) ECLS Systems Development Branch (ES62) were brought into the project to contribute expertise in operational ECLS systems. Project lead scientists chose to pursue the development of bioelectrochemical technologies to spacecraft life support. Therefore, the ECLS element of the project became essentially an effort to develop a bioelectrochemical ECLS subsystem. Bioelectrochemical systems exploit the ability of many microorganisms to drive their metabolisms by direct or indirect utilization of electrical potential gradients. Whereas many microorganisms are capable of deriving the energy required for the processes of interest (such as carbon dioxide (CO2) fixation) from sunlight, it is believed that subsystems utilizing electrotrophs will exhibit smaller mass, volume, and power requirements than those that derive their energy from sunlight. In the first 2 years of the project, MSFC personnel conducted modeling, simulation, and conceptual design efforts to assist the

Hilbert-Schmidt quantum coherence in multi-qudit systems

Science.gov (United States)

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.

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

Relativistic resonances as non-orthogonal states in Hilbert space

CERN Document Server

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'....

Moduli Spaces for Linear Differential Equations and the Painlevé Equations

NARCIS (Netherlands)

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

The NASA Advanced Space Power Systems Project

Science.gov (United States)

Mercer, Carolyn R.; Hoberecht, Mark A.; Bennett, William R.; Lvovich, Vadim F.; Bugga, Ratnakumar

2015-01-01

The goal of the NASA Advanced Space Power Systems Project is to develop advanced, game changing technologies that will provide future NASA space exploration missions with safe, reliable, light weight and compact power generation and energy storage systems. The development effort is focused on maturing the technologies from a technology readiness level of approximately 23 to approximately 56 as defined in the NASA Procedural Requirement 7123.1B. Currently, the project is working on two critical technology areas: High specific energy batteries, and regenerative fuel cell systems with passive fluid management. Examples of target applications for these technologies are: extending the duration of extravehicular activities (EVA) with high specific energy and energy density batteries; providing reliable, long-life power for rovers with passive fuel cell and regenerative fuel cell systems that enable reduced system complexity. Recent results from the high energy battery and regenerative fuel cell technology development efforts will be presented. The technical approach, the key performance parameters and the technical results achieved to date in each of these new elements will be included. The Advanced Space Power Systems Project is part of the Game Changing Development Program under NASAs Space Technology Mission Directorate.

A Novel Approach for Microgrid Protection Based upon Combined ANFIS and Hilbert Space-Based Power Setting

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

Spaces of positive and negative frequency solutions of field equations in curved space--times. I. The Klein--Gordon equation in stationary space--times

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

Geometry of spin coherent states

Science.gov (United States)

Chryssomalakos, C.; Guzmán-González, E.; Serrano-Ensástiga, E.

2018-04-01

Spin states of maximal projection along some direction in space are called (spin) coherent, and are, in many respects, the ‘most classical’ available. For any spin s, the spin coherent states form a 2-sphere in the projective Hilbert space \

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.

Space applications of Automation, Robotics and Machine Intelligence Systems (ARAMIS). Volume 2: Space projects overview

Science.gov (United States)

Miller, R. H.; Minsky, M. L.; Smith, D. B. S.

1982-01-01

Applications of automation, robotics, and machine intelligence systems (ARAMIS) to space activities, and their related ground support functions are studied so that informed decisions can be made on which aspects of ARAMIS to develop. The space project breakdowns, which are used to identify tasks ('functional elements'), are described. The study method concentrates on the production of a matrix relating space project tasks to pieces of ARAMIS.

Reflection Negative Kernels and Fractional Brownian Motion

Directory of Open Access Journals (Sweden)

Palle E. T. Jorgensen

2018-06-01

Full Text Available In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space E and show in particular that fractional Brownian motion for Hurst index 0 < H ≤ 1 / 2 is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if 0 < H < 1 / 2 . We also study projective invariance of fractional Brownian motion and relate this to the complementary series representations of GL 2 ( R . We relate this to a measure preserving action on a Gaussian L 2 -Hilbert space L 2 ( E .

Space-filling Curves

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 ...

Greedy Algorithms for Reduced Bases in Banach Spaces

KAUST Repository

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.

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.

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)

Moduli spaces of convex projective structures on surfaces

DEFF Research Database (Denmark)

Fock, V. V.; Goncharov, A. B.

2007-01-01

We introduce explicit parametrisations of the moduli space of convex projective structures on surfaces, and show that the latter moduli space is identified with the higher Teichmüller space for defined in [V.V. Fock, A.B. Goncharov, Moduli spaces of local systems and higher Teichmüller theory, math.......AG/0311149]. We investigate the cluster structure of this moduli space, and define its quantum version....

Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter.

Science.gov (United States)

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.

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.)

Hilbert-Schmidt and Sobol sensitivity indices for static and time series Wnt signaling measurements in colorectal cancer - part A.

Science.gov (United States)

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

A Proof of the Hilbert-Smith Conjecture

OpenAIRE

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...

2009 ESMD Space Grant Faculty Project Final Report

Science.gov (United States)

Murphy, Gloria; Ghanashyam, Joshi; Guo, Jiang; Conrad, James; Bandyopadhyay, Alak; Cross, William

2009-01-01

The Constellation Program is the medium by which we will maintain a presence in low Earth orbit, return to the moon for further exploration and develop procedures for Mars exploration. The foundation for its presence and success is built by the many individuals that have given of their time, talent and even lives to help propel the mission and objectives of NASA. The Exploration Systems Mission Directorate (ESMD) Faculty Fellows Program is a direct contributor to the success of directorate and Constellation Program objectives. It is through programs such as the ESMD Space Grant program that students are inspired and challenged to achieve the technological heights that will propel us to meet the goals and objectives of ESMD and the Constellation Program. It is through ESMD Space Grant programs that future NASA scientists, engineers, and mathematicians begin to dream of taking America to newer heights of space exploration. The ESMD Space Grant program is to be commended for taking the initiative to develop and implement programs that help solidify the mission of NASA. With the concerted efforts of the Kennedy Space Center educational staff, the 2009 ESMD Space Grant Summer Faculty Fellows Program allowed faculty to become more involved with NASA personnel relating to exploration topics for the senior design projects. The 2009 Project was specifically directed towards NASA's Strategic Educational Outcome 1. In-situ placement of Faculty Fellows at the NASA field Centers was essential; this allowed personal interactions with NASA scientists and engineers. In particular, this was critical to better understanding the NASA problems and begin developing a senior design effort to solve the problems. The Faculty Fellows are pleased that the ESMD Space Grant program is taking interest in developing the Senior Design courses at the university level. These courses are needed to help develop the NASA engineers and scientists of the very near future. It has been a pleasure to be

Space Mission Human Reliability Analysis (HRA) Project

Science.gov (United States)

Boyer, Roger

2014-01-01

The purpose of the Space Mission Human Reliability Analysis (HRA) Project is to extend current ground-based HRA risk prediction techniques to a long-duration, space-based tool. Ground-based HRA methodology has been shown to be a reasonable tool for short-duration space missions, such as Space Shuttle and lunar fly-bys. However, longer-duration deep-space missions, such as asteroid and Mars missions, will require the crew to be in space for as long as 400 to 900 day missions with periods of extended autonomy and self-sufficiency. Current indications show higher risk due to fatigue, physiological effects due to extended low gravity environments, and others, may impact HRA predictions. For this project, Safety & Mission Assurance (S&MA) will work with Human Health & Performance (HH&P) to establish what is currently used to assess human reliabiilty for human space programs, identify human performance factors that may be sensitive to long duration space flight, collect available historical data, and update current tools to account for performance shaping factors believed to be important to such missions. This effort will also contribute data to the Human Performance Data Repository and influence the Space Human Factors Engineering research risks and gaps (part of the HRP Program). An accurate risk predictor mitigates Loss of Crew (LOC) and Loss of Mission (LOM).The end result will be an updated HRA model that can effectively predict risk on long-duration missions.

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...

Multisymplectic unified formalism for Einstein-Hilbert gravity

Science.gov (United States)

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.

Critical Assessment Of The Issues In The Application Of Hilbert Transform To Compute The Logarithmic Decrement

OpenAIRE

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...

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.

Space-time least-squares Petrov-Galerkin projection in nonlinear model reduction.

Energy Technology Data Exchange (ETDEWEB)

Choi, Youngsoo [Sandia National Laboratories (SNL-CA), Livermore, CA (United States). Extreme-scale Data Science and Analytics Dept.; Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Carlberg, Kevin Thomas [Sandia National Laboratories (SNL-CA), Livermore, CA (United States). Extreme-scale Data Science and Analytics Dept.

2017-09-01

Our work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply Petrov-Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed method applies projection in space and time simultaneously. To accomplish this, the method first introduces a low-dimensional space-time trial subspace, which can be obtained by computing tensor decompositions of state-snapshot data. The method then computes discrete-optimal approximations in this space-time trial subspace by minimizing the residual arising after time discretization over all space and time in a weighted ℓ²-norm. This norm can be de ned to enable complexity reduction (i.e., hyper-reduction) in time, which leads to space-time collocation and space-time GNAT variants of the ST-LSPG method. Advantages of the approach relative to typical spatial-projection-based nonlinear model reduction methods such as Galerkin projection and least-squares Petrov-Galerkin projection include: (1) a reduction of both the spatial and temporal dimensions of the dynamical system, (2) the removal of spurious temporal modes (e.g., unstable growth) from the state space, and (3) error bounds that exhibit slower growth in time. Numerical examples performed on model problems in fluid dynamics demonstrate the ability of the method to generate orders-of-magnitude computational savings relative to spatial-projection-based reduced-order models without sacrificing accuracy.

The method of rigged spaces in singular perturbation theory of self-adjoint operators

CERN Document Server

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...

Linearized Jastrow-style fluctuations on spin-projected Hartree-Fock

International Nuclear Information System (INIS)

Henderson, Thomas M.; Scuseria, Gustavo E.

2013-01-01

The accurate and efficient description of strong electronic correlations remains an important objective in electronic structure theory. Projected Hartree-Fock theory, where symmetries of the Hamiltonian are deliberately broken and projectively restored, all with a mean-field computational scaling, shows considerable promise in this regard. However, the method is neither size extensive nor size consistent; in other words, the correlation energy per particle beyond broken-symmetry mean field vanishes in the thermodynamic limit, and the dissociation limit of a molecule is not the sum of the fragment energies. These two problems are closely related. Recently, Neuscamman [Phys. Rev. Lett. 109, 203001 (2012)] has proposed a method to cure the lack of size consistency in the context of the antisymmetrized geminal power wave function (equivalent to number-projected Hartree-Fock-Bogoliubov) by using a Jastrow-type correlator in Hilbert space. Here, we apply the basic idea in the context of projected Hartree-Fock theory, linearizing the correlator for computational simplicity but extending it to include spin fluctuations. Results are presented for the Hubbard Hamiltonian and for some simple molecular systems

NASA Space Flight Program and Project Management Handbook

Science.gov (United States)

Blythe, Michael P.; Saunders, Mark P.; Pye, David B.; Voss, Linda D.; Moreland, Robert J.; Symons, Kathleen E.; Bromley, Linda K.

2014-01-01

This handbook is a companion to NPR 7120.5E, NASA Space Flight Program and Project Management Requirements and supports the implementation of the requirements by which NASA formulates and implements space flight programs and projects. Its focus is on what the program or project manager needs to know to accomplish the mission, but it also contains guidance that enhances the understanding of the high-level procedural requirements. (See Appendix C for NPR 7120.5E requirements with rationale.) As such, it starts with the same basic concepts but provides context, rationale, guidance, and a greater depth of detail for the fundamental principles of program and project management. This handbook also explores some of the nuances and implications of applying the procedural requirements, for example, how the Agency Baseline Commitment agreement evolves over time as a program or project moves through its life cycle.

Cuspidal discrete series for projective hyperbolic spaces

DEFF Research Database (Denmark)

Andersen, Nils Byrial; Flensted-Jensen, Mogens

2013-01-01

Abstract. We have in [1] proposed a definition of cusp forms on semisimple symmetric spaces G/H, involving the notion of a Radon transform and a related Abel transform. For the real non-Riemannian hyperbolic spaces, we showed that there exists an infinite number of cuspidal discrete series......, and at most finitely many non-cuspidal discrete series, including in particular the spherical discrete series. For the projective spaces, the spherical discrete series are the only non-cuspidal discrete series. Below, we extend these results to the other hyperbolic spaces, and we also study the question...

On the quantization of free fields of spin 1 and 2

International Nuclear Information System (INIS)

Grigore, D.R.

2000-01-01

The second quantization of an 'elementary' particle, that is a projective unitary irreducible representation of the Poincare group (H,U) (here the first entry is the Hilbert space where the representation U acts) is a prescription of constructing an associated Hilbert space (called Fock space) H phys ≡ F ± (H), where the sign indicates the statistics. For particles of higher spin, appearing in electromagnetism, Yang-Mills theories or gravitation it is convenient to extend the Fock space by adding fictitious particles (called ghosts). If the extended Hilbert space is H gh then one tries to determine an operator Q, called supercharge which verifies Q 2 = 0 and such that the physical Hilbert space is H phys = Ker(Q) Im(Q). The rigorous proof of this equivalence seems to be missing from the literature. Although, no general theorem of this type seems to be available, this is a proof for the case of the massless particle, of helicity 1 (photon), the massive particle of spin 1, (heavy Bosons) and massless spin 2 particle (the graviton). As a consequence, we argue that the condition of gauge invariance which is generally postulated in these theories, is in fact not an independent axiom but the rather natural condition that the S-matrix factorizes to the physical Hilbert space. (author)

Frequency hopping signal detection based on wavelet decomposition and Hilbert-Huang transform

Science.gov (United States)

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.

