Some Generalizations of Jungck's Fixed Point Theorem

Directory of Open Access Journals (Sweden)

J. R. Morales

2012-01-01

Full Text Available We are going to generalize the Jungck's fixed point theorem for commuting mappings by mean of the concepts of altering distance functions and compatible pair of mappings, as well as, by using contractive inequalities of integral type and contractive inequalities depending on another function.

Proofs and generalizations of the pythagorean theorem

Directory of Open Access Journals (Sweden)

Lialda B. Cavalcanti

2011-01-01

Full Text Available This article explores a topic developed by a group of researchers of the Science and Technology Teaching School of Instituto Federal de Pernambuco, Brazil (IFPE, in assistance to the development of the Mathematics Practical and Teaching Laboratory of the distance learning Teaching Licensure, financed by the Universidad Abierta de Brasil. In this article, we describe the peculiarities present in the proofs of the Pythagorean theorem with the purpose of illustrating some of these methods. The selection of these peculiarities was founded and based on the comparison of areas by means of the superimposition of geometrical shapes and used several different class resources. Some generalizations of this important theorem in mathematical problem-solving are also shown.

A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process

International Nuclear Information System (INIS)

Okabe, Y.

1985-01-01

The [α,β,γ]-Langevin equation describes the time evolution of a real stationary process with T-positivity (reflection positivity) originating in the axiomatic quantum field theory. For this [α,β,γ]-Langevin equation a generalized fluctuation-dissipation theorem is proved. We shall obtain, as its application, a generalized fluctuation-dissipation theorem for the one-dimensional non-linear diffusion process, which presents one solution of Ryogo Kubo's problem in physics. (orig.)

Locally Hamiltonian systems with symmetry and a generalized Noether's theorem

International Nuclear Information System (INIS)

Carinena, J.F.; Ibort, L.A.

1985-01-01

An analysis of global aspects of the theory of symmetry groups G of locally Hamiltonian dynamical systems is carried out for particular cases either of the symmetry group, or the differentiable manifold M supporting the symplectic structure, or the action of G on M. In every case it is obtained a generalization of Noether's theorem. It has been looked at the classical Noether's theorem for Lagrangian systems from a modern perspective

Weak circulation theorems as a way of distinguishing between generalized gravitation theories

International Nuclear Information System (INIS)

Enosh, M.

1980-01-01

It was proved in a previous paper that a generalized circulation theorem characterizes Einstein's theory of gravitation as a special case of a more general theory of gravitation, which is also based on the principle of equivalence. Here the question of whether it is possible to weaken this circulation theorem in such ways that it would imply more general theories than Einstein's is posed. This problem is solved. Principally, there are two possibilities. One of them is essentially Weyl's theory. (author)

The 1s x-ray absorption pre-edge structures in transition metal oxides

NARCIS (Netherlands)

de Groot, Frank|info:eu-repo/dai/nl/08747610X; Vanko, Gyoergy; Glatzel, Pieter

2009-01-01

We develop a general procedure to analyse the pre-edges in 1s x-ray absorption near edge structure (XANES) of transition metal oxides and coordination complexes. Transition metal coordination complexes can be described from a local model with one metal ion. The 1s 3d quadrupole transitions are

A Borsuk-Ulam type generalization of the Leray-Schauder fixed point theorem

International Nuclear Information System (INIS)

Prykarpatsky, A.K.

2007-05-01

A generalization of the classical Leray-Schauder fixed point theorem, based on the infinite-dimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on a weak version of the well known Krein-Milman theorem are presented. (author)

Multiphonon theory: generalized Wick's theorem and recursion formulas

International Nuclear Information System (INIS)

Silvestre-Brac, B.; Piepenbring, R.

1982-04-01

Overlaps and matrix elements of one and two-body operators are calculated in a space spanned by multiphonons of different types taking properly the Pauli principle into account. Two methods are developped: a generalized Wick's theorem dealing with new contractions and recursion formulas well suited for numerical applications

A general product measurability theorem with applications to variational inequalities

Directory of Open Access Journals (Sweden)

Kenneth L. Kuttler

2016-03-01

Full Text Available This work establishes the existence of measurable weak solutions to evolution problems with randomness by proving and applying a novel theorem on product measurability of limits of sequences of functions. The measurability theorem is used to show that many important existence theorems within the abstract theory of evolution inclusions or equations have straightforward generalizations to settings that include random processes or coefficients. Moreover, the convex set where the solutions are sought is not fixed but may depend on the random variables. The importance of adding randomness lies in the fact that real world processes invariably involve randomness and variability. Thus, this work expands substantially the range of applications of models with variational inequalities and differential set-inclusions.

Generalized Fourier slice theorem for cone-beam image reconstruction.

Science.gov (United States)

Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang

2015-01-01

The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

Evolutionary trees: an integer multicommodity max-flow-min-cut theorem

NARCIS (Netherlands)

Erdös, Péter L.; Szekely, László A.

1992-01-01

In biomathematics, the extensions of a leaf-colouration of a binary tree to the whole vertex set with minimum number of colour-changing edges are extensively studied. Our paper generalizes the problem for trees; algorithms and a Menger-type theorem are presented. The LP dual of the problem is a

Generalized virial theorem and pressure relation for a strongly correlated Fermi gas

International Nuclear Information System (INIS)

Tan, Shina

2008-01-01

For a two-component Fermi gas in the unitarity limit (i.e., with infinite scattering length), there is a well-known virial theorem, first shown by J.E. Thomas et al. A few people rederived this result, and extended it to few-body systems, but their results are all restricted to the unitarity limit. Here I show that there is a generalized virial theorem for FINITE scattering lengths. I also generalize an exact result concerning the pressure to the case of imbalanced populations

X-ray imaging characterization of active edge silicon pixel sensors

International Nuclear Information System (INIS)

Ponchut, C; Ruat, M; Kalliopuska, J

2014-01-01

The aim of this work was the experimental characterization of edge effects in active-edge silicon pixel sensors, in the frame of X-ray pixel detectors developments for synchrotron experiments. We produced a set of active edge pixel sensors with 300 to 500 μm thickness, edge widths ranging from 100 μm to 150 μm, and n or p pixel contact types. The sensors with 256 × 256 pixels and 55 × 55 μm 2 pixel pitch were then bump-bonded to Timepix readout chips for X-ray imaging measurements. The reduced edge widths makes the edge pixels more sensitive to the electrical field distribution at the sensor boundaries. We characterized this effect by mapping the spatial response of the sensor edges with a finely focused X-ray synchrotron beam. One of the samples showed a distortion-free response on all four edges, whereas others showed variable degrees of distortions extending at maximum to 300 micron from the sensor edge. An application of active edge pixel sensors to coherent diffraction imaging with synchrotron beams is described

A General No-Cloning Theorem for an infinite Multiverse

Science.gov (United States)

Gauthier, Yvon

2013-10-01

In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics.

The Invariance and the General CCT Theorems

OpenAIRE

Stancu, Alin

2010-01-01

The \\begin{it} Invariance Theorem \\end{it} of M. Gerstenhaber and S. D. Schack states that if $\\mathbb{A}$ is a diagram of algebras then the subdivision functor induces a natural isomorphism between the Yoneda cohomologies of the category $\\mathbb{A}$-$\\mathbf{mod}$ and its subdivided category $\\mathbb{A}'$-$\\mathbf{mod}$. In this paper we generalize this result and show that the subdivision functor is a full and faithful functor between two suitable derived categories of $\\mathbb{A}$-$\\mathb...

A general shakedown theorem for elastic/plastic bodies with work hardening

International Nuclear Information System (INIS)

Ponter, A.R.S.

1975-01-01

In recent years the design of metallic structures under variable loading has been assisted by the application of Melan's lower bound theorem for the shakedown on an elastic/perfectly plastic structure. The design codes for both portal frames and pressure vessels have taken account of such calculations. The theory of shakedown suffers from two defects, geometry changes are ignored and the material behaviour is described by a perfectly plastic constitutive relationship which includes neither work hardening nor the Bauschinger effect. This paper is concerned with the latter problem. A very general lower bound shakedown theorem is derived for an arbitrary time-independent material in terms of functional properties of the constitutive relationship. The theorem is then applied to perfect, isotropic and kinematic hardening plasticity. (Auth.)

Optimal Shape of a Gamma-ray Collimator: single vs double knife edge

Science.gov (United States)

Metz, Albert; Hogenbirk, Alfred

2017-09-01

Gamma-ray collimators in nuclear waste scanners are used for selecting a narrow vertical segment in activity measurements of waste vessels. The system that is used by NRG uses tapered slit collimators of both the single and double knife edge type. The properties of these collimators were investigated by means of Monte Carlo simulations. We found that single knife edge collimators are highly preferable for a conservative estimate of the activity of the waste vessels. These collimators show much less dependence on the angle of incidence of the radiation than double knife edge collimators. This conclusion also applies to cylindrical collimators of the single knife edge type, that are generally used in medical imaging spectroscopy.

A hierarchical generalization of the acoustic reciprocity theorem involving higher-order derivatives and interaction quantities.

Science.gov (United States)

Lin, Ju; Li, Jie; Li, Xiaolei; Wang, Ning

2016-10-01

An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.

A proof of the Kochen–Specker theorem can always be converted to a state-independent noncontextuality inequality

International Nuclear Information System (INIS)

Yu, Xiao-Dong; Tong, D M; Guo, Yan-Qing

2015-01-01

Quantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of the Kochen–Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been found that some proofs of the Kochen-Specker theorem, such as those based on rays, can be converted to a state-independent noncontextuality inequality, but it remains open whether this is true in general, i.e., whether any proof of the Kochen-Specker theorem can always be converted to a noncontextuality inequality. In this paper, we address this issue. We prove that all kinds of proofs of the Kochen-Specker theorem, based on rays or any other observables, can always be converted to state-independent noncontextuality inequalities. Besides, our constructive proof also provides a general approach for deriving a state-independent noncontextuality inequality from a proof of the KS theorem. (paper)

The generalized Mayer theorem in the approximating hamiltonian method

International Nuclear Information System (INIS)

Bakulev, A.P.; Bogoliubov, N.N. Jr.; Kurbatov, A.M.

1982-07-01

With the help of the generalized Mayer theorem we obtain the improved inequality for free energies of model and approximating systems, where only ''connected parts'' over the approximating hamiltonian are taken into account. For the concrete system we discuss the problem of convergency of appropriate series of ''connected parts''. (author)

Nash-Williams’ cycle-decomposition theorem

DEFF Research Database (Denmark)

Thomassen, Carsten

2016-01-01

We give an elementary proof of the theorem of Nash-Williams that a graph has an edge-decomposition into cycles if and only if it does not contain an odd cut. We also prove that every bridgeless graph has a collection of cycles covering each edge at least once and at most 7 times. The two results...

Learning in neural networks based on a generalized fluctuation theorem

Science.gov (United States)

Hayakawa, Takashi; Aoyagi, Toshio

2015-11-01

Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.

Whiteheadian approach to quantum theory and the generalized bell's theorem

International Nuclear Information System (INIS)

Stapp, H.P.

1979-01-01

The model of the world proposed by Whitehead provides a natural theoretical framework in which to imbed quantum theory. This model accords with the ontological ideas of Heisenberg, and also with Einstein's view that physical theories should refer nominally to the objective physical situation, rather than our knowledge of that system. Whitehead imposed on his model the relativistic requirement that what happens in any given spacetime region be determined only by what has happened in its absolute past, i.e., in the backward light-cone drawn from that region. This requirement must be modified, for it is inconsistent with the implications of quantum theory expressed by a generalized version of Bell's theorem. Revamping the causal spacetime structure of the Whitehead-Heisenberg ontology to bring it into accord with the generalized Bell's theorem creates the possibility of a nonlocal causal covariant theory that accords with the statistical prediction of quantum theory

Poincare-Birkhoff-Witt theorems and generalized Casimir invariants for some infinite-dimensional Lie groups: II

International Nuclear Information System (INIS)

Ton-That, Tuong

2005-01-01

In a previous paper we gave a generalization of the notion of Casimir invariant differential operators for the infinite-dimensional Lie groups GL ∞ (C) (or equivalently, for its Lie algebra gj ∞ (C)). In this paper we give a generalization of the Casimir invariant differential operators for a class of infinite-dimensional Lie groups (or equivalently, for their Lie algebras) which contains the infinite-dimensional complex classical groups. These infinite-dimensional Lie groups, and their Lie algebras, are inductive limits of finite-dimensional Lie groups, and their Lie algebras, with some additional properties. These groups or their Lie algebras act via the generalized adjoint representations on projective limits of certain chains of vector spaces of universal enveloping algebras. Then the generalized Casimir operators are the invariants of the generalized adjoint representations. In order to be able to explicitly compute the Casimir operators one needs a basis for the universal enveloping algebra of a Lie algebra. The Poincare-Birkhoff-Witt (PBW) theorem gives an explicit construction of such a basis. Thus in the first part of this paper we give a generalization of the PBW theorem for inductive limits of Lie algebras. In the last part of this paper a generalization of the very important theorem in representation theory, namely the Chevalley-Racah theorem, is also discussed

The generalized back projection theorem for cone beam reconstruction

International Nuclear Information System (INIS)

Peyrin, F.C.

1985-01-01

The use of cone beam scanners raises the problem of three dimensional reconstruction from divergent projections. After a survey on bidimensional analytical reconstruction methods we examine their application to the 3D problem. Finally, it is shown that the back projection theorem can be generalized to cone beam projections. This allows to state a new inversion formula suitable for both the 4 π parallel and divergent geometries. It leads to the generalization of the ''rho-filtered back projection'' algorithm which is outlined

A Note on a Broken-Cycle Theorem for Hypergraphs

Directory of Open Access Journals (Sweden)

Trinks Martin

2014-08-01

Full Text Available Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there

Parity proofs of the Kochen–Specker theorem based on 60 complex rays in four dimensions

International Nuclear Information System (INIS)

Waegell, Mordecai; Aravind, P K

2011-01-01

It is pointed out that the 60 complex rays in four dimensions associated with a system of two qubits yield over 10 9 critical parity proofs of the Kochen–Specker theorem. The geometrical properties of the rays are described, an overview of the parity proofs contained in them is given and examples of some of the proofs are exhibited. (paper)

The Levinson theorem

International Nuclear Information System (INIS)

Ma Zhongqi

2006-01-01

The Levinson theorem is a fundamental theorem in quantum scattering theory, which shows the relation between the number of bound states and the phase shift at zero momentum for the Schroedinger equation. The Levinson theorem was established and developed mainly with the Jost function, with the Green function and with the Sturm-Liouville theorem. In this review, we compare three methods of proof, study the conditions of the potential for the Levinson theorem and generalize it to the Dirac equation. The method with the Sturm-Liouville theorem is explained in some detail. References to development and application of the Levinson theorem are introduced. (topical review)

Measurement of X-ray attenuation coefficients around K-absorption edges using Fe Kα X-rays

International Nuclear Information System (INIS)

Kerur, B.R.; Thontadarya, S.R.; Hanumaiah, B.

1993-01-01

The x-ray mass attenuation coefficients were measured around the K-absorption edges of elements in the range 16 ≤ Z ≤ 30 using Fe Kα x-rays of energy 6.400 keV, which is the weighted average energy of Kα 1 and Kα 2 x-ray components from the 57 Co radioactive source. Kβ x-rays were almost eliminated by the differential absorption technique. The small difference in energy between Kα 1 and Kα 2 , 13 eV, was shown to be inconsequential by comparing the measured and theoretical values of μ/ρ for standard materials such as Al, Cu, Mo and Ta. The effect of fine structure of the K-absorption edge on μ/ρ was elucidated by using the compounds of elements in the range 16 ≤ X ≤ 30, containing one element with its K-absorption edge energy (E k ) close to the incident photon energy (E x ). The results clearly indicate the validity of the theoretical mixture rule for all those compounds whose K edge is far away from the incident energy but show deviations of as much as 10% for the manganese compound whose K edge is 140 eV above E x and about 12% for the chromium compound whose K edge is 410 eV below E x . These deviations are attributed to the possible influence of resonance Raman scattering when the incident photon energy E x is less than the edge and to the influence of EXAFS when E x is more than the edge energy. (Author)

Fermat's Last Theorem A Theorem at Last!

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 1. Fermat's Last Theorem A Theorem at Last! C S Yogananda. General Article Volume 1 Issue 1 January 1996 pp 71-79. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/001/01/0071-0079 ...

The spectral method and ergodic theorems for general Markov chains

International Nuclear Information System (INIS)

Nagaev, S V

2015-01-01

We study the ergodic properties of Markov chains with an arbitrary state space and prove a geometric ergodic theorem. The method of the proof is new: it may be described as an operator method. Our main result is an ergodic theorem for Harris-Markov chains in the case when the return time to some fixed set has finite expectation. Our conditions for the transition function are more general than those used by Athreya-Ney and Nummelin. Unlike them, we impose restrictions not on the original transition function but on the transition function of an embedded Markov chain constructed from the return times to the fixed set mentioned above. The proof uses the spectral theory of linear operators on a Banach space

Near edge x-ray spectroscopy theory

International Nuclear Information System (INIS)

1994-01-01

We propose to develop a quantitative theory of x-ray spectroscopies in the near edge region, within about 100 eV of threshold. These spectroscopies include XAFS (X-ray absorption fine structure), photoelectron diffraction (PD), and diffraction anomalous fine structure (DAFS), all of which are important tools for structural studies using synchrotron radiation x-ray sources. Of primary importance in these studies are many-body effects, such as the photoelectron self-energy, and inelastic losses. A better understanding of these quantities is needed to obtain theories without adjustable parameters. We propose both analytical and numerical calculations, the latter based on our x-ray spectroscopy codes FEFF

Generalization of the Bogoliubov-Zubarev Theorem for Dynamic Pressure to the Case of Compressibility

Science.gov (United States)

Rudoi, Yu. G.

2018-01-01

We present the motivation, formulation, and modified proof of the Bogoliubov-Zubarev theorem connecting the pressure of a dynamical object with its energy within the framework of a classical description and obtain a generalization of this theorem to the case of dynamical compressibility. In both cases, we introduce the volume of the object into consideration using a singular addition to the Hamiltonian function of the physical object, which allows using the concept of the Bogoliubov quasiaverage explicitly already on a dynamical level of description. We also discuss the relation to the same result known as the Hellmann-Feynman theorem in the framework of the quantum description of a physical object.

Review of superconducting transition-edge sensors for x-ray and gamma-ray spectroscopy

International Nuclear Information System (INIS)

Ullom, Joel N; Bennett, Douglas A

2015-01-01

We present a review of emerging x-ray and gamma-ray spectrometers based on arrays of superconducting transition-edge sensors (TESs). Special attention will be given to recent progress in TES applications and in understanding TES physics. (paper)

Generalized Perron--Frobenius Theorem for Nonsquare Matrices

OpenAIRE

Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David

2013-01-01

The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the...

Si K EDGE STRUCTURE AND VARIABILITY IN GALACTIC X-RAY BINARIES

Energy Technology Data Exchange (ETDEWEB)

Schulz, Norbert S.; Corrales, Lia; Canizares, Claude R. [Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)

2016-08-10

We survey the Si K edge structure in various absorbed Galactic low-mass X-ray binaries (LMXBs) to study states of silicon in the inter- and circum-stellar medium. The bulk of these LMXBs lie toward the Galactic bulge region and all have column densities above 10{sup 22} cm{sup −2}. The observations were performed using the Chandra High Energy Transmission Grating Spectrometer. The Si K edge in all sources appears at an energy value of 1844 ± 0.001 eV. The edge exhibits significant substructure that can be described by a near edge absorption feature at 1849 ± 0.002 eV and a far edge absorption feature at 1865 ± 0.002 eV. Both of these absorption features appear variable with equivalent widths up to several mÅ. We can describe the edge structure using several components: multiple edge functions, near edge absorption excesses from silicates in dust form, signatures from X-ray scattering optical depths, and a variable warm absorber from ionized atomic silicon. The measured optical depths of the edges indicate much higher values than expected from atomic silicon cross sections and interstellar medium abundances, and they appear consistent with predictions from silicate X-ray absorption and scattering. A comparison with models also indicates a preference for larger dust grain sizes. In many cases, we identify Si xiii resonance absorption and determine ionization parameters between log ξ = 1.8 and 2.8 and turbulent velocities between 300 and 1000 km s{sup −1}. This places the warm absorber in close vicinity of the X-ray binaries. In some data, we observe a weak edge at 1.840 keV, potentially from a lesser contribution of neutral atomic silicon.

Generalized Panofsky-Wenzel theorem and hybrid coupling

CERN Document Server

Smirnov, A V

2001-01-01

The Panofsky-Wenzel theorem is reformulated for the case in which phase slippage between the wave and beam is not negligible. The extended theorem can be applied in analysis of detuned waveguides, RF injectors, bunchers, some tapered waveguides or high-power sources and multi-cell cavities for dipole and higher order modes. As an example, the relative contribution of the Lorentz' component of the deflecting force is calculated for a conventional circular disk-loaded waveguide.

Automated and observer based light field indicator edge evaluation in diagnostic X-ray equipment

International Nuclear Information System (INIS)

Bottaro, Marcio; Nagy, Balazs Vince; Soares, Fernanda Cristina Salvador; Rosendo, Danilo Cabral

2017-01-01

Introduction: To analyze edge detection and optical contrast calculation of light field-indicators used in X-ray via automated- and observer-based methods, and comparison with current standard approaches, which do not give exact definition for light field edge determination. Methods: Automated light sensor array was used to measure the penumbra zone of the edge in the standard X-ray equipment, while trained and naive human observers were asked to mark the light field edge according to their own determination. Different interpretations of the contrast were then calculated and compared. Results: In contrast to automated measurements of edge definition and detection, measurements by human observers showed large inter-observer variation independent of their training with X-ray equipment. Different contrast calculations considering the different edge definitions gave very different contrast values. Conclusion: As the main conclusion, we propose a more exact edge definition of the X-ray light field, corresponding well to the average human observer's edge determination. The new edge definition method with automated systems would reduce human variability in edge determination. Such errors could potentially affect the approval of X-ray equipment, and also increase the radiation dose. The automated measurement based on human observers’ edge definition and the corresponding contrast calculation may lead to a more precise light field calibration, which enables reduced irradiation doses on radiology patients. (author)

Automated and observer based light field indicator edge evaluation in diagnostic X-ray equipment

Directory of Open Access Journals (Sweden)

Márcio Bottaro

Full Text Available Abstract Introduction To analyze edge detection and optical contrast calculation of light field-indicators used in X-ray via automated- and observer-based methods, and comparison with current standard approaches, which do not give exact definition for light field edge determination. Methods Automated light sensor array was used to measure the penumbra zone of the edge in the standard X-ray equipment, while trained and naïve human observers were asked to mark the light field edge according to their own determination. Different interpretations of the contrast were then calculated and compared. Results In contrast to automated measurements of edge definition and detection, measurements by human observers showed large inter-observer variation independent of their training with X-ray equipment. Different contrast calculations considering the different edge definitions gave very different contrast values. Conclusion As the main conclusion, we propose a more exact edge definition of the X-ray light field, corresponding well to the average human observer’s edge determination. The new edge definition method with automated systems would reduce human variability in edge determination. Such errors could potentially affect the approval of X-ray equipment, and also increase the radiation dose. The automated measurement based on human observers’ edge definition and the corresponding contrast calculation may lead to a more precise light field calibration, which enables reduced irradiation doses on radiology patients.

Automated and observer based light field indicator edge evaluation in diagnostic X-ray equipment

Energy Technology Data Exchange (ETDEWEB)

Bottaro, Marcio; Nagy, Balazs Vince; Soares, Fernanda Cristina Salvador; Rosendo, Danilo Cabral, E-mail: marcio@iee.usp.br [Universidade de Sao Paulo (USP), SP (Brazil); Optics and Engineering Informatics, Budapest University of Technology and Economics, Budapest (Hungary)

2017-04-15

Introduction: To analyze edge detection and optical contrast calculation of light field-indicators used in X-ray via automated- and observer-based methods, and comparison with current standard approaches, which do not give exact definition for light field edge determination. Methods: Automated light sensor array was used to measure the penumbra zone of the edge in the standard X-ray equipment, while trained and naive human observers were asked to mark the light field edge according to their own determination. Different interpretations of the contrast were then calculated and compared. Results: In contrast to automated measurements of edge definition and detection, measurements by human observers showed large inter-observer variation independent of their training with X-ray equipment. Different contrast calculations considering the different edge definitions gave very different contrast values. Conclusion: As the main conclusion, we propose a more exact edge definition of the X-ray light field, corresponding well to the average human observer's edge determination. The new edge definition method with automated systems would reduce human variability in edge determination. Such errors could potentially affect the approval of X-ray equipment, and also increase the radiation dose. The automated measurement based on human observers’ edge definition and the corresponding contrast calculation may lead to a more precise light field calibration, which enables reduced irradiation doses on radiology patients. (author)

A generalization of Schauder's theorem and its application to Cauchy-Kovalevskaya problem

Directory of Open Access Journals (Sweden)

Oleg Zubelevich

2003-05-01

Full Text Available We extend the classical majorant functions method to a PDE system which right hand side is a mapping of one functional space to another. This extension is based on some generalization of the Schauder fixed point theorem.

ON A GENERALIZATION OF THE MAXIMUM ENTROPY THEOREM OF BURG

Directory of Open Access Journals (Sweden)

JOSÉ MARCANO

2017-01-01

Full Text Available In this article we introduce some matrix manipulations that allow us to obtain a version of the original Christoffel-Darboux formula, which is of interest in many applications of linear algebra. Using these developments matrix and Jensen’s inequality, we obtain the main result of this proposal, which is the generalization of the maximum entropy theorem of Burg for multivariate processes.

Fan beam image reconstruction with generalized Fourier slice theorem.

Science.gov (United States)

Zhao, Shuangren; Yang, Kang; Yang, Kevin

2014-01-01

For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.

Bertrand's theorem and virial theorem in fractional classical mechanics

Science.gov (United States)

Yu, Rui-Yan; Wang, Towe

2017-09-01

Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.

Algorithm/Architecture Co-design of the Generalized Sampling Theorem Based De-Interlacer.

NARCIS (Netherlands)

Beric, A.; Haan, de G.; Sethuraman, R.; Meerbergen, van J.

2005-01-01

De-interlacing is a major determinant of image quality in a modern display processing chain. The de-interlacing method based on the generalized sampling theorem (GST)applied to motion estimation and motion compensation provides the best de-interlacing results. With HDTV interlaced input material

Topological interpretation of Luttinger theorem

OpenAIRE

Seki, Kazuhiro; Yunoki, Seiji

2017-01-01

Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because i) the Luttinger volume is represented as the winding number of the single-particle Green's function and thus ii) the deviation of the theorem, expressed with a ratio between the interacting and n...

Generalized augmented space theorem for correlated disorder and cluster coherent potential approximation

International Nuclear Information System (INIS)

Mookerjee, A.; Prasad, R.

1993-09-01

We present a method for calculating the electronic structure of disordered alloys with short range order (SRO) which guarantees positive density of states for all values of the SRO parameter. The method is based on the generalized augmented space theorem which is valid for alloys with SRO. This theorem is applied to alloys with SRO in the tight-binding linear muffin-tin orbital (TB-LMTO) framework. This is done by using the augmented space formulation of Mookerjee and cluster coherent potential approximation. As an illustration, the method is applied to a single band mode TB-LMTO Hamiltonian. We find that the SRO can induce substantial changes in the density of states. (author). 22 refs, 2 figs

The s-Ordered Fock Space Projectors Gained by the General Ordering Theorem

International Nuclear Information System (INIS)

Shähandeh Farid; Bazrafkan Mohammad Reza; Ashrafi Mahmoud

2012-01-01

Employing the general ordering theorem (GOT), operational methods and incomplete 2-D Hermite polynomials, we derive the t-ordered expansion of Fock space projectors. Using the result, the general ordered form of the coherent state projectors is obtained. This indeed gives a new integration formula regarding incomplete 2-D Hermite polynomials. In addition, the orthogonality relation of the incomplete 2-D Hermite polynomials is derived to resolve Dattoli's failure

Mean energy of some interacting bosonic systems derived by virtue of the generalized Hellmann-Feynman theorem

Science.gov (United States)

Fan, Hong-yi; Xu, Xue-xiang

2009-06-01

By virtue of the generalized Hellmann-Feynman theorem [H. Y. Fan and B. Z. Chen, Phys. Lett. A 203, 95 (1995)], we derive the mean energy of some interacting bosonic systems for some Hamiltonian models without proceeding with diagonalizing the Hamiltonians. Our work extends the field of applications of the Hellmann-Feynman theorem and may enrich the theory of quantum statistics.

On Krasnoselskii's Cone Fixed Point Theorem

Directory of Open Access Journals (Sweden)

Man Kam Kwong

2008-04-01

Full Text Available In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.

X-ray speckle contrast variation at a sample-specific absorption edges

International Nuclear Information System (INIS)

Retsch, C. C.; Wang, Y.; Frigo, S. P.; Stephenson, G. B.; McNulty, I.

2000-01-01

The authors measured static x-ray speckle contrast variation with the incident photon energy across sample-specific absorption edges. They propose that the variation depends strongly on the spectral response function of the monochromator. Speckle techniques have been introduced to the x-ray regime during recent years. Most of these experiments, however, were done at photon energies above 5 keV. They are working on this technique in the 1 to 4 keV range, an energy range that includes many important x-ray absorption edges, e.g., in Al, Si, P, S, the rare-earths, and others. To their knowledge, the effect of absorption edges on speckle contrast has not yet been studied. In this paper, they present their initial measurements and understanding of the observed phenomena

Simultaneous Generalizations of the Theorems of Ceva and Menelaus for Field Planes

Science.gov (United States)

Houston, Kelly B.; Powers, Robert C.

2009-01-01

In 1992, Klamkin and Liu proved a very general result in the Extended Euclidean Plane that contains the theorems of Ceva and Menelaus as special cases. In this article, we extend the Klamkin and Liu result to projective planes "PG"(2, F) where F is a field. (Contains 2 figures.)

The exponential edge-gradient effect in x-ray computed tomography

International Nuclear Information System (INIS)

Joseph, P.M.

1981-01-01

The exponential edge-gradient effect must arise in any X-ray transmission CT scanner whenever long sharp edges of high contrast are encountered. The effect is non-linear and is due to the interaction of the exponential law of X-ray attenuation and the finite width of the scanning beam in the x-y plane. The error induced in the projection values is proved to be always negative. While the most common effect is lucent streaks emerging from single straight edges, it is demonstrated that dense streaks from pairs of edges are possible. It is shown that an exact correction of the error is possible only under very special (and rather unrealistic) circumstances in which an infinite number of samples per beam width are available and all thin rays making up the beam can be considered parallel. As a practical matter, nevertheless, increased sample density is highly desirable in making good approximate corrections; this is demonstrated with simulated scans. Two classes of approximate correction algorithms are described and their effectiveness evaluated on simulated CT phantom scans. One such algorithm is also shown to work well with a real scan of a physical phantom on a machine that provides approximately four samples per beam width. (author)

Measurement of X-ray mass attenuation coefficient of nickel around the K-edge using synchrotron radiation based X-ray absorption study

International Nuclear Information System (INIS)

Roy, Bunty Rani; Rajput, Parasmani; Jha, S.N.; Nageswara Rao, A.S.

2015-01-01

The work presents the X-ray absorption fine structure (XAFS) technique for measuring the X-ray mass attenuation coefficient of nickel metal foil in the X-ray energy range of 8271.2–8849.4 eV using scanning XAFS beam line (BL-09) at Indus-2 synchrotron radiation source facility, Raja Ramanna Centre for Advanced Technology (RRCAT) at Indore, India. The result represents the X-ray mass attenuation coefficient data for 0.02 mm thick Ni metal foil in the XAFS region of Ni K-edge. However, the results are compared to theoretical values using X-COM. There is a maximum deviation which is found exactly near the K-edge jump and decreases as we move away from the absorption edge. Oscillatory structure appears just above the observed absorption edge i.e., 8348.7 eV and is confined to around 250 eV above the edge. - Highlights: • Mass attenuation coefficient measurements of nickel using synchrotron radiation. • The measurements were taken exactly near the Ni K-edge at an energy step of 1 eV. • A maximum deviation is found near the K-edge

Nonextensive kinetic theory and H-theorem in general relativity

Science.gov (United States)

Santos, A. P.; Silva, R.; Alcaniz, J. S.; Lima, J. A. S.

2017-11-01

The nonextensive kinetic theory for degenerate quantum gases is discussed in the general relativistic framework. By incorporating nonadditive modifications in the collisional term of the relativistic Boltzmann equation and entropy current, it is shown that Tsallis entropic framework satisfies a H-theorem in the presence of gravitational fields. Consistency with the 2nd law of thermodynamics is obtained only whether the entropic q-parameter lies in the interval q ∈ [ 0 , 2 ] . As occurs in the absence of gravitational fields, it is also proved that the local collisional equilibrium is described by the extended Bose-Einstein (Fermi-Dirac) q-distributions.

The spectral method and the central limit theorem for general Markov chains

Science.gov (United States)

Nagaev, S. V.

2017-12-01

We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya-Ney and Nummelin. Our proof of the CLT is purely analytical.

Anomalous x-ray attenuation coefficients around the absorption edges using Mn Ksub(α) and Cu Ksub(α) x-rays

International Nuclear Information System (INIS)

Kerur, B.R.; Thontadarya, S.R.; Hanumaiah, B.

1994-01-01

The x-ray attenuation coefficients for three elements and for eight compounds are determined, adopting the method developed by employing a proportional counter, with a view to study the effect of fine structure on the mass attenuation coefficient values using Mn K α and Cu K α x-rays derived from K x-ray emitters, 55 Fe and 65 Zn radioactive sources, by a differential absorption technique. It is experimentally established that a small difference in energy between K α1 and K α2 (11 eV in the case of Mn K α and 24 eV in the case of the Cu K α x-ray) is inconsequential by comparing the measured and theoretical values of μ/ρ for standard elements, aluminium, copper and tantalum. The effect of fine structure on μ/ρ values is studied using the compounds containing one element with its absorption edge close to the incident photon energy. Results obtained in the present investigation show the nonvalidity of the mixture rule above the edge and also below the edge, ranging from about 600 eV below the edge to about 1500 eV about the edge. The contribution of resonance Raman scattering to the attenuation coefficient and indications to the presence of pre-edge structure similar to EXAFS are discussed. (author)

A general shakedown theorem for elastic/plastic bodies with work hardening

International Nuclear Information System (INIS)

Ponter, A.R.S.

1975-01-01

In recent years the design of metallic structures under variable loading has been assisted by the application of Melan's lower bound theorem for the shakedown of an elastic/perfectly plastic structure. The design codes for both portal frames and pressure vessels have taken account of such calculations. The theory of shakedown suffers from two defects, geometry changes are ignored and the material behavior is described by a perfectly plastic constitutive relationship which includes neither work hardening nor the Bauschinger effect. This paper is concerned with the latter problem. A very general lower bound shakedown theorem for an arbitrary time-independent material in terms of functional properties of the constitutive relationship is derived. The theorem is then applied to perfect, isotropic and kinematic hardening plasticity. It is shown that the result for all three constitutive relationships may be related to each other through certain extremal stress histories. As well as providing a sufficient condition for shakedown, the theory also provides bounds of the deflection of the structure in the process of reaching the shakedown state. The bounds are discussed and derived for two simple beam problems. Both static and dynamic problems are considered. The theory derived in this paper demonstrates that shakedown analysis may be extended to a wide range of material behavior without increasing the complexity of the resulting calculation

Origin of the chemical shift in X-ray absorption near-edge spectroscopy at the Mn K-Edge in manganese oxide compounds

NARCIS (Netherlands)

de Vries, AH; Hozoi, L.; Broer, R.

2003-01-01

The absorption edge in Mn K-edge X-ray absorption spectra of manganese oxide compounds shows a shift of several electronvolts in going from MnO through LaMnO3 to CaMnO3. On the other hand, in X-ray photoelectron spectra much smaller shifts are observed. To identify the mechanisms that cause the

Automated and observer based light field indicator edge evaluation in diagnostic X-ray equipment

OpenAIRE

Bottaro, Márcio; Nagy, Balázs Vince; Soares, Fernanda Cristina Salvador; Rosendo, Danilo Cabral

2017-01-01

Abstract Introduction To analyze edge detection and optical contrast calculation of light field-indicators used in X-ray via automated- and observer-based methods, and comparison with current standard approaches, which do not give exact definition for light field edge determination. Methods Automated light sensor array was used to measure the penumbra zone of the edge in the standard X-ray equipment, while trained and naïve human observers were asked to mark the light field edge according t...

Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport

International Nuclear Information System (INIS)

Webb, G.M.; Gleeson, L.J.

1977-01-01

Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution function F 0 (r,p), (r=heliocentric distance, p=momentum) can be determined in a region rsub(a) 0 . Examples of Green's functions are given for the case rsub(a)=0, rsub(b)=infinity and derived for the cases of finite rsub(a) and rsub(b). The diffusion coefficient kappa is assumed of the form kappa=kappa 0 (p)rsup(b). The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions. (Auth.)

Modeling Dzyaloshinskii-Moriya Interaction at Transition Metal Interfaces: Constrained Moment versus Generalized Bloch Theorem

KAUST Repository

Dong, Yao-Jun

2017-10-29

Dzyaloshinskii-Moriya interaction (DMI) at Pt/Co interfaces is investigated theoretically using two different first principles methods. The first one uses the constrained moment method to build a spin spiral in real space, while the second method uses the generalized Bloch theorem approach to construct a spin spiral in reciprocal space. We show that although the two methods produce an overall similar total DMI energy, the dependence of DMI as a function of the spin spiral wavelength is dramatically different. We suggest that long-range magnetic interactions, that determine itinerant magnetism in transition metals, are responsible for this discrepancy. We conclude that the generalized Bloch theorem approach is more adapted to model DMI in transition metal systems, where magnetism is delocalized, while the constrained moment approach is mostly applicable to weak or insulating magnets, where magnetism is localized.