Tsirelson's space

CERN Document Server

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).

On projective invariants based on non-linear connections in a Finsler space I

International Nuclear Information System (INIS)

Rastogi, S.C.

1986-05-01

The projective transformations based on linear connections in a Finsler space have been studied by Berwald, Misra, Szabo, Matsumoto, Fukai and Yamada, Rastogi and others. In almost all these papers the emphasis has been on studying Finsler spaces of scalar curvature, Finsler spaces of constant curvature and Finsler spaces of zero curvature with the help of projective curvature tensors of Weyl and Douglas. In 1981, the author studied projective transformation in a Finsler space based on non-linear connections and obtained certain projective invariants. The aim of the present paper is to study Finsler spaces of scalar curvature, constant curvature and zero curvature with the help of non-linear connections and projective invariants obtained from non-linear connections. (author)

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

Unitary Representations of Gauge Groups

Science.gov (United States)

Huerfano, Ruth Stella

I generalize to the case of gauge groups over non-trivial principal bundles representations that I. M. Gelfand, M. I. Graev and A. M. Versik constructed for current groups. The gauge group of the principal G-bundle P over M, (G a Lie group with an euclidean structure, M a compact, connected and oriented manifold), as the smooth sections of the associated group bundle is presented and studied in chapter I. Chapter II describes the symmetric algebra associated to a Hilbert space, its Hilbert structure, a convenient exponential and a total set that later play a key role in the construction of the representation. Chapter III is concerned with the calculus needed to make the space of Lie algebra valued 1-forms a Gaussian L^2-space. This is accomplished by studying general projective systems of finitely measurable spaces and the corresponding systems of sigma -additive measures, all of these leading to the description of a promeasure, a concept modeled after Bourbaki and classical measure theory. In the case of a locally convex vector space E, the corresponding Fourier transform, family of characters and the existence of a promeasure for every quadratic form on E^' are established, so the Gaussian L^2-space associated to a real Hilbert space is constructed. Chapter III finishes by exhibiting the explicit Hilbert space isomorphism between the Gaussian L ^2-space associated to a real Hilbert space and the complexification of its symmetric algebra. In chapter IV taking as a Hilbert space H the L^2-space of the Lie algebra valued 1-forms on P, the gauge group acts on the motion group of H defining in an straight forward fashion the representation desired.

Rael Artel Gallery: Non-Profit Project Space : short tale of an experimental project's space tactics / Kiwa

Index Scriptorium Estoniae

Kiwa, pseud., 1975-

2009-01-01

Aastatel 2004-2008 Pärnus ja aastatel 2006-2008 Tartus tegutsenud Rael Artel Galeriist, mille looja ja moderaator oli Rael Artel. Galerii tegevus lõppes kunstialbumi "Hotell Pärnu : Rael Arel Gallery : Non Profit Project Space 2004-2008 / kontseptsioon ja toimetamine: Rael Artel" ilmumisega 2009. aastal

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

Science.gov (United States)

Zhu, Yan-Chun; Du, Jiang; Yang, Wen-Chao; Duan, Chai-Jie; Wang, Hao-Yu; Gao, Song; Bao, Shang-Lian

2014-03-01

Radial imaging techniques, such as projection-reconstruction (PR), are used in magnetic resonance imaging (MRI) for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function (PSF). In this paper, a shaking projection (SP) k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. A SP trajectory has the same aliasing character when using half sampling frequency (or half data) for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling reconstruction. Furthermore, this method can be applied to three-dimensional (3D) hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts.

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

International Nuclear Information System (INIS)

Zhu Yan-Chun; Yang Wen-Chao; Wang Hao-Yu; Gao Song; Bao Shang-Lian; Du Jiang; Duan Chai-Jie

2014-01-01

Radial imaging techniques, such as projection-reconstruction (PR), are used in magnetic resonance imaging (MRI) for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function (PSF). In this paper, a shaking projection (SP) k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. A SP trajectory has the same aliasing character when using half sampling frequency (or half data) for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling reconstruction. Furthermore, this method can be applied to three-dimensional (3D) hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts

Probabilistic structure of quantum theory

International Nuclear Information System (INIS)

Burzynski, A.

1989-01-01

The fundamental ideas of quantum theory are presented. It is shown that two approaches to quantum theory: Heisenberg's matrix mechanics and Schroedinger's wave mechanics, can be formulated by means of the theory of operators in Hilbert space. Some remarks on Hilbert spaces, diadic and projection operators are done. States, probabilities and observables of quantum systems are discussed and time evolution of quantum states is analysed. Some remarks on two-component systems and symmetries are given. 21 refs. (M.F.W.)

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.

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.

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

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

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

Management of Service Projects in Support of Space Flight Research

Science.gov (United States)

Love, J.

2009-01-01

Goal:To provide human health and performance countermeasures, knowledge, technologies, and tools to enable safe, reliable, and productive human space exploration . [HRP-47051] Specific Objectives: 1) Develop capabilities, necessary countermeasures, and technologies in support of human space exploration, focusing on mitigating the highest risks to human health and performance. 2) Define and improve human spaceflight medical, environmental, and human factors standards. 3) Develop technologies that serve to reduce medical and environmental risks, to reduce human systems resource requirements (mass, volume, power, data, etc.) and to ensure effective human-system integration across exploration systems. 4) Ensure maintenance of Agency core competencies necessary to enable risk reduction in the following areas: A. Space medicine B. Physiological and behavioral effects of long duration spaceflight on the human body C. Space environmental effects, including radiation, on human health and performance D. Space "human factors" [HRP-47051]. Service projects can form integral parts of research-based project-focused programs to provide specialized functions. Traditional/classic project management methodologies and agile approaches are not mutually exclusive paradigms. Agile strategies can be combined with traditional methods and applied in the management of service projects functioning in changing environments. Creative collaborations afford a mechanism for mitigation of constrained resource limitations.

Design methodology and projects for space engineering

Science.gov (United States)

Nichols, S.; Kleespies, H.; Wood, K.; Crawford, R.

1993-01-01

NASA/USRA is an ongoing sponsor of space design projects in the senior design course of the Mechanical Engineering Department at The University of Texas at Austin. This paper describes the UT senior design sequence, consisting of a design methodology course and a capstone design course. The philosophical basis of this sequence is briefly summarized. A history of the Department's activities in the Advanced Design Program is then presented. The paper concludes with a description of the projects completed during the 1991-92 academic year and the ongoing projects for the Fall 1992 semester.

NASA's In-Space Manufacturing Project: A Roadmap for a Multimaterial Fabrication Laboratory in Space

Science.gov (United States)

Prater, Tracie; Werkheiser, Niki; Ledbetter, Frank

2017-01-01

Human space exploration to date has been limited to low Earth orbit and the moon. The International Space Station (ISS) provides a unique opportunity for NASA to partner with private industry for development and demonstration of the technologies needed to support exploration initiatives. One challenge that is critical to sustainable and safer exploration is the ability to manufacture and recycle materials in space. This paper provides an overview of NASA's in-space manufacturing (ISM) project, its past and current activities (2014-2017), and how technologies under development will ultimately culminate in a multimaterial fabrication laboratory ("ISM FabLab") to be deployed on the International Space Station in the early 2020s. ISM is a critical capability for the long endurance missions NASA seeks to undertake in the coming decades. An unanticipated failure that can be adapted for in low earth orbit, through a resupply launch or a return to earth, may instead result in a loss of mission while in transit to Mars. To have a suite of functional ISM capabilities that are compatible with NASA's exploration timeline, ISM must be equipped with the resources necessary to develop these technologies and deploy them for testing prior to the scheduled de-orbit of ISS in 2024. The presentation provides a broad overview of ISM projects activities culminating with the Fabrication Laboratory for ISS. In 2017, the in-space manufacturing project issued a broad agency announcement for this capability. Requirements of the Fabrication Laboratory as stated in the solicitation will be discussed. The FabLab will move NASA and private industry significantly closer to changing historical paradigms for human spaceflight where all materials used in space are launched from earth. While the current ISM FabLab will be tested on ISS, future systems are eventually intended for use in a deep space habitat or transit vehicle. The work of commercial companies funded under NASA's Small Business

Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform.

Science.gov (United States)

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)].

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.

A New Method for Non-linear and Non-stationary Time Series Analysis:
The Hilbert Spectral Analysis

CERN Multimedia

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...

Super Global Projects and Environmentally Friendly Technologies Used in Space Exploration: Realities and Prospects of the Space Age

Directory of Open Access Journals (Sweden)

Sergey Krichevsky

2018-02-01

Full Text Available The 60th anniversary of the Space Age is an important intermediate finishing point on the way of a man and the whole humanity to space. Along with the outstanding achievements, there are a number of challenges and contradictions in space exploration due to the aggravation of the global crisis on Earth, low efficiency and the backlog of space research in the transition to a new technology based reality and clean technologies. Both the international astronautics and the space exploration area nowadays face difficulties in choosing a new paradigm and a development strategy that is becoming even more complicated due to the current unstable and turbulent situation on Earth. The article reveals the optimistic scenario of further space exploration, as well as the methodological and practical aspects of new projects and technologies. The periodization of the Space Age history has been conducted. It has been also proposed a new classification of the “space” phenomenon due to concretizing the concept of “global” in the form of a three-scale structure encompassing the following levels: 1 planetary global; 2 super global; 3 universally global. The notion of “super global space exploration project” has been introduced. The concept of further space exploration is proposed, which includes four interrelated super global projects:1 Earth Protection System from Asteroid and Comet Threat; 2 Moon Exploration; 3 Mars Exploration; 4 Cosmic Humanity. Since the humanity is embarking on the practical implementation of these super global projects, it is urgent to make a transition towards a new technology based order, as well as up-to-date technologies. A couple of ecological projects and space exploration technologies of the 20th and 21st centuries have been exemplified and analyzed. It has been also worked out the list of new environmentally friendly space technologies and projects. The research makes an emphasis upon a great potential of clean and green

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

Ghost sector of vacuum string field theory and the projection equation

International Nuclear Information System (INIS)

Potting, Robertus; Raeymaekers, Joris

2002-01-01

We study the ghost sector of vacuum string field theory where the BRST operator Q is given by the midpoint insertion proposed by Gaiotto, Rastelli, Sen and Zwiebach. We introduce a convenient basis of half-string modes in terms of which Q takes a particularly simple form. We show that there exists a field redefinition which reduces the ghost sector field equation to a pure projection equation for string fields satisfying the constraint that the ghost number is equally divided over the left- and right halves of the string. When this constraint is imposed, vacuum string field theory can be reformulated as a U(∞) cubic matrix model. Ghost sector solutions can be constructed from projection operators on half-string Hilbert space just as in the matter sector. We construct the ghost sector equivalent of various well-known matter sector projectors such as the sliver, butterfly and nothing states. (author)

The use of particle accelerators for space projects

International Nuclear Information System (INIS)

Virtanen, Ari

2006-01-01

With the introduction of CMOS technology radiation effects in components became an important issue in satellite and space mission projects. At the end of the cold war, the market of radiation hard (RadHard) components crashed and during the 90's their fabrication practically stopped. The use of 'commercial-off-the-shelf' (COTS) components became more common but required increased evaluation activities at radiation test sites. Component manufacturers and space project engineers were directed towards these test sites, in particular, towards particle accelerators. Many accelerator laboratories developed special beam lines and constructed dedicated test areas for component evaluations. The space environment was simulated at these test sites and components were tested to levels often exceeding mission requirements. In general, space projects environments were predicted in respects to particle mass and energy distributions with the expected fluxes and fluences. In order to validate this information in tests, concepts like stopping power, linear energy transfer, ion penetration ranges etc. have to be understood. The knowledge from the component structure also defines the way of irradiation. For example, the higher ion energies resulting in much deeper ion penetration ranges allow successful reverse side irradiation of thinned Integrated Circuits (ICs). So overall increased demands for radiation testing attracted the European Space Agency (ESA) to the JYFL-accelerator laboratory of the University of Jyvaeskylae, Finland. A contract was signed between ESA and JYFL for the development of a 'High Penetrating Heavy Ion Test Site'. Following one year development, this test site was commissioned in May 2005. This paper addresses the various issues around the JYFL laboratory with its accelerator and radiation effects facility as the focal point in service of component evaluations for the space community

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.

Project LAUNCH: Bringing Space into Math and Science Classrooms

Science.gov (United States)

Fauerbach, M.; Henry, D. P.; Schmidt, D. L.

2005-01-01

Project LAUNCH is a K-12 teacher professional development program, which has been created in collaboration between the Whitaker Center for Science, Mathematics and Technology Education at Florida Gulf Coast University (FGCU), and the Florida Space Research Institute (FSRI). Utilizing Space as the overarching theme it is designed to improve mathematics and science teaching, using inquiry based, hands-on teaching practices, which are aligned with Florida s Sunshine State Standards. Many students are excited about space exploration and it provides a great venue to get them involved in science and mathematics. The scope of Project LAUNCH however goes beyond just providing competency in the subject area, as pedagogy is also an intricate part of the project. Participants were introduced to the Conceptual Change Model (CCM) [1] as a framework to model good teaching practices. As the CCM closely follows what scientists call the scientific process, this teaching method is also useful to actively engage institute participants ,as well as their students, in real science. Project LAUNCH specifically targets teachers in low performing, high socioeconomic schools, where the need for skilled teachers is most critical.

From Kant to Hilbert a source book in the foundations of mathematics

CERN Document Server

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...

Resolution dependence on phase extraction by the Hilbert transform in phase calibrated and dispersion compensated ultrahigh resolution spectrometer-based OCT

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....

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...

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?

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.)

Poschl-Teller potentials based solution to Hilbert's tenth problem Pöschl-Teller potentials based solution to Hilbert's tenth problem

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.

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)

Rich families and projectional skeletons in Asplund WCG spaces

Czech Academy of Sciences Publication Activity Database

Cúth, M.; Fabian, Marián

2017-01-01

Roč. 448, č. 2 (2017), s. 1618-1632 ISSN 0022-247X R&D Projects: GA ČR(CZ) GAP201/12/0290 Institutional support: RVO:67985840 Keywords : Asplund space * weakly compactly generated space * weakly Lindelöf determined space Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022247X16307715

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)

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

Science.gov (United States)

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.

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

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.

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

Strategic Project Management at the NASA Kennedy Space Center

Science.gov (United States)

Lavelle, Jerome P.

2000-01-01

This paper describes Project Management at NASA's Kennedy Space Center (KSC) from a strategic perspective. It develops the historical context of the agency and center's strategic planning process and illustrates how now is the time for KSC to become a center which has excellence in project management. The author describes project management activities at the center and details observations on those efforts. Finally the author describes the Strategic Project Management Process Model as a conceptual model which could assist KSC in defining an appropriate project management process system at the center.

International Roughness Index (IRI) measurement using Hilbert-Huang transform

Science.gov (United States)

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.

Conformal symmetries of the Einstein-Hilbert action on horizons of stationary and axisymmetric black holes

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)

Employing the Hilbert-Huang Transform to analyze observed natural complex signals: Calm wind meandering cases

Science.gov (United States)

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.

Greedy Algorithms for Reduced Bases in Banach Spaces

KAUST Repository

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

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.)

Arbitrary-order Hilbert Spectral Analysis and Intermittency in Solar Wind Density Fluctuations

Science.gov (United States)

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.

Uniform sparse bounds for discrete quadratic phase Hilbert transforms

Science.gov (United States)

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.

Superconformal compactifications in weighted projective space

International Nuclear Information System (INIS)

Greene, B.R.

1990-01-01

We discuss some aspects of string vacua constructed from orbifolded nonminimal Landau-Ginzburg theories which correspond to Calabi-Yau manifolds in weighted projective space. In contrast to previous expectations, we find that these theories allow for the construction of numerous stable (2, 0) Calabi-Yau vacua (most of which are not simply deformations of an underlying (2, 2) theory) thus indicating that this phenomenologically promising sector of the space of classical vacua is quite robust. We briefly discuss methods for extracting the phenomenology of these models and show, for example, that the full renormalizable superpotential of our SU(5) theories is not corrected by world sheet instantons and is thus given exactly by its tree-level value. (orig.)

Evaluating Quality in Educational Spaces: OECD/CELE Pilot Project

Science.gov (United States)

von Ahlefeld, Hannah

2009-01-01

CELE's International Pilot Project on Evaluating Quality in Educational Spaces aims to assist education authorities, schools and others to maximise the use of and investment in learning environments. This article provides an update on the pilot project, which is currently being implemented in Brazil, Mexico, New Zealand, Portugal and the United…

Two-shot fringe pattern phase-amplitude demodulation using Gram-Schmidt orthonormalization with Hilbert-Huang pre-filtering.

Science.gov (United States)

Trusiak, Maciej; Patorski, Krzysztof

2015-02-23

Gram-Schmidt orthonormalization is a very fast and efficient method for the fringe pattern phase demodulation. It requires only two arbitrarily phase-shifted frames. Images are treated as vectors and upon orthogonal projection of one fringe vector onto another the quadrature fringe pattern pair is obtained. Orthonormalization process is very susceptible, however, to noise, uneven background and amplitude modulation fluctuations. The Hilbert-Huang transform based preprocessing is proposed to enhance fringe pattern phase demodulation by filtering out the spurious noise and background illumination and performing fringe normalization. The Gram-Schmidt orthonormalization process error analysis is provided and its filtering-expanded capabilities are corroborated analyzing DSPI fringes and performing amplitude demodulation of Bessel fringes. Synthetic and experimental fringe pattern analyses presented to validate the proposed technique show that it compares favorably with other pre-filtering schemes, i.e., Gaussian filtering and continuous wavelet transform.

Hilbert scheme of points on cyclic quotient singularities of type (p,1)

OpenAIRE

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.

NASA Space Radiation Risk Project: Overview and Recent Results

Science.gov (United States)

Blattnig, Steve R.; Chappell, Lori J.; George, Kerry A.; Hada, Megumi; Hu, Shaowen; Kidane, Yared H.; Kim, Myung-Hee Y.; Kovyrshina, Tatiana; Norman, Ryan B.; Nounu, Hatem N.;

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.)

NASA rocket launches student project into space

OpenAIRE

Crumbley, Liz

2005-01-01

A project that began in 2002 will culminate at sunrise on Tuesday, March 15, when a team of Virginia Tech engineering students watch a payload section they designed lift off aboard a sounding rocket from a launch pad at NASA's Wallops Island Flight Facility and travel 59 miles into space.

Regular Riemann-Hilbert transforms, Baecklund transformations and hidden symmetry algebra for some linearization systems

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)

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.

Extended space expectation values of position related operators for hydrogen-like quantum system evolutions

International Nuclear Information System (INIS)

Kalay, Berfin; Demiralp, Metin

2014-01-01

The expectation value definitions over an extended space from the considered Hilbert space of the system under consideration is given in another paper of the second author in this symposium. There, in that paper, the conceptuality rather than specification is emphasized on. This work uses that conceptuality to investigate the time evolutions of the position related operators' expectation values not in its standard meaning but rather in a new version of the definition over not the original Hilbert space but in the space obtained by extensions via introducing the images of the given initial wave packet under the positive integer powers of the system Hamiltonian. These images may not be residing in the same space of the initial wave packet when certain singularities appear in the structure of the system Hamiltonian. This may break down the existence of the integrals in the definitions of the expectation values. The cure is the use of basis functions in the abovementioned extended space and the sandwiching of the target operator whose expectation value is under questioning by an appropriately chosen operator guaranteeing the existence of the relevant integrals. Work specifically focuses on the hydrogen-like quantum systems whose Hamiltonians contain a polar singularity at the origin

Geometric invariant theory for polarized curves

CERN Document Server

Bini, Gilberto; Melo, Margarida; Viviani, Filippo

2014-01-01

We investigate GIT quotients of polarized curves. More specifically, we study the GIT problem for the Hilbert and Chow schemes of curves of degree d and genus g in a projective space of dimension d-g, as d decreases with respect to g. We prove that the first three values of d at which the GIT quotients change are given by d=a(2g-2) where a=2, 3.5, 4. We show that, for a>4, L. Caporaso's results hold true for both Hilbert and Chow semistability. If 3.5Hilbert semistable locus coincides with the Chow semistable locus and it maps to the moduli stack of weakly-pseudo-stable curves. If 2Hilbert and Chow semistable loci coincide and they map to the moduli stack of pseudo-stable curves. We also analyze in detail the critical values a=3.5 and a=4, where the Hilbert semistable locus is strictly smaller than the Chow semistable locus. As an application, we obtain three compactications of the universal Jacobian over the moduli space of stable curves, weakly-pseudo-stable curves and pseu...

Life sciences payloads analyses and technical program planning studies. [project planning of space missions of space shuttles in aerospace medicine and space biology

Science.gov (United States)

1976-01-01

Contractural requirements, project planning, equipment specifications, and technical data for space shuttle biological experiment payloads are presented. Topics discussed are: (1) urine collection and processing on the space shuttle, (2) space processing of biochemical and biomedical materials, (3) mission simulations, and (4) biomedical equipment.

The solution of the sixth Hilbert problem: the ultimate Galilean revolution

Science.gov (United States)

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'.

The conditional in quantum logic

International Nuclear Information System (INIS)

Hardegree, G.M.

1976-01-01

In this article it is argued that orthodox quantum logic, which is represented by the lattice of projections on Hilbert space, does in fact admit an operation which possesses the essential properties of a material conditional. It is proposed that this connective can be interpreted as a Stalnaker (counter factual) conditional, where the nearness ordering among 'worlds' (in this case, QM pure states) derives in a natural way from the Hilbert space inner-product metric. It is a characteristic of the quantum logic conditional that the law of modus ponens is equivalent to the orthomodular law of conventional quantum logic. (B.R.H.)

On using the Hilbert transform for blind identification of complex modes: A practical approach

Science.gov (United States)

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

Projections in duals to Asplund spaces made without Simons' lemma

Czech Academy of Sciences Publication Activity Database

Cúth, M.; Fabian, Marián

2015-01-01

Roč. 143, č. 1 (2015), s. 301-308 ISSN 0002-9939 R&D Projects: GA ČR(CZ) GAP201/12/0290 Institutional support: RVO:67985840 Keywords : Asplund space * projectional resolution of identity * projectional skeleton Subject RIV: BA - General Mathematics Impact factor: 0.700, year: 2015 http://www.ams.org/journals/proc/2015-143-01/S0002-9939-2014-12300-8/

HAL/S programmer's guide. [for space shuttle project

Science.gov (United States)

Newbold, P. M.; Hotz, R. L.

1974-01-01

The structure and symbology of the HAL/S programming language are described; this language is to be used among the flight software for the space shuttle project. The data declaration, input/output statements, and replace statements are also discussed.

Operator representations of frames

DEFF Research Database (Denmark)

Christensen, Ole; Hasannasab, Marzieh

2017-01-01

of the properties of the operator T requires more work. For example it is a delicate issue to obtain a representation with a bounded operator, and the availability of such a representation not only depends on the frame considered as a set, but also on the chosen indexing. Using results from operator theory we show......The purpose of this paper is to consider representations of frames {fk}k∈I in a Hilbert space ℋ of the form {fk}k∈I = {Tkf0}k∈I for a linear operator T; here the index set I is either ℤ or ℒ0. While a representation of this form is available under weak conditions on the frame, the analysis...... that by embedding the Hilbert space ℋ into a larger Hilbert space, we can always represent a frame via iterations of a bounded operator, composed with the orthogonal projection onto ℋ. The paper closes with a discussion of an open problem concerning representations of Gabor frames via iterations of a bounded...

Moduli spaces for linear differential equations and the Painlev'e equations

NARCIS (Netherlands)

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

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.)

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.

A more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function.

Science.gov (United States)

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.

Deteksi Kerusakan Batang Rotor Pada Motor Induksi Menggunakan Analisis Arus Mula Berbasis Hilbert Transform

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.

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

Projected space-time and varying speed of light

International Nuclear Information System (INIS)

Iovane, G.; Bellucci, S.; Benedetto, E.

2008-01-01

In this paper starting from El Naschie's Cantorian space-time and our model of projected Universe, we consider its properties in connection with varying speed of light. A possible way-out of the related problem is provided by the Fantappie group approach

The ESA Space Weather Applications Pilot Project

Science.gov (United States)

Glover, A.; Hilgers, A.; Daly, E.

Following the completion in 2001 of two parallel studies to consider the feasibility of a European Space Weather Programme ESA embarked upon a space weather pilot study with the goal of prototyping European space weather services and assessing the overall market for such within Europe This pilot project centred on a number of targeted service development activities supported by a common infrastructure and making use of only existing space weather assets Each service activity included clear participation from at least one identified service user who was requested to provide initial requirements and regular feedback during the operational phase of the service These service activities are now reaching the end of their 2-year development and testing phase and are now accessible each with an element of the service in the public domain see http www esa-spaceweathet net swenet An additional crucial element of the study was the inclusion of a comprehensive and independent analysis of the benefits both economic and strategic of embarking on a programme which would include the deployment of an infrastructure with space-based elements The results of this study will be reported together with their implication for future coordinated European activities in this field

Applications of Hilbert Spectral Analysis for Speech and Sound Signals

Science.gov (United States)

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.

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

Problem and Project Based Learning in Hybrid Spaces

DEFF Research Database (Denmark)

Ryberg, Thomas; Davidsen, Jacob; Hodgson, Vivien

2016-01-01

There is a need within networked learning to understand and conceptualise the interplay between digital and physical spaces or what we could term hybrid spaces. Therefore, we discuss a recent study of students from two different programmes who are engaged in long-term, group-based problem...... and project based learning. Based on interviews, workshops and observations of students’ actual group practices in open, shared and flexible spaces in Aalborg University (AAU), we identify and discuss how students incorporate networked and digital technologies into their group work and into the study places...... they create for themselves. We describe how in one of the programmes ‘nomadic’ groups of students used different technologies and spaces for ‘placemaking’. We then show how their experience and approach to collaborative work differs to that of the more static or ‘artisan’ groups of students in the other...