Modeling Dzyaloshinskii-Moriya Interaction at Transition Metal Interfaces: Constrained Moment versus Generalized Bloch Theorem

KAUST Repository

Dong, Yao-Jun; Belabbes, Abderrezak; Manchon, Aurelien

2017-01-01

Dzyaloshinskii-Moriya interaction (DMI) at Pt/Co interfaces is investigated theoretically using two different first principles methods. The first one uses the constrained moment method to build a spin spiral in real space, while the second method uses the generalized Bloch theorem approach to construct a spin spiral in reciprocal space. We show that although the two methods produce an overall similar total DMI energy, the dependence of DMI as a function of the spin spiral wavelength is dramatically different. We suggest that long-range magnetic interactions, that determine itinerant magnetism in transition metals, are responsible for this discrepancy. We conclude that the generalized Bloch theorem approach is more adapted to model DMI in transition metal systems, where magnetism is delocalized, while the constrained moment approach is mostly applicable to weak or insulating magnets, where magnetism is localized.

On Comparison Theorems for Conformable Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Mehmet Zeki Sarikaya

2016-10-01

Full Text Available In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm's separation and Sturm's comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented to verify the proposed theorem.

EDGE DETECTION OF THE SCOLIOTIC VERTEBRAE USING X-RAY IMAGES

Directory of Open Access Journals (Sweden)

P. MOHANKUMAR

2016-02-01

Full Text Available Bones act as a mineral storage reservoir for calcium and phosphorus. Proper well grown bones give a perfect posture to the human body. In other case, if the bone has an improper growth, it might lead to an abnormal posture or an awkward posture. Scoliosis is a condition where the scoliotic vertebrae are wedge shaped and differ with the shape of normal vertebrae. Treatment for scoliosis depends on Cobb angle which can be measured using spine X-rays. Recent development in the medical imaging techniques brought us to a new research area in image processing which includes medical image enhancement, detailed visualization of internal organs & tissues and edge detection. Bone edges are important feature in an X-ray image. The purpose of application of segmentation in medical imaging is to develop a detailed framework on human anatomy, whose primary objective is to outline the anatomical structures. Whereas edge detection is a technique which extracts vital features like corners, lines, angles and curves from an image. In this study, we are going to deal with the edge detection technique on scoliotic vertebrae. The objective of this paper is to compare the performance of edge detectors using filters and operators.

Some approximation theorems

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

Abstract. The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose K is a compact set in the complex plane and 0 belongs to the boundary ∂K. Let A(K) denote the space of all functions f on K such that f is holo- morphic in a neighborhood of K and f(0) = 0. Also for any given positive integer ...

Many-body effects in the mesoscopic x-ray edge problem

International Nuclear Information System (INIS)

Hentschel, Martina; Roeder, Georg; Ullmo, Denis

2007-01-01

Many-body phenomena, a key interest in the investigation of bulk solid state systems, are studied here in the context of the x-ray edge problem for mesoscopic systems. We investigate the many-body effects associated with the sudden perturbation following the x-ray exciton of a core electron into the conduction band. For small systems with dimensions at the nanoscale we find considerable deviations from the well-understood metallic case where Anderson orthogonality catastrophe and the Mahan-Nozieres-DeDominicis response cause characteristic deviations of the photoabsorption cross section from the naive expectation. Whereas the K-edge is typically rounded in metallic systems, we find a slightly peaked K-edge in generic mesoscopic systems with chaotic-coherent electron dynamics. Thus the behavior of the photoabsorption cross section at threshold depends on the system size and is different for the metallic and the mesoscopic case. (author)

Characterization of atmospheric aerosols using Synchroton radiation total reflection X-ray fluorescence and Fe K-edge total reflection X-ray fluorescence-X-ray absorption near-edge structure

Energy Technology Data Exchange (ETDEWEB)

Fittschen, U.E.A. [Department of Chemistry, University of Hamburg, Martin-Luther-King-Platz 6, 20146 Hamburg (Germany)], E-mail: ursula.fittschen@chemie.uni-hamburg.de; Meirer, F. [Atominstitut, Vienna University of Technology, Stadionallee 2, 1020 Wien (Austria)], E-mail: fmeirer@ati.ac.at; Streli, C. [Atominstitut, Vienna University of Technology, Stadionallee 2, 1020 Wien (Austria)], E-mail: streli@ati.ac.at; Wobrauschek, P. [Atominstitut, Vienna University of Technology, Stadionallee 2, 1020 Wien (Austria)], E-mail: wobi@ati.ac.at; Thiele, J. [Department of Chemistry, University of Hamburg, Martin-Luther-King-Platz 6, 20146 Hamburg (Germany)], E-mail: Julian.Thiele@gmx.de; Falkenberg, G. [Hamburger Synchrotronstrahlungslabor at Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22603 Hamburg (Germany)], E-mail: falkenbe@mail.desy.de; Pepponi, G. [ITC-irst, Via Sommarive 18, 38050 Povo (Trento) (Italy)], E-mail: pepponi@itc.it

2008-12-15

In this study a new procedure using Synchrotron total reflection X-ray fluorescence (SR-TXRF) to characterize elemental amounts in atmospheric aerosols down to particle sizes of 0.015 um is presented. The procedure was thoroughly evaluated regarding bounce off effects and blank values. Additionally the potential of total reflection X-ray fluorescence-X-ray absorption near edge structure (SR-TXRF-XANES) for speciation of FeII/III down to amounts of 34 pg in aerosols which were collected for 1 h is shown. The aerosols were collected in the city of Hamburg with a low pressure Berner impactor on Si carriers covered with silicone over time periods of 60 and 20 min each. The particles were collected in four and ten size fractions of 10.0-8.0 {mu}m, 8.0-2.0 {mu}m, 2.0-0.13 {mu}m 0.13-0.015 {mu}m (aerodynamic particle size) and 15-30 nm, 30-60 nm, 60-130 nm, 130-250 nm, 250-500 nm, 0.5-1 {mu}m, 1-2 {mu}m, 2-4 {mu}m, 4-8 {mu}m, 8-16 {mu}m. Prior to the sampling 'bounce off' effects on Silicone and Vaseline coated Si carriers were studied with total reflection X-ray fluorescence. According to the results silicone coated carriers were chosen for the analysis. Additionally, blank levels originating from the sampling device and the calibration procedure were studied. Blank levels of Fe corresponded to 1-10% of Fe in the aerosol samples. Blank levels stemming from the internal standard were found to be negligible. The results from the Synchroton radiation total reflection X-ray fluorescence analysis of the aerosols showed that 20 min of sampling time gave still enough sample material for elemental determination of most elements. For the determination of the oxidation state of Fe in the aerosols different Fe salts were prepared as a reference from suspensions in isopropanol. The results from the Fe K-edge Synchroton radiation total reflection X-ray fluorescence-X-ray absorption near-edge structure analysis of the aerosol samples showed that mainly Fe(III) was present in

Characterization of atmospheric aerosols using Synchroton radiation total reflection X-ray fluorescence and Fe K-edge total reflection X-ray fluorescence-X-ray absorption near-edge structure

International Nuclear Information System (INIS)

Fittschen, U.E.A.; Meirer, F.; Streli, C.; Wobrauschek, P.; Thiele, J.; Falkenberg, G.; Pepponi, G.

2008-01-01

In this study a new procedure using Synchrotron total reflection X-ray fluorescence (SR-TXRF) to characterize elemental amounts in atmospheric aerosols down to particle sizes of 0.015 um is presented. The procedure was thoroughly evaluated regarding bounce off effects and blank values. Additionally the potential of total reflection X-ray fluorescence-X-ray absorption near edge structure (SR-TXRF-XANES) for speciation of FeII/III down to amounts of 34 pg in aerosols which were collected for 1 h is shown. The aerosols were collected in the city of Hamburg with a low pressure Berner impactor on Si carriers covered with silicone over time periods of 60 and 20 min each. The particles were collected in four and ten size fractions of 10.0-8.0 μm, 8.0-2.0 μm, 2.0-0.13 μm 0.13-0.015 μm (aerodynamic particle size) and 15-30 nm, 30-60 nm, 60-130 nm, 130-250 nm, 250-500 nm, 0.5-1 μm, 1-2 μm, 2-4 μm, 4-8 μm, 8-16 μm. Prior to the sampling 'bounce off' effects on Silicone and Vaseline coated Si carriers were studied with total reflection X-ray fluorescence. According to the results silicone coated carriers were chosen for the analysis. Additionally, blank levels originating from the sampling device and the calibration procedure were studied. Blank levels of Fe corresponded to 1-10% of Fe in the aerosol samples. Blank levels stemming from the internal standard were found to be negligible. The results from the Synchroton radiation total reflection X-ray fluorescence analysis of the aerosols showed that 20 min of sampling time gave still enough sample material for elemental determination of most elements. For the determination of the oxidation state of Fe in the aerosols different Fe salts were prepared as a reference from suspensions in isopropanol. The results from the Fe K-edge Synchroton radiation total reflection X-ray fluorescence-X-ray absorption near-edge structure analysis of the aerosol samples showed that mainly Fe(III) was present in all particle size fractions

A Fascinating Application of Steiner's Theorem for Trapezium: Geometric Constructions Using Straightedge Alone

Science.gov (United States)

Stupel, Moshe; Ben-Chaim, David

2013-01-01

Based on Steiner's fascinating theorem for trapezium, seven geometrical constructions using straight-edge alone are described. These constructions provide an excellent base for teaching theorems and the properties of geometrical shapes, as well as challenging thought and inspiring deeper insight into the world of geometry. In particular, this…

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.

K-edge subtraction synchrotron X-ray imaging in bio-medical research.

Science.gov (United States)

Thomlinson, W; Elleaume, H; Porra, L; Suortti, P

2018-05-01

High contrast in X-ray medical imaging, while maintaining acceptable radiation dose levels to the patient, has long been a goal. One of the most promising methods is that of K-edge subtraction imaging. This technique, first advanced as long ago as 1953 by B. Jacobson, uses the large difference in the absorption coefficient of elements at energies above and below the K-edge. Two images, one taken above the edge and one below the edge, are subtracted leaving, ideally, only the image of the distribution of the target element. This paper reviews the development of the KES techniques and technology as applied to bio-medical imaging from the early low-power tube sources of X-rays to the latest high-power synchrotron sources. Applications to coronary angiography, functional lung imaging and bone growth are highlighted. A vision of possible imaging with new compact sources is presented. Copyright © 2018 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Fluctuation-dissipation theorem in general relativity and the cosmological constant

International Nuclear Information System (INIS)

Mottola, E.

1992-01-01

Vacuum fluctuations are an essential feature of quantum field theory. Yet, the smallness of the scalar curvature of our universe suggests that the zero-point energy associated with these fluctuations does not curve spacetime. A possible way out of this paradox is suggested by the fact that microscopic fluctuations are generally accompanied by dissipative behavior in macroscopic systems. The intimate relation between the two is expressed by a fluctuation-dissipation theorem which extends to general relativity. The connection between quantum fluctuations and dissipation suggests a mechanism for the conversion of coherent stresses in the curvature of space into ordinary matter or radiation, thereby relaxing the effective cosmological ''constant'' to zero over time. The expansion of the universe may be the effect of this time-asymmetric relaxation process

Generalized Kutta–Joukowski theorem for multi-vortex and multi-airfoil flow with vortex production — A general model

Directory of Open Access Journals (Sweden)

Bai Chenyuan

2014-10-01

Full Text Available By using a special momentum approach and with the help of interchange between singularity velocity and induced flow velocity, we derive in a physical way explicit force formulas for two-dimensional inviscid flow involving multiple bound and free vortices, multiple airfoils, and vortex production. These force formulas hold individually for each airfoil thus allowing for force decomposition, and the contributions to forces from singularities (such as bound and image vortices, sources, and doublets and bodies out of an airfoil are related to their induced velocities at the locations of singularities inside this airfoil. The force contribution due to vortex production is related to the vortex production rate and the distance between each pair of vortices in production, thus frame-independent. The formulas are validated against a number of standard problems. These force formulas, which generalize the classic Kutta–Joukowski theorem (for a single bound vortex and the recent generalized Lagally theorem (for problems without a bound vortex and vortex production to more general cases, can be used to identify or understand the roles of outside vortices and bodies on the forces of the actual body, optimize arrangement of outside vortices and bodies for force enhancement or reduction, and derive analytical force formulas once the flow field is given or known.

A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption.

Science.gov (United States)

Yang, Xiuping; Min, Lequan; Wang, Xue

2015-05-01

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2(1345). As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

Local BRST cohomology in the antifield formalism. Pt. 1. General theorems

Energy Technology Data Exchange (ETDEWEB)

Barnich, G [Universite Libre de Bruxelles (Belgium). Faculte des Sciences; Henneaux, M [Universite Libre de Bruxelles (Belgium). Faculte des Sciences; Brandt, F [Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Amsterdam (Netherlands). Sectie H

1994-12-31

We establish general theorems on the cohomology H{sup *}(svertical stroke d) of the BRST differential modulo the spacetime exterior derivative, acting in the algebra of local p-forms depending on the fields and the antifields (= sources for the BRST variations). It is shown that H{sup -k}(svertical stroke d) is isomorphic H{sub k}({delta}vertical stroke d) in negative ghost degree -k (k > 0), where {delta} is the Koszul-Tate differential associated with the stationary surface. The cohomological group H{sub 1}({delta}vertical stroke d) in form degree n is proved to be isomorphic to the space of constants of the motion, thereby providing a cohomological reformulation of Noether theorem. More generally, the group H{sub k}({delta}vertical stroke d) in form degree n is isomorphic to the space of n - k forms that are closed when the equations of motion hold. The groups H{sub k}({delta}vertical stroke d) (k > 2) are shown to vanish for standard irreducible gauge theories. The group H{sub 2}({delta}vertical stroke d) is then calculated explicitly for electromagnetism, Yang-Mills models and Einstein gravity. The invariance of the groups H{sup k}(svertical stroke d) under the introduction of non minimal variables and of auxiliary fields is also demonstrated. In a companion paper, the general formalism is applied to the calculation of H{sup k}(svertical stroke d) in Yang-Mills theory, which is carried out in detail for an arbitrary compact gauge group. (orig.).

Positive energy theorem in generalized Kaluza-Klein theories of higher dimensions

International Nuclear Information System (INIS)

Moreschi, O.M.

1983-01-01

The technique of using spinors in the proof of positive energy theorems in 4 dimensions is extended to the case of Kaluza-Klein theories in spaces of 4 + n dimensions. First a useful presentation of generalized Kaluza-Klein theories is introduced, in which just from the observation of conformal symmetries it is possible to detect a nice splitting of the Ricci tensor into a 4-dimensional Ricci part and a Yang-Mills part, among others. Consideration of linear dependence among the symmetries is not excluded in this treatment. Relevant to the introduction of spinors, a discussion of Clifford Algebras is presented. In particular a real representation of these algebras is introduced for spaces of higher dimensions and its structure is analyzed. The Lie derivative of spinors is presented probably more clearly than in former treatments. After the introduction of these preliminary themes, a brief review of the relevant aspects of positive energy theorems in 4 dimensions is presented, followed by the extension of these ideas to the case of 5 dimensions. Here an earlier result involving gravitational mass and electromagnetic charges is improved. Finally the results are generalized to spaces of 4 + n dimensions, and a more complicated condition to be satisfied by the usual matter tensor is discovered. This procedure leads to a natural definition of invariant Yang-Mills charges, which is compared with former studies

X-ray absorption near-edge spectroscopic study of nickel catalysts

International Nuclear Information System (INIS)

Soldatov, Alexander V.; Smolentsev, Grigory; Kravtsova, Antonina; Yalovega, Galina; Feiters, Martin C.; Metselaar, Gerald A.; Joly, Yves

2006-01-01

Ni-isocyanide and Ni-acac complexes have been studied by X-ray absorption spectroscopy. Theoretical analysis has been done using self-consistent full multiple scattering (MS) approach within both muffin-tin (MT) model of the potential and non-MT finite deference method. For the isocyanide complex, it was shown that MS theoretical spectra reproduce all structural details of the X-ray absorption near-edge structure (XANES), but also that it is important to consider the non-MT effects in the potential for a correct simulation of the shape of the pre-edge structures. The contribution of a non-constant potential in the interstitial regions is extremely important for the interpretation of the XANES of Ni(acac) 2

Modified fluctuation-dissipation theorem for general non-stationary states and application to the Glauber–Ising chain

International Nuclear Information System (INIS)

Verley, Gatien; Lacoste, David; Chétrite, Raphaël

2011-01-01

In this paper, we present a general derivation of a modified fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary state for a system obeying Markovian dynamics. We show that the method for deriving modified fluctuation-dissipation theorems near non-equilibrium stationary states used by Prost et al (2009 Phys. Rev. Lett. 103 090601) is generalizable to non-stationary states. This result follows from both standard linear response theory and from a transient fluctuation theorem, analogous to the Hatano–Sasa relation. We show that this modified fluctuation-dissipation theorem can be interpreted at the trajectory level using the notion of stochastic trajectory entropy, in a way which is similar to what has been done recently in the case of the MFDT near non-equilibrium steady states (NESS). We illustrate this framework with two solvable examples: the first example corresponds to a Brownian particle in a harmonic trap subjected to a quench of temperature and to a time-dependent stiffness; the second example is a classic model of coarsening systems, namely the 1D Ising model with Glauber dynamics

X-ray fluorescence holography and multiple-energy x-ray holography: A critical comparison of atomic images

International Nuclear Information System (INIS)

Len, P.M.; Gog, T.; Fadley, C.S.; Materlik, G.

1997-01-01

We compare x-ray fluorescence holography (XFH) and multiple-energy x-ray holography (MEXH), two techniques that have recently been used to obtain experimental three-dimensional atomic images. For single-energy holograms, these methods are equivalent by virtue of the optical reciprocity theorem. However, XFH can only record holographic information at the characteristic fluorescence energies of the emitting species, while MEXH can record holographic information at any energy above the fluorescent edge of the emitter, thus enabling the suppression of real-twin overlaps and other aberrations and artifacts in atomic images. copyright 1997 The American Physical Society

X-Ray Absorption Near-Edge Structure (XANES) of Calcium L3,2 Edges of Various Calcium Compounds and X-Ray Excited Optical Luminescence (XEOL) Studies of Luminescent Calcium Compounds

International Nuclear Information System (INIS)

Ko, J. Y. Peter; Zhou Xingtai; Sham, T.-K.; Heigl, Franziskus; Regier, Tom; Blyth, Robert

2007-01-01

X-ray absorption at calcium L3,2 edges of various calcium compounds were measured using a high resolution Spherical Grating Monochromator (SGM) at the Canadian Light Source (CLS). We observe that each compound has its unique fine structure of L3,2 edges. This uniqueness is due to differences in local structure of compounds. We also performed (X-ray Excited Optical Luminescence) XEOL of selected luminescent calcium compounds to investigate their optical properties. XEOL is a photon-in-photon-out technique in which the optical luminescence that is excited by tunable x-rays from a synchrotron light source is monitored. Depending on excitation energy of the x-ray, relative intensities of luminescence peaks vary. Recent findings of the results will be presented here

A simple proof of the recent generalizations of Hawking's black hole topology theorem

Energy Technology Data Exchange (ETDEWEB)

Racz, Istvan [RMKI, H-1121 Budapest, Konkoly Thege Miklos ut 29-33 (Hungary)], E-mail: iracz@sunserv.kfki.hu

2008-08-21

A key result in four-dimensional black hole physics, since the early 1970s, is Hawking's topology theorem assertion that the cross-sections of an 'apparent horizon', separating the black hole region from the rest of the spacetime, are topologically 2-spheres. Later, during the 1990s, by applying a variant of Hawking's argument, Gibbons and Woolgar could also show the existence of a genus-dependent lower bound for the entropy of topological black holes with negative cosmological constant. Recently, Hawking's black hole topology theorem, along with the results of Gibbons and Woolgar, has been generalized to the case of black holes in higher dimensions. Our aim here is to give a simple self-contained proof of these generalizations, which also makes their range of applicability transparent. (fast track communication)

Refraction angle and edge visibility in X-ray diffraction enhanced imaging

International Nuclear Information System (INIS)

Chen Yu; Jia Quanjie; Li Gang; Wang Yuzhu; Xue Xianying; Jiang Xiaoming

2007-01-01

Diffraction-enhanced X-ray imaging could extract accurately the refraction angles of the sample, which is very important to increase the image contrast of low Z samples. In this paper, the DEI experiments with X-rays of different energies were performed both on wedge-shaped and rounded model samples. Refraction angles of the two samples were all obtained accurately, and the results agreed well with the calculations. Quantitative analyses based on Edge Visibility were performed for the wedge-shaped model sample. The results revealed that the calculated positions for the Best Edge Visibility of the slope with fixed refraction angle were calculable in good agreement with the experimental results. A quantitative research on the Edge Visibility of real tissues sample was carried out and the optimal condition for best contrast of DEI images were discussed. (authors)

A landing theorem for entire functions with bounded post-singular sets

OpenAIRE

Benini, Anna Miriam; Rempe-Gillen, Lasse

2017-01-01

The Douady-Hubbard landing theorem for periodic external rays is one of the cornerstones of the study of polynomial dynamics. It states that, for a complex polynomial with bounded postcritical set, every periodic external ray lands at a repelling or parabolic periodic point, and conversely every repelling or parabolic point is the landing point of at least one periodic external ray. We prove an analogue of this theorem for an entire function with bounded postsingular set: every periodic dread...

Radiobiological investigations of soft X-rays near carbon, nitrogen, oxygen K-shell edges on Aspergillus oryzae spores

International Nuclear Information System (INIS)

Chen, L.; Jiang, S. P.; Wan, L. B.; Ma, X. D.; Li, M. F.

2008-01-01

Soft X-rays at carbon, nitrogen, oxygen K-shell edges have special radiobiological effects. Using Aspergillus oryzae spores as sample, the radiation effects of soft X-rays near the K-shell edges of C, N and O elements from synchrotron radiation were investigated. Also the dose depositions of different X-ray energies in spore were discussed. At the same time, the spores were irradiated by gamma rays from 60 Co and relative biological effects were compared with those produced by soft X-rays. The results showed that soft X-rays near K-shell edges of O element had higher ability of radiation damage than that of X-rays near K-shell edges of C and N elements as compared with one another. But they all had higher killing abilities per unit dose than that of gamma rays from 60 Co. The relative biological effects (RBEs), the comparison of dose to gamma rays at 10% survival level, of the three soft X-rays were 1.65, 1.73 and 1.91, respectively. (authors)

Generalized Lions-Peetre interpolation construction and optimal embedding theorems for Sobolev spaces

International Nuclear Information System (INIS)

Ovchinnikov, V I

2014-01-01

In the paper, a new description of the generalized Lions-Peetre method of means is found, which enables one to evaluate the interpolation orbits of spaces constructed by this method. The list of these spaces includes all Lorentz spaces with functional parameters, Orlicz spaces, and spaces close to them. This leads in turn to new optimal embedding theorems for Sobolev spaces produced using the Lions-Peetre construction in rearrangement invariant spaces. It turns out that the optimal space of the embedding is also a generalized Lions-Peetre space whose parameters are explicitly evaluated. Bibliography: 18 titles

A density Corradi-Hajnal theorem

Czech Academy of Sciences Publication Activity Database

Allen, P.; Böttcher, J.; Hladký, Jan; Piguet, D.

2015-01-01

Roč. 67, č. 4 (2015), s. 721-758 ISSN 0008-414X Institutional support: RVO:67985840 Keywords : extremal graph theory * Mantel's theorem * Corradi-Hajnal theorem Subject RIV: BA - General Mathematics Impact factor: 0.618, year: 2015 http://cms.math.ca/10.4153/CJM-2014-030-6

Edge detection methods based on generalized type-2 fuzzy logic

CERN Document Server

Gonzalez, Claudia I; Castro, Juan R; Castillo, Oscar

2017-01-01

In this book four new methods are proposed. In the first method the generalized type-2 fuzzy logic is combined with the morphological gra-dient technique. The second method combines the general type-2 fuzzy systems (GT2 FSs) and the Sobel operator; in the third approach the me-thodology based on Sobel operator and GT2 FSs is improved to be applied on color images. In the fourth approach, we proposed a novel edge detec-tion method where, a digital image is converted a generalized type-2 fuzzy image. In this book it is also included a comparative study of type-1, inter-val type-2 and generalized type-2 fuzzy systems as tools to enhance edge detection in digital images when used in conjunction with the morphologi-cal gradient and the Sobel operator. The proposed generalized type-2 fuzzy edge detection methods were tested with benchmark images and synthetic images, in a grayscale and color format. Another contribution in this book is that the generalized type-2 fuzzy edge detector method is applied in the preproc...

Adiabatic theorem and spectral concentration

International Nuclear Information System (INIS)

Nenciu, G.

1981-01-01

The spectral concentration of arbitrary order, for the Stark effect is proved to exist for a large class of Hamiltonians appearing in nonrelativistic and relativistic quantum mechanics. The results are consequences of an abstract theorem about the spectral concentration for self-ad oint operators. A general form of the adiabatic theorem of quantum mechanics, generalizing an earlier result of the author as well as some results of Lenard, is also proved [ru

A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption

Energy Technology Data Exchange (ETDEWEB)

Yang, Xiuping, E-mail: yangxiuping-1990@163.com; Min, Lequan, E-mail: minlequan@sina.com; Wang, Xue, E-mail: wangxue-20130818@163.com [Schools of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083 (China)

2015-05-15

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2{sup 1345}. As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

General Correlation Theorem for Trinion Fourier Transform

OpenAIRE

Bahri, Mawardi

2017-01-01

- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.

Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs

Directory of Open Access Journals (Sweden)

Magda Dettlaff

2016-01-01

Full Text Available Given a graph \\(G=(V,E\\, the subdivision of an edge \\(e=uv\\in E(G\\ means the substitution of the edge \\(e\\ by a vertex \\(x\\ and the new edges \\(ux\\ and \\(xv\\. The domination subdivision number of a graph \\(G\\ is the minimum number of edges of \\(G\\ which must be subdivided (where each edge can be subdivided at most once in order to increase the domination number. Also, the domination multisubdivision number of \\(G\\ is the minimum number of subdivisions which must be done in one edge such that the domination number increases. Moreover, the concepts of paired domination and independent domination subdivision (respectively multisubdivision numbers are defined similarly. In this paper we study the domination, paired domination and independent domination (subdivision and multisubdivision numbers of the generalized corona graphs.

Out-of-time-order fluctuation-dissipation theorem

Science.gov (United States)

Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

2018-01-01

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.

Generalized Friedland's theorem for C0-semigroups

Science.gov (United States)

Cichon, Dariusz; Jung, Il Bong; Stochel, Jan

2008-07-01

Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.

Quasimonochromatic x-ray source using photoabsorption-edge transition radiation

International Nuclear Information System (INIS)

Piestrup, M.A.; Boyers, D.G.; Pincus, C.I.; Harris, J.L.; Maruyama, X.K.; Bergstrom, J.C.; Caplan, H.S.; Silzer, R.M.; Skopik, D.M.

1991-01-01

By designing transition radiators to emit x rays at the foil material's K-, L-, or M-shell photoabsorption edge, the x-ray spectrum is narrowed. The source is quasimonochromatic, directional, and intense and uses an electron beam whose energy is considerably lower than that needed for synchrotron sources. Depending upon the selection of foil material, the radiation can be produced wherever there is a photoabsorption edge. In this paper we report the results of the measurement of the x-ray spectrum from a transition radiator composed of 10 foils of 2-μm titanium and exposed to low-current, 90.2-MeV electrons. The measured band of emission was from 3.2 to 5 keV. In addition, a measurment was performed of the total power from a transition radiator composed of 18 foils of 2.0-μm copper exposed to a high-average-current electron beam of 40 μA and at energies of 135, 172, and 200 MeV. The maximum measured power was 4.0 mW. The calculated band of emission was from 4 to 9 keV

X-ray absorption near edge spectroscopy at the Mn K-edge in highly homogeneous GaMnN diluted magnetic semiconductors

Energy Technology Data Exchange (ETDEWEB)

Sancho-Juan, O.; Cantarero, A.; Garro, N.; Cros, A. [Materials Science Institute, University of Valencia, PO Box 22085, 46071 Valencia (Spain); Martinez-Criado, G.; Salome, M.; Susini, J. [ESRF, Polygone Scientifique Louis Neel, 6 rue Jules Horowitz, 38000 Grenoble (France); Olguin, D. [Dept. de Fisica, CINVESTAV-IPN, 07300 Mexico D.F. (Mexico); Dhar, S.; Ploog, K. [Paul Drude Institute, Hausvogteiplatz 5-7, 10117 Berlin (Germany)

2006-06-15

We have studied by X-ray absorption spectroscopy the local environment of Mn in highly homogeneous Ga{sub 1-x}Mn{sub x}N (0.06edges. In this report, we focus our attention to the X-ray absorption near edge spectroscopy (XANES) results. The comparison of the XANES spectra corresponding to the Ga and Mn edges indicates that Mn is substitutional to Ga in all samples studied. The XANES spectra measured at the Mn absorption edge shows in the near-edge region a double peak and a shoulder below the absorption edge and the main absorption peak after the edge, separated around 15 eV above the pre-edge structure. We have compared the position of the edge with that of MnO (Mn{sup 2+}) and Mn{sub 2}O{sub 3} (Mn{sup 3+}). All samples studied present the same Mn oxidation state, 2{sup +}. In order to interprete the near-edge structure, we have performed ab initio calculations with a 2 x 2 x 1supercell ({proportional_to}6% Mn) using the full potential linear augmented plane wave method as implemented in the Wien2k code. The calculations show the appearance of Mn anti-bonding t{sub 2g} bands, which are responsible for the pre-edge absorption. The shoulder and main absorption peaks are due to transitions from the valence band 1s-states of Mn to the p-contributions of the conduction bands. (copyright 2006 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Applications of 'edge-on' illuminated porous plate detectors for diagnostic X-ray imaging

CERN Document Server

Shikhaliev, P M

2002-01-01

Scanning X-ray imaging systems for non-invasive diagnostics have several advantages over conventional imaging systems using area detectors. They significantly reduce the detected scatter radiation, cover large areas and potentially provide high spatial resolution. Applications of one-dimensional gaseous detectors and 'edge-on' illuminated silicon strip detectors for scanning imaging systems are currently under intensive investigation. The purpose of this work is to investigate 'edge-on' illuminated Porous Plate (PP) detectors for applications in diagnostic X-ray imaging. MicroChannel Plate (MCP), which is a common type of PP, has previously been investigated as a detector in surface-on illumination mode for medical X-ray imaging. However, its detection efficiency was too low for medical imaging applications. In the present study, the PP are used in the 'edge-on' illumination mode. Furthermore, the structural parameters of different PP types are optimized to improve the detection efficiency in the diagnostic X...

Keller’s theorem revisited

Science.gov (United States)

Ortiz, Guillermo P.; Mochán, W. Luis

2018-02-01

Keller’s theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assumption that the response function relates an irrotational to a solenoidal field and that is valid for dispersive and dissipative anisotropic systems. We show that the usual statement of Keller’s theorem in terms of the conductivity is strictly valid only at zero frequency and we obtain a new generalization for finite frequencies. We develop applications of the theorem to the study of the optical properties of systems such as superlattices, 2D isotropic and anisotropic metamaterials and random media, to test the accuracy of theories and computational schemes, and to increase the accuracy of approximate calculations.

The Goldstone equivalence theorem and AdS/CFT

Energy Technology Data Exchange (ETDEWEB)

Anand, Nikhil; Cantrell, Sean [Department of Physics & Astronomy, Johns Hopkins University,Baltimore, MD 21218 (United States)

2015-08-03

The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the non-conserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields. We then go on to generalize the theorem using conformal blocks in two and four-dimensional CFTs. We show that when the scaling dimensions of the exchanged operators are large compared to both their spins and the dimension of the current, the conformal blocks satisfy an equivalence theorem.

The Classical Version of Stokes' Theorem Revisited

DEFF Research Database (Denmark)

Markvorsen, Steen

2005-01-01

Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we prove that the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...

Convergence estimates for iterative methods via the Kriess Matrix Theorem on a general complex domain

Energy Technology Data Exchange (ETDEWEB)

Toh, K.C.; Trefethen, L.N. [Cornell Univ., Ithaca, NY (United States)

1994-12-31

What properties of a nonsymmetric matrix A determine the convergence rate of iterations such as GMRES, QMR, and Arnoldi? If A is far from normal, should one replace the usual Ritz values {r_arrow} eigenvalues notion of convergence of Arnoldi by alternative notions such as Arnoldi lemniscates {r_arrow} pseudospectra? Since Krylov subspace iterations can be interpreted as minimization processes involving polynomials of matrices, the answers to questions such as these depend upon mathematical problems of the following kind. Given a polynomial p(z), how can one bound the norm of p(A) in terms of (1) the size of p(z) on various sets in the complex plane, and (2) the locations of the spectrum and pseudospectra of A? This talk reports some progress towards solving these problems. In particular, the authors present theorems that generalize the Kreiss matrix theorem from the unit disk (for the monomial A{sup n}) to a class of general complex domains (for polynomials p(A)).

Femtosecond Near Edge X-ray Absorption Measurement of the VO2 Phase Transition

International Nuclear Information System (INIS)

Cavalleri, A.; Chong, H.H.W.; Fourmaux, S.; Glover, T.E.; Heimann, P.A; Kieffer, J.C.; Padmore, H.A.; Schoenlein, R.W.

2004-01-01

The authors measure the insulator-to-metal transition in VO 2 using femtosecond Near-Edge X-ray Absorption. Sliced pulses of synchrotron radiation are used to detect the photo-induced dynamics at the 516-eV Vanadium L 3 edge

Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces

International Nuclear Information System (INIS)

Cho, Yeol Je; Sedghi, Shaban; Shobe, Nabi

2009-01-01

In this paper, we give some new definitions of compatible mappings of types (I) and (II) in fuzzy metric spaces and prove some common fixed point theorems for four mappings under the condition of compatible mappings of types (I) and (II) in complete fuzzy metric spaces. Our results extend, generalize and improve the corresponding results given by many authors.

Complex integration and Cauchy's theorem

CERN Document Server

Watson, GN

2012-01-01

This brief monograph by one of the great mathematicians of the early twentieth century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.Author G. N. Watson begins by reviewing various propositions of Poincaré's Analysis Situs, upon which proof of the theorem's most general form depends. Subsequent chapters examine the calculus of residues, calculus optimization, the

Portable X-Ray, K-Edge Heavy Metal Detector

International Nuclear Information System (INIS)

Fricke, V.

1999-01-01

The X-Ray, K-Edge Heavy Metal Detection System was designed and built by Ames Laboratory and the Center for Nondestructive Evaluation at Iowa State University. The system uses a C-frame inspection head with an X-ray tube mounted on one side of the frame and an imaging unit and a high purity germanium detector on the other side. the inspection head is portable and can be easily positioned around ventilation ducts and pipes up to 36 inches in diameter. Wide angle and narrow beam X-ray shots are used to identify the type of holdup material and the amount of the contaminant. Precise assay data can be obtained within minutes of the interrogation. A profile of the containerized holdup material and a permanent record of the measurement are immediately available

On the Total Edge Irregularity Strength of Generalized Butterfly Graph

Science.gov (United States)

Dwi Wahyuna, Hafidhyah; Indriati, Diari

2018-04-01

Let G(V, E) be a connected, simple, and undirected graph with vertex set V and edge set E. A total k-labeling is a map that carries vertices and edges of a graph G into a set of positive integer labels {1, 2, …, k}. An edge irregular total k-labeling λ: V(G) ∪ E(G) → {1, 2, …, k} of a graph G is a total k-labeling such that the weights calculated for all edges are distinct. The weight of an edge uv in G, denoted by wt(uv), is defined as the sum of the label of u, the label of v, and the label of uv. The total edge irregularity strength of G, denoted by tes(G), is the minimum value of the largest label k over all such edge irregular total k-labelings. A generalized butterfly graph, BFn , obtained by inserting vertices to every wing with assumption that sum of inserting vertices to every wing are same then it has 2n + 1 vertices and 4n ‑ 2 edges. In this paper, we investigate the total edge irregularity strength of generalized butterfly graph, BFn , for n > 2. The result is tes(B{F}n)=\\lceil \\frac{4n}{3}\\rceil .

A Bidirectional Generalized Synchronization Theorem-Based Chaotic Pseudo-random Number Generator

Directory of Open Access Journals (Sweden)

Han Shuangshuang

2013-07-01

Full Text Available Based on a bidirectional generalized synchronization theorem for discrete chaos system, this paper introduces a new 5-dimensional bidirectional generalized chaos synchronization system (BGCSDS, whose prototype is a novel chaotic system introduced in [12]. Numerical simulation showed that two pair variables of the BGCSDS achieve generalized chaos synchronization via a transform H.A chaos-based pseudo-random number generator (CPNG was designed by the new BGCSDS. Using the FIPS-140-2 tests issued by the National Institute of Standard and Technology (NIST verified the randomness of the 1000 binary number sequences generated via the CPNG and the RC4 algorithm respectively. The results showed that all the tested sequences passed the FIPS-140-2 tests. The confidence interval analysis showed the statistical properties of the randomness of the sequences generated via the CPNG and the RC4 algorithm do not have significant differences.

Dimensional analysis beyond the Pi theorem

CERN Document Server

Zohuri, Bahman

2017-01-01

Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First ...

A study of the Nb3Ge system by Ge K-edge extended x-ray absorption fine structure and x-ray absorption near-edge structure spectroscopy

International Nuclear Information System (INIS)

Saini, N L; Filippi, M; Wu Ziyu; Oyanagi, H; Ihara, H; Iyo, A; Agrestini, S; Bianconi, A

2002-01-01

The local structure of Nb 3 Ge intermetallic superconductor has been studied by Ge K-edge absorption spectroscopy. Extended x-ray absorption fine structure (EXAFS) experiments show two Ge-Nb distances. In addition to the crystallographic distance of ∼2.87 A, there exists a second Ge-Nb distance, shorter than the first by ∼0.2 A, assigned to a phase with short-range symmetry related to local displacements in the Nb-Nb chains. The x-ray absorption near-edge structure (XANES) spectrum has been simulated by full multiple-scattering calculations considering the local displacements determined by the EXAFS analysis. The XANES spectrum has been well reproduced by considering a cluster of 99 atoms within a radius of about 7 A from the central Ge atom and introducing determined local displacements

-Dimensional Fractional Lagrange's Inversion Theorem

Directory of Open Access Journals (Sweden)

F. A. Abd El-Salam

2013-01-01

Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.