( )f ( ) ( ) ( )

African Journals Online (AJOL)

cce

On the Minimum Norm Solution to Weber Problem. Osinuga, I. A. ... minimum norm problem in the Hilbert space and resolved by an appropriate application of the classical projection ..... Minimum orm Solution for Cooperative Games. Research.

Analysis in Banach spaces

CERN Document Server

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...

The solution of the sixth Hilbert problem: the ultimate Galilean revolution.

Science.gov (United States)

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).

A geometric Hamiltonian description of composite quantum systems and quantum entanglement

Science.gov (United States)

Pastorello, Davide

2015-05-01

Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is discussed in this paper. As summarized in the first part of this work, in the Hamiltonian formulation the phase space of a quantum system is the Kähler manifold given by the complex projective space P(H) of the Hilbert space H of the considered quantum theory. However the phase space of a bipartite system must be P(H1 ⊗ H2) and not simply P(H1) × P(H2) as suggested by the analogy with Classical Mechanics. A part of this paper is devoted to manage this problem. In the second part of the work, a definition of quantum entanglement and a proposal of entanglement measure are given in terms of a geometrical point of view (a rather studied topic in recent literature). Finally two known separability criteria are implemented in the Hamiltonian formalism.

In-Space Manufacturing Project (prior to FY15: Additive Manufacturing Technology Development)

Data.gov (United States)

National Aeronautics and Space Administration — The In-Space Manufacturing (ISM) project is responsible for developing the manufacturing capabilities that will provide on-demand, sustainable operations during NASA...

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.

Orthogonal polynomials, Laguerre Fock space, and quasi-classical asymptotics

Science.gov (United States)

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.

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.

Representations of coherent states in non-orthogonal bases

International Nuclear Information System (INIS)

Ali, S Twareque; Roknizadeh, R; Tavassoly, M K

2004-01-01

Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfand triple of (rigged) Hilbert spaces. Moreover, it is shown that in each dual pair of families of nonlinear coherent states, at least one family is related to a (generally) non-unitary projective representation of the Weyl-Heisenberg group, which can then be thought of as characterizing the dual pair

Spatio-temporal phase retrieval in speckle interferometry with Hilbert transform and two-dimensional phase unwrapping

Science.gov (United States)

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.

Elements of mathematics topological vector spaces

CERN Document Server

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).

Vector bundles on complex projective spaces

CERN Document Server

Okonek, Christian; Spindler, Heinz

1980-01-01

This expository treatment is based on a survey given by one of the authors at the Séminaire Bourbaki in November 1978 and on a subsequent course held at the University of Göttingen. It is intended to serve as an introduction to the topical question of classification of holomorphic vector bundles on complex projective spaces, and can easily be read by students with a basic knowledge of analytic or algebraic geometry. Short supplementary sections describe more advanced topics, further results, and unsolved problems.

On a Hilbert-Type Operator with a Symmetric Homogeneous Kernel of −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 −1-order in Hilbert-type operator T:lr→lr (r>1 is obtained. Two equivalent inequalities with the symmetric homogenous kernel of −λ-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.

The TERRA project, a space nuclear micro-reactor case study

International Nuclear Information System (INIS)

Guimaraes, Lamartine N.F.; Nascimento, Jamil A.; Borges, Eduardo M.; Lobo, Paulo D. Castro; Placco, Guilherme M.; Barrios Junior, Ary G.

2011-01-01

The TEcnologia de Reatores Rapidos Avancados project, also known as TERRA Project is been conducted by the Institute for Advanced Studies IEAv. The TERRA project has a general objective of understanding and developing the key technologies that will allow (Brazil) the use of nuclear technology to generate electricity in space. This electricity may power several space systems and/or a type of plasma based engine. Also, the type of reactor intended for space may be used for power generation in very inhospitable environment such as the ocean floor. Some of the mentioned technologies may include: Brayton cycles, Stirling engines, heat pipes and its coupled systems, nuclear fuel technology, new materials and several others. Once there is no mission into which apply this technology, at this moment, this research may be conducted in many forms and ways. The fact remains that when this technology becomes needed there will be no way that we (Brazilians) will be able to buy it from. This technology, in this sense, is highly strategic and will be the key to commercially explore deep space. Therefore, there is the need to face the development problems and solve them, to gain experience with our own rights and wrongs. This paper will give a brief overview of what has been done so far, on experimental facilities and hardware that could support space system development, including a Brayton cycle test facility, Tesla turbine testing, and Stirling engine development and modeling. Our great problem today is lack of human resources. To attend that problem we are starting a new graduate program that will allow overcoming that, given the proper time frame. (author)

The TERRA project, a space nuclear micro-reactor case study

Energy Technology Data Exchange (ETDEWEB)

Guimaraes, Lamartine N.F.; Nascimento, Jamil A.; Borges, Eduardo M.; Lobo, Paulo D. Castro, E-mail: guimarae@ieav.cta.br, E-mail: jamil@ieav.cta.br, E-mail: eduardo@ieav.cta.br [Divisao de Energia Nuclear. Instituto de Estudos Avancados, Sao Jose dos Campos, SP (Brazil); Placco, Guilherme M.; Barrios Junior, Ary G. [Faculdade de Tecnologia Sao Francisco (FATESF), Jacarei, SP (Brazil)

2011-07-01

The TEcnologia de Reatores Rapidos Avancados project, also known as TERRA Project is been conducted by the Institute for Advanced Studies IEAv. The TERRA project has a general objective of understanding and developing the key technologies that will allow (Brazil) the use of nuclear technology to generate electricity in space. This electricity may power several space systems and/or a type of plasma based engine. Also, the type of reactor intended for space may be used for power generation in very inhospitable environment such as the ocean floor. Some of the mentioned technologies may include: Brayton cycles, Stirling engines, heat pipes and its coupled systems, nuclear fuel technology, new materials and several others. Once there is no mission into which apply this technology, at this moment, this research may be conducted in many forms and ways. The fact remains that when this technology becomes needed there will be no way that we (Brazilians) will be able to buy it from. This technology, in this sense, is highly strategic and will be the key to commercially explore deep space. Therefore, there is the need to face the development problems and solve them, to gain experience with our own rights and wrongs. This paper will give a brief overview of what has been done so far, on experimental facilities and hardware that could support space system development, including a Brayton cycle test facility, Tesla turbine testing, and Stirling engine development and modeling. Our great problem today is lack of human resources. To attend that problem we are starting a new graduate program that will allow overcoming that, given the proper time frame. (author)

Space Geodesy Project Information and Configuration Management Procedure

Science.gov (United States)

Merkowitz, Stephen M.

2016-01-01

This plan defines the Space Geodesy Project (SGP) policies, procedures, and requirements for Information and Configuration Management (CM). This procedure describes a process that is intended to ensure that all proposed and approved technical and programmatic baselines and changes to the SGP hardware, software, support systems, and equipment are documented.

The effect of redshift-space distortions on projected 2-pt clustering measurements

OpenAIRE

Nock, Kelly; Percival, Will J.; Ross, Ashley J.

2010-01-01

Although redshift-space distortions only affect inferred distances and not angles, they still distort the projected angular clustering of galaxy samples selected using redshift dependent quantities. From an Eulerian view-point, this effect is caused by the apparent movement of galaxies into or out of the sample. From a Lagrangian view-point, we find that projecting the redshift-space overdensity field over a finite radial distance does not remove all the anisotropic distortions. We investigat...

Project Mercury: NASA's first manned space programme

Science.gov (United States)

Catchpole, John

Project Mercury will offer a developmental resume of the first American manned spaceflight programme and its associated infrastructure, including accounts of space launch vehicles. The book highlights the differences in Redstone/Atlas technology, drawing similar comparisons between ballistic capsules and alternative types of spacecraft. The book also covers astronaut selection and training, as well as tracking systems, flight control, basic principles of spaceflight and detailed accounts of individual flights.

MAGDAS Project for Space Weather Research and Application

International Nuclear Information System (INIS)

Yumoto, Kiyohumi

2009-01-01

The Space Environment Research Center (SERC), Kyushu University, is currently deploying a new ground-based magnetometer network of MAGnetic Data Acqusition System (MAGDAS), in cooperation with about 30 organizations in the world, in order to understand the complex Sun-Earth system for space weather research and application. SERC will conducts MAGDAS observation at 50 stations in the Circum-pan Pacific Magnetometer Network (CPMN) region, and FM-CW radar observation along the 210 deg. magnetic meridian (MM) during the IHY/ILWS/CAWSES periods. This project is actively providing the following space weather monitoring:(1) Global 3-dimensional current system to know electromagnetic coupling of the region 1 and 2 field-aligned currents, auroral electrojet current, Sq current, and equatorial electrojet current. (2) Plasma mass density along the 210 deg. MM to understand plasma environment change during space storms. (3) Ionospheric electric field intensity with 10-sec sampling at L = 1.26 to understand how the external electric field penetrates into the equatorial ionosphere.

The Koslowski-Sahlmann representation: quantum configuration space

Science.gov (United States)

Campiglia, Miguel; Varadarajan, Madhavan

2014-09-01

The Koslowski-Sahlmann (KS) representation is a generalization of the representation underlying the discrete spatial geometry of loop quantum gravity (LQG), to accommodate states labelled by smooth spatial geometries. As shown recently, the KS representation supports, in addition to the action of the holonomy and flux operators, the action of operators which are the quantum counterparts of certain connection dependent functions known as ‘background exponentials’. Here we show that the KS representation displays the following properties which are the exact counterparts of LQG ones: (i) the abelian * algebra of SU(2) holonomies and ‘U(1)’ background exponentials can be completed to a C* algebra, (ii) the space of semianalytic SU(2) connections is topologically dense in the spectrum of this algebra, (iii) there exists a measure on this spectrum for which the KS Hilbert space is realized as the space of square integrable functions on the spectrum, (iv) the spectrum admits a characterization as a projective limit of finite numbers of copies of SU(2) and U(1), (v) the algebra underlying the KS representation is constructed from cylindrical functions and their derivations in exactly the same way as the LQG (holonomy-flux) algebra except that the KS cylindrical functions depend on the holonomies and the background exponentials, this extra dependence being responsible for the differences between the KS and LQG algebras. While these results are obtained for compact spaces, they are expected to be of use for the construction of the KS representation in the asymptotically flat case.

Non-Archimedean analogues of orthogonal and symmetric operators

International Nuclear Information System (INIS)

Albeverio, S; Bayod, J M; Perez-Garsia, C; Khrennikov, A Yu; Cianci, R

1999-01-01

We study orthogonal and symmetric operators on non-Archimedean Hilbert spaces in connection with the p-adic quantization. This quantization describes measurements with finite precision. Symmetric (bounded) operators on p-adic Hilbert spaces represent physical observables. We study the spectral properties of one of the most important quantum operators, namely, the position operator (which is represented on p-adic Hilbert L 2 -space with respect to the p-adic Gaussian measure). Orthogonal isometric isomorphisms of p-adic Hilbert spaces preserve the precision of measurements. We study properties of orthogonal operators. It is proved that every orthogonal operator on non-Archimedean Hilbert space is continuous. However, there are discontinuous operators with dense domain of definition that preserve the inner product. There exist non-isometric orthogonal operators. We describe some classes of orthogonal isometric operators on finite-dimensional spaces. We study some general questions in the theory of non-Archimedean Hilbert spaces (in particular, general connections between the topology, norm and inner product)

Structure and properties of Hughston's stochastic extension of the Schroedinger equation

International Nuclear Information System (INIS)

Adler, Stephen L.; Horwitz, Lawrence P.

2000-01-01

Hughston has recently proposed a stochastic extension of the Schroedinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston's equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston's equation to earlier work on norm-preserving stochastic equations, and show that Hughston's equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston's, suffices to give an objective interpretation of the measurement process in quantum mechanics. (c) 2000 American Institute of Physics

Numerical optimization with computational errors

CERN Document Server

Zaslavski, Alexander J

2016-01-01

This book studies the approximate solutions of optimization problems in the presence of computational errors. A number of results are presented on the convergence behavior of algorithms in a Hilbert space; these algorithms are examined taking into account computational errors. The author illustrates that algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant. Known computational errors are examined with the aim of determining an approximate solution. Researchers and students interested in the optimization theory and its applications will find this book instructive and informative. This monograph contains 16 chapters; including a chapters devoted to the subgradient projection algorithm, the mirror descent algorithm, gradient projection algorithm, the Weiszfelds method, constrained convex minimization problems, the convergence of a proximal point method in a Hilbert space, the continuous subgradient method, penalty methods and Newton’s meth...

Transition probability spaces in loop quantum gravity

Science.gov (United States)

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.

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.)

The Unification of Space Qualified Integrated Circuits by Example of International Space Project GAMMA-400

Science.gov (United States)

Bobkov, S. G.; Serdin, O. V.; Arkhangelskiy, A. I.; Arkhangelskaja, I. V.; Suchkov, S. I.; Topchiev, N. P.

The problem of electronic component unification at the different levels (circuits, interfaces, hardware and software) used in space industry is considered. The task of computer systems for space purposes developing is discussed by example of scientific data acquisition system for space project GAMMA-400. The basic characteristics of high reliable and fault tolerant chips developed by SRISA RAS for space applicable computational systems are given. To reduce power consumption and enhance data reliability, embedded system interconnect made hierarchical: upper level is Serial RapidIO 1x or 4x with rate transfer 1.25 Gbaud; next level - SpaceWire with rate transfer up to 400 Mbaud and lower level - MIL-STD-1553B and RS232/RS485. The Ethernet 10/100 is technology interface and provided connection with the previously released modules too. Systems interconnection allows creating different redundancy systems. Designers can develop heterogeneous systems that employ the peer-to-peer networking performance of Serial RapidIO using multiprocessor clusters interconnected by SpaceWire.

Strong convergence with a modified iterative projection method for hierarchical fixed point problems and variational inequalities

Directory of Open Access Journals (Sweden)

Ibrahim Karahan

2016-04-01

Full Text Available Let C be a nonempty closed convex subset of a real Hilbert space H. Let {T_{n}}:C›H be a sequence of nearly nonexpansive mappings such that F:=?_{i=1}^{?}F(T_{i}?Ø. Let V:C›H be a ?-Lipschitzian mapping and F:C›H be a L-Lipschitzian and ?-strongly monotone operator. This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem. It is shown that under certain approximate assumptions on the operators and parameters, the modified iterative sequence {x_{n}} converges strongly to x^{*}?F which is also the unique solution of the following variational inequality: ?0, ?x?F. As a special case, this projection method can be used to find the minimum norm solution of above variational inequality; namely, the unique solution x^{*} to the quadratic minimization problem: x^{*}=argmin_{x?F}?x?². The results here improve and extend some recent corresponding results of other authors.

Normal pure states of the von Nuemann algebra of bounded operators as Kaehler manifold

International Nuclear Information System (INIS)

Cirelli, R.; Lanzavecchia, P.; Mania, A.

1983-01-01

The projective space of a complex Hilbert space H is considered both as a Kaehler manifold and as the set of pure states of the von Neumann algebra B(H). A link is given between these two structures. Special attention is devoted to topology, orientation and automorphisms of the structures and Wigner's theorem. (author)

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

Jauch-Piron system of imprimitivities for phonons. I. Localizability in discrete space

Science.gov (United States)

Banach, Zbigniew; Piekarski, Sławomir

1993-01-01

This paper is devoted to a discussion of the notion of localizability for phonons, i.e., quasiparticles arising from the harmonic vibrations of a system of n atoms bound to one another by elastic forces. The natural tools for the analysis of localizability are the projection operators Ê(Δ) acting on the Hilbert space of one-phonon states, where Δ is an arbitrary subset of the set that consists of n vectors specifying the equilibrium positions of n atoms. The expectation value of Ê(Δ) is the probability that the phonon belongs to the atoms whose equilibrium positions are characterized by the elements of Δ. For a strongly localizable phonon all of the projection operators Ê(Δ) commute with one another, whereas in the case of a weakly localizable phonon the operators Ê(Δ1) and Ê(Δ2) do not commute when Δ1 and Δ2 overlap. With the aid of the Jauch-Piron quantum theory of localization in space, the present paper describes the method of obtaining Ê(Δ) and also shows that if in the system of n atoms there exist normal modes of zero frequency, then the phonon is only weakly localizable. Given the explicit expression for Ê(Δ), one can define the number-of-phonons operator as well as the quasiparticle analogue (given in a companion paper) of the Wigner distribution function.

Axiomatic method of partitions in the theory of Noebeling spaces. I. Improvement of partition connectivity

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.

Weibull Distribution for Estimating the Parameters and Application of Hilbert Transform in case of a Low Wind Speed at Kolaghat

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.

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.

Systematic approach to the application of automation, robotics, and machine intelligence systems (aramis) to future space projects

Energy Technology Data Exchange (ETDEWEB)

Smith, D B.S.

1983-01-01

The potential applications of automation, robotics and machine intelligence systems (ARAMIS) to space projects are investigated, through a systematic method. In this method selected space projects are broken down into space project tasks, and 69 of these tasks are selected for study. Candidate ARAMIS options are defined for each task. The relative merits of these options are evaluated according to seven indices of performance. Logical sequences of ARAMIS development are also defined. Based on this data, promising applications of ARAMIS are identified for space project tasks. General conclusions and recommendations for further study are also presented. 6 references.

Public channel cryptography: chaos synchronization and Hilbert's tenth problem.

Science.gov (United States)

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.

Problem and Project Based Learning in Hybrid Spaces:Nomads and Artisans

OpenAIRE

Ryberg, Thomas; Davidsen, Jacob; Hodgson, Vivien

2016-01-01

There is a need within networked learning to understand and conceptualise the interplay between digital and physical spaces or what we could term hybrid spaces. Therefore, we discuss a recent study of students from two different programmes who are engaged in long-term, group-based problem and project based learning. Based on interviews, workshops and observations of students’ actual group practices in open, shared and flexible spaces in Aalborg University (AAU), we identify and discuss how st...

Certainty relations between local and nonlocal observables

International Nuclear Information System (INIS)

Diaz, R Garcia; Romero, J L; Bjoerk, G; Bourennane, M

2005-01-01

We point out that for an arbitrary number of identical particles, each defined on a Hilbert space of arbitrary dimension, there exists a whole ladder of relations of complementarity between certain local and nonlocal measurements corresponding to every conceivable grouping of the particles, e.g., the more accurately we can know (by a measurement) some joint property of three qubits (projecting the state onto a tripartite-entangled state), the less accurate some other property, local to the three qubits, becomes. We investigate the relation between these complementarity relations and a similar relation based on interference visibilities. We also show that the complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces

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.

Riesz basis for strongly continuous groups.

NARCIS (Netherlands)

Zwart, Heiko J.

Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if the span of the corresponding eigenvectors is dense, then these eigenvectors form a Riesz basis (or unconditional basis) of the Hilbert space.

Geometry of Moishezon and 1-convex spaces II: Projectivity of Moishezon spaces and its non-compact version

International Nuclear Information System (INIS)

Sitaramayya, M.

1993-11-01

After a brief review of the geometry of Moishezon spaces, their relation with l-convex spaces and a reasonable and up to date understanding of the obstructions for projectivity of Moishezon objects both in singular and non-singular case is given. The geometry of l-convex manifolds and with l-dimensional exceptional set is studied and some problems and conjectures are stated. The tools of cohomology vanishing theorems important for the subject are briefly sketched. Compactifications of C 3 and Stein spaces are finally outlined. given. 111 refs, 2 figs

Photonic Hilbert transformers based on laterally apodized integrated waveguide Bragg gratings on a SOI wafer.

Science.gov (United States)

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.

INTERDISCIPLINARITY IN PUBLIC SPACE PARTICIPATIVE PROJECTS: METHODS AND RESULTS IN PRACTICE AND TEACHING

Directory of Open Access Journals (Sweden)

Pedro Brandão

2015-06-01

• In the development of design practice and studio teaching methods We shall see in this paper how interdisciplinary approaches correspond to new and complex urban transformations, focusing on the importance of actors’ interaction processes, combining professional and non-professional knowledge and theory-practice relations. Therefore, we aim at a deepening in public space area of knowledge under the growing complexity of urban life. We see it as a base for further development of collaborative projects and their implications on community empowerment and urban governance at local level. Motivations of this line of work are persistent in several ongoing research projects, aiming to: - Understand public space as a cohesion factor both in urban life and urban form - Manage processes and strategies as elements of urban transformation, - Stimulate the understanding of actors’ roles in urban design practices. - Favoring the questioning of emerging aspects of urban space production… The paper presents and analyses processes, methods and results from civic participation projects developed in the neighbourhood of Barò de Viver (Barcelona and in the District of Marvila (Lisbon. In the first case, a long process initiated in 2004 and partially completed in 2011, neighbours developed the projects "Memory Wall" and Ciutat d'Asuncion Promenade as part of identity construction in public space, in collaboration  with a team of facilitators from CrPolis group. In the second case, different participatory processes dated from 2001 and 2003 have resulted in the implementation of a specific identity urban brand and communication system with an ongoing project of "maps" construction according to the neighbours perception and representation systems. We may conclude that processes of urban governance require more active participation of citizens in projects regarding the improvement of quality of life. At the same time, the implementation of these processes requires a clear

Least square regularized regression in sum space.

Science.gov (United States)

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.

The NASA In-Space Propulsion Technology Project, Products, and Mission Applicability

Science.gov (United States)

Anderson, David J.; Pencil, Eric; Liou, Larry; Dankanich, John; Munk, Michelle M.; Kremic, Tibor

2009-01-01

The In-Space Propulsion Technology (ISPT) Project, funded by NASA s Science Mission Directorate (SMD), is continuing to invest in propulsion technologies that will enable or enhance NASA robotic science missions. This overview provides development status, near-term mission benefits, applicability, and availability of in-space propulsion technologies in the areas of aerocapture, electric propulsion, advanced chemical thrusters, and systems analysis tools. Aerocapture investments improved: guidance, navigation, and control models of blunt-body rigid aeroshells; atmospheric models for Earth, Titan, Mars, and Venus; and models for aerothermal effects. Investments in electric propulsion technologies focused on completing NASA s Evolutionary Xenon Thruster (NEXT) ion propulsion system, a 0.6 to 7 kW throttle-able gridded ion system. The project is also concluding its High Voltage Hall Accelerator (HiVHAC) mid-term product specifically designed for a low-cost electric propulsion option. The primary chemical propulsion investment is on the high-temperature Advanced Material Bipropellant Rocket (AMBR) engine providing higher performance for lower cost. The project is also delivering products to assist technology infusion and quantify mission applicability and benefits through mission analysis and tools. In-space propulsion technologies are applicable, and potentially enabling for flagship destinations currently under evaluation, as well as having broad applicability to future Discovery and New Frontiers mission solicitations.

Metropolis-Hastings Algorithms in Function Space for Bayesian Inverse Problems

KAUST Repository

Ernst, Oliver

2015-01-07

We consider Markov Chain Monte Carlo methods adapted to a Hilbert space setting. Such algorithms occur in Bayesian inverse problems where the solution is a probability measure on a function space according to which one would like to integrate or sample. We focus on Metropolis-Hastings algorithms and, in particular, we introduce and analyze a generalization of the existing pCN-proposal. This new proposal allows to exploit the geometry or anisotropy of the target measure which in turn might improve the statistical efficiency of the corresponding MCMC method. Numerical experiments for a real-world problem confirm the improvement.

Metropolis-Hastings Algorithms in Function Space for Bayesian Inverse Problems

KAUST Repository

Ernst, Oliver

2015-01-01

We consider Markov Chain Monte Carlo methods adapted to a Hilbert space setting. Such algorithms occur in Bayesian inverse problems where the solution is a probability measure on a function space according to which one would like to integrate or sample. We focus on Metropolis-Hastings algorithms and, in particular, we introduce and analyze a generalization of the existing pCN-proposal. This new proposal allows to exploit the geometry or anisotropy of the target measure which in turn might improve the statistical efficiency of the corresponding MCMC method. Numerical experiments for a real-world problem confirm the improvement.

Introduction to probability and measure theories

International Nuclear Information System (INIS)

Partasarati, K.

1983-01-01

Chapters of probability and measured theories are presented. The Borele images of spaces with the measure into each other and in separate metric spaces are studied. The Kolmogorov theorem on the continuation of probabilies is drawn from the theorem on the measure continuation to the projective limits of spaces with measure. The integration theory is plotted, measures on multiplications of spaces are studied. The theory of conventional mathematical expectations by projections in Hilbert space is presented. In conclusion, the theory of weak convergence of measures of elements of the theory of characteristic functions and the theory of invariant and quasi-invariant measures on groups and homogeneous spaces is given

Space applications of Automation, Robotics and Machine Intelligence Systems (ARAMIS). Volume 4: Application of ARAMIS capabilities to space project functional elements

Science.gov (United States)

Miller, R. H.; Minsky, M. L.; Smith, D. B. S.

1982-01-01

Applications of automation, robotics, and machine intelligence systems (ARAMIS) to space activities and their related ground support functions are studied, so that informed decisions can be made on which aspects of ARAMIS to develop. The specific tasks which will be required by future space project tasks are identified and the relative merits of these options are evaluated. The ARAMIS options defined and researched span the range from fully human to fully machine, including a number of intermediate options (e.g., humans assisted by computers, and various levels of teleoperation). By including this spectrum, the study searches for the optimum mix of humans and machines for space project tasks.

Classification theorem for principal fibre bundles, Berry's phase, and exact cycle evolution

International Nuclear Information System (INIS)

Bohm, A.; Boya, L.J.; Mostafazadeh, A.; Rudolph, G.

1993-03-01

The relation between the two mathematical interpretations of the geometric (Berry) phase is discussed, using either the fibre bundle over parameter space or over projective Hilbert space. It turns out that these two geometric constructions are linked by the classification theorem for vector bundles. The classification theorem provides the means to classify the parameter space bundles for adiabatic evolution and for non-adiabatic cyclic evolution of the statevectors

Space Sciences Education and Outreach Project of Moscow State University

Science.gov (United States)

Krasotkin, S.