Feasibility of photon-counting K-edge imaging in X-ray and computed tomographic systems: Monte Carlo simulation studies

International Nuclear Information System (INIS)

Lee, Seung-Wan; Choi, Yu-Na; Cho, Hyo-Min; Lee, Young-Jin; Ryu, Hyun-Ju; Kim, Hee-Joung

2011-01-01

Conventional X-ray systems and X-ray computed tomography (CT) systems, which use detectors operated in the integrating mode, are not able to reflect spectral information because the detector output is proportional to the energy fluence integrated over the whole spectrum. Photon-counting detectors have been considered as alternative devices. These detectors can measure the photon energy deposited by each event and improve the image quality. In this study, we investigated the feasibility of K-edge imaging using a photon-counting detector and evaluated the capability of material decomposition in X-ray images. The geometries of X-ray imaging systems equipped with cadmium telluride (CdTe) detectors and phantoms consisting of different materials were designed using Geant4 Application for Tomographic Emission (GATE) version 6.0. To observe the effect of a discontinuity in the attenuation due to the K-edge of a high atomic number material, we chose the energy windows to be one below and one above the K-edge absorption energy of the target material. The contrast-to-noise ratios (CNRs) of the target materials were increased at selective energy levels above the K-edge absorption energy because the attenuation is more dramatically increased at energies above the K-edge absorption energy of the material than at energies below that. The CNRs for the target materials in the K-edge image were proportional to the material concentration. The results of this study show that K-edge imaging can be carried out in conventional X-ray systems and X-ray CT systems using CdTe photon-counting detectors and that the target materials can be separated from background materials by using K-edge imaging. The photon-counting detector has potential to provide improved image quality, and this study will be used as a basis for future studies on photon-counting X-ray imaging.

Edge effects in a small pixel CdTe for X-ray imaging

Science.gov (United States)

Duarte, D. D.; Bell, S. J.; Lipp, J.; Schneider, A.; Seller, P.; Veale, M. C.; Wilson, M. D.; Baker, M. A.; Sellin, P. J.; Kachkanov, V.; Sawhney, K. J. S.

2013-10-01

Large area detectors capable of operating with high detection efficiency at energies above 30 keV are required in many contemporary X-ray imaging applications. The properties of high Z compound semiconductors, such as CdTe, make them ideally suitable to these applications. The STFC Rutherford Appleton Laboratory has developed a small pixel CdTe detector with 80 × 80 pixels on a 250 μm pitch. Historically, these detectors have included a 200 μm wide guard band around the pixelated anode to reduce the effect of defects in the crystal edge. The latest version of the detector ASIC is capable of four-side butting that allows the tiling of N × N flat panel arrays. To limit the dead space between modules to the width of one pixel, edgeless detector geometries have been developed where the active volume of the detector extends to the physical edge of the crystal. The spectroscopic performance of an edgeless CdTe detector bump bonded to the HEXITEC ASIC was tested with sealed radiation sources and compared with a monochromatic X-ray micro-beam mapping measurements made at the Diamond Light Source, U.K. The average energy resolution at 59.54 keV of bulk and edge pixels was 1.23 keV and 1.58 keV, respectively. 87% of the edge pixels present fully spectroscopic performance demonstrating that edgeless CdTe detectors are a promising technology for the production of large panel radiation detectors for X-ray imaging.

Development of X-ray microcalorimeters using transition edge sensors

International Nuclear Information System (INIS)

Ukibe, M; Hirayama, F.; Tanaka, K.; Koyanagi, M.; Ohkubo, M.; Kobayashi, N.; Morooka, T.; Chinone, K.

2000-01-01

We are developing X-ray microcalorimeters using superconducting transition edge sensors (TESs), which can be operated at relatively high temperatures in a 3 He cryostat, and DC-SQUID current amplifiers to realize an X-ray spectroscopy with a high energy resolution and a high counting rate. The TESs are proximity bilayers of Ti and Au on SiN x membranes with 500-1000 nm thicknesses. The typical TES has a T c value of 0.4 K and a ΔT c value of 2 mK. Two types of DC-SQUID amplifiers were developed; the single stage with 200-series SQUIDs and the double stage with an input SQUID and 50-series SQUIDs. The X-ray detection experiment is in progress. (author)

There is No Quantum Regression Theorem

International Nuclear Information System (INIS)

Ford, G.W.; OConnell, R.F.

1996-01-01

The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem. copyright 1996 The American Physical Society

Bell's theorem based on a generalized EPR criterion of reality

International Nuclear Information System (INIS)

Eberhard, P.H.; Rosselet, P.

1995-01-01

First, the demonstration of Bell's theorem, i.e., of the nonlocal character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedanken experiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almost with certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future

Image reconstruction for x-ray K-edge imaging with a photon counting detector

Science.gov (United States)

Meng, Bo; Cong, Wenxiang; Xi, Yan; Wang, Ge

2014-09-01

Contrast agents with high-Z elements have K-absorption edges which significantly change X-ray attenuation coefficients. The K-edge characteristics is different for various kinds of contrast agents, which offers opportunities for material decomposition in biomedical applications. In this paper, we propose a new K-edge imaging method, which not only quantifies a distribution of a contrast agent but also provides an optimized contrast ratio. Our numerical simulation tests demonstrate the feasibility and merits of the proposed methodology.

Effects of phonon broadening on x-ray near-edge spectra in molecular crystals

Science.gov (United States)

Vinson, John; Jach, Terrence; Elam, Tim; Denlinger, Jonathon

2014-03-01

Calculations of near-edge x-ray spectra are often carried out using the average atomic coordinates from x-ray or neutron scattering experiments or from density functional theory (DFT) energy minimization. This neglects disorder from thermal and zero-point vibrations. Here we look at the nitrogen K-edge of ammonium chloride and ammonium nitrate, comparing Bethe-Salpeter calculations of absorption and fluorescence to experiment. We find that intra-molecular vibrational effects lead to significant, non-uniform broadening of the spectra, and that for some features zero-point motion is the primary source of the observed shape.

Quantum work fluctuation theorem: Nonergodic Brownian motion case

International Nuclear Information System (INIS)

Bai, Zhan-Wu

2014-01-01

The work fluctuations of a quantum Brownian particle driven by an external force in a general nonergodic heat bath are studied under a general initial state. The exact analytical expression of the work probability distribution function is derived. Results show the existence of a quantum asymptotic fluctuation theorem, which is in general not a direct generalization of its classical counterpart. The form of this theorem is dependent on the structure of the heat bath and the specified initial condition.

Optimal no-go theorem on hidden-variable predictions of effect expectations

Science.gov (United States)

Blass, Andreas; Gurevich, Yuri

2018-03-01

No-go theorems prove that, under reasonable assumptions, classical hidden-variable theories cannot reproduce the predictions of quantum mechanics. Traditional no-go theorems proved that hidden-variable theories cannot predict correctly the values of observables. Recent expectation no-go theorems prove that hidden-variable theories cannot predict the expectations of observables. We prove the strongest expectation-focused no-go theorem to date. It is optimal in the sense that the natural weakenings of the assumptions and the natural strengthenings of the conclusion make the theorem fail. The literature on expectation no-go theorems strongly suggests that the expectation-focused approach is more general than the value-focused one. We establish that the expectation approach is not more general.

EDGE: Explorer of diffuse emission and gamma-ray burst explosions

DEFF Research Database (Denmark)

Den Herder, J.W.; Hermsen, W.; Hoevers, H.

2007-01-01

cluster formation, down to the very low redshift Universe, when between a third and one half of the baryons are expected to reside in cosmic filaments undergoing gravitational collapse by dark matter (the so-called warm hot intragalactic medium). In addition EDGE, with its unprecedented capabilities......How structures of various scales formed and evolved from the early Universe up to present time is a fundamental question of astrophysics. EDGE1 will trace the cosmic history of the baryons from the early generations of massive stars by Gamma-Ray Burst (GRB) explosions, through the period of galaxy...

EDGE: Explorer of diffuse emission and gamma-ray burst explosions

DEFF Research Database (Denmark)

Piro, L; den Herder, J W; Ohashi, T

2009-01-01

, through the period of galaxy cluster formation, down to the very low redshift Universe, when between a third and one half of the baryons are expected to reside in cosmic filaments undergoing gravitational collapse by dark matter (the so-called warm hot intragalactic medium). In addition EDGE, with its......How structures of various scales formed and evolved from the early Universe up to present time is a fundamental question of astrophysical cosmology. EDGE (Piro et al., 2007) will trace the cosmic history of the baryons from the early generations of massive stars by Gamma-Ray Burst (GRB) explosions...

EDGE: explorer of diffuse emission and gamma-ray burst explosions

NARCIS (Netherlands)

den Herder, J.W.; Piro, L.; Ohashi, T.; Amati, L.; Atteia, J.; Barthelmy, S.D.; Barbera, M.; Barret, D.; Basso, S.; de Boer, M.; Borgani, S.; Boyarskiy, O.; Branchini, E.; Branduardi-Raymont, G.; Briggs, M.; Brunetti, G.; Budtz-Jorgensenf, C.; Burrows, D.N.; Campana, S.; Caroli, E.; Chincarini, G.; Christensen, F.; Cocchi, M.; Comastri, A.; Corsi, A.; Cotroneo, V.; Conconi, P.; Colasanti, L.; Cusamano, G.; Rosa, A.; Del Santo, M.; Ettori, S.; Ezoe, Y.; Ferrari, L.; Feroci, M.; Finger, M.; Fishman, G.; Fujimoto, R.; Galeazzi, M.; Galli, A.; Gatti, F.; Gehrels, N.; Gendre, B.; Ghirlanda, G.; Ghisellini, G.; Giommi, P.; Girardi, M.; Guzzo, L.; Haardt, F.; Hepburn, I.; Hermsen, W.; Hoevers, H.; Holland, A.; in 't Zand, J.J.M.; Ishisaki, Y.; Kawahara, H.; Kawai, N.; Kaastra, J.; Kippen, M.; de Korte, P.A.J.; Kouveliotou, C.; Kusenko, A.; Labanti, C.; Lieu, R.; Macculi, C.; Makishima, K.; Matt, G.; Mazotta, P.; McCammon, D.; Méndez, M.; Mineo, T.; Mitchell, S.; Mitsuda, K.; Molendi, S.; Moscardini, L.; Mushotzky, R.; Natalucci, L.; Nicastro, F.; O'Brien, P.; Osborne, J.; Paerels, F.; Page, M.; Paltani, S.; Pareschi, G.; Perinati, E.; Perola, C.; Ponman, T.; Rasmussen, A.; Roncarelli, M.; Rosati, P.; Ruchayskiy, O.; Quadrini, E.; Sakurai, I.; Salvaterra, R.; Sasaki, S.; Wijers, R.; et al., [Unknown

2007-01-01

How structures of various scales formed and evolved from the early Universe up to present time is a fundamental question of astrophysics. EDGE will trace the cosmic history of the baryons from the early generations of massive stars by Gamma-Ray Burst (GRB) explosions, through the period of galaxy

The relativistic virial theorem

International Nuclear Information System (INIS)

Lucha, W.; Schoeberl, F.F.

1989-11-01

The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)

Bell's theorem based on a generalized EPR criterion of reality

International Nuclear Information System (INIS)

Eberhard, P.H.; Rosselet, P.

1993-04-01

First, the demonstration of Bell's theorem, i.e. of the non-local character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedanken experiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almost with certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future. (author) 1 fig., 11 refs

Investigation of the spatial generalization of Kato's theorem by a variational density-functional approach

International Nuclear Information System (INIS)

Csavinszky, P.

1990-01-01

In a recent work, March has considered the quantum-mechanical system of an arbitrary number of closed electronic shells around an atomic nucleus of charge Z a e. March has assumed that the shells are filled by noninteracting electrons, moving in the bare Coulomb potential energy of V(r) = -Z a e 2 /r. In this framework, the basic quantity is the total electron (number) density ρ(r), built by summing the (number) density ρ n (r) of the nth closed electronic shell over the principal quantum number n. March has shown that Kato's theorem, (∂ρ(r)/∂r) r=0 = -(2Z a /a 0 )ρ (r = 0), with a 0 = ℎ 2 /me 2 , is amenable to a spatially dependent generalization that can be expressed by ∂ρ(r)/∂r = -(2Z a /a 0 )ρ s (r), where ρ s (r) is the s-state contribution from the n closed electronic shells to ρ(r). The present work investigates the spatially dependent generalization of Kato's theorem for the Ne atom by making use of a variational density-functional approach and adopting several expressions for the kinetic-energy functional of the electrons. The intriguing question of identifying the best kinetic-energy functional is raised and discussed

The Boundary Crossing Theorem and the Maximal Stability Interval

Directory of Open Access Journals (Sweden)

Jorge-Antonio López-Renteria

2011-01-01

useful tools in the study of the stability of family of polynomials. Although both of these theorem seem intuitively obvious, they can be used for proving important results. In this paper, we give generalizations of these two theorems and we apply such generalizations for finding the maximal stability interval.

Evaluate More General Integrals Involving Universal Associated Legendre Polynomials via Taylor's Theorem

Institute of Scientific and Technical Information of China (English)

G.Ya(n)ez-Navarro; Guo-Hua Sun; Dong-Sheng Sun; Chang-Yuan Chen; Shi-Hai Dong

2017-01-01

A few important integrals involving the product of two universal associated Legendre polynomials Pl'm'(x),Pk'n'(x) and x2a(1-x2)-p-1,xb(1 ±x)-p-1 and xc(1-x2)-p-1 (1 ±-x) are evaluated using the operator form of Taylor's theorem and an integral over a single universal associated Legendre polynomial.These integrals are more general since the quantum numbers are unequal,i.e.l'≠ k'and m'≠ n'.Their selection rules are also given.We also verify the correctness of those integral formulas numerically.

K-edge resonant x-ray magnetic scattering from a transition-metal oxide: NiO

DEFF Research Database (Denmark)

Hill, J.P.; Kao, C.C.; McMorrow, D.F.

1997-01-01

We report the observation of resonant x-ray magnetic scattering in the vicinity of the Ni K edge in the antiferromagnet NiO. An approximately twofold increase in the scattering is observed as the incident photon energy is tuned through a pre-edge feature in the absorption spectrum, associated...

Central limit theorem in quantum field theory, generalized partons and application to deep-inelastic scattering

International Nuclear Information System (INIS)

Manoukian, E.B.

1986-01-01

We prove the following elementary theorem. If diameter 1 ,...,diametersub(N) is a sequence of fields having identical, though arbitrary, interactions but not interacting with each other and =0, i=1,...,N, then the generating functional of the ''average'' field diametersup((N))=(diameter 1 +...+diametersub((N))/√N, for N->infinite, may be explicitly obtained and may be written in terms of the two-point function of any of the fields diametersub(i). The theorem is then applied to define generalized parton fields PSIsub(j)=Σsup(N)sub(i)=1 PSIij/√N as ''averages'' of basic fields PSIsub(ij) having arbitrary interactions but not interacting with each other. We show that in the limit N->infinite Bjorken scaling, as observed at energies not too high, may be obtained if only quanta associated with generalized parton fields are excited in the hadron by the virtual photon with no reference to the details of the underlying dynamics. For N< infinite, and the excitation of other quanta as well lead to a systematic breaking of scale invariance and the details of the dynamics are necessarily recovered which are expected to be applicable at higher energy regimes. (orig.)

The Osgood-Schoenflies theorem revisited

International Nuclear Information System (INIS)

Siebenmann, L C

2005-01-01

The very first unknotting theorem of a purely topological character established that every compact subset of the Euclidean plane homeomorphic to a circle can be moved onto a round circle by a globally defined self-homeomorphism of the plane. This difficult hundred-year-old theorem is here celebrated with a partly new elementary proof, and a first but tentative account of its history. Some quite fundamental corollaries of the proof are sketched, and some generalizations are mentioned

X-ray absorption near edge structure (XANES) study of some hydroxamic mixed ligand copper complexes

International Nuclear Information System (INIS)

Mishra, A; Parsai, N; Shrivastava, B D; Soni, N

2012-01-01

With the advent of modern bright synchrotron radiation sources, X-ray absorption spectra has emerged as a powerful technique for local structure determination, which can be applied to any type of material. The X-ray absorption measurements of four hydroxamic mixed ligand copper complexes have been performed at the recently developed BL-8 Dispersive EXAFS beamline at 2.5 GeV Indus-2 synchrotron at RRCAT, Indore, India. The X-ray absorption near edge structure (XANES) data obtained has been processed using data analysis program Athena. The energies of the K absorption edge, chemical shifts, edge-widths, shifts of the principal absorption maximum in the complexes have been determined. The values of the chemical shift suggest that copper is in oxidation state +2 in all of the complexes. The chemical shift data has been utilized to estimate effective nuclear charge on copper atom. The order of the chemical shifts has been correlated to the relative ionic character of the bonding in these complexes.

A survey of weighted substitution operators and generalizations of Banach-stone theorem

OpenAIRE

R. K. Singh

2005-01-01

The classical Banach-Stone theorem characterizes linear surjective isometries between C(K)-spaces. The main aim of this paper is to present a survey of Banach-Stone-theorem-type results between some function spaces. The weighted substitution operators play an important role in characterization of isometries, disjointness preserving operators, and lattice homomorphisms. Some open problems are given for further investigation.

Sensitivity of photon-counting based K-edge imaging in X-ray computed tomography.

Science.gov (United States)

Roessl, Ewald; Brendel, Bernhard; Engel, Klaus-Jürgen; Schlomka, Jens-Peter; Thran, Axel; Proksa, Roland

2011-09-01

The feasibility of K-edge imaging using energy-resolved, photon-counting transmission measurements in X-ray computed tomography (CT) has been demonstrated by simulations and experiments. The method is based on probing the discontinuities of the attenuation coefficient of heavy elements above and below the K-edge energy by using energy-sensitive, photon counting X-ray detectors. In this paper, we investigate the dependence of the sensitivity of K-edge imaging on the atomic number Z of the contrast material, on the object diameter D , on the spectral response of the X-ray detector and on the X-ray tube voltage. We assume a photon-counting detector equipped with six adjustable energy thresholds. Physical effects leading to a degradation of the energy resolution of the detector are taken into account using the concept of a spectral response function R(E,U) for which we assume four different models. As a validation of our analytical considerations and in order to investigate the influence of elliptically shaped phantoms, we provide CT simulations of an anthropomorphic Forbild-Abdomen phantom containing a gold-contrast agent. The dependence on the values of the energy thresholds is taken into account by optimizing the achievable signal-to-noise ratios (SNR) with respect to the threshold values. We find that for a given X-ray spectrum and object size the SNR in the heavy element's basis material image peaks for a certain atomic number Z. The dependence of the SNR in the high- Z basis-material image on the object diameter is the natural, exponential decrease with particularly deteriorating effects in the case where the attenuation from the object itself causes a total signal loss below the K-edge. The influence of the energy-response of the detector is very important. We observed that the optimal SNR values obtained with an ideal detector and with a CdTe pixel detector whose response, showing significant tailing, has been determined at a synchrotron differ by factors of

Functional characterization of planar sensors with active edges using laser and X-ray beam scans

International Nuclear Information System (INIS)

Povoli, M.; Bagolini, A.; Boscardin, M.; Dalla Betta, G.-F.; Giacomini, G.; Hasi, J.; Oh, A.; Zorzi, N.

2013-01-01

We report on the functional characterization of planar sensors with active edges fabricated at Fondazione Bruno Kessler (FBK), Trento, Italy. The measurements here reported were performed by means of laser and X-ray beam scans mainly focusing on the signal efficiency of the edge region of the devices. Results are very encouraging and show very good sensitivity up to few microns away from the device physical edge

Functional characterization of planar sensors with active edges using laser and X-ray beam scans

Energy Technology Data Exchange (ETDEWEB)

Povoli, M., E-mail: povoli@disi.unitn.it [Dipartimento di Ingegneria e Scienza dell' Informazione, Università di Trento, Via Sommarive, 14, I-38123 Povo di Trento (Italy); INFN, Sezione di Padova (Gruppo Collegato di Trento),Via Sommarive, 14, I-38123 Povo di Trento (Italy); Bagolini, A.; Boscardin, M. [Fondazione Bruno Kessler, Centro per i Materiali e i Microsistemi (FBK-CMM), Via Sommarive, 18, I-38123 Povo di Trento (Italy); Dalla Betta, G.-F. [Dipartimento di Ingegneria e Scienza dell' Informazione, Università di Trento, Via Sommarive, 14, I-38123 Povo di Trento (Italy); INFN, Sezione di Padova (Gruppo Collegato di Trento),Via Sommarive, 14, I-38123 Povo di Trento (Italy); Giacomini, G. [Fondazione Bruno Kessler, Centro per i Materiali e i Microsistemi (FBK-CMM), Via Sommarive, 18, I-38123 Povo di Trento (Italy); Hasi, J. [SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025-7015 (United States); Oh, A. [The University of Manchester, Oxford Road, Manchester M13 9PL (United Kingdom); Zorzi, N. [Fondazione Bruno Kessler, Centro per i Materiali e i Microsistemi (FBK-CMM), Via Sommarive, 18, I-38123 Povo di Trento (Italy)

2013-08-01

We report on the functional characterization of planar sensors with active edges fabricated at Fondazione Bruno Kessler (FBK), Trento, Italy. The measurements here reported were performed by means of laser and X-ray beam scans mainly focusing on the signal efficiency of the edge region of the devices. Results are very encouraging and show very good sensitivity up to few microns away from the device physical edge.

Notes on the area theorem

International Nuclear Information System (INIS)

Park, Mu-In

2008-01-01

Hawking's area theorem can be understood from a quasi-stationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual BTZ black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon 'can decrease', rather than increase, with the quasi-stationary process. However, I find that the area for the outer horizon 'never decreases' such that the usual area theorem still works in our examples, though this is quite non-trivial in general. There exists an instability problem of the inner horizons but it seems that the instability is not important in my analysis. I also find a generalized area theorem by combining those of the outer and inner horizons

Projection-slice theorem based 2D-3D registration

Science.gov (United States)

van der Bom, M. J.; Pluim, J. P. W.; Homan, R.; Timmer, J.; Bartels, L. W.

2007-03-01

In X-ray guided procedures, the surgeon or interventionalist is dependent on his or her knowledge of the patient's specific anatomy and the projection images acquired during the procedure by a rotational X-ray source. Unfortunately, these X-ray projections fail to give information on the patient's anatomy in the dimension along the projection axis. It would be very profitable to provide the surgeon or interventionalist with a 3D insight of the patient's anatomy that is directly linked to the X-ray images acquired during the procedure. In this paper we present a new robust 2D-3D registration method based on the Projection-Slice Theorem. This theorem gives us a relation between the pre-operative 3D data set and the interventional projection images. Registration is performed by minimizing a translation invariant similarity measure that is applied to the Fourier transforms of the images. The method was tested by performing multiple exhaustive searches on phantom data of the Circle of Willis and on a post-mortem human skull. Validation was performed visually by comparing the test projections to the ones that corresponded to the minimal value of the similarity measure. The Projection-Slice Theorem Based method was shown to be very effective and robust, and provides capture ranges up to 62 degrees. Experiments have shown that the method is capable of retrieving similar results when translations are applied to the projection images.

On Pythagoras Theorem for Products of Spectral Triples

OpenAIRE

D'Andrea, Francesco; Martinetti, Pierre

2013-01-01

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some un...

Virial theorem and hypervirial theorem in a spherical geometry

International Nuclear Information System (INIS)

Li Yan; Chen Jingling; Zhang Fulin

2011-01-01

The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)

Cancellation of spurious arrivals in Green's function extraction and the generalized optical theorem

Science.gov (United States)

Snieder, R.; Van Wijk, K.; Haney, M.; Calvert, R.

2008-01-01

The extraction of the Green's function by cross correlation of waves recorded at two receivers nowadays finds much application. We show that for an arbitrary small scatterer, the cross terms of scattered waves give an unphysical wave with an arrival time that is independent of the source position. This constitutes an apparent inconsistency because theory predicts that such spurious arrivals do not arise, after integration over a complete source aperture. This puzzling inconsistency can be resolved for an arbitrary scatterer by integrating the contribution of all sources in the stationary phase approximation to show that the stationary phase contributions to the source integral cancel the spurious arrival by virtue of the generalized optical theorem. This work constitutes an alternative derivation of this theorem. When the source aperture is incomplete, the spurious arrival is not canceled and could be misinterpreted to be part of the Green's function. We give an example of how spurious arrivals provide information about the medium complementary to that given by the direct and scattered waves; the spurious waves can thus potentially be used to better constrain the medium. ?? 2008 The American Physical Society.

Quantization of edge currents for continuous magnetic operators

CERN Document Server

Kellendonk, J

2003-01-01

For a magnetic Hamiltonian on a half-plane given as the sum of the Landau operator with Dirichlet boundary conditions and a random potential, a quantization theorem for the edge currents is proven. This shows that the concept of edge channels also makes sense in presence of disorder. Moreover, gaussian bounds on the heat kernel and its covariant derivatives are obtained.

Mammographic x-ray unit kilovoltage test tool based on k-edge absorption effect.

Science.gov (United States)

Napolitano, Mary E; Trueblood, Jon H; Hertel, Nolan E; David, George

2002-09-01

A simple tool to determine the peak kilovoltage (kVp) of a mammographic x-ray unit has been designed. Tool design is based on comparing the effect of k-edge discontinuity of the attenuation coefficient for a series of element filters. Compatibility with the mammography accreditation phantom (MAP) to obtain a single quality control film is a second design objective. When the attenuation of a series of sequential elements is studied simultaneously, differences in the absorption characteristics due to the k-edge discontinuities are more evident. Specifically, when the incident photon energy is higher than the k-edge energy of a number of the elements and lower than the remainder, an inflection may be seen in the resulting attenuation data. The maximum energy of the incident photon spectra may be determined based on this inflection point for a series of element filters. Monte Carlo photon transport analysis was used to estimate the photon transmission probabilities for each of the sequential k-edge filter elements. The photon transmission corresponds directly to optical density recorded on mammographic x-ray film. To observe the inflection, the element filters chosen must have k-edge energies that span a range greater than the expected range of the end point energies to be determined. For the design, incident x-ray spectra ranging from 25 to 40 kVp were assumed to be from a molybdenum target. Over this range, the k-edge energy changes by approximately 1.5 keV between sequential elements. For this design 21 elements spanning an energy range from 20 to 50 keV were chosen. Optimum filter element thicknesses were calculated to maximize attenuation differences at the k-edge while maintaining optical densities between 0.10 and 3.00. Calculated relative transmission data show that the kVp could be determined to within +/-1 kV. To obtain experimental data, a phantom was constructed containing 21 different elements placed in an acrylic holder. MAP images were used to determine

Mammographic x-ray unit kilovoltage test tool based on k-edge absorption effect

International Nuclear Information System (INIS)

Napolitano, Mary E.; Trueblood, Jon H.; Hertel, Nolan E.; David, George

2002-01-01

A simple tool to determine the peak kilovoltage (kVp) of a mammographic x-ray unit has been designed. Tool design is based on comparing the effect of k-edge discontinuity of the attenuation coefficient for a series of element filters. Compatibility with the mammography accreditation phantom (MAP) to obtain a single quality control film is a second design objective. When the attenuation of a series of sequential elements is studied simultaneously, differences in the absorption characteristics due to the k-edge discontinuities are more evident. Specifically, when the incident photon energy is higher than the k-edge energy of a number of the elements and lower than the remainder, an inflection may be seen in the resulting attenuation data. The maximum energy of the incident photon spectra may be determined based on this inflection point for a series of element filters. Monte Carlo photon transport analysis was used to estimate the photon transmission probabilities for each of the sequential k-edge filter elements. The photon transmission corresponds directly to optical density recorded on mammographic x-ray film. To observe the inflection, the element filters chosen must have k-edge energies that span a range greater than the expected range of the end point energies to be determined. For the design, incident x-ray spectra ranging from 25 to 40 kVp were assumed to be from a molybdenum target. Over this range, the k-edge energy changes by approximately 1.5 keV between sequential elements. For this design 21 elements spanning an energy range from 20 to 50 keV were chosen. Optimum filter element thicknesses were calculated to maximize attenuation differences at the k-edge while maintaining optical densities between 0.10 and 3.00. Calculated relative transmission data show that the kVp could be determined to within ±1 kV. To obtain experimental data, a phantom was constructed containing 21 different elements placed in an acrylic holder. MAP images were used to determine

Wigner's Symmetry Representation Theorem

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...

Two fixed point theorems on quasi-metric spaces via mw- distances

Energy Technology Data Exchange (ETDEWEB)

Alegre, C.

2017-07-01

In this paper we prove a Banach-type fixed point theorem and a Kannan-type theorem in the setting of quasi-metric spaces using the notion of mw-distance. These theorems generalize some results that have recently appeared in the literature. (Author)

On the Leray-Hirsch Theorem for the Lichnerowicz cohomology

International Nuclear Information System (INIS)

Ait Haddoul, Hassan

2004-03-01

The purpose of this paper is to prove the Leray-Hirsch theorem for the Lichnerowicz; cohomology with respect to basic and vertical closed 1-forms. This is a generalization of the Kfirmeth theorem to fiber bundles. (author)

Radon-Nikodym type theorem for α-completely positive maps

International Nuclear Information System (INIS)

Heo, Jaeseong; Ji, Un Cig

2010-01-01

We introduce a new notion of α-completely positive map on a C*-algebra as a generalization of the notion of completely positive map. Then we study a theorem of the Radon-Nikodym type that there is a one-to-one correspondence between α-completely positive maps and positive operators and, as an application of the Radon-Nikodym type theorem, we give a characterization of pure α-completely positive maps. Finally, we study a covariant version of the Stinespring's theorem for a covariant α-completely positive map (see Theorem 4.3).

Probing single magnon excitations in Sr₂IrO₄ using O K-edge resonant inelastic x-ray scattering.

Science.gov (United States)

Liu, X; Dean, M P M; Liu, J; Chiuzbăian, S G; Jaouen, N; Nicolaou, A; Yin, W G; Rayan Serrao, C; Ramesh, R; Ding, H; Hill, J P

2015-05-27

Resonant inelastic x-ray scattering (RIXS) at the L-edge of transition metal elements is now commonly used to probe single magnon excitations. Here we show that single magnon excitations can also be measured with RIXS at the K-edge of the surrounding ligand atoms when the center heavy metal elements have strong spin-orbit coupling. This is demonstrated with oxygen K-edge RIXS experiments on the perovskite Sr2IrO4, where low energy peaks from single magnon excitations were observed. This new application of RIXS has excellent potential to be applied to a wide range of magnetic systems based on heavy elements, for which the L-edge RIXS energy resolution in the hard x-ray region is usually poor.

Observation of Phase Objects by Using an X-ray Microscope with a Foucault Knife-Edge

Science.gov (United States)

Watanabe, N.; Sasaya, T.; Imai, Y.; Iwata, S.; Zama, K.; Aoki, S.

2011-09-01

An x-ray microscope with a zone plate was assembled at the synchrotron radiation source of BL3C, Photon Factory. A Foucault knife-edge was set at the back focal plate of the objective zone plate and phase retrieval was tested by scanning the knife-edge. A preliminary result shows that scanning the knife-edge during exposure was effective for phase retrieval. Phase-contrast tomography was investigated using differential projection images calculated from two Schlieren images with the oppositely oriented knife-edges. Fairly good reconstruction images of polystyrene beads and spores could be obtained.

Observation of Phase Objects by Using an X-ray Microscope with a Foucault Knife-Edge

International Nuclear Information System (INIS)

Watanabe, N.; Sasaya, T.; Imai, Y.; Iwata, S.; Zama, K.; Aoki, S.

2011-01-01

An x-ray microscope with a zone plate was assembled at the synchrotron radiation source of BL3C, Photon Factory. A Foucault knife-edge was set at the back focal plate of the objective zone plate and phase retrieval was tested by scanning the knife-edge. A preliminary result shows that scanning the knife-edge during exposure was effective for phase retrieval. Phase-contrast tomography was investigated using differential projection images calculated from two Schlieren images with the oppositely oriented knife-edges. Fairly good reconstruction images of polystyrene beads and spores could be obtained.

A General Representation Theorem for Integrated Vector Autoregressive Processes

DEFF Research Database (Denmark)

Franchi, Massimo

We study the algebraic structure of an I(d) vector autoregressive process, where d is restricted to be an integer. This is useful to characterize its polynomial cointegrating relations and its moving average representation, that is to prove a version of the Granger representation theorem valid...

Fixed-point theorems for families of weakly non-expansive maps

Science.gov (United States)

Mai, Jie-Hua; Liu, Xin-He

2007-10-01

In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.

On the Riesz representation theorem and integral operators ...

African Journals Online (AJOL)

We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions. Keywords: Vector integral, integral operators, operator ...

Multi-energy soft-x-ray technique for impurity transport measurements in the fusion plasma edge

International Nuclear Information System (INIS)

Clayton, D J; Tritz, K; Stutman, D; Finkenthal, M; Kumar, D; Kaye, S M; LeBlanc, B P; Paul, S; Sabbagh, S A

2012-01-01

A new diagnostic technique was developed to produce high-resolution impurity transport measurements of the steep-gradient edge of fusion plasmas. Perturbative impurity transport measurements were performed for the first time in the NSTX plasma edge (r/a ∼ 0.6 to the SOL) with short neon gas puffs, and the resulting line and continuum emission was measured with the new edge multi-energy soft-x-ray (ME-SXR) diagnostic. Neon transport is modeled with the radial impurity transport code STRAHL and the resulting x-ray emission is computed using the ADAS atomic database. The radial transport coefficient profiles D(r) and v(r), and the particle flux from the gas puff Φ(t), are the free parameters in this model and are varied to find the best fit to experimental x-ray emissivity measurements, with bolometry used to constrain the impurity source. Initial experiments were successful and results were consistent with previous measurements of core impurity transport and neoclassical transport calculations. New diagnostic tools will be implemented on NSTX-U to further improve these transport measurements. (paper)

Arsenic K-edge X-ray absorption near-edge spectroscopy to determine oxidation states of arsenic of a coastal aquifer–aquitard system

International Nuclear Information System (INIS)

Wang, Ya; Jiao, Jiu Jimmy; Zhu, Sanyuan; Li, Yiliang

2013-01-01

Determination of oxidation states of solid-phase arsenic in bulk sediments is a valuable step in the evaluation of its bioavailability and environmental fate in deposits, but is difficult when the sediments have low arsenic contents and heterogeneous distribution of arsenic species. As K-edge X-ray absorption near-edge spectroscopy (XANES) was used to determine quantitatively the oxidation states of arsenic in sediments collected from different depths of boreholes in the Pearl River Delta, China, where the highest aquatic arsenic concentration is 161.4 μg/L, but the highest solid arsenic content only 39.6 mg/kg. The results demonstrated that XANES is efficient in determining arsenic oxidation states of the sediments with low arsenic contents and multiple arsenic species. The study on the high-resolution vertical variations of arsenic oxidation states also indicated that these states are influenced strongly by groundwater activities. With the help of geochemical data, solid arsenic speciation, toxicity and availability were further discussed. -- Highlights: •XANES is efficient in determining arsenic oxidation states of the bulk sediments. •Distribution of arsenic oxidation states is consistent with geochemical conditions. •Arsenic oxidation states are influenced strongly by groundwater activities. -- As K-edge X-ray absorption near-edge spectroscopy is efficient in determining arsenic oxidation states of the bulk sediments with low arsenic contents and heterogeneous distribution of arsenic species

Field demonstration of a portable, X-ray, K-edge heavy-metal detector

International Nuclear Information System (INIS)

Jensen, T.; Aljundi, T.; Whitmore, C.; Zhong, H.; Gray, J.N.

1997-01-01

Under the Characterization, Monitoring, and Sensor Technology Crosscutting Program, the authors have designed and built a K-edge heavy metal detector that measures the level of heavy metal contamination inside closed containers in a nondestructive, non-invasive way. The device employs a volumetric technique that takes advantage of the X-ray absorption characteristics of heavy elements, and is most suitable for characterization of contamination inside pipes, processing equipment, closed containers, and soil samples. The K-edge detector is a fast, efficient, and cost-effective in situ characterization tool. More importantly, this device will enhance personnel safety while characterizing radioactive and toxic waste. The prototype K-edge system was operated at the Materials and Chemistry Laboratory User Facility at the Oak Ridge K-25 Site during February 1997. Uranium contaminated pipes and valves from a UF 6 feed facility were inspected using the K-edge technique as well as a baseline nondestructive assay method. Operation of the K-edge detector was demonstrated for uranium contamination ranging from 10 to 6,000 mg/cm 2 and results from the K-edge measurements were found to agree very well with nondestructive assay measurements

The Fluctuation Theorem and Dissipation Theorem for Poiseuille Flow

International Nuclear Information System (INIS)

Brookes, Sarah J; Reid, James C; Evans, Denis J; Searles, Debra J

2011-01-01

The fluctuation theorem and the dissipation theorem provide relationships to describe nonequilibrium systems arbitrarily far from, or close to equilibrium. They both rely on definition of a central property, the dissipation function. In this manuscript we apply these theorems to examine a boundary thermostatted system undergoing Poiseuille flow. The relationships are verified computationally and show that the dissipation theorem is potentially useful for study of boundary thermostatted systems consisting of complex molecules undergoing flow in the nonlinear regime.

Green's Theorem for Sign Data

OpenAIRE

Houston, Louis M.

2012-01-01

Sign data are the signs of signal added to noise. It is well known that a constant signal can be recovered from sign data. In this paper, we show that an integral over variant signal can be recovered from an integral over sign data based on the variant signal. We refer to this as a generalized sign data average. We use this result to derive a Green's theorem for sign data. Green's theorem is important to various seismic processing methods, including seismic migration. Results in this paper ge...

Fully Quantum Fluctuation Theorems

Science.gov (United States)

Åberg, Johan

2018-02-01

Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.

Identifying anthropogenic uranium compounds using soft X-ray near-edge absorption spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Ward, Jesse D.; Bowden, Mark; Tom Resch, C.; Eiden, Gregory C.; Pemmaraju, C. D.; Prendergast, David; Duffin, Andrew M.

2017-01-01

Uranium ores mined for industrial use are typically acid-leached to produce yellowcake and then converted into uranium halides for enrichment and purification. These anthropogenic chemical forms of uranium are distinct from their mineral counterparts. The purpose of this study is to use soft X-ray absorption spectroscopy to characterize several common anthropogenic uranium compounds important to the nuclear fuel cycle. Non-destructive chemical analyses of these compounds is important for process and environmental monitoring and X-ray absorption techniques have several advantages in this regard, including element-specificity, chemical sensitivity, and high spectral resolution. Oxygen K-edge spectra were collected for uranyl nitrate, uranyl fluoride, and uranyl chloride, and fluorine K-edge spectra were collected for uranyl fluoride and uranium tetrafluoride. Interpretation of the data is aided by comparisons to calculated spectra. These compounds have unique spectral signatures that can be used to identify unknown samples.

Silicon K-edge XANES spectra of silicate minerals

Science.gov (United States)

Li, Dien; Bancroft, G. M.; Fleet, M. E.; Feng, X. H.

1995-03-01

Silicon K-edge x-ray absorption near-edge structure (XANES) spectra of a selection of silicate and aluminosilicate minerals have been measured using synchrotron radiation (SR). The spectra are qualitatively interpreted based on MO calculation of the tetrahedral SiO{4/4-}cluster. The Si K-edge generally shifts to higher energy with increased polymerization of silicates by about 1.3 eV, but with considerable overlap for silicates of different polymerization types. The substitution of Al for Si shifts the Si K-edge to lower energy. The chemical shift of Si K-edge is also sensitive to cations in more distant atom shells; for example, the Si K-edge shifts to lower energy with the substitution of Al for Mg in octahedral sites. The shifts of the Si K-edge show weak correlation with average Si-O bond distance (dSi-O), Si-O bond valence (sSi-O) and distortion of SiO4 tetrahedra, due to the crystal structure complexity of silicate minerals and multiple factors effecting the x-ray absorption processes.

Nitrogen K-edge X-ray absorption near edge structure (XANES) spectra of purine-containing nucleotides in aqueous solution

Energy Technology Data Exchange (ETDEWEB)

Shimada, Hiroyuki; Fukao, Taishi; Minami, Hirotake; Ukai, Masatoshi [Department of Applied Physics, Tokyo University of Agriculture and Technology, Koganei-shi, Tokyo 184-8588 (Japan); Fujii, Kentaro; Yokoya, Akinari [Advanced Science Research Center, Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki 319-1195 (Japan); Fukuda, Yoshihiro; Saitoh, Yuji [Synchrotron Radiation Research Center, Japan Atomic Energy Agency, Sayo-gun, Hyougo 679-5148 (Japan)

2014-08-07

The N K-edge X-ray absorption near edge structure (XANES) spectra of the purine-containing nucleotide, guanosine 5{sup ′}-monophosphate (GMP), in aqueous solution are measured under various pH conditions. The spectra show characteristic peaks, which originate from resonant excitations of N 1s electrons to π* orbitals inside the guanine moiety of GMP. The relative intensities of these peaks depend on the pH values of the solution. The pH dependence is explained by the core-level shift of N atoms at specific sites caused by protonation and deprotonation. The experimental spectra are compared with theoretical spectra calculated by using density functional theory for GMP and the other purine-containing nucleotides, adenosine 5{sup ′}-monophosphate, and adenosine 5{sup ′}-triphosphate. The N K-edge XANES spectra for all of these nucleotides are classified by the numbers of N atoms with particular chemical bonding characteristics in the purine moiety.

Unified quantum no-go theorems and transforming of quantum pure states in a restricted set

Science.gov (United States)

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

2017-12-01

The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.

A note on the homomorphism theorem for hemirings

Directory of Open Access Journals (Sweden)

D. M. Olson

1978-01-01

Full Text Available The fundamental homomorphism theorem for rings is not generally applicable in hemiring theory. In this paper, we show that for the class of N-homomorphism of hemirings the fundamental theorem is valid. In addition, the concept of N-homomorphism is used to prove that every hereditarily semisubtractive hemiring is of type (K.

An extension of Brosowski-Meinardus theorem on invariant approximation

International Nuclear Information System (INIS)

Liaqat Ali Khan; Abdul Rahim Khan.

1991-07-01

We obtain a generalization of a fixed point theorem of Dotson for non-expansive mappings on star-shaped sets and then use it to prove a unified Brosowski-Meinardus theorem on invariant approximation in the setting of p-normed linear spaces. (author). 13 refs

On Pythagoras Theorem for Products of Spectral Triples

Science.gov (United States)

D'Andrea, Francesco; Martinetti, Pierre

2013-05-01

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.

Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

Science.gov (United States)

Evans, Denis J.; Searles, Debra J.; Mittag, Emil

2001-05-01

For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.

Action-angle variables and a KAM theorem for b-Poisson manifolds

OpenAIRE

Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey

2015-01-01

In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [14] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved.

Poncelet's theorem

CERN Document Server

Flatto, Leopold

2009-01-01

Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. The theorem is of great depth in that it relates to a large and diverse body of mathematics. There are several proofs of the theorem, none of which is elementary. A particularly attractive feature of the theorem, which is easily understood but difficult to prove, is that it serves as a prism through which one can learn and appreciate a lot of beautiful mathematics. This book stresses the modern appro

Optimizing Transition Edge Sensors for High-Resolution X-ray Spectroscopy

International Nuclear Information System (INIS)

Saab, Tarek; Bandler, Simon R.; Boyce, Kevin; Chervenak, James A.; Figueroa-Feliciano, Enectali; Iyomoto, Naoko; Kelley, Richard L.; Kilbourne, Caroline A.; Porter, Frederick S.; Sadleir, John E.

2006-01-01

Transition Edge Sensors (TES) have found applications as astronomical detectors ranging from the microwave to the gamma ray energy bands. Each energy band, however, imposes a different set of requirements on the TES such as energy and timing resolution, focal plane coverage, and the mechanisms by which the signal is coupled to the detector. This paper focuses on the development of TESs optimized for the 0.1-10 keV energy range at the NASA Goddard Space Flight Center. Such detectors are suitable candidates for some of the upcoming X-ray observatories such as NeXT and Constellation-X. Ongoing efforts at producing, characterizing, and modeling such devices, as well as the latest results, are discussed

A new proof of the positive energy theorem

International Nuclear Information System (INIS)

Witten, E.

1981-01-01

A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by Schoen and Yau). The relevance of these results to the stability of Minkowski space is discussed. (orig.)

Four theorems on the psychometric function.

Science.gov (United States)

May, Keith A; Solomon, Joshua A

2013-01-01

In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus

Four theorems on the psychometric function.

Directory of Open Access Journals (Sweden)

Keith A May

Full Text Available In a 2-alternative forced-choice (2AFC discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise x β(Transducer, where β(Noise is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer depends on the transducer. We derive general expressions for β(Noise and β(Transducer, from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx(b, β ≈ β(Noise x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is

K- and L-edge X-ray Absorption Spectroscopy (XAS) and Resonant Inelastic X-ray Scattering (RIXS) Determination of Differential Orbital Covalency (DOC) of Transition Metal Sites.

Science.gov (United States)

Baker, Michael L; Mara, Michael W; Yan, James J; Hodgson, Keith O; Hedman, Britt; Solomon, Edward I

2017-08-15

Continual advancements in the development of synchrotron radiation sources have resulted in X-ray based spectroscopic techniques capable of probing the electronic and structural properties of numerous systems. This review gives an overview of the application of metal K-edge and L-edge X-ray absorption spectroscopy (XAS), as well as K resonant inelastic X-ray scattering (RIXS), to the study of electronic structure in transition metal sites with emphasis on experimentally quantifying 3d orbital covalency. The specific sensitivities of K-edge XAS, L-edge XAS, and RIXS are discussed emphasizing the complementary nature of the methods. L-edge XAS and RIXS are sensitive to mixing between 3d orbitals and ligand valence orbitals, and to the differential orbital covalency (DOC), that is, the difference in the covalencies for different symmetry sets of the d orbitals. Both L-edge XAS and RIXS are highly sensitive to and enable separation of and donor bonding and back bonding contributions to bonding. Applying ligand field multiplet simulations, including charge transfer via valence bond configuration interactions, DOC can be obtained for direct comparison with density functional theory calculations and to understand chemical trends. The application of RIXS as a probe of frontier molecular orbitals in a heme enzyme demonstrates the potential of this method for the study of metal sites in highly covalent coordination sites in bioinorganic chemistry.

Absorber Materials for Transition-Edge Sensor X-ray Microcalorimeters

Science.gov (United States)

Brown, Ari-David; Bandler, Simon; Brekosky, Regis; Chervenak, James; Figueroa-Feliciano, Enectali; Finkbeiner, Fred; Sadleir, Jack; Iyomoto, Naoko; Kelley, Richard; Kilbourne, Caroline;

Attractive Hubbard model with disorder and the generalized Anderson theorem

International Nuclear Information System (INIS)

Kuchinskii, E. Z.; Kuleeva, N. A.; Sadovskii, M. V.

2015-01-01

Using the generalized DMFT+Σ approach, we study the influence of disorder on single-particle properties of the normal phase and the superconducting transition temperature in the attractive Hubbard model. A wide range of attractive potentials U is studied, from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong-coupling region, where the superconducting transition is due to Bose-Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures much higher than the superconducting transition temperature. We study two typical models of the conduction band with semi-elliptic and flat densities of states, respectively appropriate for three-dimensional and two-dimensional systems. For the semi-elliptic density of states, the disorder influence on all single-particle properties (e.g., density of states) is universal for an arbitrary strength of electronic correlations and disorder and is due to only the general disorder widening of the conduction band. In the case of a flat density of states, universality is absent in the general case, but still the disorder influence is mainly due to band widening, and the universal behavior is restored for large enough disorder. Using the combination of DMFT+Σ and Nozieres-Schmitt-Rink approximations, we study the disorder influence on the superconducting transition temperature T c for a range of characteristic values of U and disorder, including the BCS-BEC crossover region and the limit of strong-coupling. Disorder can either suppress T c (in the weak-coupling region) or significantly increase T c (in the strong-coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of the superconducting critical temperature are essentially due to only the general disorder widening of the conduction band

Uniqueness theorems for differential pencils with eigenparameter boundary conditions and transmission conditions

Science.gov (United States)

Yang, Chuan-Fu

Inverse spectral problems are considered for differential pencils with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions. We give formulations of the associated inverse problems such as Titchmarsh-Weyl theorem, Hochstadt-Lieberman theorem and Mochizuki-Trooshin theorem, and prove corresponding uniqueness theorems. The obtained results are generalizations of the similar results for the classical Sturm-Liouville operator on a finite interval.

Level comparison theorems and supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Baumgartner, B.; Grosse, H.

1986-01-01

The sign of the Laplacian of the spherical symmetric potential determines the order of energy levels with the same principal Coulomb quantum number. This recently derived theorem has been generalized, extended and applied to various situations in particle, nuclear and atomic physics. Besides a comparison theorem the essential step was the use of supersymmetric quantum mechanics. Recently worked out applications of supersymmetric quantum mechanics to index problems of Dirac operators are mentioned. (Author)

Measurement of mass attenuation coefficients around the K absorption edge by parametric X-rays

International Nuclear Information System (INIS)

Tamura, Masaya; Akimoto, Tadashi; Aoki, Yohei; Ikeda, Jiro; Sato, Koichi; Fujita, Fumiyuki; Homma, Akira; Sawamura, Teruko; Narita, Masakuni

2002-01-01

When electrons at relativistic velocities pass through a crystal plate, such as silicon, photons are emitted around the Bragg angle for X-ray diffraction. This phenomenon is called parametric X-ray radiation (PXR). The monochromaticity and directivity of PXR are adequate and the energy can be changed continuously by rotating the crystal. This study measured the mass attenuation coefficient around the K-shell absorption edge of Nb, Zr and Mo as a PXR application of monochromatic hard X-ray radiation sources

Measurement of mass attenuation coefficients around the K absorption edge by parametric X-rays

CERN Document Server

Tamura, M; Aoki, Y; Ikeda, J; Sato, K; Fujita, F; Homma, A; Sawamura, T; Narita, M

2002-01-01

When electrons at relativistic velocities pass through a crystal plate, such as silicon, photons are emitted around the Bragg angle for X-ray diffraction. This phenomenon is called parametric X-ray radiation (PXR). The monochromaticity and directivity of PXR are adequate and the energy can be changed continuously by rotating the crystal. This study measured the mass attenuation coefficient around the K-shell absorption edge of Nb, Zr and Mo as a PXR application of monochromatic hard X-ray radiation sources.

Study of non-validity of mixture rule near K-absorption edges by X-ray spectrometric technique

International Nuclear Information System (INIS)

Sharanabasappa; Chitralekha, A.; Kerur, B.R.; Anilkumar, S.

2012-01-01

X-ray spectrometric technique has been described to determine the X-ray mass attenuation coefficient, μ/ρ, of X-rays employing HPGe X-ray detector and radioactive sources. The photon intensity is measured by gating the channel of the spectrometer at FWHM/photo peak. Using the technique the 'best value' values of μ/ρ were obtained for those thicknesses which lie in the transmission (T) range 0.5 ≥ T ≥ 0.02. Total attenuation cross sections for other elements and lead compounds were measured at photon energies from 17 to 88 keV to study the Bragg's additivity law near the absorption edge of the lead. The measured values of mass attenuation coefficient values are compared with theoretical values obtained using Winxcom (programme). This study suggests that measured mass attenuation coefficient values at and near absorption edges differ from the theoretical value by about 17-23%. (author)

Fabrication of Transition Edge Sensor Microcalorimeters for X-Ray Focal Planes

Science.gov (United States)

Chervenak, James A.; Adams, Joseph S.; Audley, Heather; Bandler, Simon R.; Betancourt-Martinez, Gabriele; Eckart, Megan E.; Finkbeiner, Fred M.; Kelley, Richard L.; Kilbourne, Caroline; Lee, Sang Jun;

Detecting edges in the X-ray surface brightness of galaxy clusters

Science.gov (United States)

Sanders, J. S.; Fabian, A. C.; Russell, H. R.; Walker, S. A.; Blundell, K. M.

2016-08-01

The effects of many physical processes in the intracluster medium of galaxy clusters imprint themselves in X-ray surface brightness images. It is therefore important to choose optimal methods for extracting information from and enhancing the interpretability of such images. We describe in detail a gradient filtering edge detection method that we previously applied to images of the Centaurus cluster of galaxies. The Gaussian gradient filter measures the gradient in the surface brightness distribution on particular spatial scales. We apply this filter on different scales to Chandra X-ray observatory images of two clusters with active galactic nucleus feedback, the Perseus cluster and M 87, and a merging system, A 3667. By combining filtered images on different scales using radial filters spectacular images of the edges in a cluster are produced. We describe how to assess the significance of features in filtered images. We find the gradient filtering technique to have significant advantages for detecting many kinds of features compared to other analysis techniques, such as unsharp masking. Filtering cluster images in this way in a hard energy band allows shocks to be detected.

Integrable equations, addition theorems, and the Riemann-Schottky problem

International Nuclear Information System (INIS)

Buchstaber, Viktor M; Krichever, I M

2006-01-01

The classical Weierstrass theorem claims that, among the analytic functions, the only functions admitting an algebraic addition theorem are the elliptic functions and their degenerations. This survey is devoted to far-reaching generalizations of this result that are motivated by the theory of integrable systems. The authors discovered a strong form of the addition theorem for theta functions of Jacobian varieties, and this form led to new approaches to known problems in the geometry of Abelian varieties. It is shown that strong forms of addition theorems arise naturally in the theory of the so-called trilinear functional equations. Diverse aspects of the approaches suggested here are discussed, and some important open problems are formulated.

A Maximal Element Theorem in FWC-Spaces and Its Applications

Science.gov (United States)

Hu, Qingwen; Miao, Yulin

2014-01-01

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672

Study of the L2,3 edges of 3d transition metals by X-ray absorption spectroscopy

International Nuclear Information System (INIS)

Akguel, G.; Aksoy, F.; Bozduman, A.; Ozkendir, O.M.; Ufuktepe, Y.; Luening, J.

2008-01-01

In the soft X-rays energy region, near edge X-ray absorption fine structure (NEXAFS) spectra are generally recorded by monitoring yield signals of secondary particles. These secondary particles, electrons or fluorescence photons, follow from the decay of the core hole excited in the primary absorption process. In general the yield signals are, to a good approximation, proportional to the absorption coefficient. However, in several applications it would be desirable to measure the absorption coefficient quantitatively. To derive the absorption coefficient quantitatively from a yield spectrum, one needs to know the escape depth of the emitted electrons (λ e ) of the applied yield technique in the material of interest. Since this quantity is difficult to calculate, it is unknown for most materials. In this paper we present the first results of our systematic investigation of the total electron-yield (TEY) escape depth of the 3d transition metals (Fe, Co and Cu). In addition our results gave important information on the variation of the TEY escape depth with the filling of the 3d band

Study of the L2,3 Edges of 3d Transition Metals By X-Ray Absorption Spectroscopy

International Nuclear Information System (INIS)

Akgul, G.; Aksoy, F.; Bozduman, A.; Ozkendir, O.M.; Ufuktepe, Y.; Luning, J.

2008-01-01

In the soft X-rays energy region, near edge X-ray absorption fine structure (NEXAFS) spectra are generally recorded by monitoring yield signals of secondary particles. These secondary particles, electrons or fluorescence photons, follow from the decay of the core hole excited in the primary absorption process. In general the yield signals are, to a good approximation, proportional to the absorption coefficient. However, in several applications it would be desirable to measure the absorption coefficient quantitatively. To derive the absorption coefficient quantitatively from a yield spectrum, one needs to know the escape depth of the emitted electrons (λ e ) of the applied yield technique in the material of interest. Since this quantity is difficult to calculate, it is unknown for most materials. In this paper we present the first results of our systematic investigation of the total electron-yield (TEY) escape depth of the 3d transition metals (Fe, Co and Cu). In addition our results gave important information on the variation of the TEY escape depth with the filling of the 3d band.

High-resolution Al L2,3-edge x-ray absorption near edge structure spectra of Al-containing crystals and glasses: coordination number and bonding information from edge components

International Nuclear Information System (INIS)

Weigel, C; Calas, G; Cormier, L; Galoisy, L; Henderson, G S

2008-01-01

High-resolution Al L 2,3 -edge x-ray absorption near edge structure (XANES) spectra have been measured in selected materials containing aluminium in 4-, 5- and 6-coordination. A shift of 1.5 eV is observed between the onset of [4] Al and [6] Al L 2,3 -edge XANES, in agreement with the magnitude of the shift observed at the Al K-edge. The differences in the position and shape of low-energy components of Al L 2,3 -edge XANES spectra provide a unique fingerprint of the geometry of the Al site and of the nature of Al-O chemical bond. The high resolution allows the calculation of electronic parameters such as the spin-orbit coupling and exchange energy using intermediate coupling theory. The electron-hole exchange energy decreases in tetrahedral as compared to octahedral symmetry, in relation with the increased screening of the core hole in the former. Al L 2,3 -edge XANES spectra confirm a major structural difference between glassy and crystalline NaAlSi 2 O 6 , with Al in 4- and 6-coordination, respectively, Al coordination remaining unchanged in NaAl 1-x Fe x Si 2 O 6 glasses, as Fe is substituted for Al

Generalized virial theorem for the Liénard-type systems

Indian Academy of Sciences (India)

for second-order differential equations of the Liénard type. The explicit ... Keywords. Virial theorem; Liénard-type equation; Jacobi last multiplier; symplectic form; Banach manifold. ..... 3.1 Application to Gierer–Meinhardt system ..... financial support by the research projects MTMÐ2012/33575 (MINECO, Madrid) and.

The X-ray photoabsorption spectrum of potassium near the K-edge

International Nuclear Information System (INIS)

Azuma, Y.; Berry, H.G.; Cowan, P.L.; Gemmell, D.S.; LeBrun, T.

1996-01-01

The authors have used a heat-pipe target in an X-ray beam to obtain photoabsorption spectra of potassium at the K- and KM-edges, in the photon energy range 3,600 to 3,650 eV. Preliminary identifications of most of the peaks observed are made using Dirac Hartree-Fock calculations. They compare these results with those obtained previously in closed-shell rare gas absorption spectra

Probing single magnon excitations in Sr2IrO4 using O K-edge resonant inelastic x-ray scattering

International Nuclear Information System (INIS)

Liu, X; Ding, H; Dean, M P M; Yin, W G; Hill, J P; Liu, J; Ramesh, R; Chiuzbăian, S G; Jaouen, N; Nicolaou, A; Serrao, C Rayan

2015-01-01

Resonant inelastic x-ray scattering (RIXS) at the L-edge of transition metal elements is now commonly used to probe single magnon excitations. Here we show that single magnon excitations can also be measured with RIXS at the K-edge of the surrounding ligand atoms when the center heavy metal elements have strong spin–orbit coupling. This is demonstrated with oxygen K-edge RIXS experiments on the perovskite Sr 2 IrO 4 , where low energy peaks from single magnon excitations were observed. This new application of RIXS has excellent potential to be applied to a wide range of magnetic systems based on heavy elements, for which the L-edge RIXS energy resolution in the hard x-ray region is usually poor. (fast track communication)

More on Weinberg's no-go theorem in quantum gravity

Science.gov (United States)

Nagahama, Munehiro; Oda, Ichiro

2018-05-01

We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.

Chemical shift of Mn and Cr K-edges in X-ray absorption

Indian Academy of Sciences (India)

... Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Bulletin of Materials Science; Volume 36; Issue 6. Chemical shift of Mn and Cr K-edges in X-ray absorption spectroscopy with synchrotron radiation. D Joseph A K Yadav S N Jha D Bhattacharyya. Volume 36 Issue 6 November 2013 pp ...

Applications of square-related theorems

Science.gov (United States)

Srinivasan, V. K.

2014-04-01

The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.

Microstructure Analysis of Bismuth Absorbers for Transition-Edge Sensor X-ray Microcalorimeters

Science.gov (United States)

Yan, Daikang; Divan, Ralu; Gades, Lisa M.; Kenesei, Peter; Madden, Timothy J.; Miceli, Antonino; Park, Jun-Sang; Patel, Umeshkumar M.; Quaranta, Orlando; Sharma, Hemant; Bennett, Douglas A.; Doriese, William B.; Fowler, Joseph W.; Gard, Johnathon D.; Hays-Wehle, James P.; Morgan, Kelsey M.; Schmidt, Daniel R.; Swetz, Daniel S.; Ullom, Joel N.

2018-03-01

Given its large X-ray stopping power and low specific heat capacity, bismuth (Bi) is a promising absorber material for X-ray microcalorimeters and has been used with transition-edge sensors (TESs) in the past. However, distinct X-ray spectral features have been observed in TESs with Bi absorbers deposited with different techniques. Evaporated Bi absorbers are widely reported to have non-Gaussian low-energy tails, while electroplated ones do not show this feature. In this study, we fabricated Bi absorbers with these two methods and performed microstructure analysis using scanning electron microscopy and X-ray diffraction microscopy. The two types of material showed the same crystallographic structure, but the grain size of the electroplated Bi was about 40 times larger than that of the evaporated Bi. This distinction in grain size is likely to be the cause of their different spectral responses.

X-ray K-edge analysis of drain lines in Wilhelm Hall, Ames Laboratory

International Nuclear Information System (INIS)

Jensen, T.; Whitmore, C.; Iowa State Univ., Ames, IA

1999-01-01

From August 12--27, 1998 X-ray K-edge measurements were made on drain lines in seven rooms in Wilhelm Hall, Ames Laboratory. The purpose of these measurements was to determine the extent of thorium (and other heavy metal) contamination inside these pipes. The K-edge method is a noninvasive inspection technique that can provide accurate quantification of heavy metal contamination interior to an object. Of the seven drain lines inspected, one was found to have no significant contamination, three showed significant thorium deposits, two showed mercury contamination, and one line was found to contain mercury, thorium and uranium. The K-edge measurements were found to be consistent with readings from hand-held survey meters, and provided much greater detail on the location and amount of heavy metal contamination

Generalization of the variational principle and the Hohenberg and Kohn theorems for excited states of Fermion systems

Energy Technology Data Exchange (ETDEWEB)

Gonis, A., E-mail: gonis@comcast.net

2017-01-05

Through the entanglement of a collection of K non-interacting replicas of a system of N interacting Fermions, and making use of the properties of reduced density matrices the variational principle and the theorems of Hohenberg and Kohn are generalized to excited states. The generalization of the variational principle makes use of the natural orbitals of an N-particle density matrix describing the state of lowest energy of the entangled state. The extension of the theorems of Hohenberg and Kohn is based on the ground-state formulation of density functional theory but with a new interpretation of the concept of a ground state: It is the state of lowest energy of a system of KN Fermions that is described in terms of the excited states of the N-particle interacting system. This straightforward implementation of the line of reasoning of ground-state density functional theory to a new domain leads to a unique and logically valid extension of the theory to excited states that allows the systematic treatment of all states in the spectrum of the Hamiltonian of an interacting system. - Highlights: • Use of entanglement in connection with the properties of density matrices. • An anti-symmetric entangled state of order KN expressed in terms of excited states of an interacting N-particle system.

Several properties of generalized multivariate integrals and theorems of the du Bois-Reymond type for Haar series

International Nuclear Information System (INIS)

Plotnikov, M G

2007-01-01

Several properties of generalized multivariate integrals are considered. In the two-dimensional case the consistency of the regular Perron integral is proved, as well as the consistency of a generalized integral solving the problem of the recovery of the coefficients of double Haar series in a certain class. Several generalizations of Skvortsov's well-known theorem are obtained as consequences, for instance, the following result: if a double Haar series converges for some ρ element of (0,1/2] ρ-regularly everywhere in the unit square to a finite function that is Perron-integrable in the ρ-regular sense, then the series in question is the Fourier-Perron series of its sum. Bibliography: 20 titles.

Kolmogorov-Arnold-Moser Theorem

Indian Academy of Sciences (India)

system (not necessarily the 2-body system). Kolmogorov was the first to provide a solution to the above general problem in a theorem formulated in 1954 (see Suggested. Reading). However, he provided only an outline of the proof. The actual proof (with all the details) turned to be quite difficult and was provided by Arnold ...

The origin of luminescence from di[4-(4-diphenylaminophenyl)phenyl]sulfone (DAPSF), a blue light emitter: an X-ray excited optical luminescence (XEOL) and X-ray absorption near edge structure (XANES) study.

Science.gov (United States)

Zhang, Duo; Zhang, Hui; Zhang, Xiaohong; Sham, Tsun-Kong; Hu, Yongfeng; Sun, Xuhui

2016-03-07

The electronic structure and optical properties of di[4-(4-diphenylaminophenyl)phenyl]sulfone (denoted as DAPSF), a highly efficient fluorophor, have been investigated using X-ray excited optical luminescence (XEOL) and X-ray absorption near edge structure (XANES) spectroscopy at excitation energies across the C, N, O K-edges and the sulfur K-edge. The results indicate that the blue luminescence is mainly related to the sulfur functional group.

Fixed point theorems in spaces and -trees

Directory of Open Access Journals (Sweden)

Kirk WA

2004-01-01

Full Text Available We show that if is a bounded open set in a complete space , and if is nonexpansive, then always has a fixed point if there exists such that for all . It is also shown that if is a geodesically bounded closed convex subset of a complete -tree with , and if is a continuous mapping for which for some and all , then has a fixed point. It is also noted that a geodesically bounded complete -tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.

X-ray K-absorption edge of zirconium in some perovskite type zirconates

Energy Technology Data Exchange (ETDEWEB)

Chougule, B K; Patil, R N [Shivaji Univ., Kolhapur (India). Dept. of Physics

1979-01-01

The chemical shifts in the X-ray K-absorption edges of zirconium in the zirconates of calcium, strontium, barium and lead and zirconium oxide have been investigated employing a 400 mm bent crystal X-ray spectrograph. It has been found that the discontinuity shifts towards the high energy side with respect to that in the pure metal and that the chemical shift depends upon the size of the next nearest cation. The larger the size of the cation, smaller is the chemical shift. Dependence of the shift on the crystal structure and the packing factor of the perovskite is also reported.

Fermi-edge singularity and the functional renormalization group

Science.gov (United States)

Kugler, Fabian B.; von Delft, Jan

2018-05-01

We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two-particle-irreducible, multi-channel Hubbard–Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the x-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the x-ray-edge singularity and does not generalize.

Microanalysis of iron oxidation state in iron oxides using X Ray Absorption Near Edge Structure (XANES)

Science.gov (United States)

Sutton, S. R.; Delaney, J.; Bajt, S.; Rivers, M. L.; Smith, J. V.

1993-01-01

An exploratory application of x ray absorption near edge structure (XANES) analysis using the synchrotron x ray microprobe was undertaken to obtain Fe XANES spectra on individual sub-millimeter grains in conventional polished sections. The experiments concentrated on determinations of Fe valence in a suite of iron oxide minerals for which independent estimates of the iron speciation could be made by electron microprobe analysis and x ray diffraction.

Restriction Theorem for Principal bundles in Arbitrary Characteristic

DEFF Research Database (Denmark)

Gurjar, Sudarshan

2015-01-01

The aim of this paper is to prove two basic restriction theorem for principal bundles on smooth projective varieties in arbitrary characteristic generalizing the analogues theorems of Mehta-Ramanathan for vector bundles. More precisely, let G be a reductive algebraic group over an algebraically...... closed field k and let X be a smooth, projective variety over k together with a very ample line bundle O(1). The main result of the paper is that if E is a semistable (resp. stable) principal G-bundle on X w.r.t O(1), then the restriction of E to a general, high multi-degree, complete-intersection curve...

Fueter's theorem and its generalizations in Dunkl-Clifford analysis

International Nuclear Information System (INIS)

Fei Minggang; Cerejeiras, Paula; Kaehler, Uwe

2009-01-01

In this paper, we give a construction of Dunkl monogenic and Dunkl harmonic functions starting from holomorphic functions in the plane. This construction has the advantage of not needing Dunkl's intertwining operator or Dunkl spherical harmonics. To this end we study Vekua-type systems and prove a version of Fueter's theorem in the case of finite reflection groups. Important examples, such as a Dunkl monogenic Gaussian distribution or a Cauchy kernel, will be given at the end.

Differentiation of retarded integrals and the divergence theorem for retarded functions with discontinuities

International Nuclear Information System (INIS)

Cooperstock, F.I.; Lim, P.H.

1986-01-01

Theorems expressing the time derivatives of retarded volume and surface integrals are presented as well as the Gauss divergence theorem for retarded functions with discontinuities. These theorems greatly facilitate the analysis of gravitational radiation from the motion of disjoint matter distributions in general relativity and could find useful application in other branches of physics

Frege's theorem

CERN Document Server

Heck, Richard G

2011-01-01

Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterlyfundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that a

Asymptotic representation theorems for poverty indices | Lo | Afrika ...

African Journals Online (AJOL)

Abstract. We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotic of the bulk of poverty indices and issues in poverty ...

A Density Turán Theorem

Czech Academy of Sciences Publication Activity Database

Narins, L.; Tran, Tuan

2017-01-01

Roč. 85, č. 2 (2017), s. 496-524 ISSN 0364-9024 Institutional support: RVO:67985807 Keywords : Turán’s theorem * stability method * multipartite version Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.601, year: 2016

A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications

Directory of Open Access Journals (Sweden)

Mei Zhang

2015-01-01

Full Text Available Firstly, this study introduces a definition of generalized stability (GST in discrete-time nonautonomous chaos system (DNCS, which is an extension for chaos generalized synchronization. Secondly, a constructive theorem of DNCS has been proposed. As an example, a GST DNCS is constructed based on a novel 4-dimensional discrete chaotic map. Numerical simulations show that the dynamic behaviors of this map have chaotic attractor characteristics. As one application, we design a chaotic pseudorandom number generator (CPRNG based on the GST DNCS. We use the SP800-22 test suite to test the randomness of four 100-key streams consisting of 1,000,000 bits generated by the CPRNG, the RC4 algorithm, the ZUC algorithm, and a 6-dimensional CGS-based CPRNG, respectively. The numerical results show that the randomness performances of the two CPRNGs are promising. In addition, theoretically the key space of the CPRNG is larger than 21116. As another application, this study designs a stream avalanche encryption scheme (SAES in RGB image encryption. The results show that the GST DNCS is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs.

Testing the No-Hair Theorem with Sgr A*

Directory of Open Access Journals (Sweden)

Tim Johannsen

2012-01-01

Full Text Available The no-hair theorem characterizes the fundamental nature of black holes in general relativity. This theorem can be tested observationally by measuring the mass and spin of a black hole as well as its quadrupole moment, which may deviate from the expected Kerr value. Sgr A*, the supermassive black hole at the center of the Milky Way, is a prime candidate for such tests thanks to its large angular size, high brightness, and rich population of nearby stars. In this paper, I discuss a new theoretical framework for a test of the no-hair theorem that is ideal for imaging observations of Sgr A* with very long baseline interferometry (VLBI. The approach is formulated in terms of a Kerr-like spacetime that depends on a free parameter and is regular everywhere outside of the event horizon. Together with the results from astrometric and timing observations, VLBI imaging of Sgr A* may lead to a secure test of the no-hair theorem.

Complex proofs of real theorems

CERN Document Server

Lax, Peter D

2011-01-01

Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, "The shortest and best way between two truths of the real domain often passes through the imaginary one." Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Müntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Żelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime ...

Dispersive approach to the axial anomaly and nonrenormalization theorem

International Nuclear Information System (INIS)

Pasechnik, R.S.; Teryaev, O.V.

2006-01-01

Anomalous triangle graphs for the divergence of the axial-vector current are studied using the dispersive approach generalized for the case of higher orders of perturbation theory. The validity of this procedure is proved up to the two-loop level. By direct calculation in the framework of dispersive approach we have obtained that the two-loop axial-vector-vector (AVV) amplitude is equal to zero. According to the Vainshtein's theorem, the transversal part of the anomalous triangle is not renormalized in the chiral limit. We generalize this theorem for the case of finite fermion mass in the triangle loop

Extension and reconstruction theorems for the Urysohn universal metric space

Czech Academy of Sciences Publication Activity Database

Kubiś, Wieslaw; Rubin, M.

2010-01-01

Roč. 60, č. 1 (2010), s. 1-29 ISSN 0011-4642 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Urysohn space * bilipschitz homeomorphism * modulus of continuity * reconstruction theorem * extension theorem Subject RIV: BA - General Mathematics Impact factor: 0.265, year: 2010 http://dml.cz/handle/10338.dmlcz/140544

Kochen-Specker theorem studied with neutron interferometer.

Science.gov (United States)

Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut

2011-04-01

The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

Kochen-Specker theorem studied with neutron interferometer

Energy Technology Data Exchange (ETDEWEB)

Hasegawa, Yuji, E-mail: Hasegawa@ati.ac.a [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria); Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria)

2011-04-01

The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291{+-}0.008 not {<=} 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

The BRST quantization and the no-ghost theorem for AdS3

International Nuclear Information System (INIS)

Asano, Masako; Natsuume, Makoto

2003-01-01

In our previous papers, we prove the no-ghost theorem without light-cone directions. We point out that our results are valid for more general backgrounds. In particular, we prove the no-ghost theorem for AdS 3 in the context of the BRST quantization (with the standard restriction on the spin). We compare our BRST proof with the OCQ proof and establish the BRST-OCQ equivalence for AdS 3 . The key in both approaches lies in the certain structure of the matter Hilbert space as a product of two Verma modules. We also present the no-ghost theorem in the most general form. (author)

Gap and density theorems

CERN Document Server

Levinson, N

1940-01-01

A typical gap theorem of the type discussed in the book deals with a set of exponential functions { \\{e^{{{i\\lambda}_n} x}\\} } on an interval of the real line and explores the conditions under which this set generates the entire L_2 space on this interval. A typical gap theorem deals with functions f on the real line such that many Fourier coefficients of f vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various propertie

An improved version of the Mar otto Theorem

International Nuclear Information System (INIS)

Li Changpin; Chen Guanrong

2003-01-01

In 1975, Li and Yorke introduced the first precise definition of discrete chaos and established a very simple criterion for chaos in one-dimensional difference equations, 'period three implies chaos' for brevity. After three years. Marotto generalized this result to n-dimensional difference equations, showing that the existence of a snap-back repeller implies chaos in the sense of Li-Yorke. This theorem is up to now the best one in predicting and analyzing discrete chaos in multidimensional difference equations. Yet, it is well known that there exists an error in the condition of the original Marotto Theorem, and several authors had tried to correct it in different ways. In this paper, we further clarify the issue, with an improved version of the Marotto Theorem derived

The quantitative Morse theorem

OpenAIRE

Loi, Ta Le; Phien, Phan

2013-01-01

In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \\cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse function theorem and the quantitative Morse lemma.

Sulfur K-edge X-ray absorption spectroscopy as an experimental probe for S-nitroso proteins

International Nuclear Information System (INIS)

Szilagyi, Robert K.; Schwab, David E.

2005-01-01

X-ray absorption spectroscopy at the sulfur K-edge (2.4-2.6 keV) provides a sensitive and specific technique to identify S-nitroso compounds, which have significance in nitric oxide-based cell signaling. Unique spectral features clearly distinguish the S-nitroso-form of a cysteine residue from the sulfhydryl-form or from a methionine thioether. Comparison of the sulfur K-edge spectra of thiolate, thiol, thioether, and S-nitroso thiolate compounds indicates high sensitivity of energy positions and intensities of XAS pre-edge features as determined by the electronic environment of the sulfur absorber. A new experimental setup is being developed for reaching the in vivo concentration range of S-nitroso thiol levels in biological samples

Supersymmetric extension of the Adler-Bardeen theorem

International Nuclear Information System (INIS)

Novikov, V.A.; Zakharov, V.I.; Shifman, M.A.; Vainshtein, A.I.