2006-11-01

sergekras@mail.ru The space sciences education and outreach project was initiated at Moscow State University in order to incorporate modern space research into the curriculum popularize the basics of space physics, and enhance public interest in space exploration. On 20 January 2005 the first Russian University Satellite “Universitetskiy-Tatyana” was launched into circular polar orbit (inclination 83 deg., altitude 940-980 km). The onboard scientific complex “Tatyana“, as well as the mission control and information receiving centre, was designed and developed at Moscow State University. The scientific programme of the mission includes measurements of space radiation in different energy channels and Earth UV luminosity and lightning. The current education programme consists of basic multimedia lectures “Life of the Earth in the Solar Atmosphere” and computerized practice exercises “Space Practice” (based on the quasi-real-time data obtained from “Universitetskiy-Tatyana” satellite and other Internet resources). A multimedia lectures LIFE OF EARTH IN THE SOLAR ATMOSPHERE containing the basic information and demonstrations of heliophysics (including Sun structure and solar activity, heliosphere and geophysics, solar-terrestrial connections and solar influence on the Earth’s life) was created for upper high-school and junior university students. For the upper-university students there a dozen special computerized hands-on exercises were created based on the experimental quasi-real-time data obtained from our satellites. Students specializing in space physics from a few Russian universities are involved in scientific work. Educational materials focus on upper high school, middle university and special level for space physics students. Moscow State University is now extending its space science education programme by creating multimedia lectures on remote sensing, space factors and materials study, satellite design and development, etc. The space

A remark on the unitary part of contractions

International Nuclear Information System (INIS)

Duggal, B.P.

1992-07-01

Considering operators on a complex infinite dimensional Hilbert space H and denoting by T * a construction with C .O completely non-unitary part, it is proved that A T is projection which commutes with T and H (u) T = A T H. 3 refs

Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit

Czech Academy of Sciences Publication Activity Database

Kwiatkowski, E.; Mandel, Jan

2015-01-01

Roč. 3, č. 1 (2015), s. 1-17 ISSN 2166-2525 R&D Projects: GA ČR GA13-34856S Institutional support: RVO:67985807 Keywords : data assimilation * Lp laws of large numbers * Hilbert space * ensemble Kalman filter Subject RIV: IN - Informatics, Computer Science

Perturbative universal state-selective correction for state-specific multi-reference coupled cluster methods

Czech Academy of Sciences Publication Activity Database

Brabec, Jiří; Banik, Subrata; Kowalski, K.; Pittner, Jiří

2016-01-01

Roč. 145, č. 16 (2016), s. 164106 ISSN 0021-9606 R&D Projects: GA MŠk LH13117; GA ČR GAP208/11/2222 Grant - others:GA ČR(CZ) Ga15-00058Y Institutional support: RVO:61388955 Keywords : INCOMPLETE MODEL SPACES * BRILLOUIN-WIGNER * HILBERT-SPACE Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.965, year: 2016

Classification of the spaces Cp*(X) within the Borel-Wadge hierarchy for a projective space X

Czech Academy of Sciences Publication Activity Database

Doležal, Martin; Vejnar, B.

2015-01-01

Roč. 183, March (2015), s. 11-17 ISSN 0166-8641 Institutional support: RVO:67985840 Keywords : function spaces * pointwise convergence * projective determinacy Subject RIV: BA - General Mathematics Impact factor: 0.493, year: 2015 http://www.sciencedirect.com/science/article/pii/S0166864114004854

Spectral Analysis and Computation of Effective Diffusivities in Space-time Periodic Incompressible Flows

Science.gov (United States)

2015-11-01

diffusive tracer fluxes, directed normal to the tracer gradient [64], are generally equivalent to antisymmetric components in the effective diffusivity...tensor D∗, while the symmetric part of D∗ represents irreversible diffusive effects [83, 87, 39] directed down the tracer gradient . The mixing of eddy...provides an operational calculus in Hilbert space which yields powerful integral representations involving the Stieltjes measures displayed in equation

Moduli of mathematical instanton vector bundles with odd c2 on projective space

International Nuclear Information System (INIS)

Tikhomirov, Aleksandr S

2012-01-01

We study the moduli space I n of mathematical instanton vector bundles of rank 2 with second Chern class n≥1 on the projective space P 3 , and prove the irreducibility of I n for arbitrary odd n≥1.

An “unreasonable effectiveness” of Hilbert transform for the transition phase behavior in an Aharonov–Bohm two-path interferometer

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.

Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Degroote, M. [Rice Univ., Houston, TX (United States); Henderson, T. M. [Rice Univ., Houston, TX (United States); Zhao, J. [Rice Univ., Houston, TX (United States); Dukelsky, J. [Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Inst. de Estructura de la Materia; Scuseria, G. E. [Rice Univ., Houston, TX (United States)

2018-01-03

We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.

VLBI2010 in NASA's Space Geodesy Project

Science.gov (United States)

Ma, Chopo

2012-01-01

In the summer of 20 11 NASA approved the proposal for the Space Geodesy Project (SGP). A major element is developing at the Goddard Geophysical and Astronomical Observatory a prototype of the next generation of integrated stations with co-located VLBI, SLR, GNSS and DORIS instruments as well as a system for monitoring the vector ties. VLBI2010 is a key component of the integrated station. The objectives ofSGP, the role of VLBI20 lOin the context of SGP, near term plans and possible future scenarios will be discussed.

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.

Space Versus Time: Unimodular Versus Non-Unimodular Projective Ring Geometries?

Czech Academy of Sciences Publication Activity Database

Saniga, M.; Pracna, Petr

2010-01-01

Roč. 4, - (2010), s. 719-735 ISSN 2159-063X Institutional research plan: CEZ:AV0Z40400503 Keywords : projective ring lines * smallest ring of ternions * Germas: of space-time Subject RIV: CF - Physical ; Theoretical Chemistry http://journalofcosmology.com/Multiverse4.html

Non-commutative geometry on quantum phase-space

International Nuclear Information System (INIS)

Reuter, M.

1995-06-01

A non-commutative analogue of the classical differential forms is constructed on the phase-space of an arbitrary quantum system. The non-commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. They are constructed by applying the Weyl-Wigner symbol map to the differential envelope of the linear operators on the quantum mechanical Hilbert space. This leads to a representation of the non-commutative forms considered by A. Connes in terms of multiscalar functions on the classical phase-space. In an appropriate coincidence limit they define a quantum deformation of the classical tensor fields and both commutative and non-commutative forms can be studied in a unified framework. We interprete the quantum differential forms in physical terms and comment on possible applications. (orig.)

Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space

Directory of Open Access Journals (Sweden)

Hanifa Zekraoui

2013-01-01

Full Text Available We introduce some new algebraic and topological properties of the Minkowski inverse A⊕ of an arbitrary matrix A∈Mm,n (including singular and rectangular in a Minkowski space μ. Furthermore, we show that the Minkowski inverse A⊕ in a Minkowski space and the Moore-Penrose inverse A+ in a Hilbert space are different in many properties such as the existence, continuity, norm, and SVD. New conditions of the Minkowski inverse are also given. These conditions are related to the existence, continuity, and reverse order law. Finally, a new representation of the Minkowski inverse A⊕ is also derived.

A Hilbert transform method for parameter identification of time-varying structures with observer techniques

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)

The Hilbert-Huang Transform-Based Denoising Method for the TEM Response of a PRBS Source Signal

Science.gov (United States)

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.

Wide Bandpass and Narrow Bandstop Microstrip Filters based on Hilbert fractal geometry: design and simulation results.

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.

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

Multichannel photonic Hilbert transformers based on complex modulated integrated Bragg gratings.

Science.gov (United States)

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.

Bohrification of operator algebras and quantum logic

NARCIS (Netherlands)

Heunen, C.; Landsman, N.P.; Spitters, B.A.W.

2012-01-01

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by

Bohrification of operator algebras and quantum logic

NARCIS (Netherlands)

Heunen, C.; Landsman, N.P.; Spitters, B.A.W.

2009-01-01

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by

Supporting Multiple Programs and Projects at NASA's Kennedy Space Center

Science.gov (United States)

Stewart, Camiren L.

2014-01-01

With the conclusion of the shuttle program in 2011, the National Aeronautics and Space Administration (NASA) had found itself at a crossroads for finding transportation of United States astronauts and experiments to space. The agency would eventually hand off the taxiing of American astronauts to the International Space Station (ISS) that orbits in Low Earth Orbit (LEO) about 210 miles above the earth under the requirements of the Commercial Crew Program (CCP). By privatizing the round trip journey from Earth to the ISS, the space agency has been given the additional time to focus funding and resources to projects that operate beyond LEO; however, adding even more stress to the agency, the premature cancellation of the program that would succeed the Shuttle Program - The Constellation Program (CxP) -it would inevitably delay the goal to travel beyond LEO for a number of years. Enter the Space Launch System (SLS) and the Orion Multipurpose Crew Vehicle (MPCV). Currently, the SLS is under development at NASA's Marshall Spaceflight Center in Huntsville, Alabama, while the Orion Capsule, built by government contractor Lockheed Martin Corporation, has been assembled and is currently under testing at the Kennedy Space Center (KSC) in Florida. In its current vision, SLS will take Orion and its crew to an asteroid that had been captured in an earlier mission in lunar orbit. Additionally, this vehicle and its configuration is NASA's transportation to Mars. Engineers at the Kennedy Space Center are currently working to test the ground systems that will facilitate the launch of Orion and the SLS within its Ground Services Development and Operations (GSDO) Program. Firing Room 1 in the Launch Control Center (LCC) has been refurbished and outfitted to support the SLS Program. In addition, the Spaceport Command and Control System (SCCS) is the underlying control system for monitoring and launching manned launch vehicles. As NASA finds itself at a junction, so does all of its

Hamiltonian Dynamics of Doubly-Foliable Space-Times

Directory of Open Access Journals (Sweden)

Cecília Gergely

2018-01-01

Full Text Available The 2 + 1 + 1 decomposition of space-time is useful in monitoring the temporal evolution of gravitational perturbations/waves in space-times with a spatial direction singled-out by symmetries. Such an approach based on a perpendicular double foliation has been employed in the framework of dark matter and dark energy-motivated scalar-tensor gravitational theories for the discussion of the odd sector perturbations of spherically-symmetric gravity. For the even sector, however, the perpendicularity has to be suppressed in order to allow for suitable gauge freedom, recovering the 10th metric variable. The 2 + 1 + 1 decomposition of the Einstein–Hilbert action leads to the identification of the canonical pairs, the Hamiltonian and momentum constraints. Hamiltonian dynamics is then derived via Poisson brackets.

Clifford coherent state transforms on spheres

Science.gov (United States)

Dang, Pei; Mourão, José; Nunes, João P.; Qian, Tao

2018-01-01

We introduce a one-parameter family of transforms, U(m)t,t > 0, from the Hilbert space of Clifford algebra valued square integrable functions on the m-dimensional sphere, L2(Sm , dσm) ⊗Cm+1, to the Hilbert spaces, ML2(R m + 1 ∖ { 0 } , dμt) , of solutions of the Euclidean Dirac equation on R m + 1 ∖ { 0 } which are square integrable with respect to appropriate measures, dμt. We prove that these transforms are unitary isomorphisms of the Hilbert spaces and are extensions of the Segal-Bargman coherent state transform, U(1) :L2(S1 , dσ1) ⟶ HL2(C ∖ { 0 } , dμ) , to higher dimensional spheres in the context of Clifford analysis. In Clifford analysis it is natural to replace the analytic continuation from Sm to SCm as in (Hall, 1994; Stenzel, 1999; Hall and Mitchell, 2002) by the Cauchy-Kowalewski extension from Sm to R m + 1 ∖ { 0 } . One then obtains a unitary isomorphism from an L2-Hilbert space to a Hilbert space of solutions of the Dirac equation, that is to a Hilbert space of monogenic functions.

SpaceScience@Home: Authentic Research Projects that Use Citizen Scientists

Science.gov (United States)

Méndez, B. J. H.

2008-06-01

In recent years, several space science research projects have enlisted the help of large numbers of non-professional volunteers, ``citizen scientists'', to aid in performing tasks that are critical to a project, but require more person-time (or computing time) than a small professional research team can practically perform themselves. Examples of such projects include SETI@home, which uses time from volunteers computers to process radio-telescope observation looking for signals originating from extra-terrestrial intelligences; Clickworkers, which asks volunteers to review images of the surface of Mars to identify craters; Spacewatch, which used volunteers to review astronomical telescopic images of the sky to identify streaks made by possible Near Earth Asteroids; and Stardust@home, which asks volunteers to review ``focus movies'' taken of the Stardust interstellar dust aerogel collector to search for possible impacts from interstellar dust particles. We shall describe these and other similar projects and discuss lessons learned from carrying out such projects, including the educational opportunities they create.

Quantum mechanics in Hilbert space

CERN Document Server

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

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 space and quantum mechanics

CERN Document Server

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...

Implementing Kernel Methods Incrementally by Incremental Nonlinear Projection Trick.

Science.gov (United States)

Kwak, Nojun

2016-05-20

Recently, the nonlinear projection trick (NPT) was introduced enabling direct computation of coordinates of samples in a reproducing kernel Hilbert space. With NPT, any machine learning algorithm can be extended to a kernel version without relying on the so called kernel trick. However, NPT is inherently difficult to be implemented incrementally because an ever increasing kernel matrix should be treated as additional training samples are introduced. In this paper, an incremental version of the NPT (INPT) is proposed based on the observation that the centerization step in NPT is unnecessary. Because the proposed INPT does not change the coordinates of the old data, the coordinates obtained by INPT can directly be used in any incremental methods to implement a kernel version of the incremental methods. The effectiveness of the INPT is shown by applying it to implement incremental versions of kernel methods such as, kernel singular value decomposition, kernel principal component analysis, and kernel discriminant analysis which are utilized for problems of kernel matrix reconstruction, letter classification, and face image retrieval, respectively.

Product numerical range in a space with tensor product structure

OpenAIRE

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 ...

Large-Scale Urban Projects, Production of Space and Neo-liberal Hegemony: A Comparative Study of Izmir

Directory of Open Access Journals (Sweden)

Mehmet PENPECİOĞLU

2013-04-01

Full Text Available With the rise of neo-liberalism, large-scale urban projects (LDPs have become a powerful mechanism of urban policy. Creating spaces of neo-liberal urbanization such as central business districts, tourism centers, gated residences and shopping malls, LDPs play a role not only in the reproduction of capital accumulation relations but also in the shift of urban political priorities towards the construction of neo-liberal hegemony. The construction of neo-liberal hegemony and the role played by LDPs in this process could not only be investigated by the analysis of capital accumulation. For such an investigation; the role of state and civil society actors in LDPs, their collaborative and conflictual relationships should be researched and their functions in hegemony should be revealed. In the case of Izmir’s two LDPs, namely the New City Center (NCC and Inciraltı Tourism Center (ITC projects, this study analyzes the relationship between the production of space and neo-liberal hegemony. In the NCC project, local governments, investors, local capital organizations and professional chambers collaborated and disseminated hegemonic discourse, which provided social support for the project. Through these relationships and discourses, the NCC project has become a hegemonic project for producing space and constructed neo-liberal hegemony over urban political priorities. In contrast to the NCC project, the ITC project saw no collaboration between state and organized civil society actors. The social opposition against the ITC project, initiated by professional chambers, has brought legal action against the ITC development plans in order to prevent their implementation. As a result, the ITC project did not acquire the consent of organized social groups and failed to become a hegemonic project for producing space.

Monitoring of Space and Earth electromagnetic environment by MAGDAS project: Collaboration with IKIR - Introduction to ICSWSE/MAGDAS project

Directory of Open Access Journals (Sweden)

Yoshikawa Akimasa

2017-01-01

Full Text Available For study of coupling processes in the Solar-Terrestrial System, International Center for Space Weather Science and Education (ICSWSE, Kyushu University has developed a real time magnetic data acquisition system (the MAGDAS project around the world. The number of observational sites is increasing every year with the collaboration of host countries. Now at this time, the MAGDAS Project has installed 78 real time magnetometers – so it is the largest magnetometer array in the world. The history of global observation at Kyushu University is over 30 years and number of developed observational sites is over 140. Especially, Collaboration between IKIR is extended back to 1990's. Now a time, we are operating Flux-gate magnetometer and FM-CW Radar. It is one of most important collaboration for space weather monitoring. By using MAGDAS data, ICSWSE produces many types of space weather index, such as EE-index (for monitoring long tern and shot term variation of equatorial electrojet, Pc5 index (for monitoring solar-wind velocity and high energy electron flux, Sq-index (for monitoring global change of ionospheric low and middle latitudinal current system, and Pc3 index (for monitoring of plasma density variation at low latitudes. In this report, we will introduce recent development of MAGDAS/ICSWSE Indexes project and topics for new open policy for MAGDAS data will be also discussed.

Monitoring of Space and Earth electromagnetic environment by MAGDAS project: Collaboration with IKIR - Introduction to ICSWSE/MAGDAS project

Science.gov (United States)

Yoshikawa, Akimasa; Fujimoto, Akiko; Ikeda, Akihiro; Uozumi, Teiji; Abe, Shuji

2017-10-01

For study of coupling processes in the Solar-Terrestrial System, International Center for Space Weather Science and Education (ICSWSE), Kyushu University has developed a real time magnetic data acquisition system (the MAGDAS project) around the world. The number of observational sites is increasing every year with the collaboration of host countries. Now at this time, the MAGDAS Project has installed 78 real time magnetometers - so it is the largest magnetometer array in the world. The history of global observation at Kyushu University is over 30 years and number of developed observational sites is over 140. Especially, Collaboration between IKIR is extended back to 1990's. Now a time, we are operating Flux-gate magnetometer and FM-CW Radar. It is one of most important collaboration for space weather monitoring. By using MAGDAS data, ICSWSE produces many types of space weather index, such as EE-index (for monitoring long tern and shot term variation of equatorial electrojet), Pc5 index (for monitoring solar-wind velocity and high energy electron flux), Sq-index (for monitoring global change of ionospheric low and middle latitudinal current system), and Pc3 index (for monitoring of plasma density variation at low latitudes). In this report, we will introduce recent development of MAGDAS/ICSWSE Indexes project and topics for new open policy for MAGDAS data will be also discussed.

The use of Wigner transformation for the description of the classical aspects of the quantum systems

International Nuclear Information System (INIS)

Baran, V.

1990-01-01

The mutual relation between the classical phase space and the Hilbert space of operators are explicitly written down.In particular, the Wigner transformation maps the Hilbert space onto the classical space of functions defined on two dimensional manifold. (Author)

Projecting technology change to improve space technology planning and systems management

Science.gov (United States)

Walk, Steven Robert

2011-04-01

Projecting technology performance evolution has been improving over the years. Reliable quantitative forecasting methods have been developed that project the growth, diffusion, and performance of technology in time, including projecting technology substitutions, saturation levels, and performance improvements. These forecasts can be applied at the early stages of space technology planning to better predict available future technology performance, assure the successful selection of technology, and improve technology systems management strategy. Often what is published as a technology forecast is simply scenario planning, usually made by extrapolating current trends into the future, with perhaps some subjective insight added. Typically, the accuracy of such predictions falls rapidly with distance in time. Quantitative technology forecasting (QTF), on the other hand, includes the study of historic data to identify one of or a combination of several recognized universal technology diffusion or substitution patterns. In the same manner that quantitative models of physical phenomena provide excellent predictions of system behavior, so do QTF models provide reliable technological performance trajectories. In practice, a quantitative technology forecast is completed to ascertain with confidence when the projected performance of a technology or system of technologies will occur. Such projections provide reliable time-referenced information when considering cost and performance trade-offs in maintaining, replacing, or migrating a technology, component, or system. This paper introduces various quantitative technology forecasting techniques and illustrates their practical application in space technology and technology systems management.

Differential calculus in normed linear spaces

CERN Document Server

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...

Quantum mechanics on phase space: The hydrogen atom and its Wigner functions

Science.gov (United States)

Campos, P.; Martins, M. G. R.; Fernandes, M. C. B.; Vianna, J. D. M.

2018-03-01

Symplectic quantum mechanics (SQM) considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ, to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article the Coulomb potential in three dimensions (3D) is resolved completely by using the phase space Schrödinger equation. The Kustaanheimo-Stiefel(KS) transformation is applied and the Coulomb and harmonic oscillator potentials are connected. In this context we determine the energy levels, the amplitude of probability in phase space and correspondent Wigner quasi-distribution functions of the 3D-hydrogen atom described by Schrödinger equation in phase space.

Some Remarks on Space-Time Decompositions, and Degenerate Metrics, in General Relativity

Science.gov (United States)

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.

Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces

Directory of Open Access Journals (Sweden)

Messaoud Bounkhel

2013-01-01

Full Text Available In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, ẋ(t∈F(t,x(t a.e. on I, x(t∈S, ∀t∈I, x(0=x0∈S, (*, where S is a closed subset in a Banach space , I=[0,T], (T>0, F:I×S→, is an upper semicontinuous set-valued mapping with convex values satisfying F(t,x⊂c(tx+xp, ∀(t,x∈I×S, where p∈ℝ, with p≠1, and c∈C([0,T],ℝ+. The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.

The scientific data acquisition system of the GAMMA-400 space project

Science.gov (United States)

Bobkov, S. G.; Serdin, O. V.; Gorbunov, M. S.; Arkhangelskiy, A. I.; Topchiev, N. P.

2016-02-01

The description of scientific data acquisition system (SDAS) designed by SRISA for the GAMMA-400 space project is presented. We consider the problem of different level electronics unification: the set of reliable fault-tolerant integrated circuits fabricated on Silicon-on-Insulator 0.25 mkm CMOS technology and the high-speed interfaces and reliable modules used in the space instruments. The characteristics of reliable fault-tolerant very large scale integration (VLSI) technology designed by SRISA for the developing of computation systems for space applications are considered. The scalable net structure of SDAS based on Serial RapidIO interface including real-time operating system BAGET is described too.

Symmetry-adapted Liouville space. Pt. 8

International Nuclear Information System (INIS)

Temme, F.P.

1990-01-01

A generalized hierarchy over lexical weight-sets is shown to provide significant insight into the structure of identical higher I i spin clusters under the S n /SO(3) dual groups. The use of combinatorial S n word-lengths allows one to derive the dual irreps directly from the combinatorics inherent in the adapted spin space. These advantages arise from the intimate connections between the scalar invariants of Cayley algebra over a field and their lexical combinatorics over vertical strokeI, Σ i M i , ()> space, which itself is a consequence of the S n -group representational algebra. By taking the highest SO(3) weight as the lexical origin, the calculations become recursive over all further expansions of the spin space, i.e., arising from an enhanced magnitude for the component nuclear spins, I i . The method over Hilbert space for spin clusters of I i ≤ 9/2 is more direct than those associated with unitary group algebras; in addition, the cogent beauty of combinatorial concepts derived from Cayley algebra deserves wider recognition in the physical sciences. (orig.)

Hilbert and Blaschke phases in the temporal coherence function of stationary broadband light.

Science.gov (United States)

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 systematic approach to the application of Automation, Robotics, and Machine Intelligence Systems /ARAMIS/ to future space projects

Science.gov (United States)

Smith, D. B. S.

1982-01-01

The potential applications of Automation, Robotics, and Machine Intelligence Systems (ARAMIS) to space projects are investigated, through a systematic method. In this method selected space projects are broken down into space project tasks, and 69 of these tasks are selected for study. Candidate ARAMIS options are defined for each task. The relative merits of these options are evaluated according to seven indices of performance. Logical sequences of ARAMIS development are also defined. Based on this data, promising applications of ARAMIS are

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

Information Presentation: Human Research Program - Space Human Factors and Habitability, Space Human Factors Engineering Project

Science.gov (United States)

Holden, Kristina L.; Sandor, Aniko; Thompson, Shelby G.; Kaiser, Mary K.; McCann, Robert S.; Begault, D. R.; Adelstein, B. D.; Beutter, B. R.; Wenzel, E. M.; Godfroy, M.;

Parallel Implementation of Multireference Coupled-Cluster Theories Based on the Reference-Level Parallelism

Czech Academy of Sciences Publication Activity Database

Brabec, Jiří; Pittner, Jiří; van Dam, H. J. J.; Apra, E.; Kowalski, K.

2012-01-01

Roč. 8, č. 2 (2012), s. 487-497 ISSN 1549-9618 R&D Projects: GA ČR GAP208/11/2222 Institutional research plan: CEZ:AV0Z40400503 Keywords : Blast forum standard * Hilbert-space * State-universal Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 5.389, year: 2012

Some open problems in noncommutative probability

International Nuclear Information System (INIS)

Kruszynski, P.

1981-01-01

A generalization of probability measures to non-Boolean structures is discussed. The starting point of the theory is the Gleason theorem about the form of measures on closed subspaces of a Hilbert space. The problems are formulated in terms of probability on lattices of projections in arbitrary von Neumann algebras. (Auth.)

Tensor spherical harmonics and tensor multipoles. II. Minkowski space

International Nuclear Information System (INIS)

Daumens, M.; Minnaert, P.

1976-01-01

The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation

String partition functions, Hilbert schemes and affine Lie algebra representations on homology groups

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)

Projective embeddings of homogeneous spaces with small boundary

International Nuclear Information System (INIS)

Arzhantsev, Ivan V

2009-01-01

We study open equivariant projective embeddings of homogeneous spaces such that the complement of the open orbit has codimension at least 2. We establish a criterion for the existence of such an embedding, prove that the set of isomorphism classes of such embeddings is finite, and give a construction of the embeddings in terms of Geometric Invariant Theory. A generalization of Cox's construction and the theory of bunched rings enable us to describe in combinatorial terms the basic geometric properties of embeddings with small boundary

Upper ankle joint space detection on low contrast intraoperative fluoroscopic C-arm projections

Science.gov (United States)

Thomas, Sarina; Schnetzke, Marc; Brehler, Michael; Swartman, Benedict; Vetter, Sven; Franke, Jochen; Grützner, Paul A.; Meinzer, Hans-Peter; Nolden, Marco

2017-03-01

Intraoperative mobile C-arm fluoroscopy is widely used for interventional verification in trauma surgery, high flexibility combined with low cost being the main advantages of the method. However, the lack of global device-to- patient orientation is challenging, when comparing the acquired data to other intrapatient datasets. In upper ankle joint fracture reduction accompanied with an unstable syndesmosis, a comparison to the unfractured contralateral site is helpful for verification of the reduction result. To reduce dose and operation time, our approach aims at the comparison of single projections of the unfractured ankle with volumetric images of the reduced fracture. For precise assessment, a pre-alignment of both datasets is a crucial step. We propose a contour extraction pipeline to estimate the joint space location for a prealignment of fluoroscopic C-arm projections containing the upper ankle joint. A quadtree-based hierarchical variance comparison extracts potential feature points and a Hough transform is applied to identify bone shaft lines together with the tibiotalar joint space. By using this information we can define the coarse orientation of the projections independent from the ankle pose during acquisition in order to align those images to the volume of the fractured ankle. The proposed method was evaluated on thirteen cadaveric datasets consisting of 100 projections each with manually adjusted image planes by three trauma surgeons. The results show that the method can be used to detect the joint space orientation. The correlation between angle deviation and anatomical projection direction gives valuable input on the acquisition direction for future clinical experiments.