1985-01-01

A supersymmetric generalization of the Adler-Bardeen theorem in SUSY gauge theories is given. We show that within the Adler-Bardeen procedure, both the conformal and axial anomalies are exhausted by one loop. (orig.)

Exotic sources of x-rays for iodine K-edge angiography

International Nuclear Information System (INIS)

Carr, R.

1993-08-01

Digital Subtractive Angiography (DSA) has been performed to image human coronary arteries using wiggler radiation from electron storage rings. The significant medical promise of this procedure motivates the development of smaller and less costly x-ray sources. Several exotic sources are candidates for consideration, using effects such as Cherenkov, channeling, coherent bremsstrahlung, laser backscattering, microundulator, parametric, Smith-Purcell, and transition radiation. In this work we present an analysis of these effects as possible sources of intense x-rays at the iodine K-edge at 33.169 key. The criteria we use are energy, efficiency, flux, optical properties, and technical realizability. For each of the techniques, we find that they suffer either from low flux, a low energy cutoff, target materials heating, too high electron beam energy requirement, optical mismatch to angiography, or a combination of these. We conclude that the foreseeable state-of-the-art favors a compact storage ring design

Understanding band gaps of solids in generalized Kohn-Sham theory.

Science.gov (United States)

Perdew, John P; Yang, Weitao; Burke, Kieron; Yang, Zenghui; Gross, Eberhard K U; Scheffler, Matthias; Scuseria, Gustavo E; Henderson, Thomas M; Zhang, Igor Ying; Ruzsinszky, Adrienn; Peng, Haowei; Sun, Jianwei; Trushin, Egor; Görling, Andreas

2017-03-14

The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. However, the gap in the band structure of the exact multiplicative Kohn-Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS density-functional theory. Here, we give a simple proof of a theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from metageneralized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.

Koopmans' theorem in the Hartree-Fock method. General formulation

Science.gov (United States)

Plakhutin, Boris N.

2018-03-01

This work presents a general formulation of Koopmans' theorem (KT) in the Hartree-Fock (HF) method which is applicable to molecular and atomic systems with arbitrary orbital occupancies and total electronic spin including orbitally degenerate (OD) systems. The new formulation is based on the full set of variational conditions imposed upon the HF orbitals by the variational principle for the total energy and the conditions imposed by KT on the orbitals of an ionized electronic shell [B. N. Plakhutin and E. R. Davidson, J. Chem. Phys. 140, 014102 (2014)]. Based on these conditions, a general form of the restricted open-shell HF method is developed, whose eigenvalues (orbital energies) obey KT for the whole energy spectrum. Particular attention is paid to the treatment of OD systems, for which the new method gives a number of unexpected results. For example, the present method gives four different orbital energies for the triply degenerate atomic level 2p in the second row atoms B to F. Based on both KT conditions and a parallel treatment of atoms B to F within a limited configuration interaction approach, we prove that these four orbital energies, each of which is triply degenerate, are related via KT to the energies of different spin-dependent ionization and electron attachment processes (2p)N → (2p ) N ±1. A discussion is also presented of specific limitations of the validity of KT in the HF method which arise in OD systems. The practical applicability of the theory is verified by comparing KT estimates of the ionization potentials I2s and I2p for the second row open-shell atoms Li to F with the relevant experimental data.

The Completeness Theorem of Godel

Indian Academy of Sciences (India)

GENERAL I ARTICLE. The Completeness Theorem of Godel. 2. Henkin's Proof for First Order Logic. S M Srivastava is with the. Indian Statistical,. Institute, Calcutta. He received his PhD from the Indian Statistical. Institute in 1980. His research interests are in descriptive set theory. I Part 1. An Introduction to Math- ematical ...

K-edge x-ray-absorption spectroscopy of laser-generated Kr+ and Kr2+

International Nuclear Information System (INIS)

Southworth, S. H.; Arms, D. A.; Dufresne, E. M.; Dunford, R. W.; Ederer, D. L.; Hoehr, C.; Kanter, E. P.; Kraessig, B.; Landahl, E. C.; Peterson, E. R.; Rudati, J.; Santra, R.; Walko, D. A.; Young, L.

2007-01-01

Tunable, polarized, microfocused x-ray pulses were used to record x-ray absorption spectra across the K edges of Kr + and Kr 2+ produced by laser ionization of Kr. Prominent 1s→4p and 5p excitations are observed below the 1s ionization thresholds in accord with calculated transition energies and probabilities. Due to alignment of 4p hole states in the laser-ionization process, the Kr + 1s→4p cross section varies with respect to the angle between the laser and x-ray polarization vectors. This effect is used to determine the Kr + 4p 3/2 and 4p 1/2 quantum state populations, and these are compared with results of an adiabatic strong-field ionization theory that includes spin-orbit coupling

Quantitative investigation of two metallohydrolases by X-ray absorption spectroscopy near-edge spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Zhao, W. [Hefei National Laboratory for Physical Sciences at Microscale and School of Life Sciences, University of Science and Technology of China, Hefei, Anhui 230027 (China); Chu, W.S.; Yang, F.F.; Yu, M.J.; Chen, D.L.; Guo, X.Y. [Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 (China); Zhou, D.W.; Shi, N. [Hefei National Laboratory for Physical Sciences at Microscale and School of Life Sciences, University of Science and Technology of China, Hefei, Anhui 230027 (China); Marcelli, A. [Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, P.O. Box 13, Frascati 00044 (Italy); Niu, L.W.; Teng, M.K. [Hefei National Laboratory for Physical Sciences at Microscale and School of Life Sciences, University of Science and Technology of China, Hefei, Anhui 230027 (China); Gong, W.M. [Institute of Biophysics, Chinese Academy of Sciences, Beijing 100101 (China); Benfatto, M. [Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, P.O. Box 13, Frascati 00044 (Italy); Wu, Z.Y. [Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 (China); Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, P.O. Box 13, Frascati 00044 (Italy)], E-mail: wuzy@ihep.ac.cn

2007-09-21

The last several years have witnessed a tremendous increase in biological applications using X-ray absorption spectroscopy (BioXAS), thanks to continuous advancements in synchrotron radiation (SR) sources and detector technology. However, XAS applications in many biological systems have been limited by the intrinsic limitations of the Extended X-ray Absorption Fine Structure (EXAFS) technique e.g., the lack of sensitivity to bond angles. As a consequence, the application of the X-ray absorption near-edge structure (XANES) spectroscopy changed this scenario that is now continuously changing with the introduction of the first quantitative XANES packages such as Minut XANES (MXAN). Here we present and discuss the XANES code MXAN, a novel XANES-fitting package that allows a quantitative analysis of experimental data applied to Zn K-edge spectra of two metalloproteins: Leptospira interrogans Peptide deformylase (LiPDF) and acutolysin-C, a representative of snake venom metalloproteinases (SVMPs) from Agkistrodon acutus venom. The analysis on these two metallohydrolases reveals that proteolytic activities are correlated to subtle conformation changes around the zinc ion. In particular, this quantitative study clarifies the occurrence of the LiPDF catalytic mechanism via a two-water-molecules model, whereas in the acutolysin-C we have observed a different proteolytic activity correlated to structural changes around the zinc ion induced by pH variations.

Quantitative investigation of two metallohydrolases by X-ray absorption spectroscopy near-edge spectroscopy

International Nuclear Information System (INIS)

Zhao, W.; Chu, W.S.; Yang, F.F.; Yu, M.J.; Chen, D.L.; Guo, X.Y.; Zhou, D.W.; Shi, N.; Marcelli, A.; Niu, L.W.; Teng, M.K.; Gong, W.M.; Benfatto, M.; Wu, Z.Y.

2007-01-01

The last several years have witnessed a tremendous increase in biological applications using X-ray absorption spectroscopy (BioXAS), thanks to continuous advancements in synchrotron radiation (SR) sources and detector technology. However, XAS applications in many biological systems have been limited by the intrinsic limitations of the Extended X-ray Absorption Fine Structure (EXAFS) technique e.g., the lack of sensitivity to bond angles. As a consequence, the application of the X-ray absorption near-edge structure (XANES) spectroscopy changed this scenario that is now continuously changing with the introduction of the first quantitative XANES packages such as Minut XANES (MXAN). Here we present and discuss the XANES code MXAN, a novel XANES-fitting package that allows a quantitative analysis of experimental data applied to Zn K-edge spectra of two metalloproteins: Leptospira interrogans Peptide deformylase (LiPDF) and acutolysin-C, a representative of snake venom metalloproteinases (SVMPs) from Agkistrodon acutus venom. The analysis on these two metallohydrolases reveals that proteolytic activities are correlated to subtle conformation changes around the zinc ion. In particular, this quantitative study clarifies the occurrence of the LiPDF catalytic mechanism via a two-water-molecules model, whereas in the acutolysin-C we have observed a different proteolytic activity correlated to structural changes around the zinc ion induced by pH variations

Quantitative phase tomography by using x-ray microscope with Foucault knife-edge scanning filter

Energy Technology Data Exchange (ETDEWEB)

Watanabe, Norio; Tsuburaya, Yuji; Shimada, Akihiro; Aoki, Sadao [Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki, 305-8573 (Japan)

2016-01-28

Quantitative phase tomography was evaluated by using a differential phase microscope with a Foucault knife-edge scanning filter. A 3D x-ray phase image of polystyrene beads was obtained at 5.4 keV. The reconstructed refractive index was fairly good agreement with the Henke’s tabulated data.

Quantitative phase tomography by using x-ray microscope with Foucault knife-edge scanning filter

International Nuclear Information System (INIS)

Watanabe, Norio; Tsuburaya, Yuji; Shimada, Akihiro; Aoki, Sadao

2016-01-01

Quantitative phase tomography was evaluated by using a differential phase microscope with a Foucault knife-edge scanning filter. A 3D x-ray phase image of polystyrene beads was obtained at 5.4 keV. The reconstructed refractive index was fairly good agreement with the Henke’s tabulated data

Quantitative phase tomography by using x-ray microscope with Foucault knife-edge scanning filter

Science.gov (United States)

Watanabe, Norio; Tsuburaya, Yuji; Shimada, Akihiro; Aoki, Sadao

2016-01-01

Quantitative phase tomography was evaluated by using a differential phase microscope with a Foucault knife-edge scanning filter. A 3D x-ray phase image of polystyrene beads was obtained at 5.4 keV. The reconstructed refractive index was fairly good agreement with the Henke's tabulated data.

A laboratory-based hard x-ray monochromator for high-resolution x-ray emission spectroscopy and x-ray absorption near edge structure measurements

Energy Technology Data Exchange (ETDEWEB)

Seidler, G. T., E-mail: seidler@uw.edu; Mortensen, D. R.; Remesnik, A. J.; Pacold, J. I.; Ball, N. A.; Barry, N.; Styczinski, M.; Hoidn, O. R. [Physics Department, University of Washington, Seattle, Washington 98195-1560 (United States)

2014-11-15

We report the development of a laboratory-based Rowland-circle monochromator that incorporates a low power x-ray (bremsstrahlung) tube source, a spherically bent crystal analyzer, and an energy-resolving solid-state detector. This relatively inexpensive, introductory level instrument achieves 1-eV energy resolution for photon energies of ∼5 keV to ∼10 keV while also demonstrating a net efficiency previously seen only in laboratory monochromators having much coarser energy resolution. Despite the use of only a compact, air-cooled 10 W x-ray tube, we find count rates for nonresonant x-ray emission spectroscopy comparable to those achieved at monochromatized spectroscopy beamlines at synchrotron light sources. For x-ray absorption near edge structure, the monochromatized flux is small (due to the use of a low-powered x-ray generator) but still useful for routine transmission-mode studies of concentrated samples. These results indicate that upgrading to a standard commercial high-power line-focused x-ray tube or rotating anode x-ray generator would result in monochromatized fluxes of order 10{sup 6}–10{sup 7} photons/s with no loss in energy resolution. This work establishes core technical capabilities for a rejuvenation of laboratory-based hard x-ray spectroscopies that could have special relevance for contemporary research on catalytic or electrical energy storage systems using transition-metal, lanthanide, or noble-metal active species.

Beyond the Floquet theorem: generalized Floquet formalisms and quasienergy methods for atomic and molecular multiphoton processes in intense laser fields

International Nuclear Information System (INIS)

Chu, S.-I.; Telnov, D.A.

2004-01-01

The advancement of high-power and short-pulse laser technology in the past two decades has generated considerable interest in the study of multiphoton and very high-order nonlinear optical processes of atomic and molecular systems in intense and superintense laser fields, leading to the discovery of a host of novel strong-field phenomena which cannot be understood by the conventional perturbation theory. The Floquet theorem and the time-independent Floquet Hamiltonian method are powerful theoretical framework for the study of bound-bound multiphoton transitions driven by periodically time-dependent fields. However, there are a number of significant strong-field processes cannot be directly treated by the conventional Floquet methods. In this review article, we discuss several recent developments of generalized Floquet theorems, formalisms, and quasienergy methods, beyond the conventional Floquet theorem, for accurate nonperturbative treatment of a broad range of strong-field atomic and molecular processes and phenomena of current interests. Topics covered include (a) artificial intelligence (AI)-most-probable-path approach (MPPA) for effective treatment of ultralarge Floquet matrix problem; (b) non-Hermitian Floquet formalisms and complex quasienergy methods for nonperturbative treatment of bound-free and free-free processes such as multiphoton ionization (MPI) and above-threshold ionization (ATI) of atoms and molecules, multiphoton dissociation (MPD) and above-threshold dissociation (ATD) of molecules, chemical bond softening and hardening, charge-resonance enhanced ionization (CREI) of molecular ions, and multiple high-order harmonic generation (HHG), etc.; (c) many-mode Floquet theorem (MMFT) for exact treatment of multiphoton processes in multi-color laser fields with nonperiodic time-dependent Hamiltonian; (d) Floquet-Liouville supermatrix (FLSM) formalism for exact nonperturbative treatment of time-dependent Liouville equation (allowing for relaxations and

Beyond the Floquet theorem: generalized Floquet formalisms and quasienergy methods for atomic and molecular multiphoton processes in intense laser fields

Science.gov (United States)

Chu, Shih-I.; Telnov, Dmitry A.

2004-02-01

The advancement of high-power and short-pulse laser technology in the past two decades has generated considerable interest in the study of multiphoton and very high-order nonlinear optical processes of atomic and molecular systems in intense and superintense laser fields, leading to the discovery of a host of novel strong-field phenomena which cannot be understood by the conventional perturbation theory. The Floquet theorem and the time-independent Floquet Hamiltonian method are powerful theoretical framework for the study of bound-bound multiphoton transitions driven by periodically time-dependent fields. However, there are a number of significant strong-field processes cannot be directly treated by the conventional Floquet methods. In this review article, we discuss several recent developments of generalized Floquet theorems, formalisms, and quasienergy methods, beyond the conventional Floquet theorem, for accurate nonperturbative treatment of a broad range of strong-field atomic and molecular processes and phenomena of current interests. Topics covered include (a) artificial intelligence (AI)-most-probable-path approach (MPPA) for effective treatment of ultralarge Floquet matrix problem; (b) non-Hermitian Floquet formalisms and complex quasienergy methods for nonperturbative treatment of bound-free and free-free processes such as multiphoton ionization (MPI) and above-threshold ionization (ATI) of atoms and molecules, multiphoton dissociation (MPD) and above-threshold dissociation (ATD) of molecules, chemical bond softening and hardening, charge-resonance enhanced ionization (CREI) of molecular ions, and multiple high-order harmonic generation (HHG), etc.; (c) many-mode Floquet theorem (MMFT) for exact treatment of multiphoton processes in multi-color laser fields with nonperiodic time-dependent Hamiltonian; (d) Floquet-Liouville supermatrix (FLSM) formalism for exact nonperturbative treatment of time-dependent Liouville equation (allowing for relaxations and

Kochen-Specker theorem studied with neutron interferometer

International Nuclear Information System (INIS)

Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut

2011-01-01

The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008 not ≤ 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

Some commutativity theorems for a certain class of rings

International Nuclear Information System (INIS)

Khan, M.A.

1994-08-01

In the present paper we first establish the commutativity theorem for semiprime ring satisfying the polynomial identity [x n ,y]x r = ±y s [x,y m ]y t for all x,y in R, where m,n,r,s and t are fixed nonnegative integers, and further, we investigate commutativity of rings with unity under some additional hypothesis. Moreover, it is also shown that the above result is true for s-unital. Also, we provide some counter examples which show that the hypothesis of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital. (author). 21 refs

Towards a Novel no-hair Theorem for Black Holes

CERN Document Server

Hertog, T

2006-01-01

We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.

Extensions of the stability theorem of the Minkowski space in general relativity

CERN Document Server

Bieri, Lydia

2009-01-01

A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this book, Bieri and Zipser provide two extensions to this result. In the first part, Bieri solves the Cauchy problem for the Einstein vacuum equations with more general, asymptotically flat initial data, and describes precisely the asymptotic behavior. In particular, she assumes less decay in the power of r and one less derivative than in the Christodoulou-Klainerman result. She proves that in this case, too, the initial data, being globally close to the trivial data, yields a solution which is a complete spacetime, tending to the Minkowski spacetime at infinity along any geodesic. In contrast to the original situation, certain estimates in this proof are borderline in view of decay, indicating that the conditions in the main theorem on the decay at infinity on the initial data are sharp. In the second part, Zipser proves the existence of smooth, global solutions to the Einstein-Maxwell equations. A n...

Non-renormalization theorems andN=2 supersymmetric backgrounds

International Nuclear Information System (INIS)

Butter, Daniel; Wit, Bernard de; Lodato, Ivano

2014-01-01

The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed

Dispersion relation for the 3. -->. 3 forward scattering amplitude and the generalized optical theorem. [Crossing properties, dispersion relations

Energy Technology Data Exchange (ETDEWEB)

Logunov, A A; Medvedev, B V; Mestvirishvili, M A; Pavlov, V P; Polivanov, M K; Sukhanov, A D [Gosudarstvennyj Komitet po Ispol' zovaniyu Atomnoj Ehnergii SSSR, Serpukhov. Inst. Fiziki Vysokikh Ehnergij

1977-11-01

Investigation of analytical structure of the three-particle forward scattering amplitude with respect to energy variable of one of particles is performed. The results obtained make it possible to draw the conclusions on crossing properties of the amplitude and to derive the generalized optical theorem relating the discontinuity of the amplitude to the distribution function of an inclusive process. For a special case when two of three particles are of zero mass, a dispersion relation is proved.

Joint probability distributions and fluctuation theorems

International Nuclear Information System (INIS)

García-García, Reinaldo; Kolton, Alejandro B; Domínguez, Daniel; Lecomte, Vivien

2012-01-01

We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation–dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators

X-ray spectroscopy at the Mn K edge in LaMnO3 : An ab initio study

NARCIS (Netherlands)

Hozoi, L.; Vries, A.H. de; Broer, R.

2001-01-01

We present ab initio quantum chemical embedded cluster calculations of Mn core-valence and d-d transitions in LaMnO3. The results are also important for the analysis of recent x-ray absorption and x-ray scattering experiments at the Mn K edge in LaMnO3. We find that the first two peaks of the

Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems

DEFF Research Database (Denmark)

Nest, Ryszard; Tsygan, Boris

2001-01-01

Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely the Poisson structures coming from symplectic Lie algebroids......, as well as holomorphic symplectic structures. For deformations of these structures we prove the classification theorems and a general a general index theorem....

Radon transformation on reductive symmetric spaces:Support theorems

DEFF Research Database (Denmark)

Kuit, Job Jacob

2013-01-01

We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and derive support theorems for these transforms. A reductive symmetric space is a homogeneous space G/H for a reductive Lie group G of the Harish-Chandra class, where H is an open sub...... is based on the relation between the Radon transform and the Fourier transform on G/H, and a Paley–Wiener-shift type argument. Our results generalize the support theorem of Helgason for the Radon transform on a Riemannian symmetric space....

Convergence theorems for Banach space valued integrable multifunctions

Directory of Open Access Journals (Sweden)

Nikolaos S. Papageorgiou

1987-01-01

Full Text Available In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω (1≤p≤∞. Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.

General proof of the Greenberger-Horne-Zeilinger theorem

International Nuclear Information System (INIS)

Chen Zeqian

2004-01-01

It is proved that all states of three spin-(1/2) particles exhibiting an 'all versus nothing' contradiction between quantum mechanics and the local realism of Einstein, Podolsky, and Rosen are exactly the Greenberger-Horne-Zeilinger (GHZ) states and the states obtained from them by local unitary transformations. The proof is obtained by showing that there are at most four elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the three-qubit system and using the certain algebraic properties that Pauli's matrices satisfy. We show that only does such a set of four nonlocal spin observables present a Greenberger-Horne-Zeilinger-Mermin-like argument. This also reveals the equivalence between the GHZ theorem and maximal violation of the Bell inequality

A non-renormalization theorem for conformal anomalies

International Nuclear Information System (INIS)

Petkou, Anastasios; Skenderis, Kostas

1999-01-01

We provide a non-renormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal anomaly of 2-point functions both by a computation in the conformal field theory and via the AdS/CFT correspondence. Our results imply that 2- and 3-point functions of chiral primary operators in N=4 SU(N) SYM will not renormalize provided that a 'generalized Adler-Bardeen theorem' holds. We further show that recent arguments connecting the non-renormalizability of the above-mentioned correlation functions to a bonus U(1) Y symmetry are incomplete due to possible U(1) Y violating contact terms. The tree level contribution to the contact terms may be set to zero by considering appropriately normalized operators. Non-renormalizability of the above-mentioned correlation functions, however, will follow only if these contact terms saturate by free fields

Attenuation studies near K-absorption edges using Compton scattered 241Am gamma rays

International Nuclear Information System (INIS)

Abdullah, K.K.; Ramachandran, N.; Karunakaran Nair, K.; Babu, B.R.S.; Joseph, Antony; Thomas, Rajive; Varier, K.M.

2008-01-01

We have carried out photon attenuation measurements at several energies in the range from 49.38 keV to 57.96 keV around the K-absorption edges of the rare earth elements Sm, Eu, Gd, Tb, Dy and Er using 59.54 keV gamma rays from 241 Am source after Compton scattering from an aluminium target. Pellets of oxides of the rare earth elements were chosen as mixture absorbers in these investigations. A narrow beam good geometry set-up was used for the attenuation measurements. The scattered gamma rays were detected by an HPGe detector. The results are consistent with theoretical values derived from the XCOM package. (author)

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).

Study of X-ray L2 absorption edges of Gd, Dy, Ho and Er in metals and compounds

International Nuclear Information System (INIS)

Agarwal, B.K.; Agarwal, B.R.K.

1978-01-01

The positions and shapes of L2 X-ray absorption edges of Gd, Dy, Ho and Er have been studied in metals and in oxides and chlorides, using a forty centimetre bent mica crystal spectrograph. It has been found that the L2 edge shifts towards the high energy side in the compounds and that the chemical shift ΔE depends on the degree of covalency involved. The white line structure at the edge has been analysed in terms of transitions of L2 shell electron to optical nd (n >= 5) states. (author)

Absolute determination of zero-energy phase shifts for multiparticle single-channel scattering: Generalized Levinson theorem

International Nuclear Information System (INIS)

Rosenberg, L.; Spruch, L.

1996-01-01

Levinson close-quote s theorem relates the zero-energy phase shift δ for potential scattering in a given partial wave l, by a spherically symmetric potential that falls off sufficiently rapidly, to the number of bound states of that l supported by the potential. An extension of this theorem is presented that applies to single-channel scattering by a compound system initially in its ground state. As suggested by Swan [Proc. R. Soc. London Ser. A 228, 10 (1955)], the extended theorem differs from that derived for potential scattering; even in the absence of composite bound states δ may differ from zero as a consequence of the Pauli principle. The derivation given here is based on the introduction of a continuous auxiliary open-quote open-quote length phase close-quote close-quote η, defined modulo π for l=0 by expressing the scattering length as A=acotη, where a is a characteristic length of the target. Application of the minimum principle for the scattering length determines the branch of the cotangent curve on which η lies and, by relating η to δ, an absolute determination of δ is made. The theorem is applicable, in principle, to single-channel scattering in any partial wave for e ± -atom and nucleon-nucleus systems. In addition to a knowledge of the number of composite bound states, information (which can be rather incomplete) concerning the structure of the target ground-state wave function is required for an explicit, absolute, determination of the phase shift δ. As for Levinson close-quote s original theorem for potential scattering, no additional information concerning the scattering wave function or scattering dynamics is required. copyright 1996 The American Physical Society

A high resolution x-ray fluorescence spectrometer for near edge absorption studies

International Nuclear Information System (INIS)

Stojanoff, V.; Hamalainen, K.; Siddons, D.P.; Hastings, J.B.; Berman, L.E.; Cramer, S.; Smith, G.

1991-01-01

A high resolution fluorescence spectrometer using a Johann geometry in a back scattering arrangement was developed. The spectrometer, with a resolution of 0.3 eV at 6.5 keV, combined with an incident beam, with a resolution of 0.7 eV, form the basis of a high resolution instrument for measuring x-ray absorption spectra. The advantages of the instrument are illustrated with the near edge absorption spectrum of dysprosium nitrate. 10 refs., 4 figs

Electronic Structure from Iron L-edge Spectroscopy : An Example of Spin Transition Evidenced by Soft X-ray Absorption Spectroscopy

NARCIS (Netherlands)

Cartier dit Moulin, Ch.; Flank, A.M.; Rudolf, P.; Chen, C.T.

1993-01-01

Soft X-ray Absorption Spectroscopy at the transition metal L2,3 edges provides information about the 3d unoccupied states by dipole allowed transitions. We have recorded iron L2,3 edges in order to follow the reversible thermal spin interconversion (S=2 S=0) of the Fe(II)(o-phenantroline)2(NCS)2.

A Meinardus Theorem with Multiple Singularities

Science.gov (United States)

Granovsky, Boris L.; Stark, Dudley

2012-09-01

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.

Multi-Absorber Transition-Edge Sensors for X-Ray Astronomy Applications

Science.gov (United States)

Smith, S. J.; Adams, J. S.; Bandler, S. R.; Busch, S. E.; Chervenak, J. A.; Eckart, M. E.; Ewin, A. J.; Finkbeiner, F. M.; Kelley, R. L.; Kelly, D. P.;

Study on Coloration Mechanism of Chinese Ancient Ceramics by X-ray Absorption Near-edge Structure

Science.gov (United States)

Peng, Y. H.; Xie, Z.; He, J. F.; Liu, Q. H.; Pan, Z. Y.; Cheng, W. R.; Wei, S. Q.

2013-04-01

The Fe K-edge X-ray absorption near-edge structure (XANES) spectra of a series of ceramic shards were measured by fluorescence mode to reveal the color-generating techniques of Chinese porcelain. The analysis disclosed relationships among the chemical form of the iron, the firing conditions and the colors of the ceramics. The results indicate that the coloration for different ceramics depend on the valence states of iron as the main color element in glaze and the proportion of Fe2+ and Fe3+ was attributed to the baking technology. The findings provide important information for archaeologist on the coloration researches.

Further results for crack-edge mappings by ray methods

International Nuclear Information System (INIS)

Norris, A.N.; Achenbach, J.D.; Ahlberg, L.; Tittman, B.R.

1984-01-01

This chapter discusses further extensions of the local edge mapping method to the pulse-echo case and to configurations of water-immersed specimens and transducers. Crack edges are mapped by the use of arrival times of edge-diffracted signals. Topics considered include local edge mapping in a homogeneous medium, local edge mapping algorithms, local edge mapping through an interface, and edge mapping through an interface using synthetic data. Local edge mapping is iterative, with two or three iterations required for convergence

Phonon-mediated superconducting transition-edge sensor X-ray detectors for use in astronomy

Science.gov (United States)

Leman, Steven W.; Martinez-Galarce, Dennis S.; Brink, Paul L.; Cabrera, Blas; Castle, Joseph P.; Morse, Kathleen; Stern, Robert A.; Tomada, Astrid

2004-09-01

Superconducting Transition-Edge Sensors (TESs) are generating a great deal of interest in the areas of x-ray astrophysics and space science, particularly to develop them as large-array, imaging x-ray spectrometers. We are developing a novel concept that is based on position-sensitive macro-pixels placing TESs on the backside of a silicon or germanium absorber. Each x-ray absorbed will be position (X/δX and Y/δY ~ 100) and energy (E/δE ~ 1000) resolved via four distributed TES readouts. In the future, combining such macropixels with advances in multiplexing could lead to 30 by 30 arrays of close-packed macro-pixels equivalent to imaging instruments of 10 megapixels or more. We report on our progress to date and discuss its application to a plausible solar satellite mission and plans for future development.

K-Edge Subtraction Angiography with Synchrotron X-Rays

CERN Document Server

Giacomini, J C

1996-01-01

The purpose of this project was to utilize dual energy, monochromatic X-rays produced from synchrotrons radiation in order to obtain noninvasive medical imaging. The application of synchrotrons radiation to medical imaging is based on the principle of iodine dichromography, first described by Bertil Jacobson of the Karolinska Institute in 1953. Medical imaging using synchrotrons radiation and K-edge dichromography was pioneered at Stanford University under the leadership of Dr. Ed Rubenstein, and the late Nobel Laureate in Physics, Dr. Robert Hofstadter. With progressive refinements in hardware, clinical-quality images were obtained of human coronary arteries utilizing peripheral injections of iodinated contrast agent. These images even now are far superior to those being presented by investigators using MRI as an imaging tool for coronary arteries. However, new supplies and instruments in the cardiac catheterization laboratory have served to transform coronary angiography into an outpatient procedure, with r...

MVT a most valuable theorem

CERN Document Server

Smorynski, Craig

2017-01-01

This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mat...

Trace Formulae of Characteristic Polynomial and Cayley-Hamilton's Theorem, and Applications to Chiral Perturbation Theory and General Relativity

International Nuclear Information System (INIS)

Zhang Honghao; Yan Wenbin; Li Xuesong

2008-01-01

By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and we further obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace formulae of the Cayley-Hamilton's theorem with all coefficients explicitly given. This implies a byproduct, a complete expression for the determinant of any finite-dimensional matrix in terms of the traces of its successive powers. And we discuss some of their applications to chiral perturbation theory and general relativity

On the proof of the first Carnot theorem in thermodynamics

International Nuclear Information System (INIS)

Morad, M R; Momeni, F

2013-01-01

The proof of the first Carnot theorem in classical thermodynamics is revisited in this study. The underlying conditions of a general proof of this principle presented by Senft (1978 Phys. Educ. 13 35–37) are explored and discussed. These conditions are analysed in more detail using a physical description of heat and work to present a simpler proof of the first principle prior to using the violation of the second law of thermodynamics. Finally, a new simple proof is also presented based on Gibbs relation. This discussion will benefit the teaching of classical thermodynamics and promote better understanding of the proof of the first Carnot theorem in general form. (paper)

Charge-transfer and Mott-Hubbard Excitations in FeBo3: Fe K-edge resonant Inelastic x-ray scattering study

International Nuclear Information System (INIS)

Kim, J.; Shvydko, Y.

2011-01-01

Momentum-resolved resonant inelastic x-ray scattering (RIXS) spectroscopy has been carried out successfully at the Fe K-edge for the first time. The RIXS spectra of a FeBO 3 single crystal reveal a wealth of information on ∼ 1-10 eV electronic excitations. The IXS signal resonates when the incident photon energy approaches the pre-edge (1s - -3d) and the main-edge (1s - -4p) of the Fe K-edge absorption spectrum. The RIXS spectra measured at the pre-edge and the main-edge show quantitatively different dependences on the incident photon energy, momentum transfer, photon polarization, and temperature. We present a multielectron analysis of the Mott-Hubbard (MH) and charge transfer (CT) excitations, and calculate their energies. Electronic excitations observed in the pre-edge and main-edge RIXS spectra are interpreted as MH and CT excitations, respectively. We propose the electronic structure around the chemical potential in FeBO 3 based on the experimental data.

Pyrimidine and halogenated pyrimidines near edge x-ray absorption fine structure spectra at C and N K-edges: experiment and theory

International Nuclear Information System (INIS)

Bolognesi, P.; O'Keeffe, P.; Ovcharenko, Y.; Coreno, M.; Avaldi, L.; Feyer, V.; Plekan, O.; Prince, K. C.; Zhang, W.; Carravetta, V.

2010-01-01

The inner shell excitation of pyrimidine and some halogenated pyrimidines near the C and N K-edges has been investigated experimentally by near edge x-ray absorption fine structure spectroscopy and theoretically by density functional theory calculations. The selected targets, 5-Br-pyrimidine, 2-Br-pyrimidine, 2-Cl-pyrimidine, and 5-Br-2-Cl-pyrimidine, allow the effects of the functionalization of the pyrimidine ring to be studied either as a function of different halogen atoms bound to the same molecular site or as a function of the same halogen atom bound to different molecular sites. The results show that the individual characteristics of the different spectra of the substituted pyrimidines can be rationalized in terms of variations in electronic and geometrical structures of the molecule depending on the localization and the electronegativity of the substituent.

An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

Science.gov (United States)

Waller, Niels

2018-01-01

Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.

X-ray L/sub III/-edge densitometer for assay of mixed S.N.M. solutions

International Nuclear Information System (INIS)

Russo, P.A.; Canada, T.R.; Langner, D.G.; Tape, J.W.; Hsue, S.T.; Cowder, L.R.; Mosley, W.C.; Reynolds, L.; Thompson, M.C.

1979-01-01

Simultaneous nondestructive analysis of uranium and plutonium in coprocessed solutions is accomplished using L/sub III/-edge densitometry in at-line instrumentation. The densitometer measures the transmission through solutions of a continuous x-ray spectrum, and gives accuracies of approximately one-half percent and three percent for uranium and plutonium concentrations respectively

Monitoring of health of trees by gamma-ray tomographic scanners and the first Kanpur error theorem

International Nuclear Information System (INIS)

Verma, Ruchi; Razdan, Mayuri; Quraishi, A.M.; Munshi, Prabhat

2004-01-01

CT scanners produce nondestructively images of a given cross-section with the help of radiation source-detector system and a suitable tomographic reconstruction algorithm. These CT images have inherent error associated with them and for unknown objects it is not possible to calculate it directly. Careful application of the first Kanpur theorem, however, gives an indirect estimate of the inaccuracy of these images. An interesting outcome of this theorem is monitoring of health of trees. (author)

Factor and Remainder Theorems: An Appreciation

Science.gov (United States)

Weiss, Michael

2016-01-01

The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…

Analysis of X-ray adsorption edges: L_2,3 edge of FeCl₄^-

Energy Technology Data Exchange (ETDEWEB)

Bagus, Paul S. [Department of Chemistry, University of North Texas, Denton, Texas 76203-5017, USA; Nelin, Connie J. [Consultant, Austin, Texas 78730, USA; Ilton, Eugene S. [Pacific Northwest National Laboratory, Richland, Washington 99352, USA; Sassi, Michel J. [Pacific Northwest National Laboratory, Richland, Washington 99352, USA; Rosso, Kevin M. [Pacific Northwest National Laboratory, Richland, Washington 99352, USA

2017-12-14

We describe a detailed analysis of the features of the X-ray adsorption spectra at the Fe L_2,3 edge of FeCl₄. The objective of this analysis is to explain the origin of the complex features in relation to properties of the wavefunctions, especially for the excited states. These properties include spin-orbit and ligand field splittings where a novel aspect of the dipole selection rules is applied to understand the influence of these splittings on the spectra. We also explicitly take account of the intermediate coupling of the open core and valence shell electrons. Our analysis also includes comparison of theory and experiment for the Fe L_2,3 edge and comparison of theoretical predictions for the Fe³⁺ cation and FeCl₄-. The electronic structure is obtained from theoretical wavefunctions for the ground and excited states.

Generalized Bloch Theorem for Complex Periodic Potentials - A Powerful Application to Quantum Transport Calculations

International Nuclear Information System (INIS)

Zhang, Xiaoguang; Varga, Kalman; Pantelides, Sokrates T

2007-01-01

Band-theoretic methods with periodically repeated supercells have been a powerful approach for ground-state electronic structure calculations, but have not so far been adapted for quantum transport problems with open boundary conditions. Here we introduce a generalized Bloch theorem for complex periodic potentials and use a transfer-matrix formulation to cast the transmission probability in a scattering problem with open boundary conditions in terms of the complex wave vectors of a periodic system with absorbing layers, allowing a band technique for quantum transport calculations. The accuracy and utility of the method is demonstrated by the model problems of the transmission of an electron over a square barrier and the scattering of a phonon in an inhomogeneous nanowire. Application to the resistance of a twin boundary in nanocrystalline copper yields excellent agreement with recent experimental data

Delocalization and occupancy effects of 5f orbitals in plutonium intermetallics using L3-edge resonant X-ray emission spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Booth, C. H.; Medling, S. A.; Jiang, Yu; Bauer, E. D.; Tobash, P. H.; Mitchell, J. N.; Veirs, D. K.; Wall, M. A.; Allen, P. G.; Kas, J. J.; Sokaras, D.; Nordlund, D.; Weng, T. -C.

2014-06-24

Although actinide (An) L3 -edge X-ray absorption near-edge structure (XANES) spectroscopy has been very effective in determining An oxidation states in insulating, ionically bonded materials, such as in certain coordination compounds and mineral systems, the technique fails in systems featuring more delocalized 5f orbitals, especially in metals. Recently, actinide L3-edge resonant X-ray emission spec- troscopy (RXES) has been shown to be an effective alternative. This technique is further demonstrated here using a parameterized partial unoccupied density of states method to quantify both occupancy and delocalization of the 5f orbital in ?-Pu, ?-Pu, PuCoGa5 , PuCoIn5 , and PuSb2. These new results, supported by FEFF calculations, highlight the effects of strong correlations on RXES spectra and the technique?s ability to differentiate between f-orbital occupation and delocalization.

Chemical shift of U L3 edges in different uranium compounds obtained by X-ray absorption spectroscopy with synchrotron radiation

International Nuclear Information System (INIS)

Joseph, D.; Jha, S.N.; Nayak, C.; Bhattacharyya, D.; Babu, P. Venu

2014-01-01

Uranium L 3 X-ray absorption edge was measured in various compounds containing uranium in U 4+ , U 5+ and U 5+ oxidation states. The measurements have been carried out at the Energy Dispersive EXAFS beamline (BL-08) at INDUS-2 synchrotron radiation source at RRCAT, Indore. Energy shifts of ∼ 2-3 eV were observed for U L 3 edge in the U-compounds compared to their value in elemental U. The different chemical shifts observed for the compounds having the same oxidation state of the cation but different anions or ligands show the effect of different chemical environments surrounding the cations in determining their X-ray absorption edges in the above compounds. The above chemical effect has been quantitatively described by determining the effective charges on U cation in the above compounds. (author)

The Patchwork Divergence Theorem

OpenAIRE

Dray, Tevian; Hellaby, Charles

1994-01-01

The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting "patchwork divergence theorem" which is independent of the metric signature in either region, and which is thus valid if the signature changes. (PA...

The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory

Directory of Open Access Journals (Sweden)

Claude Semay

2015-01-01

Full Text Available The envelope theory is a convenient method to compute approximate solutions for bound state equations in quantum mechanics. It is shown that these approximate solutions obey a kind of Hellmann–Feynman theorem, and that the comparison theorem can be applied to these approximate solutions for two ordered Hamiltonians.

Another look at the second incompleteness theorem

NARCIS (Netherlands)

Visser, A.

2017-01-01

In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is xed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the interpretation

Another look at the second incompleteness theorem

NARCIS (Netherlands)

Visser, Albert

2017-01-01

In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is fixed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the

Vapour–to–liquid nucleation: Nucleation theorems for nonisothermal–nonideal case

Energy Technology Data Exchange (ETDEWEB)

Malila, J.; McGraw, R.; Napari, I.; Laaksonen, A.

2010-08-29

Homogeneous vapour-to-liquid nucleation, a basic process of aerosol formation, is often considered as a type example of nucleation phenomena, while most treatment of the subject introduce several simplifying assumptions (ideal gas phase, incompressible nucleus, isothermal kinetics, size-independent surface free energy...). During last decades, nucleation theorems have provided new insights into properties of critical nuclei facilitating direct comparison between laboratory experiments and molecular simulations. These theorems are, despite of their generality, often applied in forms where the aforementioned assumptions are made. Here we present forms of nucleation theorems that explicitly take into account these effects and allow direct estimation of their importance. Only assumptions are Arrhenius-type kinetics of nucleation process and exclusion carrier gas molecules from the critical nucleus.

Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

Science.gov (United States)

Li, Lei; Liu, Jian-Guo; Lu, Jianfeng

2017-10-01

We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.

K-Edge Subtraction Angiography with Synchrotron X-Rays

International Nuclear Information System (INIS)

Giacomini, John C.

1996-01-01

The purpose of this project was to utilize dual energy, monochromatic X-rays produced from synchrotrons radiation in order to obtain noninvasive medical imaging. The application of synchrotrons radiation to medical imaging is based on the principle of iodine dichromography, first described by Bertil Jacobson of the Karolinska Institute in 1953. Medical imaging using synchrotrons radiation and K-edge dichromography was pioneered at Stanford University under the leadership of Dr. Ed Rubenstein, and the late Nobel Laureate in Physics, Dr. Robert Hofstadter. With progressive refinements in hardware, clinical-quality images were obtained of human coronary arteries utilizing peripheral injections of iodinated contrast agent. These images even now are far superior to those being presented by investigators using MRI as an imaging tool for coronary arteries. However, new supplies and instruments in the cardiac catheterization laboratory have served to transform coronary angiography into an outpatient procedure, with relatively little morbidity. We extended the principles learned with coronary angiography to noninvasive imaging of the human bronchial tree. For these images, we utilized xenon as the contrast agent, as it has a K-edge very similar to that of iodine. In this case, there is no true competing diagnostic test, and pulmonary neoplasm is an enormous public health concern. In early experiments, we demonstrated remarkably clear images of the human bronchial tree. These images have been shown internationally; however, funding difficulties primarily with the Department of Energy have not allowed for progression of this promising avenue of research. One potential criticism of the project is that in order to obtain these images, we utilized national laboratories. Some have questioned whether this would lead to a practical imaging modality. However, we have shown that the technology exists to allow for construction of a miniature storage ring, with a superconducting

Optical properties of boron carbide near the boron K edge evaluated by soft-x-ray reflectometry from a Ru/B4C multilayer

Energy Technology Data Exchange (ETDEWEB)

Ksenzov, Dmitriy; Panzner, Tobias; Schlemper, Christoph; Morawe, Christian; Pietsch, Ullrich

2009-12-10

Soft-x-ray Bragg reflection from two Ru/B4C multilayers with 10 and 63 periods was used for independent determination of both real and imaginary parts of the refractive index n = 1 -{delta} + i{beta} close to the boron K edge ({approx}188 eV). Prior to soft x-ray measurements, the structural parameters of the multilayers were determined by x-ray reflectometry using hard x rays. For the 63-period sample, the optical properties based on the predictions made for elemental boron major deviations were found close to the K edge of boron for the 10-period sample explained by chemical bonding of boron to B4C and various boron oxides.

Near-edge X-ray absorption fine structure studies of Cr{sub 1−x}M{sub x}N coatings

Energy Technology Data Exchange (ETDEWEB)

Mahbubur Rahman, M. [School of Engineering and Information Technology, Murdoch University, Murdoch, WA 6150 (Australia); Department of Physics, Jahangirnagar University, Savar, Dhaka 1342 (Bangladesh); Duan, Alex [School of Chemistry, The University of Melbourne, Parkville, VIC 3010 (Australia); Jiang, Zhong-Tao, E-mail: Z.Jiang@murdoch.edu.au [School of Engineering and Information Technology, Murdoch University, Murdoch, WA 6150 (Australia); Xie, Zonghan [School of Mechanical Engineering, University of Adelaide, SA 5005 (Australia); School of Engineering, Edith Cowan University, WA 6027 (Australia); Wu, Alex [School of Chemistry, The University of Melbourne, Parkville, VIC 3010 (Australia); Amri, Amun [Department of Chemical Engineering, Riau University, Pekanbaru (Indonesia); Cowie, Bruce [Australian Synchrotron, 800 Blackburn Rd., Clayton, VIC 3168 (Australia); Yin, Chun-Yang [Chemical and Analytical Sciences, Murdoch University, Murdoch, WA 6150 (Australia)

2013-11-25

Highlights: •Al or Si is doped on CrN and AlN coatings using magnetron sputtering system. •NEXAFS analysis is conducted to measure the Al and Si K-edges, and chromium L-edge. •Structural evolution of CrN matrix with addition of Al or Si element is investigated. -- Abstract: Cr{sub 1−x}M{sub x}N coatings, with doping concentrations (Si or Al) varying from 14.3 to 28.5 at.%, were prepared on AISI M2 tool steel substrates using a TEER UDP 650/4 closed field unbalanced magnetron sputtering system. Near-edge X-ray absorption fine structure (NEXAFS) characterization was carried out to measure the aluminum and silicon K-edges, as well as chromium L-edge, in the coatings. Two soft X-ray techniques, Auger electron yield (AEY) and total fluorescence yield (TFY), were employed to investigate the surface and inner structural properties of the materials in order to understand the structural evolution of CrN matrix with addition of Al (or Si) elements. Investigations on the local bonding states and grain boundaries of the coatings, using NEXAFS technique, provide significant information which facilitates understanding of the local electronic structure of the atoms and shed light on the origins of the high mechanical strength and oxidation resistance of these technologically important coatings.

Experimental and theoretical study of X-ray absorption around the chlorine L edge in vinyl chloride

International Nuclear Information System (INIS)

Kawerk, Elie; Carniato, Stéphane; Iwayama, Hiroshi; Shigemasa, Eiji; Piancastelli, Maria Novella; Wassaf, Joseph; Khoury, Antonio; Simon, Marc

2013-01-01

Highlights: ► We measured the X-ray absorption spectrum of C 2 H 3 Cl around the chlorine L edge. ► Ab-initio calculations of the spectrum shed light on eventual electronic resonances. ► Vibrational substructures for particular core excited states are considered. ► The potential energy surfaces of the core excited electronic states are evaluated. ► Sharp or narrow spectral bands are associated to bound or dissociative surfaces. -- Abstract: We present a combined experimental and theoretical study of the high-resolution chlorine L edge X-ray absorption spectrum in gas-phase vinyl chloride (C 2 H 3 Cl). With the help of ab-initio calculations, we interpret the experimental spectrum and attribute each band to its corresponding electronic transitions terminating at states characterized by an either binding or dissociative potential energy surface (PES). Vibrational substructures in some specific core-excited electronic states are taken into account

Experimental and theoretical study of X-ray absorption around the chlorine L edge in vinyl chloride

Energy Technology Data Exchange (ETDEWEB)

Kawerk, Elie, E-mail: elie.kawerk@etu.upmc.fr [Université Pierre et Marie Curie, Laboratoire de Chimie Physique-Matière et Rayonnement, UMR 7614, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05 (France); Université Libanaise, Faculté des Sciences II Fanar, Laboratoire de Physique Appliquée, 90656 Jdeidet el Metn (Lebanon); Carniato, Stéphane [Université Pierre et Marie Curie, Laboratoire de Chimie Physique-Matière et Rayonnement, UMR 7614, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05 (France); Iwayama, Hiroshi; Shigemasa, Eiji [Ultraviolet Synchrotron Orbital Radiation Facility, Institute for Molecular Science, Okazaki 444-8585 (Japan); Piancastelli, Maria Novella [Université Pierre et Marie Curie, Laboratoire de Chimie Physique-Matière et Rayonnement, UMR 7614, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05 (France); Wassaf, Joseph; Khoury, Antonio [Université Libanaise, Faculté des Sciences II Fanar, Laboratoire de Physique Appliquée, 90656 Jdeidet el Metn (Lebanon); Simon, Marc [Université Pierre et Marie Curie, Laboratoire de Chimie Physique-Matière et Rayonnement, UMR 7614, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05 (France)

2013-02-15

Highlights: ► We measured the X-ray absorption spectrum of C{sub 2}H{sub 3}Cl around the chlorine L edge. ► Ab-initio calculations of the spectrum shed light on eventual electronic resonances. ► Vibrational substructures for particular core excited states are considered. ► The potential energy surfaces of the core excited electronic states are evaluated. ► Sharp or narrow spectral bands are associated to bound or dissociative surfaces. -- Abstract: We present a combined experimental and theoretical study of the high-resolution chlorine L edge X-ray absorption spectrum in gas-phase vinyl chloride (C{sub 2}H{sub 3}Cl). With the help of ab-initio calculations, we interpret the experimental spectrum and attribute each band to its corresponding electronic transitions terminating at states characterized by an either binding or dissociative potential energy surface (PES). Vibrational substructures in some specific core-excited electronic states are taken into account.

Quantization of Chirikov Map and Quantum KAM Theorem.

Science.gov (United States)

Shi, Kang-Jie

KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions

On the first case of Fermat's theorem for cyclotomic fields

International Nuclear Information System (INIS)

Kolyvagin, V A

1999-01-01

The classical criteria of Kummer, Mirimanov and Vandiver for the validity of the first case of Fermat's theorem for the field Q of rationals and prime exponent l are generalized to the field Q( l √1) and exponent l. As a consequence, some simpler criteria are established. For example, the validity of the first case of Fermat's theorem is proved for the field Q( l √1) and exponent l on condition that l 2 does not divide 2 l -2

Radon transformation on reductive symmetric spaces: support theorems

NARCIS (Netherlands)

Kuit, J.J.|info:eu-repo/dai/nl/313872589

2011-01-01

In this thesis we introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and study some of their properties. In particular we obtain a generalization of Helgason's support theorem for the horospherical transform on a Riemannian symmetric space.

Discovering the Theorem of Pythagoras

Science.gov (United States)

Lattanzio, Robert (Editor)

1988-01-01

In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.

Bit-Blasting ACL2 Theorems

Directory of Open Access Journals (Sweden)

Sol Swords

2011-10-01

Full Text Available Interactive theorem proving requires a lot of human guidance. Proving a property involves (1 figuring out why it holds, then (2 coaxing the theorem prover into believing it. Both steps can take a long time. We explain how to use GL, a framework for proving finite ACL2 theorems with BDD- or SAT-based reasoning. This approach makes it unnecessary to deeply understand why a property is true, and automates the process of admitting it as a theorem. We use GL at Centaur Technology to verify execution units for x86 integer, MMX, SSE, and floating-point arithmetic.

K-edge Radiography and applications to Cultural Heritage

OpenAIRE

Albertin, Fauzia

2011-01-01

The present work of thesis is focused on application of X-ray K-edge technique to paintings. This technique allows one to achieve a topographic map of a pigment on the whole surface of the painting. The digital acquisition of radiographic images by using monochromatic X-ray beams allows to take advantage of the sharp rise of X-ray absorption coefficient of the elements, the K-edge discontinuity. Working at different energies, bracketing the K-edge peak, allows recognition ...

Eliminating the non-Gaussian spectral response of X-ray absorbers for transition-edge sensors

Science.gov (United States)

Yan, Daikang; Divan, Ralu; Gades, Lisa M.; Kenesei, Peter; Madden, Timothy J.; Miceli, Antonino; Park, Jun-Sang; Patel, Umeshkumar M.; Quaranta, Orlando; Sharma, Hemant; Bennett, Douglas A.; Doriese, William B.; Fowler, Joseph W.; Gard, Johnathon D.; Hays-Wehle, James P.; Morgan, Kelsey M.; Schmidt, Daniel R.; Swetz, Daniel S.; Ullom, Joel N.

2017-11-01

Transition-edge sensors (TESs) as microcalorimeters for high-energy-resolution X-ray spectroscopy are often fabricated with an absorber made of materials with high Z (for X-ray stopping power) and low heat capacity (for high resolving power). Bismuth represents one of the most compelling options. TESs with evaporated bismuth absorbers have shown spectra with undesirable and unexplained low-energy tails. We have developed TESs with electroplated bismuth absorbers over a gold layer that are not afflicted by this problem and that retain the other positive aspects of this material. To better understand these phenomena, we have studied a series of TESs with gold, gold/evaporated bismuth, and gold/electroplated bismuth absorbers, fabricated on the same die with identical thermal coupling. We show that the bismuth morphology is linked to the spectral response of X-ray TES microcalorimeters.

The universality of the Carnot theorem

International Nuclear Information System (INIS)

Gonzalez-Ayala, Julian; Angulo-Brown, F

2013-01-01

It is common in many thermodynamics textbooks to illustrate the Carnot theorem through the use of diverse state equations for gases, paramagnets, and other simple thermodynamic systems. As is well known, the universality of the Carnot efficiency is easily demonstrated in a temperature–entropy diagram, which means that η C is independent of the working substance. In this paper we remark that the universality of the Carnot theorem goes beyond conventional state equations, and is fulfilled by gas state equations that do not correspond to an ideal gas in the dilution limit, namely V → ∞. Some of these unconventional state equations have certain thermodynamic ‘anomalies’ that nonetheless do not forbid them from obeying the Carnot theorem. We discuss how this very general behaviour arises from Maxwell relations, which are connected with a geometrical property expressed through preserving area transformations. A rule is proposed to calculate the Maxwell relations associated with a thermodynamic system by using the preserving area relationships. In this way it is possible to calculate the number of possible preserving area mappings by giving the number of possible Jacobian identities between all pairs of thermodynamic variables included in the corresponding Gibbs equation. This paper is intended for undergraduates and specialists in thermodynamics and related areas. (paper)

ACCURATE MODELING OF X-RAY EXTINCTION BY INTERSTELLAR GRAINS

International Nuclear Information System (INIS)

Hoffman, John; Draine, B. T.

2016-01-01

Interstellar abundance determinations from fits to X-ray absorption edges often rely on the incorrect assumption that scattering is insignificant and can be ignored. We show instead that scattering contributes significantly to the attenuation of X-rays for realistic dust grain size distributions and substantially modifies the spectrum near absorption edges of elements present in grains. The dust attenuation modules used in major X-ray spectral fitting programs do not take this into account. We show that the consequences of neglecting scattering on the determination of interstellar elemental abundances are modest; however, scattering (along with uncertainties in the grain size distribution) must be taken into account when near-edge extinction fine structure is used to infer dust mineralogy. We advertise the benefits and accuracy of anomalous diffraction theory for both X-ray halo analysis and near edge absorption studies. We present an open source Fortran suite, General Geometry Anomalous Diffraction Theory (GGADT), that calculates X-ray absorption, scattering, and differential scattering cross sections for grains of arbitrary geometry and composition

ACCURATE MODELING OF X-RAY EXTINCTION BY INTERSTELLAR GRAINS

Energy Technology Data Exchange (ETDEWEB)

Hoffman, John; Draine, B. T., E-mail: jah5@astro.princeton.edu, E-mail: draine@astro.princeton.edu [Princeton University Observatory, Peyton Hall, Princeton, NJ 08544-1001 (United States)

2016-02-01

Interstellar abundance determinations from fits to X-ray absorption edges often rely on the incorrect assumption that scattering is insignificant and can be ignored. We show instead that scattering contributes significantly to the attenuation of X-rays for realistic dust grain size distributions and substantially modifies the spectrum near absorption edges of elements present in grains. The dust attenuation modules used in major X-ray spectral fitting programs do not take this into account. We show that the consequences of neglecting scattering on the determination of interstellar elemental abundances are modest; however, scattering (along with uncertainties in the grain size distribution) must be taken into account when near-edge extinction fine structure is used to infer dust mineralogy. We advertise the benefits and accuracy of anomalous diffraction theory for both X-ray halo analysis and near edge absorption studies. We present an open source Fortran suite, General Geometry Anomalous Diffraction Theory (GGADT), that calculates X-ray absorption, scattering, and differential scattering cross sections for grains of arbitrary geometry and composition.

High-resolution X-ray emission spectroscopy with transition-edge sensors: present performance and future potential

Energy Technology Data Exchange (ETDEWEB)

Uhlig, J.; Doriese, W. B.; Fowler, J. W.; Swetz, D. S.; Jaye, C.; Fischer, D. A.; Reintsema, C. D.; Bennett, D. A.; Vale, L. R.; Mandal, U.; O' Neil, G. C.; Miaja-Avila, L.; Joe, Y. I.; El Nahhas, A.; Fullagar, W.; Parnefjord Gustafsson, F.; Sundström, V.; Kurunthu, D.; Hilton, G. C.; Schmidt, D. R.; Ullom, J. N.

2015-04-21

X-ray emission spectroscopy (XES) is a powerful element-selective tool to analyze the oxidation states of atoms in complex compounds, determine their electronic configuration, and identify unknown compounds in challenging environments. Until now the low efficiency of wavelength-dispersive X-ray spectrometer technology has limited the use of XES, especially in combination with weaker laboratory X-ray sources. More efficient energy-dispersive detectors have either insufficient energy resolution because of the statistical limits described by Fano or too low counting rates to be of practical use. This paper updates an approach to high-resolution X-ray emission spectroscopy that uses a microcalorimeter detector array of superconducting transition-edge sensors (TESs). TES arrays are discussed and compared with conventional methods, and shown under which circumstances they are superior. It is also shown that a TES array can be integrated into a table-top time-resolved X-ray source and a soft X-ray synchrotron beamline to perform emission spectroscopy with good chemical sensitivity over a very wide range of energies.

A Decomposition Theorem for Finite Automata.

Science.gov (United States)

Santa Coloma, Teresa L.; Tucci, Ralph P.

1990-01-01

Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)

X-ray absorption near-edge structure of GaN with high Mn concentration grown on SiC

International Nuclear Information System (INIS)

Sancho-Juan, O; Cantarero, A; Garro, N; Cros, A; Martinez-Criado, G; Salome, M; Susini, J; Olguin, D; Dhar, S

2009-01-01

By means of x-ray absorption near-edge structure (XANES) several Ga 1-x Mn x N (0.03 2 ↑ band localized in the gap region, and the corresponding anti-bonding state t 2 ↓, which seem to be responsible for the double structure which appears at the pre-edge absorption region. The shoulders and main absorption peak of the XANES spectra are attributed to transitions from the Mn(1s) band to the conduction bands, which are partially dipole allowed because of the Mn(4p) contribution to these bands.

Formalization of the Integral Calculus in the PVS Theorem Prover

Science.gov (United States)

Butler, Ricky W.

2004-01-01

The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

Noether's theorems applications in mechanics and field theory

CERN Document Server

Sardanashvily, Gennadi

2016-01-01

The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.

Birkhoff-Kellogg theorems on invariant directions for multimaps

Directory of Open Access Journals (Sweden)

Donal O'Regan

2003-04-01

Full Text Available We establish Birkhoff-Kellogg type theorems on invariant directions for a general class of maps. Our results, in particular, apply to Kakutani, acyclic, O'Neill, approximable, admissible, and 𝒰cκ maps.

Strong converse theorems using Rényi entropies

Energy Technology Data Exchange (ETDEWEB)

Leditzky, Felix; Datta, Nilanjana [Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WB (United Kingdom); Wilde, Mark M. [Department of Physics and Astronomy, Center for Computation and Technology, Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)

2016-08-15

We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint http://arxiv.org/abs/1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.

The Second Noether Theorem on Time Scales

Directory of Open Access Journals (Sweden)

Agnieszka B. Malinowska

2013-01-01

Full Text Available We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus.

Comparative study of radiation dose between digital panoramic X-ray unit and general panoramic X-ray unit

International Nuclear Information System (INIS)

Li Qingshan; Duan Tao; Wang Xiaoyun; Zhao Li; Dong Jian; Wei Lei

2010-01-01

Objective: To compare the actual dose of patients who receive the same medical practice by either digital panoramic X-ray unit and general panoramic X-ray unit and give evidence for better selection of oral X-ray examination method. Methods: Round sheet lithium fluoride (LiF) thermoluminescent dosimeters (TLD) were used. The experiment was divided into natural background contrast group, general panoramic X-ray children group, general panoramic X-ray adults group, digital panoramic X-ray children group and digital panoramic X-ray adults group. The dosimeter of natural background radiation was placed at the office of the doctor, the dosimeters of general panoramic X-ray children group and general panoramic X-ray adults group were irradiated by different conditions according to the clinical application of panoramic X-ray to children and adults, the dosimeters of digital panoramic X-ray children group and digital panoramic X-ray adults group were irradiated by different conditions according to the clinical application of digital panoramic X-ray to children and adults. The thermoluminescent dosimeter was used to count and calculate the exposure doses in various groups. Results: The dose of children exposed in general panoramic X-ray unit was 1.28 times of that in digital panoramic X-ray unit, there was significant difference (t=6.904, P<0.01). The dose of adults exposed in general panoramic X-ray unit was 1.55 times of that in the digital panoramic X-ray unit, there also was significant difference (t=-11.514. P< 0.01). Conclusion: The digital panoramic X-ray unit can reduce the dose of patients, so the digital panoramic X-ray unit should be used as far as possible. (authors)

Testing subleading multiple soft graviton theorem for CHY prescription

Science.gov (United States)

Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay

2018-01-01

In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.

Nonextensive Pythagoras' Theorem

OpenAIRE

Dukkipati, Ambedkar

2006-01-01

Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And hence, this property is referred to as Pythagoras' theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches of statistical estimation theory like information geometry. Equvalent of Pythagoras' theo...

Theoretical Mn K-edge XANES for Li2MnO3: DFT + U study

International Nuclear Information System (INIS)

Tamura, Tomoyuki; Ohwaki, Tsukuru; Ito, Atsushi; Ohsawa, Yasuhiko; Kobayashi, Ryo; Ogata, Shuji

2012-01-01

Spectral features of Mn K-edge x-ray absorption near-edge structure (XANES) for Li 2 MnO 3 were calculated using the first-principles full projector augmented wave method with the general gradient approximation plus U method. We demonstrated that the U parameter affects the spectral features in the pre-edge region while it does not affect those in the major absorption region. From the comparison with the experimental spectra and those of reference compounds, we showed that the spectral features of Mn K-edge XANES and the differences in the valence state can be reproduced well. (paper)

Optical theorem, depolarization and vector tomography

International Nuclear Information System (INIS)

Toperverg, B.P.

2003-01-01

A law of the total flux conservation is formulated in the form of the optical theorem. It is employed to explicitly derive equations for the description of the neutron polarization within the range of the direct beam defined by its angular divergence. General considerations are illustrated by calculations using the Born and Eikonal approximations. Results are briefly discussed as applied to Larmor-Fourier tomography

Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator

Science.gov (United States)

Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

2018-03-01

Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.

Extension of Kirk-Saliga Fixed Point Theorem in a Metric Space with a Reflexive Digraph

Directory of Open Access Journals (Sweden)

Karim Chaira

2018-01-01

Full Text Available We extend the result of Kirk-Saliga and we generalize Alfuraidan and Khamsi theorem for reflexive graphs. As a consequence, we obtain the ordered version of Caristi’s fixed point theorem. Some concrete examples are given to support the obtained results.

Coupled-cluster response theory for near-edge x-ray-absorption fine structure of atoms and molecules

DEFF Research Database (Denmark)

Coriani, Sonia; Christiansen, Ove; Fransson, Thomas

2012-01-01

triple corrected excitation energies CCSDR(3). This work is a first step toward the extension of these theoretical electronic structure methods of well-established high accuracy in UV-vis absorption spectroscopies to applications concerned with x-ray radiation. From the imaginary part of the linear...... response function, the near K-edge x-ray absorption spectra of neon, water, and carbon monoxide are determined and compared with experiment. Results at the CCSD level show relative peak intensities in good agreement with experiment with discrepancies in transition energies due to incomplete treatment...

Perron–Frobenius theorem for nonnegative multilinear forms and extensions

OpenAIRE

Friedland, S.; Gaubert, S.; Han, L.

2013-01-01

We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector.

Szegö's theorem on Parreau-Widom sets

DEFF Research Database (Denmark)

Christiansen, Jacob Stordal

2012-01-01

In this paper, we generalize Szego's theorem for orthogonal polynomials on the real line to infinite gap sets of Parreau–Widom type. This notion includes Cantor sets of positive measure. The Szego condition involves the equilibrium measure which in turn is absolutely continuous. Our approach builds...

Pascal’s Theorem in Real Projective Plane

OpenAIRE

Coghetto Roland

2017-01-01

In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines.

Uniform physical theory of diffraction equivalent edge currents for implementation in general computer codes

DEFF Research Database (Denmark)

Johansen, Peter Meincke

1996-01-01

New uniform closed-form expressions for physical theory of diffraction equivalent edge currents are derived for truncated incremental wedge strips. In contrast to previously reported expressions, the new expressions are well-behaved for all directions of incidence and observation and take a finite...... value for zero strip length. Consequently, the new equivalent edge currents are, to the knowledge of the author, the first that are well-suited for implementation in general computer codes...

Edge multi-energy soft x-ray diagnostic in Experimental Advanced Superconducting Tokamak

Energy Technology Data Exchange (ETDEWEB)

Li, Y. L.; Xu, G. S.; Wan, B. N.; Lan, H.; Liu, Y. L.; Wei, J.; Zhang, W.; Hu, G. H.; Wang, H. Q.; Duan, Y. M.; Zhao, J. L.; Wang, L.; Liu, S. C.; Ye, Y.; Li, J.; Lin, X.; Li, X. L. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Tritz, K. [Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218 (United States); Zhu, Y. B. [Department of Physics and Astronomy, University of California, Irvine, California 92697-4575 (United States)

2015-12-15

A multi-energy soft x-ray (ME-SXR) diagnostic has been built for electron temperature profile in the edge plasma region in Experimental Advanced Superconducting Tokamak (EAST) after two rounds of campaigns. Originally, five preamplifiers were mounted inside the EAST vacuum vessel chamber attached to five vertically stacked compact diode arrays. A custom mechanical structure was designed to protect the detectors and electronics under constraints of the tangential field of view for plasma edge and the allocation of space. In the next experiment, the mechanical structure was redesigned with a barrel structure to absolutely isolate it from the vacuum vessel. Multiple shielding structures were mounted at the pinhole head to protect the metal foils from lithium coating. The pre-amplifiers were moved to the outside of the vacuum chamber to avoid introducing interference. Twisted copper cooling tube was embedded into the back-shell near the diode to limit the temperature of the preamplifiers and diode arrays during vacuum vessel baking when the temperature reached 150 °C. Electron temperature profiles were reconstructed from ME-SXR measurements using neural networks.

Edge multi-energy soft x-ray diagnostic in Experimental Advanced Superconducting Tokamak

International Nuclear Information System (INIS)

Li, Y. L.; Xu, G. S.; Wan, B. N.; Lan, H.; Liu, Y. L.; Wei, J.; Zhang, W.; Hu, G. H.; Wang, H. Q.; Duan, Y. M.; Zhao, J. L.; Wang, L.; Liu, S. C.; Ye, Y.; Li, J.; Lin, X.; Li, X. L.; Tritz, K.; Zhu, Y. B.

2015-01-01

A multi-energy soft x-ray (ME-SXR) diagnostic has been built for electron temperature profile in the edge plasma region in Experimental Advanced Superconducting Tokamak (EAST) after two rounds of campaigns. Originally, five preamplifiers were mounted inside the EAST vacuum vessel chamber attached to five vertically stacked compact diode arrays. A custom mechanical structure was designed to protect the detectors and electronics under constraints of the tangential field of view for plasma edge and the allocation of space. In the next experiment, the mechanical structure was redesigned with a barrel structure to absolutely isolate it from the vacuum vessel. Multiple shielding structures were mounted at the pinhole head to protect the metal foils from lithium coating. The pre-amplifiers were moved to the outside of the vacuum chamber to avoid introducing interference. Twisted copper cooling tube was embedded into the back-shell near the diode to limit the temperature of the preamplifiers and diode arrays during vacuum vessel baking when the temperature reached 150 °C. Electron temperature profiles were reconstructed from ME-SXR measurements using neural networks

Pascal’s Theorem in Real Projective Plane

Directory of Open Access Journals (Sweden)

Coghetto Roland

2017-07-01

Full Text Available In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem1. Pappus’ theorem is a special case of a degenerate conic of two lines.

From Einstein's theorem to Bell's theorem: a history of quantum non-locality

Science.gov (United States)

Wiseman, H. M.

2006-04-01

In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.

Limit theorems for multi-indexed sums of random variables

CERN Document Server

Klesov, Oleg

2014-01-01

Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who ...

Birkhoff’s theorem in Lovelock gravity for general base manifolds

Science.gov (United States)

Ray, Sourya

2015-10-01

We extend the Birkhoff’s theorem in Lovelock gravity for arbitrary base manifolds using an elementary method. In particular, it is shown that any solution of the form of a warped product of a two-dimensional transverse space and an arbitrary base manifold must be static. Moreover, the field equations restrict the base manifold such that all the non-trivial intrinsic Lovelock tensors of the base manifold are constants, which can be chosen arbitrarily, and the metric in the transverse space is determined by a single function of a spacelike coordinate which satisfies an algebraic equation involving the constants characterizing the base manifold along with the coupling constants.

Functional limit theorems for generalized variations of the fractional Brownian sheet

DEFF Research Database (Denmark)

Pakkanen, Mikko; Réveillac, Anthony

and on the smallest component of the Hurst parameter vector of the fBs. The limiting process in the former result is another fBs, independent of the original fBs, whereas the limit given by the latter result is an Hermite sheet, which is driven by the same white noise as the original fBs. As an application, we derive...... functional limit theorems for power variations of the fBs and discuss what is a proper way to interpolate them to ensure functional convergence....

Functional limit theorems for generalized variations of the fractional Brownian sheet

DEFF Research Database (Denmark)

Pakkanen, Mikko; Réveillac, Anthony

2016-01-01

and on the smallest component of the Hurst parameter vector of the fBs. The limiting process in the former result is another fBs, independent of the original fBs, whereas the limit given by the latter result is an Hermite sheet, which is driven by the same white noise as the original fBs. As an application, we derive...... functional limit theorems for power variations of the fBs and discuss what is a proper way to interpolate them to ensure functional convergence....

Formalization of the Integral Calculus in the PVS Theorem Prover

Directory of Open Access Journals (Sweden)

Ricky Wayne Butler

2009-04-01

Full Text Available The PVS Theorem prover is a widely used formal verification tool used for the analysis of safetycritical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht’s classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

High-resolution gamma-ray spectroscopy with a microwave-multiplexed transition-edge sensor array

Energy Technology Data Exchange (ETDEWEB)

Noroozian, Omid [National Institute of Standards and Technology, Boulder, Colorado 80305 (United States); Center for Astrophysics and Space Astronomy, University of Colorado, Boulder, Colorado 80309 (United States); Mates, John A. B.; Bennett, Douglas A.; Brevik, Justus A.; Fowler, Joseph W.; Gao, Jiansong; Hilton, Gene C.; Horansky, Robert D.; Irwin, Kent D.; Schmidt, Daniel R.; Vale, Leila R.; Ullom, Joel N. [National Institute of Standards and Technology, Boulder, Colorado 80305 (United States); Kang, Zhao [Department of Physics, University of Colorado, Boulder, Colorado 80309 (United States)

2013-11-11

We demonstrate very high resolution photon spectroscopy with a microwave-multiplexed two-pixel transition-edge sensor (TES) array. We measured a {sup 153}Gd photon source and achieved an energy resolution of 63 eV full-width-at-half-maximum at 97 keV and an equivalent readout system noise of 86 pA/√(Hz) at the TES. The readout circuit consists of superconducting microwave resonators coupled to radio-frequency superconducting-quantum-interference-devices and transduces changes in input current to changes in phase of a microwave signal. We use flux-ramp modulation to linearize the response and evade low-frequency noise. This demonstration establishes one path for the readout of cryogenic X-ray and gamma-ray sensor arrays with more than 10{sup 3} elements and spectral resolving powers R=λ/Δλ>10{sup 3}.

Probing the influence of X-rays on aqueous copper solutions using time-resolved in situ combined video/X-ray absorption near-edge/ultraviolet-visible spectroscopy

NARCIS (Netherlands)

Mesu, J. Gerbrand; Beale, Andrew M.; de Groot, Frank M. F.; Weckhuysen, Bert M.

2006-01-01

Time-resolved in situ video monitoring and ultraviolet-visible spectroscopy in combination with X-ray absorption near-edge spectroscopy (XANES) have been used for the first time in a combined manner to study the effect of synchrotron radiation on a series of homogeneous aqueous copper solutions in a

Comparison of methods for suppressing edge and aliasing artefacts in iterative x-ray CT reconstruction

International Nuclear Information System (INIS)

Zbijewski, Wojciech; Beekman, Freek J

2006-01-01

X-ray CT images obtained with iterative reconstruction (IR) can be hampered by the so-called edge and aliasing artefacts, which appear as interference patterns and severe overshoots in the areas of sharp intensity transitions. Previously, we have demonstrated that these artefacts are caused by discretization errors during the projection simulation step in IR. Although these errors are inherent to IR, they can be adequately suppressed by reconstruction on an image grid that is finer than that typically used for analytical methods such as filtered back-projection. Two other methods that may prevent edge artefacts are: (i) smoothing the projections prior to reconstruction or (ii) using an image representation different from voxels; spherically symmetric Kaiser-Bessel functions are a frequently employed example of such a representation. In this paper, we compare reconstruction on a fine grid with the two above-mentioned alternative strategies for edge artefact reduction. We show that the use of a fine grid results in a more adequate suppression of artefacts than the smoothing of projections or using the Kaiser-Bessel image representation

Differentiability in density-functional theory: Further study of the locality theorem

International Nuclear Information System (INIS)

Lindgren, Ingvar; Salomonson, Sten

2004-01-01

The locality theorem in density-functional theory (DFT) states that the functional derivative of the Hohenberg-Kohn universal functional can be expressed as a local multiplicative potential function, and this is the basis of DFT and of the successful Kohn-Sham model. Nesbet has in several papers [Phys. Rev. A 58, R12 (1998); ibid.65, 010502 (2001); Adv. Quant. Chem, 43, 1 (2003)] claimed that this theorem is in conflict with fundamental quantum physics, and as a consequence that the Hohenberg-Kohn theory cannot be generally valid. We have commented upon these works [Comment, Phys. Rev. A 67, 056501 (2003)] and recently extended the arguments [Adv. Quantum Chem. 43, 95 (2003)]. We have shown that there is no such conflict and that the locality theorem is inherently exact. In the present work we have furthermore verified this numerically by constructing a local Kohn-Sham potential for the 1s2s 3 S state of helium that generates the many-body electron density and shown that the corresponding 2s Kohn-Sham orbital eigenvalue agrees with the ionization energy to nine digits. Similar result is obtained with the Hartree-Fock density. Therefore, in addition to verifying the locality theorem, this result also confirms the so-called ionization-potential theorem

''Vanishing theorem'' for a positive holomorphic vector bundle of undefined rank

International Nuclear Information System (INIS)

Le Potier, J.

1974-01-01

Let M ba a compact complex manifold of dimension n and let E→M be a holomorphic vector bundle over M. Theorem: If E is positive of rank r and if Hsup(p,q)(M,E) is the cohomology of type (p,q) of M with values in E, then Hsup(p,q)(M,E) = O as soon as p+q >=n+r. If r = 1, this is the ''precise vanishing theorem'' due to Kodaira and Nakano; the present paper contains a proof of the general case

State Prices and Implementation of the Recovery Theorem

Directory of Open Access Journals (Sweden)

Alex Backwell

2015-01-01

Full Text Available It is generally held that derivative prices do not contain useful predictive information, that is, information relating to the distribution of future financial variables under the real-world measure. This is because the market’s implicit forecast of the future becomes entangled with market risk preferences during derivative price formation. A result derived by Ross [1], however, recovers the real-world distribution of an equity index, requiring only current prices and mild restrictions on risk preferences. In addition to being of great interest to the theorist, the potential practical value of the result is considerable. This paper addresses implementation of the Ross Recovery Theorem. The theorem is formalised, extended, proved and discussed. Obstacles to application are identified and a workable implementation methodology is developed.