A Space-Time Study of Hemorrhagic Fever with Renal Syndrome (HFRS and Its Climatic Associations in Heilongjiang Province, China

Directory of Open Access Journals (Sweden)

Junyu He

2017-08-01

Full Text Available Background: Hemorrhagic fever with renal syndrome (HFRS is highly endemic in China, especially in Heilongjiang province (90% of all reported HFRS cases worldwide occur in China. The dynamic identification of high HFRS incidence spatiotemporal regions and the quantitative assessment of HFRS associations with climate change in Heilongjiang province can provide valuable guidance for HFRS monitoring, preventing and control. Yet, so far there exist very few and of limited scope quantitative studies of the spatiotemporal HFRS spread and its climatic associations in Heilongjiang province. Making up for this lack of quantitative studies is the reason for the development of the present work.Method: To address this need, the well-known Bayesian maximum entropy (BME method of space-time modeling and mapping together with its recently proposed variant, the projected BME (P-BME method, were employed in this work to perform a composite space-time analysis and mapping of HFRS incidence in Heilongjiang province during the years 2005–2013. Also, using multivariate El Niño-Southern Oscillation index as a proxy, we proposed a combination of Hilbert-Huang transform and wavelet analysis to study the “HFRS incidence-climate change” associations.Results: The main results of this work were two-fold: (1 three core areas were identified with high HFRS incidences that were spatially distributed and exhibited distinct biomodal temporal patterns in the eastern, western, and southern parts of Heilongjiang province; and (2 there exists a considerable association between HFRS incidence and climate change, particularly, an ~6 months period coherency was clearly detected.Conclusions: The combination of modern space-time modeling and mapping techniques (P-BME theory, Hilbert-Huang spectrum analysis, and wavelet analysis used in this work led to valuable quantitative findings concerning the spatiotemporal spread of HFRS incidence in Heilongjiang province and its association

On a canonical quantization of 3D Anti de Sitter pure gravity

Science.gov (United States)

Kim, Jihun; Porrati, Massimo

2015-10-01

We perform a canonical quantization of pure gravity on AdS 3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,{R})× SL(2,{R}) . We first quantize the theory canonically on an asymptotically AdS space -which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kähler quantization of Teichmüller space. After explicitly computing the Kähler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2,{R}) Chern-Simons theory are conformal blocks. We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous spectrum and a lower bound on operator dimensions. A projection defined by topology changing amplitudes in Euclidean gravity is proposed. It defines an invariant subspace that allows for a dual interpretation in terms of a Liouville CFT. Problems and features of the CFT dual are assessed and a new definition of the Hilbert space, exempt from those problems, is proposed in the case of highly-curved AdS 3.

On a canonical quantization of 3D Anti de Sitter pure gravity

Energy Technology Data Exchange (ETDEWEB)

Kim, Jihun [Center for Cosmology and Particle Physics, Department of Physics,New York University, 4 Washington Place, New York, NY 10003 (United States); Porrati, Massimo [Center for Cosmology and Particle Physics, Department of Physics,New York University, 4 Washington Place, New York, NY 10003 (United States); CERN PH-TH, CH 1211,Geneva 23 (Switzerland)

2015-10-14

We perform a canonical quantization of pure gravity on AdS{sub 3} using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,ℝ)×SL(2,ℝ). We first quantize the theory canonically on an asymptotically AdS space –which is topologically the real line times a Riemann surface with one connected boundary. Using the “constrain first” approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kähler quantization of Teichmüller space. After explicitly computing the Kähler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2,ℝ) Chern-Simons theory are conformal blocks. We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous spectrum and a lower bound on operator dimensions. A projection defined by topology changing amplitudes in Euclidean gravity is proposed. It defines an invariant subspace that allows for a dual interpretation in terms of a Liouville CFT. Problems and features of the CFT dual are assessed and a new definition of the Hilbert space, exempt from those problems, is proposed in the case of highly-curved AdS{sub 3}.

Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings

Directory of Open Access Journals (Sweden)

Watcharaporn Cholamjiak

2009-01-01

Full Text Available We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006 and Nakajo and Takahashi (2003.

High Efficiency Space Power Systems Project Advanced Space-Rated Batteries

Science.gov (United States)

Reid, Concha M.

2011-01-01

Case Western Reserve University (CWRU) has an agreement with China National Offshore Oil Corporation New Energy Investment Company, Ltd. (CNOOC), under the United States-China EcoPartnerships Framework, to create a bi-national entity seeking to develop technically feasible and economically viable solutions to energy and environmental issues. Advanced batteries have been identified as one of the initial areas targeted for collaborations. CWRU invited NASA Glenn Research Center (GRC) personnel from the Electrochemistry Branch to CWRU to discuss various aspects of advanced battery development as they might apply to this partnership. Topics discussed included: the process for the selection of a battery chemistry; the establishment of an integrated development program; project management/technical interactions; new technology developments; and synergies between batteries for automotive and space operations. Additional collaborations between CWRU and NASA GRC's Electrochemistry Branch were also discussed.

Properties of Griffin-Hill-Wheeler spaces - 2. one-parameters and two-conjugate parameter families of generator states

International Nuclear Information System (INIS)

Passos, E.J.V. de; Toledo Piza, A.F.R. de.

The properties of the subspaces of the many-body Hilbert space which are associated with the use of the Generator Coordinate Method (GCM) in connection with one parameter, and with two-conjugate parameter families of generator states are examined in detail. It is shown that natural orthonormal base vectors in each case are immediately related to Peierls-Voccoz and Peierls-Thouless projections respectively. Through the formal consideration of a canonical transformation to collective, P and Q, and intrinsic degrees of freedom, the properties of the GCM subspaces with respect to the kinematical separation of these degrees of freedom are discussed in detail. An application is made, using the ideas developed in this paper, a) to translation; b) to illustrate the qualitative understanting of the content of existing GCM calculations of giant ressonances in light nuclei and c) to the definition of appropriate asymptotic states in current GCM descriptions of scattering [pt

A novel background field removal method for MRI using projection onto dipole fields (PDF).

Science.gov (United States)

Liu, Tian; Khalidov, Ildar; de Rochefort, Ludovic; Spincemaille, Pascal; Liu, Jing; Tsiouris, A John; Wang, Yi

2011-11-01

For optimal image quality in susceptibility-weighted imaging and accurate quantification of susceptibility, it is necessary to isolate the local field generated by local magnetic sources (such as iron) from the background field that arises from imperfect shimming and variations in magnetic susceptibility of surrounding tissues (including air). Previous background removal techniques have limited effectiveness depending on the accuracy of model assumptions or information input. In this article, we report an observation that the magnetic field for a dipole outside a given region of interest (ROI) is approximately orthogonal to the magnetic field of a dipole inside the ROI. Accordingly, we propose a nonparametric background field removal technique based on projection onto dipole fields (PDF). In this PDF technique, the background field inside an ROI is decomposed into a field originating from dipoles outside the ROI using the projection theorem in Hilbert space. This novel PDF background removal technique was validated on a numerical simulation and a phantom experiment and was applied in human brain imaging, demonstrating substantial improvement in background field removal compared with the commonly used high-pass filtering method. Copyright © 2011 John Wiley & Sons, Ltd.

Instanton tunneling for de Sitter space with real projective spatial sections

Energy Technology Data Exchange (ETDEWEB)

Ong, Yen Chin [Center for Astronomy and Astrophysics, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Yeom, Dong-han, E-mail: ongyenchin@sjtu.edu.cn, E-mail: innocent.yeom@gmail.com [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)

2017-04-01

The physics of tunneling from one spacetime to another is often understood in terms of instantons. For some instantons, it was recently shown in the literature that there are two complementary ''interpretations'' for their analytic continuations. Dubbed ''something-to-something'' and ''nothing-to-something'' interpretations, respectively, the former involves situation in which the initial and final hypersurfaces are connected by a Euclidean manifold, whereas the initial and final hypersurfaces in the latter case are not connected in such a way. We consider a de Sitter space with real projective space RP{sup 3} spatial sections, as was originally understood by de Sitter himself. This original version of de Sitter space has several advantages over the usual de Sitter space with S{sup 3} spatial sections. In particular, the interpretation of the de Sitter entropy as entanglement entropy is much more natural. We discuss the subtleties involved in the tunneling of such a de Sitter space.

Information Theoretic Characterization of Physical Theories with Projective State Space

Science.gov (United States)

Zaopo, Marco

2015-08-01

Probabilistic theories are a natural framework to investigate the foundations of quantum theory and possible alternative or deeper theories. In a generic probabilistic theory, states of a physical system are represented as vectors of outcomes probabilities and state spaces are convex cones. In this picture the physics of a given theory is related to the geometric shape of the cone of states. In quantum theory, for instance, the shape of the cone of states corresponds to a projective space over complex numbers. In this paper we investigate geometric constraints on the state space of a generic theory imposed by the following information theoretic requirements: every non completely mixed state of a system is perfectly distinguishable from some other state in a single shot measurement; information capacity of physical systems is conserved under making mixtures of states. These assumptions guarantee that a generic physical system satisfies a natural principle asserting that the more a state of the system is mixed the less information can be stored in the system using that state as logical value. We show that all theories satisfying the above assumptions are such that the shape of their cones of states is that of a projective space over a generic field of numbers. Remarkably, these theories constitute generalizations of quantum theory where superposition principle holds with coefficients pertaining to a generic field of numbers in place of complex numbers. If the field of numbers is trivial and contains only one element we obtain classical theory. This result tells that superposition principle is quite common among probabilistic theories while its absence gives evidence of either classical theory or an implausible theory.

Planning and managing future space facility projects. [management by objectives and group dynamics

Science.gov (United States)

Sieber, J. E.; Wilhelm, J. A.; Tanner, T. A.; Helmreich, R. L.; Burgenbauch, S. F.

1979-01-01

To learn how ground-based personnel of a space project plan and organize their work and how such planning and organizing relate to work outcomes, longitudinal study of the management and execution of the Space Lab Mission Development Test 3 (SMD 3) was performed at NASA Ames Research Center. A view of the problems likely to arise in organizations and some methods of coping with these problems are presented as well as the conclusions and recommendations that pertain strictly to SMD 3 management. Emphasis is placed on the broader context of future space facility projects and additional problems that may be anticipated. A model of management that may be used to facilitate problem solving and communication - management by objectives (MBO) is presented. Some problems of communication and emotion management that MBO does not address directly are considered. Models for promoting mature, constructive and satisfying emotional relationships among group members are discussed.

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

KAUST Repository

Migliorati, Giovanni; Nobile, Fabio; von Schwerin, Erik; Tempone, Raul

2014-01-01

We analyze the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is uncertainty quantification for computational models. We prove an optimal convergence estimate, up to a logarithmic factor, in the univariate case, when the observation points are sampled in a bounded domain from a probability density function bounded away from zero and bounded from above, provided the number of samples scales quadratically with the dimension of the polynomial space. Optimality is meant in the sense that the weighted L2 norm of the error committed by the random discrete projection is bounded with high probability from above by the best L∞ error achievable in the given polynomial space, up to logarithmic factors. Several numerical tests are presented in both the univariate and multivariate cases, confirming our theoretical estimates. The numerical tests also clarify how the convergence rate depends on the number of sampling points, on the polynomial degree, and on the smoothness of the target function. © 2014 SFoCM.

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

KAUST Repository

Migliorati, Giovanni

2014-03-05

We analyze the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is uncertainty quantification for computational models. We prove an optimal convergence estimate, up to a logarithmic factor, in the univariate case, when the observation points are sampled in a bounded domain from a probability density function bounded away from zero and bounded from above, provided the number of samples scales quadratically with the dimension of the polynomial space. Optimality is meant in the sense that the weighted L2 norm of the error committed by the random discrete projection is bounded with high probability from above by the best L∞ error achievable in the given polynomial space, up to logarithmic factors. Several numerical tests are presented in both the univariate and multivariate cases, confirming our theoretical estimates. The numerical tests also clarify how the convergence rate depends on the number of sampling points, on the polynomial degree, and on the smoothness of the target function. © 2014 SFoCM.

A Riemann-Hilbert formulation for the finite temperature Hubbard model