Relationships between the generalized functional method and other methods of nonimaging optical design.

Science.gov (United States)

Bortz, John; Shatz, Narkis

2011-04-01

The recently developed generalized functional method provides a means of designing nonimaging concentrators and luminaires for use with extended sources and receivers. We explore the mathematical relationships between optical designs produced using the generalized functional method and edge-ray, aplanatic, and simultaneous multiple surface (SMS) designs. Edge-ray and dual-surface aplanatic designs are shown to be special cases of generalized functional designs. In addition, it is shown that dual-surface SMS designs are closely related to generalized functional designs and that certain computational advantages accrue when the two design methods are combined. A number of examples are provided. © 2011 Optical Society of America

K-Edge Subtraction Angiography with Synchrotron X-Rays; TOPICAL

International Nuclear Information System (INIS)

Giacomini, John C.

1996-01-01

The purpose of this project was to utilize dual energy, monochromatic X-rays produced from synchrotrons radiation in order to obtain noninvasive medical imaging. The application of synchrotrons radiation to medical imaging is based on the principle of iodine dichromography, first described by Bertil Jacobson of the Karolinska Institute in 1953. Medical imaging using synchrotrons radiation and K-edge dichromography was pioneered at Stanford University under the leadership of Dr. Ed Rubenstein, and the late Nobel Laureate in Physics, Dr. Robert Hofstadter. With progressive refinements in hardware, clinical-quality images were obtained of human coronary arteries utilizing peripheral injections of iodinated contrast agent. These images even now are far superior to those being presented by investigators using MRI as an imaging tool for coronary arteries. However, new supplies and instruments in the cardiac catheterization laboratory have served to transform coronary angiography into an outpatient procedure, with relatively little morbidity. We extended the principles learned with coronary angiography to noninvasive imaging of the human bronchial tree. For these images, we utilized xenon as the contrast agent, as it has a K-edge very similar to that of iodine. In this case, there is no true competing diagnostic test, and pulmonary neoplasm is an enormous public health concern. In early experiments, we demonstrated remarkably clear images of the human bronchial tree. These images have been shown internationally; however, funding difficulties primarily with the Department of Energy have not allowed for progression of this promising avenue of research. One potential criticism of the project is that in order to obtain these images, we utilized national laboratories. Some have questioned whether this would lead to a practical imaging modality. However, we have shown that the technology exists to allow for construction of a miniature storage ring, with a superconducting

Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

Science.gov (United States)

Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.

2018-04-01

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.

Sturm-Picone type theorems for second-order nonlinear differential equations

Directory of Open Access Journals (Sweden)

Aydin Tiryaki

2014-06-01

Full Text Available The aim of this article is to give Sturm-Picone type theorems for the pair of second-order nonlinear differential equations $$\\displaylines{ (p_1(t|x'|^{\\alpha-1}x''+q_1(tf_1(x=0 \\cr (p_2(t|y'|^{\\alpha-1}y''+q_2(tf_2(y=0,\\quad t_1generalize the well-known comparison theorems given by Sturm [19], Picone [18] and Leighton [5] which play a key role in the qualitative behaviour of the solutions.

Convergence theorems for quasi-contractive mappings

International Nuclear Information System (INIS)

Chidume, C.E.

1992-01-01

It is proved that each of two well known fixed point iteration methods (the Mann and Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of a quasi-contractive map in real Banach spacers with property (U, α, m+1, m). These Banach spaces include the L p (or l p ) spaces, p ≥ 2. Our theorems generalize important known results. (author). 29 refs

Morley’s Trisector Theorem

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Coghetto Roland

2015-06-01

Full Text Available Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].

Annealed central limit theorems for the ising model on random graphs

NARCIS (Netherlands)

Giardinà, C.; Giberti, C.; van der Hofstad, R.W.; Prioriello, M.L.

2016-01-01

The aim of this paper is to prove central limit theorems with respect to the annealed measure for the magnetization rescaled by √N of Ising models on random graphs. More precisely, we consider the general rank-1 inhomogeneous random graph (or generalized random graph), the 2-regular configuration

X-ray reflectivity of cobalt and titanium in the vicinity of the Lsub(2,3) absorption edges

International Nuclear Information System (INIS)

Bremer, J.; Kaihola, L.; Keski-Kuha, R.

1980-01-01

X-ray reflectivity across cobalt and titanium Lsub(2,3) absorption edges was measured as a function of energy by means of continuous radiation from a tungsten anode in a grating spectrometer. The real and imaginary parts of the refractive index were obtained from the absorption curves and an exact Kramers-Kronig analysis. A measured fine structure in the reflected intensities was interpreted as an effect of white lines in the absorption spectra. The x-ray intensity was calculated as a function of energy by means of the Fresnel formula. (author)

Riemannian and Lorentzian flow-cut theorems

Science.gov (United States)

Headrick, Matthew; Hubeny, Veronika E.

2018-05-01

We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.

The radiation effects of aspergillus oryzae spores with soft x-rays near the K shell absorption edges of C, N, O elements from synchrotron radiation

International Nuclear Information System (INIS)

Chen Liang; Jiang Shiping; Wan Libiao; Ma Xiaodong; Li Meifang

2007-01-01

The dose deposition of different parts of Aspergillus oryzae spores were analyzed with soft X-ray energies near the K-shell absorption edges of C, N, O elements (4.4nm, 3.2nm and 2.3nm), respectively. At the same time, the spores were irradiated with the three wavelengths of soft X-rays on the soft X-ray microscopy from synchrotron radiation at NSRL, and the survivals were compared. The theoretical analyses showed that the deposition doses of different parts of the spore were varying with X-ray energies because of the effects of C, N, O K-shell absorption edges and elemental contents of the different parts of spore. The experimental studies proved three wavelengths of soft X-rays all had high killing abilities. Among these, 2.3nm wavelength X-rays had higher radiation damage to spore than that of 3.2nm, 4.4nm. (authors)

An extended characterisation theorem for quantum logics

International Nuclear Information System (INIS)

Sharma, C.S.; Mukherjee, M.K.

1977-01-01

Two theorems are proved. In the first properties of an important mapping from an orthocomplemented lattice to itself are studied. In the second the characterisation theorem of Zierler (Pacific J. Math.; 11:1151 (1961)) is extended to obtain a very useful theorem characterising orthomodular lattices. Since quantum logics are merely sigma-complete orthomodular lattices, the principal result is, for application in quantum physics, a characterisation theorem for quantum logics. (author)

A Brooks type theorem for the maximum local edge connectivity

DEFF Research Database (Denmark)

Stiebitz, Michael; Toft, Bjarne

2018-01-01

For a graph $G$, let $\\cn(G)$ and $\\la(G)$ denote the chromatic number of $G$ and the maximum local edge connectivity of $G$, respectively. A result of Dirac \\cite{Dirac53} implies that every graph $G$ satisfies $\\cn(G)\\leq \\la(G)+1$. In this paper we characterize the graphs $G$ for which $\\cn......(G)=\\la(G)+1$. The case $\\la(G)=3$ was already solved by Alboulker {\\em et al.\\,} \\cite{AlboukerV2016}. We show that a graph $G$ with $\\la(G)=k\\geq 4$ satisfies $\\cn(G)=k+1$ if and only if $G$ contains a block which can be obtained from copies of $K_{k+1}$ by repeated applications of the Haj\\'os join....

Electronic structure and optical properties of CdS{sub x}Se{sub 1−x} solid solution nanostructures from X-ray absorption near edge structure, X-ray excited optical luminescence, and density functional theory investigations

Energy Technology Data Exchange (ETDEWEB)

Murphy, M. W. [DESY (Deutsches Elektronen-Synchrotron), FS-PEX, Notkestrasse 85, 22607 Hamburg (Germany); Yiu, Y. M., E-mail: yyiu@uwo.ca; Sham, T. K. [Department of Chemistry, University of Western Ontario, London, ON N6A5B7 (Canada); Ward, M. J. [Cornell High Energy Synchrotron Source (CHESS), Cornell University, Ithaca, NY 14853 (United States); Liu, L. [Institute of Functional Nano and Soft Materials (FUNSOM) and Soochow University-Western University Center for Synchrotron Radiation Research, Soochow University, Suzhou, Jiangsu, 215123 (China); Hu, Y. [Canadian Light Source, University of Saskatchewan, Saskatoon, SK S7N2V3 (Canada); Zapien, J. A. [Center Of Super-Diamond and Advanced Films (COSDAF) and Department of Physics and Materials Science, City University of Hong Kong, Hong Kong SAR (China); Liu, Yingkai [Institute of Physics and Electronic Information, Yunnan Normal University, Kunming, Yunnan, 650500 (China)

2014-11-21

The electronic structure and optical properties of a series of iso-electronic and iso-structural CdS{sub x}Se{sub 1−x} solid solution nanostructures have been investigated using X-ray absorption near edge structure, extended X-ray absorption fine structure, and X-ray excited optical luminescence at various absorption edges of Cd, S, and Se. It is found that the system exhibits compositions, with variable local structure in-between that of CdS and CdSe accompanied by tunable optical band gap between that of CdS and CdSe. Theoretical calculation using density functional theory has been carried out to elucidate the observations. It is also found that luminescence induced by X-ray excitation shows new optical channels not observed previously with laser excitation. The implications of these observations are discussed.

The Semantic Isomorphism Theorem in Abstract Algebraic Logic

Czech Academy of Sciences Publication Activity Database

Moraschini, Tommaso

2016-01-01

Roč. 167, č. 12 (2016), s. 1298-1331 ISSN 0168-0072 R&D Projects: GA ČR GA13-14654S Institutional support: RVO:67985807 Keywords : algebra izable logics * abstract algebra ic logic * structural closure operators * semantic isomorphism theorem * evaluational frames * compositional lattice Subject RIV: BA - General Mathematics Impact factor: 0.647, year: 2016

The Levy sections theorem revisited

International Nuclear Information System (INIS)

Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Silva, Sergio Da

2007-01-01

This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets

The Levy sections theorem revisited

Science.gov (United States)

Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Da Silva, Sergio

2007-06-01

This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.

A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems

Science.gov (United States)

Dragičević, D.; Froyland, G.; González-Tokman, C.; Vaienti, S.

2018-01-01

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance is the extension of the spectral method, commonly used in limit laws for deterministic maps, to the general random setting. We achieve this via multiplicative ergodic theory and the development of a general framework to control the regularity of Lyapunov exponents of twisted transfer operator cocycles with respect to a twist parameter. While some versions of the LDP and CLT have previously been proved with other techniques, the local central limit theorem is, to our knowledge, a completely new result, and one that demonstrates the strength of our method. Applications include non-autonomous (piecewise) expanding maps, defined by random compositions of the form {T_{σ^{n-1} ω} circ\\cdotscirc T_{σω}circ T_ω} . An important aspect of our results is that we only assume ergodicity and invertibility of the random driving {σ:Ω\\toΩ} ; in particular no expansivity or mixing properties are required.

The Completeness Theorem of Gödel - An Introduction to ...

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 7. The Completeness Theorem of Gödel - An Introduction to Mathematical Logic. S M Srivastava. General Article Volume 6 Issue 7 July 2001 pp 29-41. Fulltext. Click here to view fulltext PDF. Permanent link:

Definable davies' theorem

DEFF Research Database (Denmark)

Törnquist, Asger Dag; Weiss, W.

2009-01-01

We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible.......We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible....

Demonstration of iodine K-edge imaging by use of an energy-discrimination X-ray computed tomography system with a cadmium telluride detector.

Science.gov (United States)

Abudurexiti, Abulajiang; Kameda, Masashi; Sato, Eiichi; Abderyim, Purkhet; Enomoto, Toshiyuki; Watanabe, Manabu; Hitomi, Keitaro; Tanaka, Etsuro; Mori, Hidezo; Kawai, Toshiaki; Takahashi, Kiyomi; Sato, Shigehiro; Ogawa, Akira; Onagawa, Jun

2010-07-01

An energy-discrimination K-edge X-ray computed tomography (CT) system is useful for increasing the contrast resolution of a target region by utilizing contrast media. The CT system has a cadmium telluride (CdTe) detector, and a projection curve is obtained by linear scanning with use of the CdTe detector in conjunction with an X-stage. An object is rotated by a rotation step angle with use of a turntable between the linear scans. Thus, CT is carried out by repetition of the linear scanning and the rotation of an object. Penetrating X-ray photons from the object are detected by the CdTe detector, and event signals of X-ray photons are produced with use of charge-sensitive and shaping amplifiers. Both the photon energy and the energy width are selected by use of a multi-channel analyzer, and the number of photons is counted by a counter card. For performing energy discrimination, a low-dose-rate X-ray generator for photon counting was developed; the maximum tube voltage and the minimum tube current were 110 kV and 1.0 microA, respectively. In energy-discrimination CT, the tube voltage and the current were 60 kV and 20.0 microA, respectively, and the X-ray intensity was 0.735 microGy/s at 1.0 m from the source and with a tube voltage of 60 kV. Demonstration of enhanced iodine K-edge X-ray CT was carried out by selection of photons with energies just beyond the iodine K-edge energy of 33.2 keV.

Green's theorem and Gorenstein sequences

OpenAIRE

Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su

2016-01-01

We study consequences, for a standard graded algebra, of extremal behavior in Green's Hyperplane Restriction Theorem. First, we extend his Theorem 4 from the case of a plane curve to the case of a hypersurface in a linear space. Second, assuming a certain Lefschetz condition, we give a connection to extremal behavior in Macaulay's theorem. We apply these results to show that $(1,19,17,19,1)$ is not a Gorenstein sequence, and as a result we classify the sequences of the form $(1,a,a-2,a,1)$ th...

Cosmological singularity theorems for f ( R ) gravity theories

International Nuclear Information System (INIS)

Alani, Ivo; Santillán, Osvaldo P.

2016-01-01

In the present work some generalizations of the Hawking singularity theorems in the context of f ( R ) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition ( T ij −( g ij /2) T ) k i k j ≥ 0 for any generic unit time like field k i ; the scalaron takes bounded positive values during its evolution and the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper-surface Σ for which the expansion parameter θ of the geodesic congruence emanating orthogonally from Σ satisfies some specific bounds, then the resulting space time is geodesically incomplete. Some mathematical results of reference [92] are very important for proving this. The generalized theorems presented here apply directly for some specific models such as the Hu-Sawicki or Starobinsky ones [27,38]. For other scenarios, some extra assumptions should be implemented in order to have a geodesically incomplete space time. The hypothesis considered in this text are sufficient, but not necessary. In other words, their negation does not imply that a singularity is absent.

Low Z elements (Mg, Al, and Si) K-edge X-ray absorption spectroscopy in minerals and disordered systems

International Nuclear Information System (INIS)

Ildefonse, P.; Calas, G.; Flank, A.M.; Lagarde, P.

1995-01-01

Soft X-ray absorption near edge spectroscopy (XANES) and extended X-ray absorption fine structure (EXAFS) spectroscopy have been performed at the Mg-, Al- and Si-K edges in order to establish the ability of this spectroscopy to derive structural information in disordered solids such as glasses and gels. Mg- and Al-K XANES are good structural probes to determine the coordination state of these elements in important minerals, glasses and gels. In a CaO-MgO-2SiO 2 glass Mg XANES spectra differ from that found in the crystalline equivalent, with a significant shift of the edge maxima to lower energy, consistent with a CN lower than 6. Mg-EXAFS on the same sample are in agreement and indicate the presence of 5-coordinated Mg with Mg-O distances of 2.01 A. In aluminosilicate gels, Al-K XANES has been used to investigate the [4]Al/Al total ratios. These ratios increase as the Al/Si ratios decrease. Aluminosilicate and ferric-silicate gels were studied by using Si-K edge XANES. XANES spectra differ significantly among the samples studied. Aluminosilicate gels with Al/Si=1 present a different Al and Si local environment from that known in clay minerals with the same Al/Si ratio. The gel-to-mineral transformation thus implies a dissolution-recrystallization mechanism. On the contrary, ferric-silicate gel presents a Si local environment close to that found in nontronite which may be formed by a long range ordering of the initial gels. (orig.)

Low Z elements (Mg, Al, and Si) K-edge X-ray absorption spectroscopy in minerals and disordered systems

Science.gov (United States)

Ildefonse, Ph.; Calas, G.; Flank, A. M.; Lagarde, P.

1995-05-01

Soft X-ray absorption near edge spectroscopy (XANES) and extended X-ray absorption fine structure (EXAFS) spectroscopy have been performed at the Mg-, Al- and Si-K edges in order to establish the ability of this spectroscopy to derive structural information in disordered solids such as glasses and gels. Mg- and Al-K XANES are good structural probes to determine the coordination state of these elements in important minerals, glasses and gels. In a CaOsbnd MgOsbnd 2SiO2 glass Mg XANES spectra differ from that found in the crystalline equivalent, with a significant shift of the edge maxima to lower energy, consistent with a CN lower than 6. Mg-EXAFS on the same sample are in agreement and indicate the presence of 5-coordinated Mg with Mgsbnd O distances of 2.01Å. In aluminosilicate gels, Alsbnd K XANES has been used to investigate the [4]Al/Altotal ratios. These ratios increase as the Al/Si ratios decrease. Aluminosilicate and ferric-silicate gels were studied by using Sisbnd K edge XANES. XANES spectra differ significantly among the samples studied. Aluminosilicate gels with Al/Si= 1 present a different Al and Si local environment from that known in clay minerals with the same Al/Si ratio. The gel-to-mineral transformation thus implies a dissolution-recrystallization mechanism. On the contrary, ferric-silicate gel presents a Si local environment close to that found in nontronite which may be formed by a long range ordering of the initial gels.

Simulation of Near-Edge X-ray Absorption Fine Structure with Time-Dependent Equation-of-Motion Coupled-Cluster Theory.

Science.gov (United States)

Nascimento, Daniel R; DePrince, A Eugene

2017-07-06

An explicitly time-dependent (TD) approach to equation-of-motion (EOM) coupled-cluster theory with single and double excitations (CCSD) is implemented for simulating near-edge X-ray absorption fine structure in molecular systems. The TD-EOM-CCSD absorption line shape function is given by the Fourier transform of the CCSD dipole autocorrelation function. We represent this transform by its Padé approximant, which provides converged spectra in much shorter simulation times than are required by the Fourier form. The result is a powerful framework for the blackbox simulation of broadband absorption spectra. K-edge X-ray absorption spectra for carbon, nitrogen, and oxygen in several small molecules are obtained from the real part of the absorption line shape function and are compared with experiment. The computed and experimentally obtained spectra are in good agreement; the mean unsigned error in the predicted peak positions is only 1.2 eV. We also explore the spectral signatures of protonation in these molecules.

Kerr-de Sitter spacetime, Penrose process, and the generalized area theorem

Science.gov (United States)

Bhattacharya, Sourav

2018-04-01

We investigate various aspects of energy extraction via the Penrose process in the Kerr-de Sitter spacetime. We show that the increase in the value of a positive cosmological constant, Λ , always reduces the efficiency of this process. The Kerr-de Sitter spacetime has two ergospheres associated with the black hole and the cosmological event horizons. We prove by analyzing turning points of the trajectory that the Penrose process in the cosmological ergoregion is never possible. We next show that in this process both the black hole and cosmological event horizons' areas increase, and the latter becomes possible when the particle coming from the black hole ergoregion escapes through the cosmological event horizon. We identify a new, local mass function instead of the mass parameter, to prove this generalized area theorem. This mass function takes care of the local spacetime energy due to the cosmological constant as well, including that which arises due to the frame-dragging effect due to spacetime rotation. While the current observed value of Λ is quite small, its effect in this process could be considerable in the early Universe scenario where its value is much larger, where the two horizons could have comparable sizes. In particular, the various results we obtain here are also evaluated in a triply degenerate limit of the Kerr-de Sitter spacetime we find, in which radial values of the inner, the black hole and the cosmological event horizons are nearly coincident.

No-Hair Theorem for Black Holes in Astrophysical Environments

Science.gov (United States)

Gürlebeck, Norman

2015-04-01

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

No-hair theorem for black holes in astrophysical environments.

Science.gov (United States)

Gürlebeck, Norman

2015-04-17

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

X-ray metrology of an array of active edge pixel sensors for use at synchrotron light sources

Science.gov (United States)

Plackett, R.; Arndt, K.; Bortoletto, D.; Horswell, I.; Lockwood, G.; Shipsey, I.; Tartoni, N.; Williams, S.

2018-01-01

We report on the production and testing of an array of active edge silicon sensors as a prototype of a large array. Four Medipix3RX.1 chips were bump bonded to four single chip sized Advacam active edge n-on-n sensors. These detectors were then mounted into a 2 by 2 array and tested on B16 at Diamond Light Source with an x-ray beam spot of 2um. The results from these tests, compared with optical metrology demonstrate that this type of sensor is sensitive to the physical edge of the silicon, with only a modest loss of efficiency in the final two rows of pixels. We present the efficiency maps recorded with the microfocus beam and a sample powder diffraction measurement. These results give confidence that this sensor technology can be used effectively in larger arrays of detectors at synchrotron light sources.

Edge corrections to electromagnetic Casimir energies from general-purpose Mathieu-function routines

Science.gov (United States)

Blose, Elizabeth Noelle; Ghimire, Biswash; Graham, Noah; Stratton-Smith, Jeremy

2015-01-01

Scattering theory methods make it possible to calculate the Casimir energy of a perfectly conducting elliptic cylinder opposite a perfectly conducting plane in terms of Mathieu functions. In the limit of zero radius, the elliptic cylinder becomes a finite-width strip, which allows for the study of edge effects. However, existing packages for computing Mathieu functions are insufficient for this calculation because none can compute Mathieu functions of both the first and second kind for complex arguments. To address this shortcoming, we have written a general-purpose Mathieu-function package, based on algorithms developed by Alhargan. We use these routines to find edge corrections to the proximity force approximation for the Casimir energy of a perfectly conducting strip opposite a perfectly conducting plane.

Macroscopic proof of the Jarzynski–Wójcik fluctuation theorem for heat exchange

International Nuclear Information System (INIS)

Sughiyama, Yuki; Abe, Sumiyoshi

2008-01-01

In a recent work, Jarzynski and Wójcik (2004 Phys. Rev. Lett. 92 230602) have shown by using the properties of Hamiltonian dynamics and a statistical mechanical consideration that heat exchange through contact between two systems initially prepared at different temperatures obeys a fluctuation theorem. Here, another proof is presented, in which only macroscopic thermodynamic quantities are employed. The detailed balance condition is found to play an essential role. As a result, the theorem is found to hold under very general conditions

Determination of the separation between the soft X-ray K-emission and K-absorption edges in beryllium metal from self-absorption studies

International Nuclear Information System (INIS)

Crisp, R.S.

1979-01-01

Recent theoretical studies have aroused interest in the phonon broadening of the soft X-ray emission and absorption edges and the shift between them. Using a self-absorption technique a separation of about 0.2 eV is shown to exist between the edges in Be metal. This shift explains the very small self-absorption effects previously observed in Be. (Auth.)

Distributed transition-edge sensors for linearized position response in a phonon-mediated X-ray imaging spectrometer

Science.gov (United States)

Cabrera, Blas; Brink, Paul L.; Leman, Steven W.; Castle, Joseph P.; Tomada, Astrid; Young, Betty A.; Martínez-Galarce, Dennis S.; Stern, Robert A.; Deiker, Steve; Irwin, Kent D.

2004-03-01

For future solar X-ray satellite missions, we are developing a phonon-mediated macro-pixel composed of a Ge crystal absorber with four superconducting transition-edge sensors (TES) distributed on the backside. The X-rays are absorbed on the opposite side and the energy is converted into phonons, which are absorbed into the four TES sensors. By connecting together parallel elements into four channels, fractional total energy absorbed between two of the sensors provides x-position information and the other two provide y-position information. We determine the optimal distribution for the TES sub-elements to obtain linear position information while minimizing the degradation of energy resolution.

A p-adic Perron-Frobenius Theorem

OpenAIRE

Costa, Robert; Dynes, Patrick; Petsche, Clayton

2015-01-01

We prove that if an $n\\times n$ matrix defined over ${\\mathbb Q}_p$ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in ${\\mathbb Q}_p$, and that iteration of the (normalized) matrix converges to a projection operator onto the corresponding eigenspace. This result may be viewed as a $p$-adic analogue of the Perron-Frobenius theorem for positive real matrices.

Graph-like continua, augmenting arcs, and Menger's theorem

DEFF Research Database (Denmark)

Thomassen, Carsten; Vella, Antoine

2008-01-01

We show that an adaptation of the augmenting path method for graphs proves Menger's Theorem for wide classes of topological spaces. For example, it holds for locally compact, locally connected, metric spaces, as already known. The method lends itself particularly well to another class of spaces......, connected graph. While closed subsets of such a space behave nicely in that they are compact and locally connected (and therefore locally arcwise connected), the general subspaces do not: They may be connected without being arcwise connected. Nevertheless, they satisfy Menger's Theorem......., namely the locally arcwise connected, hereditarily locally connected, metric spaces. Finally, it applies to every space where every point can be separated from every closed set not containing it by a finite set, in particular to every subspace of the Freudenthal compactification of a locally finite...

Quantum Many-Body Virial Theorem And Matsubara Green's Function

International Nuclear Information System (INIS)

Anma, D.; Fukuda, T.; Fujita, M.; Toyoda, T.; Takiuchi, K.

2004-01-01

We discuss the quantum field theoretical formulation of the virial theorem on the basis of the canonical field theory of the generalized coordinate transformation and show the equation of motion of a charged Fermion system coupled to an electromagnetic field. Possible application to Fermion-Boson mixtures is also discussed

Surface modification study of borate materials from B K-edge X-ray absorption spectroscopy

Science.gov (United States)

Kasrai, Masoud; Fleet, Michael E.; Muthupari, Swaminathan; Li, D.; Bancroft, G. M.

The B K-edge X-ray absorption near-edge structure (XANES) spectra of two borates with tetrahedrally-coordinated B [[4]B; natural danburite (CaB2Si2O8) and synthetic boron phosphate (BPO4)] have been recorded in total electron yield (TEY) and fluorescence yield (FY) modes to investigate the surface and bulk structure of these materials. The TEY XANES measurement shows that danburite is susceptible to surface damage involving conversion of [4]B sites to [3]B sites by reaction with moisture and/or mechanical abrasion (grinding, polishing, etc.). The bulk of the mineral is essentially unaffected. Commercial boron phosphate powder exhibits more extensive surface and bulk damage, which increases with air exposure but is recovered on heating at 650°C. In contrast to ELNES, the XANES technique is not affected by beam damage and when collected in the FY mode is capable of yielding meaningful information on the coordination and intermediate-range structure of B in borate and borosilicate materials.

Gibbs' theorem for open systems with incomplete statistics

International Nuclear Information System (INIS)

Bagci, G.B.

2009-01-01

Gibbs' theorem, which is originally intended for canonical ensembles with complete statistics has been generalized to open systems with incomplete statistics. As a result of this generalization, it is shown that the stationary equilibrium distribution of inverse power law form associated with the incomplete statistics has maximum entropy even for open systems with energy or matter influx. The renormalized entropy definition given in this paper can also serve as a measure of self-organization in open systems described by incomplete statistics.

The supersymmetric Adler-Bardeen theorem and regularization by dimensional reduction

International Nuclear Information System (INIS)

Ensign, P.; Mahanthappa, K.T.

1987-01-01

We examine the subtraction scheme dependence of the anomaly of the supersymmetric, gauge singlet axial current in pure and coupled supersymmetric Yang-Mills theories. Preserving supersymmetry and gauge invariance explicitly by using supersymmetric background field theory and dimensional reduction, we show that only the one-loop value of the axial anomaly is subtraction scheme independent, and that one can always define a subtraction scheme in which the Adler-Bardeen theorem is satisfied to all orders in perturbation theory. In general this subtraction scheme may be non-minimal, but in both the pure and the coupled theories, the Adler-Bardeen theorem is satisfied to two loops in minimal subtraction. (orig.)

Non-compact random generalized games and random quasi-variational inequalities

OpenAIRE

Yuan, Xian-Zhi

1994-01-01

In this paper, existence theorems of random maximal elements, random equilibria for the random one-person game and random generalized game with a countable number of players are given as applications of random fixed point theorems. By employing existence theorems of random generalized games, we deduce the existence of solutions for non-compact random quasi-variational inequalities. These in turn are used to establish several existence theorems of noncompact generalized random ...

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 ...

Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories

International Nuclear Information System (INIS)

Ensign, P.W.

1987-01-01

By the Adler-Bardeen theorem, only one-loop Feynman diagrams contribute to the anomalous divergences of quantum axial currents. The anomalous nature of scale transformations is manifested by an anomalous trace of the energy-momentum tensor, T/sup μ//sub μ/. Renormalization group arguments show that the quantum T/sup μ//sub μ/ must be proportional to the β-function. Since the β-function receives contributions at all loop levels, the Adler-Bardeen theorem appears to conflict with supersymmetry. Recently Grisaru, Milewski and Zanon constructed a supersymmetric axial current for pure supersymmetric Yang-Mills theory which satisfies the Adler-Bardeen theorem to two-loops. They used supersymmetric background field theory and regularization by dimensional reduction to maintain manifest supersymmetry and gauge invariance. In this thesis, their construction is extended to supersymmetric Yang-Mills theory coupled to chiral matter fields. The Adler-Bardeen theorem is then proven to all orders in perturbation theory for both the pure and coupled theories. The extension to coupled supersymmetric Yang-Mills supports the general validity of these techniques, and adds considerable insight into the structure of the anomalies. The all orders proof demonstrates that there is no conflict between supersymmetry and the Adler-Bardeen theorem

Generalized theory of resonance scattering (GTRS) using the translational addition theorem for spherical wave functions.

Science.gov (United States)

Mitri, Farid

2014-11-01

The generalized theory of resonance scattering (GTRS) by an elastic spherical target in acoustics is extended to describe the arbitrary scattering of a finite beam using the addition theorem for the spherical wave functions of the first kind under a translation of the coordinate origin. The advantage of the proposed method over the standard discrete spherical harmonics transform previously used in the GTRS formalism is the computation of the off-axial beam-shape coefficients (BSCs) stemming from a closed-form partial-wave series expansion representing the axial BSCs in spherical coordinates. With this general method, the arbitrary acoustical scattering can be evaluated for any particle shape and size, whether the particle is partially or completely illuminated by the incident beam. Numerical examples for the axial and off-axial resonance scattering from an elastic sphere placed arbitrarily in the field of a finite circular piston transducer with uniform vibration are provided. Moreover, the 3-D resonance directivity patterns illustrate the theory and reveal some properties of the scattering. Numerous applications involving the scattering phenomenon in imaging, particle manipulation, and the characterization of multiphase flows can benefit from the present analysis because all physically realizable beams radiate acoustical waves from finite transducers as opposed to waves of infinite extent.

Ray Tracing through the Edge Focusing of Rectangular Benders and an Improved Model for the Los Alamos Proton Storage Ring

Energy Technology Data Exchange (ETDEWEB)

Kolski, Jeffrey S. [Los Alamos National Laboratory; Barlow, David B. [Los Alamos National Laboratory; Macek, Robert J. [Los Alamos National Laboratory; McCrady, Rodney C. [Los Alamos National Laboratory

2011-01-01

Particle ray tracing through simulated 3D magnetic fields was executed to investigate the effective quadrupole strength of the edge focusing of the rectangular bending magnets in the Los Alamos Proton Storage Ring (PSR). The particle rays receive a kick in the edge field of the rectangular dipole. A focal length may be calculated from the particle tracking and related to the fringe field integral (FINT) model parameter. This tech note introduces the baseline lattice model of the PSR and motivates the need for an improvement in the baseline model's vertical tune prediction, which differs from measurement by .05. An improved model of the PSR is created by modifying the fringe field integral parameter to those suggested by the ray tracing investigation. This improved model is then verified against measurement at the nominal PSR operating set point and at set points far away from the nominal operating conditions. Lastly, Linear Optics from Closed Orbits (LOCO) is employed in an orbit response matrix method for model improvement to verify the quadrupole strengths of the improved model.

Determination of the separation between the soft X-ray K-emission and K-absorption edges in beryllium metal from self-absorption studies

International Nuclear Information System (INIS)

Crisp, R.S.

1979-01-01

Recent theoretical studies have aroused interest in the phonon broadening of the soft X-ray emission and absorption edges and the shift between them. Using a self-absorption technique a separation of about 0.2 eV is shown to exist between the edges in Be metal. This shift explains the very small self-absorption effects previously observed in Be by Crisp (1977). (Auth.)

New theoretical investigation resolving discrepancies of atomic form factors and attenuation coefficients in the near-edge soft x-ray regime

International Nuclear Information System (INIS)

Chantler, C.T.

2000-01-01

Full text: Reliable knowledge of the complex X-ray form factor and the photoelectric attenuation coefficient is required for crystallography, medical diagnosis, refractive index studies and XAFS. Discrepancies between currently used theoretical approaches of 200% exist for numerous elements from 1 keV to 3 keV X-ray energies. This work derives new theoretical results in near-edge soft X-ray regions and improves upon the theoretical uncertainty in these regions by a factor of 10. This work was also reported in J.Phys.Chem.Ref.Data (2000)

"A Separation Theorem of Active Management and Synthetic Enhanced Active Strategies"(in Japanese)

OpenAIRE

Takao Kobayashi; Seiji Minami

2008-01-01

We propose a Separation Theorem of Active Management. It asserts that in the so-called Enhanced Active Portfolio framework the efficient frontier is linear in the active return/active risk space, and one can separate the determination of optimal active portfolio weights from the determination of optimal leverage ratio. The risk preference of investors does not play any role in the former decision. The theorem holds under a fairly general set of conditions on portfolio restrictions. As such it...

Symbolic logic and mechanical theorem proving

CERN Document Server

Chang, Chin-Liang

1969-01-01

This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.

On a theorem of Cattabriga related to Stokes equations

International Nuclear Information System (INIS)

Georgescu, V.

1978-01-01

We study the ''generalized Stokes boundary value problem'', which is a (generalization of a) linearized version of Navier-Stokes equations and we show the existence and unicity of the weak solution. It is known that these results can be used to prove the existence of weak (local) solutions to the Navier-Stokes equations. However, we are mainly interested in the method of proving it will be seen how easy the result follows from some general theorems about differential forms on a Riemannian manifold. (author)

Near K-edge measurement of the X-ray attenuation coefficient of heavy elements using a tuneable X-ray source based on an electron LINAC

CERN Document Server

Materna, T; Mondelaers, W; Masschaele, B

2000-01-01

The X-ray attenuation coefficients of bismuth and of uranium were measured in the regions of 40-240 and 70-240 keV, respectively, using a tuneable hard X-ray source based on the linear electron accelerator at the University of Ghent. Results were compared with the semi-empirical values of Storm and Israel and to the theoretical values of Berger and Hubbell. We also propose a simple function for the attenuation coefficient in the vicinity of the K-edge for uranium and in an extended range of energy for bismuth. The set-up of the source at Ghent is described and the future improvements are explained.

X-ray diffraction and X-ray K absorption near edge studies of copper (II) complexes with amino acids

Science.gov (United States)

Sharma, P. K.; Mishra, Ashutosh; Malviya, Varsha; Kame, Rashmi; Malviya, P. K.

2017-05-01

Synthesis of copper (II) complexes [CuL1L2X].nH2O, where n=1, 2,3 (X=Cl,Br,NO3) (L1is 2,2’-bipyridine and L2 is L-tyrosine) by the chemical root method. The XRD data for the samples have been recorded. EXAFS spectra have also been recorded at the K-edge of Cu using the dispersive beam line BL-8 at 2.5 Gev Indus-2 Synchrotron radiation source at RRCAT, Indore, India. XRD and EXAFS data have been analysed using the computer software. X-ray diffraction studies of all complexes indicate their crystalline nature. Lattice parameter, bond length, particle size have been determined from XRD data.

Feynman-Hellmann theorem for resonances and the quest for QCD exotica

Energy Technology Data Exchange (ETDEWEB)

Ruiz de Elvira, J. [University of Bern, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Meissner, U.G. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen-und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Juelich Center for Hadron Physics and JARA-HPC, Forschungszentrum Juelich, Institute for Advanced Simulation (IAS-4), Institut fuer Kernphysik (IKP-3), Juelich (Germany); Rusetsky, A. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen-und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Schierholz, G. [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany)

2017-10-15

The generalization of the Feynman-Hellmann theorem for resonance states in quantum field theory is derived. On the basis of this theorem, a criterion is proposed to study the possible exotic nature of certain hadronic states emerging in QCD. It is shown that this proposal is supported by explicit calculations in chiral perturbation theory and by large-N{sub c} arguments. Analyzing recent lattice data on the quark mass dependence in the pseudoscalar, vector meson, baryon octet and baryon decuplet sectors, we conclude that, as expected, these are predominately quark-model states, albeit the corrections are non-negligible. (orig.)

Asymptotic form of the reciprocity theorem with applications in x-ray scattering

International Nuclear Information System (INIS)

Caticha, Ariel

2000-01-01

The emission of electromagnetic waves from a source within or near a nontrivial medium (with or without boundaries, crystalline or amorphous, with inhomogeneities, absorption, and so on) is sometimes studied using the reciprocity principle which is a variation of the method of Green's functions. If one is only interested in the asymptotic radiation fields the generality of these methods may actually be a shortcoming: obtaining expressions valid for the uninteresting near fields is not just a wasted effort but may be prohibitively difficult. In this work we obtain a modified form of the reciprocity principle which gives the asymptotic radiation field directly. The method may also be used to study scattering problems. We give a few pedagogical examples and then, as more challenging applications, we calculate the specular reflection of x rays by a rough surface and by a smoothly graded surface taking polarization effects into account. In conventional treatments of reflection, x rays are treated as scalar waves; polarization effects are neglected. This is a good approximation at grazing incidence but becomes increasingly questionable for soft x rays and UV at higher incidence angles

Coalgebraic Lindström Theorems

NARCIS (Netherlands)

Kurz, A.; Venema, Y.

2010-01-01

We study modal Lindström theorems from a coalgebraic perspective. We provide three different Lindström theorems for coalgebraic logic, one of which is a direct generalisation of de Rijke's result for Kripke models. Both the other two results are based on the properties of bisimulation invariance,

Generalized Synchronization of Time-Delayed Discrete Systems

International Nuclear Information System (INIS)

Jing Jianyi; Min Lequan

2009-01-01

This paper establishes two theorems for two time-delayed (chaotic) discrete systems to achieve time-delayed generalized synchronization (TDGS). These two theorems uncover the general forms of two TDGS systems via a prescribed transformation. As examples, we convert the Lorenz three-dimensional chaotic map to an equal time-delayed system as the driving system, and construct the TDGS driven systems according to the Theorems 1 and 2. Numerical simulations demonstrate the effectiveness of the proposed theorems. (interdisciplinary physics and related areas of science and technology)

Modulus of smoothness and theorems concerning approximation on compact groups

Directory of Open Access Journals (Sweden)

H. Vaezi

2003-01-01

Full Text Available We consider the generalized shift operator defined by (Shuf(g=∫Gf(tut−1gdt on a compact group G, and by using this operator, we define “spherical” modulus of smoothness. So, we prove Stechkin and Jackson-type theorems.

Strong versions of Bell's theorem

International Nuclear Information System (INIS)

Stapp, H.P.

1994-01-01

Technical aspects of a recently constructed strong version of Bell's theorem are discussed. The theorem assumes neither hidden variables nor factorization, and neither determinism nor counterfactual definiteness. It deals directly with logical connections. Hence its relationship with modal logic needs to be described. It is shown that the proof can be embedded in an orthodox modal logic, and hence its compatibility with modal logic assured, but that this embedding weakens the theorem by introducing as added assumptions the conventionalities of the particular modal logic that is adopted. This weakening is avoided in the recent proof by using directly the set-theoretic conditions entailed by the locality assumption

Scattering of ECRF waves by edge density fluctuations and blobs

Directory of Open Access Journals (Sweden)

Ram Abhay K.

2015-01-01

Full Text Available The scattering of electron cyclotron waves by density blobs embedded in the edge region of a fusion plasma is studied using a full-wave model. The full-wave theory is a generalization of the usual approach of geometric optics ray scattering by blobs. While the latter allows for only refraction of waves, the former, more general formulation, includes refraction, reflection, and diffraction of waves. Furthermore, the geometric optics, ray tracing, model is limited to blob densities that are slightly different from the background plasma density. Observations in tokamak experiments show that the fluctuating density differs from the background plasma density by 20% or more. Thus, the geometric optics model is not a physically realistic model of scattering of electron cyclotron waves by plasma blobs. The differences between the ray tracing approach and the full-wave approach to scattering are illustrated in this paper.

An Experiment on a Physical Pendulum and Steiner's Theorem

Science.gov (United States)

Russeva, G. B.; Tsutsumanova, G. G.; Russev, S. C.

2010-01-01

Introductory physics laboratory curricula usually include experiments on the moment of inertia, the centre of gravity, the harmonic motion of a physical pendulum, and Steiner's theorem. We present a simple experiment using very low cost equipment for investigating these subjects in the general case of an asymmetrical test body. (Contains 3 figures…

Structural Disorder in Colloidal InAs and CdSe Nanocrystals Observed by X-Ray Absorption Near-Edge Spectroscopy

International Nuclear Information System (INIS)

Hamad, K.S.; Hamad, K.S.; Roth, R.; Roth, R.; Rockenberger, J.; Rockenberger, J.; Alivisatos, A.P.; Alivisatos, A.P.; Buuren, T. van

1999-01-01

We report the observation of size dependent structural disorder by x-ray absorption near-edge spectroscopy (XANES) in InAs and CdSe nanocrystals 17 - 80 Angstrom in diameter. XANES of the In and Cd M 4,5 edges yields features that are sharp for the bulk solid but broaden considerably as the size of the particle decreases. FEFF7 multiple-scattering simulations reproduce the size dependent broadening of the spectra if a bulklike surface reconstruction of a spherical nanocrystal model is included. This illustrates that XANES is sensitive to the structure of the entire nanocrystal including the surface. copyright 1999 The American Physical Society

RATIONAL APPROXIMATIONS TO GENERALIZED HYPERGEOMETRIC FUNCTIONS.

Science.gov (United States)

Under weak restrictions on the various free parameters, general theorems for rational representations of the generalized hypergeometric functions...and certain Meijer G-functions are developed. Upon specialization, these theorems yield a sequency of rational approximations which converge to the

X-rays in the eye of the general public

International Nuclear Information System (INIS)

Stegie, R.; Guenther, D.; Stender, K.H.

1979-01-01

For a pilot study, a random sample of 181 office personnel in steel companies were interviewed about their knowledge and feelings on X-rays and other forms of ionizing radiation. The general knowledge about the beneficial and detrimental aspects of X-rays was good, with education at school and news media reports being the main sources of information (70%). In general, the news media are considered to give objective and correct reports on this matter. 85% of the interviewed held ionizing radiation to be at least somewhat dangerous. Those with higher education (college/university) were significantly more vocal on the dangerous aspects. Concerning personal fear of X-rays, 30% were at least somewhat fearful. A significant correlation was found between statements on the dangerous aspects and subjective feelings of fear (anxiety). Interestingly, there was no correlation between general fearfulness (manifest anxiety) and fear of X-rays. (orig.) [de

Parity proofs of the Kochen–Specker theorem based on the Lie algebra E8

International Nuclear Information System (INIS)

Waegell, Mordecai; Aravind, P K

2015-01-01

The 240 root vectors of the Lie algebra E8 lead to a system of 120 rays in a real eight-dimensional Hilbert space that contains a large number of parity proofs of the Kochen–Specker (KS) theorem. After introducing the rays in a triacontagonal representation due to Coxeter, we present their KS diagram in the form of a ‘basis table’ showing all 2025 bases (i.e., sets of eight mutually orthogonal rays) formed by the rays. Only a few of the bases are actually listed, but simple rules are given, based on the symmetries of E8, for obtaining all the other bases from the ones shown. The basis table is an object of great interest because all the parity proofs of E8 can be exhibited as subsets of it. We show how the triacontagonal representation of E8 facilitates the identification of substructures that are more easily searched for their parity proofs. We have found hundreds of different types of parity proofs, ranging from 9 bases (or contexts) at the low end to 35 bases at the high end, and involving projectors of various ranks and multiplicities. After giving an overview of the proofs we found, we present a few concrete examples of the proofs that illustrate both their generic features as well as some of their more unusual properties. In particular, we present a proof involving 34 rays and 9 bases that appears to provide the most compact proof of the KS theorem found to date in eight-dimensions. (paper)

Debris of potassium–magnesium silicate glass generated by femtosecond laser-induced ablation in air: An analysis by near edge X-ray absorption spectroscopy, micro Raman and energy dispersive X-ray spectroscopy

International Nuclear Information System (INIS)

Grehn, M.; Seuthe, T.; Reinhardt, F.; Höfner, M.; Griga, N.; Eberstein, M.; Bonse, J.

2014-01-01

The redeposited material (debris) resulting from ablation of a potassium–magnesium silicate glass upon scanning femtosecond laser pulse irradiation (130 fs, 800 nm) in air environment is investigated by means of three complementary surface analytical methods. Changes in the electronic band structure of the glass constituent Magnesium (Mg) were identified by X-ray Absorption Near Edge Structure spectroscopy (XANES) using synchrotron radiation. An up-shift of ≈0.8 eV of a specific Magnesium K-edge absorption peak in the spectrum of the redeposited material along with a significant change in its leading edge position was detected. In contrast, the surface left after laser ablation exhibits a downshift of the peak position by ≈0.9 eV. Both observations may be related to a change of the Mg coordinative state of the laser modified/redeposited glass material. The presence of carbon in the debris is revealed by micro Raman spectroscopy (μ-RS) and was confirmed by energy dispersive X-ray spectroscopy (EDX). These observations are attributed to structural changes and chemical reactions taking place during the ablation process.

Using X-ray, K-edge densitometry in spent fuel characterization

International Nuclear Information System (INIS)

Jensen, T.; Aljundi, T.; Gray, J.N.

1998-01-01

There are instances where records for spent nuclear fuel are incomplete, as well as cases where fuel assemblies have deteriorated during storage. To bring these materials into compliance for long term storage will require determination of parameters such as enrichment, total fissionable material, and burnup. To obtain accurate estimates of these parameters will require the combination of information from different inspection techniques. A method which can provide an accurate measure of the total uranium in the spent fuel is X-ray K-edge densitometry. To assess the potential for applying this method in spent fuel characterization, the authors have measured the amount of uranium in stacks of reactor fuel plates containing nuclear materials of different enrichments and alloys. They have obtained good agreement with expected uranium concentrations ranging from 60 mg/cm 2 to 3,000 mg/cm 2 , and have demonstrated that these measurements can be made in a high radiation field (> 200 mR/hr)

Proofs of the Kochen–Specker theorem based on a system of three qubits

International Nuclear Information System (INIS)

Waegell, Mordecai; Aravind, P K

2012-01-01

A number of new proofs of the Kochen–Specker theorem are given based on the observables of the three-qubit Pauli group. Each proof is presented in the form of a diagram from which it is obvious by inspection. Each of our observable-based proofs leads to a system of projectors and bases that generally yields a large number of ‘parity proofs’ of the Kochen–Specker theorem. Some examples of such proofs are given and some of their applications are discussed. (paper)

Abstract decomposition theorem and applications

CERN Document Server

Grossberg, R; Grossberg, Rami; Lessmann, Olivier

2005-01-01

Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies a main gap result for the class K. The setting is general enough to cover \\aleph_0-stable first-order theories (proved by Shelah in 1982), Excellent Classes of atomic models of a first order tehory (proved Grossberg and Hart 1987) and the class of submodels of a large sequentially homogenuus \\aleph_0-stable model (which is new).

Approximation theorems by Meyer-Koenig and Zeller type operators

International Nuclear Information System (INIS)

Ali Ozarslan, M.; Duman, Oktay

2009-01-01

This paper is mainly connected with the approximation properties of Meyer-Koenig and Zeller (MKZ) type operators. We first introduce a general sequence of MKZ operators based on q-integers and then obtain a Korovkin-type approximation theorem for these operators. We also compute their rates of convergence by means of modulus of continuity and the elements of Lipschitz class functionals. Furthermore, we give an rth order generalization of our operators in order to get some explicit approximation results.

A noncommutative mean ergodic theorem for partial W*-dynamical semigroups

International Nuclear Information System (INIS)

Ekhaguere, G.O.S.

1992-12-01

A noncommutative mean ergodic theorem for dynamical semigroups of maps on partial W*-algebras of linear operators from a pre-Hilbert space into its completion is proved. This generalizes a similar result of Watanabe for dynamical semigroups of maps on W*-algebras of operators. (author). 14 refs

Cosmological singularity theorems for f ( R ) gravity theories

Energy Technology Data Exchange (ETDEWEB)

Alani, Ivo [Departamento de Física and IFIBA, Facultad de Ciencias Exactas y Naturales UBA Pabellón 1, Ciudad Universitaria (1428) C.A.B.A, Buenos Aires (Argentina); Santillán, Osvaldo P., E-mail: firenzecita@hotmail.com, E-mail: osantil@dm.uba.ar [Instituto de Matemáticas Luis Santaló (IMAS), Facultad de Ciencias Exactas y Naturales UBA Pabellón 1, Ciudad Universitaria (1428) C.A.B.A, Buenos Aires (Argentina)

2016-05-01

In the present work some generalizations of the Hawking singularity theorems in the context of f ( R ) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition ( T {sub ij} −( g {sub ij} /2) T ) k {sup i} k {sup j} ≥ 0 for any generic unit time like field k {sup i} ; the scalaron takes bounded positive values during its evolution and the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper-surface Σ for which the expansion parameter θ of the geodesic congruence emanating orthogonally from Σ satisfies some specific bounds, then the resulting space time is geodesically incomplete. Some mathematical results of reference [92] are very important for proving this. The generalized theorems presented here apply directly for some specific models such as the Hu-Sawicki or Starobinsky ones [27,38]. For other scenarios, some extra assumptions should be implemented in order to have a geodesically incomplete space time. The hypothesis considered in this text are sufficient, but not necessary. In other words, their negation does not imply that a singularity is absent.

Geometry of the Adiabatic Theorem

Science.gov (United States)

Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas

2012-01-01

We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…

The Marotto Theorem on planar monotone or competitive maps

International Nuclear Information System (INIS)

Yu Huang

2004-01-01

In 1978, Marotto generalized Li-Yorke's results on the criterion for chaos from one-dimensional discrete dynamical systems to n-dimensional discrete dynamical systems, showing that the existence of a non-degenerate snap-back repeller implies chaos in the sense of Li-Yorke. This theorem is very useful in predicting and analyzing discrete chaos in multi-dimensional dynamical systems. Yet, besides it is well known that there exists an error in the conditions of the original Marotto Theorem, and several authors had tried to correct it in different way, Chen, Hsu and Zhou pointed out that the verification of 'non-degeneracy' of a snap-back repeller is the most difficult in general and expected, 'almost beyond reasonable doubt', that the existence of only degenerate snap-back repeller still implies chaotic, which was posed as a conjecture by them. In this paper, we shall give necessary and sufficient conditions of chaos in the sense of Li-Yorke for planar monotone or competitive discrete dynamical systems and solve Chen-Hsu-Zhou Conjecture for such kinds of systems

Design of three-dimensional nonimaging concentrators with inhomogeneous media

Science.gov (United States)

Minano, J. C.

1986-09-01

A three-dimensional nonimaging concentrator is an optical system that transforms a given four-parametric manifold of rays reaching a surface (entry aperture) into another four-parametric manifold of rays reaching the receiver. A procedure of design of such concentrators is developed. In general, the concentrators use mirrors and inhomogeneous media (i.e., gradient-index media). The concentrator has the maximum concentration allowed by the theorem of conservation of phase-space volume. This is the first known concentrator with such properties. The Welford-Winston edge-ray principle in three-dimensional geometry is proven under several assumptions. The linear compound parabolic concentrator is derived as a particular case of the procedure of design.

A definability theorem for first order logic

NARCIS (Netherlands)

Butz, C.; Moerdijk, I.

1997-01-01

In this paper we will present a definability theorem for first order logic This theorem is very easy to state and its proof only uses elementary tools To explain the theorem let us first observe that if M is a model of a theory T in a language L then clearly any definable subset S M ie a subset S

Note on Deduction Theorems in contraction-free logics

Czech Academy of Sciences Publication Activity Database

Chvalovský, Karel; Cintula, Petr

2012-01-01

Roč. 58, č. 3 (2012), s. 236-243 ISSN 0942-5616 R&D Projects: GA ČR GAP202/10/1826 Grant - others:Austrian Science Fund (FWF)(AT) START Y544-N23 Institutional research plan: CEZ:AV0Z10300504 Keywords : Local Deduction Theorem * BCI-logic * Substructural logics * Rule of contraction Subject RIV: BA - General Mathematics Impact factor: 0.376, year: 2012

On Newton’s shell theorem

Science.gov (United States)

Borghi, Riccardo

2014-03-01

In the present letter, Newton’s theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton’s Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.

Convergence theorems for renormalized Feynman integrals with zero-mass propagators

International Nuclear Information System (INIS)

Lowenstein, J.H.

1976-01-01

A general momentum-space subtraction procedure is proposed for the removal of both ultraviolet and infrared divergences of Feynman integrals. Convergence theorems are proved which allow one to define time-ordered Green functions, as tempered distributions for a wide class of theories with zero-mass propagators. (orig.) [de

The coding theorem for a class of quantum channels with long-term memory

International Nuclear Information System (INIS)

Datta, Nilanjana; Dorlas, Tony C

2007-01-01

In this paper, we consider the transmission of classical information through a class of quantum channels with long-term memory, which are convex combinations of memoryless channels. Hence, the memory of such channels can be considered to be given by a Markov chain which is aperiodic but not irreducible. We prove the coding theorem and weak converse for this class of channels. The main techniques that we employ are a quantum version of Feinstein's fundamental lemma (Feinstein A 1954 IRE Trans. PGIT 4 2-22, Khinchin A I 1957 Mathematical Foundations of Information Theory: II. On the Fundamental Theorems of Information Theory (New York: Dover) chapter IV) and a generalization of Helstrom's theorem (Helstrom C W 1976 Quantum detection and estimation theory Mathematics in Science and Engineering vol 123 (London: Academic))

X-ray absorption near-edge structure of GaN with high Mn concentration grown on SiC

Science.gov (United States)

Sancho-Juan, O.; Cantarero, A.; Garro, N.; Cros, A.; Martínez-Criado, G.; Salomé, M.; Susini, J.; Olguín, D.; Dhar, S.

2009-07-01

By means of x-ray absorption near-edge structure (XANES) several Ga1-xMnxN (0.03edges. All samples studied present a similar Mn ionization state, very close to 2+, and tetrahedral coordination. In order to interpret the near-edge structure, we have performed ab initio calculations using the full potential linear augmented plane wave method as implemented in the Wien2k code. The calculations show the appearance of a Mn bonding \\mathrm {t_{2}}\\uparrow band localized in the gap region, and the corresponding anti-bonding state \\mathrm {t_{2}}\\downarrow , which seem to be responsible for the double structure which appears at the pre-edge absorption region. The shoulders and main absorption peak of the XANES spectra are attributed to transitions from the Mn(1s) band to the conduction bands, which are partially dipole allowed because of the Mn(4p) contribution to these bands.

Illustrating the Central Limit Theorem through Microsoft Excel Simulations

Science.gov (United States)

Moen, David H.; Powell, John E.

2005-01-01

Using Microsoft Excel, several interactive, computerized learning modules are developed to demonstrate the Central Limit Theorem. These modules are used in the classroom to enhance the comprehension of this theorem. The Central Limit Theorem is a very important theorem in statistics, and yet because it is not intuitively obvious, statistics…

Relativistic corrections for the conventional, classical Nyquist theorem

International Nuclear Information System (INIS)

Theimer, O.; Dirk, E.H.

1983-01-01

New expressions for the Nyquist theorem are derived under the condition in which the random thermal speed of electrons, in a system of charged particles, can approach the speed of light. Both the case in which, the electron have not drift velocity relative to the ions or neutral particles and the case in which drift occours are investigated. In both instances, the new expressions for the Nyquist theorem are found to contain relativistic correction terms; however for electron temperatures T approx. 10 9 K and drift velocity magnitudes w approx. 0.5c, where c is the speed of light, the effects of these correction terms are generally small. The derivation of these relativistic corrections is carried out by means of procedures developed in an earlier work. A relativistic distribution function, which incorporates a constant drift velocity with a random thermal velocity for a given particle species, is developed

The implicit function theorem history, theory, and applications

CERN Document Server

Krantz, Steven G

2003-01-01

The implicit function theorem is part of the bedrock of mathematics analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth function, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash-Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex store, and intimately bound up with the development of fundamental ideas in a...

In situ time-resolved X-ray near-edge absorption spectroscopy of selenite reduction by siderite

International Nuclear Information System (INIS)

Badaut, V.; Schlegel, M.L.; Descostes, M.; Moutiers, G.

2012-01-01

The reduction oxidation-reaction between aqueous selenite (SeO 3 2- ) and siderite (FeCO 3 (s)) was monitored by in situ, time-resolved X-ray absorption near-edge structure (XANES) spectroscopy at the selenium K edge in a controlled electrochemical environment. Spectral evolutions showed that more than 60% of selenite was reduced at the siderite surface after 20 h of experiment, at which time the reaction was still incomplete. Fitting of XANES spectra by linear combination of reference spectra showed that selenite reaction with siderite is essentially a two-step process, selenite ions being immobilized on siderite surface prior to their reduction. A kinetic model of the reduction step is proposed, allowing to identify the specific contribution of surface reduction. These results have strong implications for the retention of selenite by corrosion products in nuclear waste repositories and in a larger extent for the fate of selenium in the environment. (authors)

X-ray Faraday effect at the L.sub.2,3./sub. edges of Fe, Co, and Ni: theory and experiment

Czech Academy of Sciences Publication Activity Database

Kuneš, Jan; Oppeneer, P. M.; Mertins, H. Ch.; Schäfers, F.; Gaupp, A.; Gudat, W.; Novák, Pavel

2001-01-01

Roč. 64, - (2001), s. 174417-1-174417-10 ISSN 0163-1829 Institutional research plan: CEZ:AV0Z1010914 Keywords : X-ray Faraday effect * L 2 * 3 edges * 3d ferromagnets Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.070, year: 2001

Heuristic analogy in Ars Conjectandi: From Archimedes' De Circuli Dimensione to Bernoulli's theorem.

Science.gov (United States)

Campos, Daniel G

2018-02-01

This article investigates the way in which Jacob Bernoulli proved the main mathematical theorem that undergirds his art of conjecturing-the theorem that founded, historically, the field of mathematical probability. It aims to contribute a perspective into the question of problem-solving methods in mathematics while also contributing to the comprehension of the historical development of mathematical probability. It argues that Bernoulli proved his theorem by a process of mathematical experimentation in which the central heuristic strategy was analogy. In this context, the analogy functioned as an experimental hypothesis. The article expounds, first, Bernoulli's reasoning for proving his theorem, describing it as a process of experimentation in which hypothesis-making is crucial. Next, it investigates the analogy between his reasoning and Archimedes' approximation of the value of π, by clarifying both Archimedes' own experimental approach to the said approximation and its heuristic influence on Bernoulli's problem-solving strategy. The discussion includes some general considerations about analogy as a heuristic technique to make experimental hypotheses in mathematics. Copyright © 2018 Elsevier Ltd. All rights reserved.

On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem.

Directory of Open Access Journals (Sweden)

Jiawei Li

Full Text Available In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games.

On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem

Science.gov (United States)

Li, Jiawei; Kendall, Graham

2015-01-01

In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games. PMID:26288088

HIGHER ORDER SPECIATION EFFECTS ON PLUTONIUM L3 X-RAY ABSORPTION NEAR EDGE SPECTRA.

Energy Technology Data Exchange (ETDEWEB)

Conradson, Steven D.; Abney, Kent D.; Begg, Bruce D.; Brady, Erik D.; Clark, David L.; den Auwer, Christophe; Ding, Mei; Dorhout, Peter K.; Espinosa-Faller, Francisco J.; Gordon, Pamela L.; Hess, Nancy J.; Hess, Ryan F.; Keogh, D. Webster; Lander, Gerard H.; Lupinetti, Anthony J.; Neu, Mary P.; Palmer, Phillip D.; Paviet-Hartmann, Patricia; Reilly, Sean D.; Runde, Wolfgang H.; Tait, C. Drew; Veirs, D. Kirk

2003-06-09

Pu L{sub 3} X-ray Near Edge Absorption Spectra for Pu(0-VII) are reported for more than 50 chalcogenides, chlorides, hydrates, hydroxides, nitrates, carbonates, oxy-hydroxides, and other compounds both as solids and in solution, and substituted in zirconlite, perovksite, and borosilicate glass. This large data base extends the known correlations between the energy and shape of these spectra from the usual association of the XANES with valence and site symmetry to higher order chemical effects. Because of the large number of compounds of these different types a number of novel and unexpected behaviors are observed.

Anomalous scaling due to correlations: limit theorems and self-similar processes

International Nuclear Information System (INIS)

Stella, Attilio L; Baldovin, Fulvio

2010-01-01

We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling forms, explain their universal character, and specify universality domains in the spaces of joint probability density functions of the summand variables. These density functions are assumed to be invariant under arbitrary permutations of their arguments. Examples from the theory of critical phenomena are discussed. The novel notion of stability implied by the limit theorems also allows us to define sequences of random variables whose sum satisfies anomalous scaling for any finite number of summands. If regarded as developing in time, the stochastic processes described by these variables are non-Markovian generalizations of Gaussian processes with uncorrelated increments, and provide, e.g., explicit realizations of a recently proposed model of index evolution in finance

Liftings in Finite Graphs and Linkages in Infinite Graphs with Prescribed Edge-Connectivity

DEFF Research Database (Denmark)

Ok, Seongmin; Richter, R. Bruce; Thomassen, Carsten

2016-01-01

Let G be a graph and let s be a vertex of G. We consider the structure of the set of all lifts of two edges incident with s that preserve edge-connectivity. Mader proved that two mild hypotheses imply there is at least one pair that lifts, while Frank showed (with the same hypotheses......) that there are at least (deg(s) - 1)/2 disjoint pairs that lift. We consider the lifting graph: its vertices are the edges incident with s, two being adjacent if they form a liftable pair. We have three main results, the first two with the same hypotheses as for Mader’s Theorem. (i)Let F be a subset of the edges incident...... with s. We show that F is independent in the lifting graph of G if and only if there is a single edge-cut C in G of size at most r + 1 containing all the edges in F, where r is the maximum number of edge-disjoint paths from a vertex (not s) in one component of G - C to a vertex (not s) in another...

Resonant inelastic x-ray scattering on iso-C₂H₂Cl₂ around the chlorine K-edge: structural and dynamical aspects.

Science.gov (United States)

Kawerk, Elie; Carniato, Stéphane; Journel, Loïc; Marchenko, Tatiana; Piancastelli, Maria Novella; Žitnik, Matjaž; Bučar, Klemen; Bohnic, Rok; Kavčič, Matjaž; Céolin, Denis; Khoury, Antonio; Simon, Marc

2014-10-14

We report a theoretical and experimental study of the high resolution resonant K(α) X-ray emission lines around the chlorine K-edge in gas phase 1,1-dichloroethylene. With the help of ab initio electronic structure calculations and cross section evaluation, we interpret the lowest lying peak in the X-ray absorption and emission spectra. The behavior of the K(α) emission lines with respect to frequency detuning highlights the existence of femtosecond nuclear dynamics on the dissociative Potential Energy Surface of the first K-shell core-excited state.

No-go theorems for the minimization of potentials

International Nuclear Information System (INIS)

Chang, D.; Kumar, A.

1985-01-01

Using a theorem in linear algebra, we prove some no-go theorems in the minimization of potentials related to the problem of symmetry breaking. Some applications in the grand unified model building are mentioned. Another application of the algebraic theorem is also included to demonstrate its usefulness

Simulations of iron K pre-edge X-ray absorption spectra using the restricted active space method.

Science.gov (United States)

Guo, Meiyuan; Sørensen, Lasse Kragh; Delcey, Mickaël G; Pinjari, Rahul V; Lundberg, Marcus

2016-01-28

The intensities and relative energies of metal K pre-edge features are sensitive to both geometric and electronic structures. With the possibility to collect high-resolution spectral data it is important to find theoretical methods that include all important spectral effects: ligand-field splitting, multiplet structures, 3d-4p orbital hybridization, and charge-transfer excitations. Here the restricted active space (RAS) method is used for the first time to calculate metal K pre-edge spectra of open-shell systems, and its performance is tested against on six iron complexes: [FeCl6](n-), [FeCl4](n-), and [Fe(CN)6](n-) in ferrous and ferric oxidation states. The method gives good descriptions of the spectral shapes for all six systems. The mean absolute deviation for the relative energies of different peaks is only 0.1 eV. For the two systems that lack centrosymmetry [FeCl4](2-/1-), the ratios between dipole and quadrupole intensity contributions are reproduced with an error of 10%, which leads to good descriptions of the integrated pre-edge intensities. To gain further chemical insight, the origins of the pre-edge features have been analyzed with a chemically intuitive molecular orbital picture that serves as a bridge between the spectra and the electronic structures. The pre-edges contain information about both ligand-field strengths and orbital covalencies, which can be understood by analyzing the RAS wavefunction. The RAS method can thus be used to predict and rationalize the effects of changes in both the oxidation state and ligand environment in a number of hard X-ray studies of small and medium-sized molecular systems.

A maximum modulus theorem for the Oseen problem

Czech Academy of Sciences Publication Activity Database

Kračmar, S.; Medková, Dagmar; Nečasová, Šárka; Varnhorn, W.

2013-01-01

Roč. 192, č. 6 (2013), s. 1059-1076 ISSN 0373-3114 R&D Projects: GA ČR(CZ) GAP201/11/1304; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : Oseen problem * maximum modulus theorem * Oseen potentials Subject RIV: BA - General Mathematics Impact factor: 0.909, year: 2013 http://link.springer.com/article/10.1007%2Fs10231-012-0258-x

Parameters Influencing Sulfur Speciation in Environmental Samples Using Sulfur K-Edge X-Ray Absorption Near-Edge Structure

Directory of Open Access Journals (Sweden)

Siwatt Pongpiachan

2012-01-01

Full Text Available This paper aims to enhance the credibility of applying the sulfur K-edge XANES spectroscopy as an innovative “fingerprint” for characterizing environmental samples. The sensitivities of sulfur K-edge XANES spectra of ten sulfur compound standards detected by two different detectors, namely, Lytle detector (LyD and Germanium detector (GeD, were studied and compared. Further investigation on “self-absorption” effect revealed that the maximum sensitivities of sulfur K-edge XANES spectra were achieved when diluting sulfur compound standards with boron nitride (BN at the mixing ratio of 0.1%. The “particle-size” effect on sulfur K-edge XANES spectrum sensitivities was examined by comparing signal-to-noise ratios of total suspended particles (TSP and particulate matter of less than 10 millionths of a meter (PM10 collected at three major cities of Thailand. The analytical results have demonstrated that the signal-to-noise ratios of sulfur K-edge XANES spectra were positively correlated with sulfate content in aerosols and negatively connected with particle sizes. The combination of hierarchical cluster analysis (HCA and principal component analysis (PCA has proved that sulfur K-edge XANES spectrum can be used to characterize German terrestrial soils and Andaman coastal sediments. In addition, this study highlighted the capability of sulfur K-edge XANES spectra as an innovative “fingerprint” to distinguish tsunami backwash deposits (TBD from typical marine sediments (TMS.

The matrix Euler-Fermat theorem

International Nuclear Information System (INIS)

Arnol'd, Vladimir I

2004-01-01

We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem

A note on Robinson-Ursescu and Lyusternik-Graves theorem

Czech Academy of Sciences Publication Activity Database

Cibulka, R.; Fabian, Marián

2013-01-01

Roč. 139, 1-2 (2013), s. 89- 101 ISSN 0025-5610 R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional research plan: CEZ:AV0Z10190503 Keywords : open mapping * restrictive metricregularity * graves theorem Subject RIV: BA - General Mathematics Impact factor: 1.984, year: 2013 http://link.springer.com/article/10.1007%2Fs10107-013-0662-z

A Converse to the Cayley-Hamilton Theorem

Indian Academy of Sciences (India)

follows that qj = api, where a is a unit. Thus, we must have that the expansion of I into irreducibles is unique. Hence, K[x] is a UFD. A famous theorem of Gauss implies that K[XI' X2,. ,xn] is also an UFD. Gauss's Theorem: R[x] is a UFD, if and only if R is a UFD. For a proof of Gauss's theorem and a detailed proof of the fact that ...

Converse Barrier Certificate Theorem

DEFF Research Database (Denmark)

Wisniewski, Rafael; Sloth, Christoffer

2013-01-01

This paper presents a converse barrier certificate theorem for a generic dynamical system.We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold. Other authors have developed a related result, by assuming that the dynamical system has no singular...... points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work...

Generalized Uncertainty Quantification for Linear Inverse Problems in X-ray Imaging

Energy Technology Data Exchange (ETDEWEB)

Fowler, Michael James [Clarkson Univ., Potsdam, NY (United States)

2014-04-25

In industrial and engineering applications, X-ray radiography has attained wide use as a data collection protocol for the assessment of material properties in cases where direct observation is not possible. The direct measurement of nuclear materials, particularly when they are under explosive or implosive loading, is not feasible, and radiography can serve as a useful tool for obtaining indirect measurements. In such experiments, high energy X-rays are pulsed through a scene containing material of interest, and a detector records a radiograph by measuring the radiation that is not attenuated in the scene. One approach to the analysis of these radiographs is to model the imaging system as an operator that acts upon the object being imaged to produce a radiograph. In this model, the goal is to solve an inverse problem to reconstruct the values of interest in the object, which are typically material properties such as density or areal density. The primary objective in this work is to provide quantitative solutions with uncertainty estimates for three separate applications in X-ray radiography: deconvolution, Abel inversion, and radiation spot shape reconstruction. For each problem, we introduce a new hierarchical Bayesian model for determining a posterior distribution on the unknowns and develop efficient Markov chain Monte Carlo (MCMC) methods for sampling from the posterior. A Poisson likelihood, based on a noise model for photon counts at the detector, is combined with a prior tailored to each application: an edge-localizing prior for deconvolution; a smoothing prior with non-negativity constraints for spot reconstruction; and a full covariance sampling prior based on a Wishart hyperprior for Abel inversion. After developing our methods in a general setting, we demonstrate each model on both synthetically generated datasets, including those from a well known radiation transport code, and real high energy radiographs taken at two U. S. Department of Energy

Anisotropic interpolation theorems of Musielak-Orlicz type

Directory of Open Access Journals (Sweden)

Jinxia Li

2016-10-01

Full Text Available Abstract Anisotropy is a common attribute of Nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathematics, can be expressed by a fairly general discrete group of dilations { A k : k ∈ Z } $\\{A^{k}: k\\in\\mathbb{Z}\\}$ , where A is a real n × n $n\\times n$ matrix with all its eigenvalues λ satisfy | λ | > 1 $|\\lambda|>1$ . Let φ : R n × [ 0 , ∞ → [ 0 , ∞ $\\varphi: \\mathbb{R}^{n}\\times[0, \\infty\\to[0,\\infty$ be an anisotropic Musielak-Orlicz function such that φ ( x , ⋅ $\\varphi(x,\\cdot$ is an Orlicz function and φ ( ⋅ , t $\\varphi(\\cdot,t$ is a Muckenhoupt A ∞ ( A $\\mathbb {A}_{\\infty}(A$ weight. The aim of this article is to obtain two anisotropic interpolation theorems of Musielak-Orlicz type, which are weighted anisotropic extension of Marcinkiewicz interpolation theorems. The above results are new even for the isotropic weighted settings.

Stacked spheres and lower bound theorem

Indian Academy of Sciences (India)

BASUDEB DATTA

2011-11-20

Nov 20, 2011 ... Preliminaries. Lower bound theorem. On going work. Definitions. An n-simplex is a convex hull of n + 1 affinely independent points. (called vertices) in some Euclidean space R. N . Stacked spheres and lower bound theorem. Basudeb Datta. Indian Institute of Science. 2 / 27 ...

The divergence theorem for divergence measure vectorfields on sets with fractal boundaries

Czech Academy of Sciences Publication Activity Database

Šilhavý, Miroslav

2009-01-01

Roč. 14, č. 5 (2009), s. 445-455 ISSN 1081-2865 Institutional research plan: CEZ:AV0Z10190503 Keywords : divergence measure vectorfields * fractal s * divergence theorem Subject RIV: BA - General Mathematics Impact factor: 1.065, year: 2009

X-ray absorption near-edge structure of hexagonal ternary phases in sputter-deposited TiAlN films

Energy Technology Data Exchange (ETDEWEB)

Gago, R., E-mail: rgago@icmm.csic.es [Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, E-28049 Madrid (Spain); Soldera, F. [Department of Materials Science and Engineering, Saarland University, D-66123 Saarbruecken (Germany); Hübner, R.; Lehmann, J.; Munnik, F. [Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, D-01314 Dresden (Germany); Vázquez, L. [Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, E-28049 Madrid (Spain); Redondo-Cubero, A. [Instituto Tecnológico e Nuclear, Instituto Superior Técnico, Universidade Técnica de Lisboa, 2686-953 Sacavém (Portugal); Endrino, J.L. [Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, E-28049 Madrid (Spain); Abengoa Research S.L., c/Energía Solar 1, Palmas Altas, E-41014 Seville (Spain)

2013-06-05

Highlights: ► Growth of ternary TiAlN films with nearly single-phase wurzite structure. ► Soft X-rays XANES measurements of ternary TiAlN films with wurzite structure. ► Identification of ternary TiAlN hexagonal phases by XANES. ► Correlation of XANES measurements with reported theoretical calculations. -- Abstract: Titanium aluminium nitride (TiAlN) coatings have been grown by reactive (Ar/N{sub 2}) direct-current magnetron sputtering from a Ti{sub 50}Al{sub 50} compound target. The film composition has been quantified by ion beam analysis showing the formation of Al-rich nitrides (Ti/Al ∼ 0.3), with stoichiometric films for N{sub 2} contents in the gas mixture equal or above ∼25%. The surface morphology of the films has been imaged by atomic force microscopy, showing very smooth surfaces with roughness values below 2 nm. X-ray and electron diffraction patterns reveal that the films are nanocrystalline with a wurzite (w) structure of lattice parameters larger (∼2.5%) than those for w-AlN. The lattice expansion correlates with the Ti/Al ratio in stoichiometric films, which suggests the incorporation of Ti into w-AlN. The atomic environments around Ti, Al and N sites have been extracted from the X-ray absorption near-edge structure (XANES) by recording the Ti2p, Al1s and N1s edges, respectively. The analysis of the XANES spectral lineshape and comparison with reported theoretical calculations confirm the formation of a ternary hexagonal phase.

Theorems for asymptotic safety of gauge theories

Energy Technology Data Exchange (ETDEWEB)

Bond, Andrew D.; Litim, Daniel F. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)

2017-06-15

We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated. (orig.)

Automated theorem proving theory and practice

CERN Document Server

Newborn, Monty

2001-01-01

As the 21st century begins, the power of our magical new tool and partner, the computer, is increasing at an astonishing rate. Computers that perform billions of operations per second are now commonplace. Multiprocessors with thousands of little computers - relatively little! -can now carry out parallel computations and solve problems in seconds that only a few years ago took days or months. Chess-playing programs are on an even footing with the world's best players. IBM's Deep Blue defeated world champion Garry Kasparov in a match several years ago. Increasingly computers are expected to be more intelligent, to reason, to be able to draw conclusions from given facts, or abstractly, to prove theorems-the subject of this book. Specifically, this book is about two theorem-proving programs, THEO and HERBY. The first four chapters contain introductory material about automated theorem proving and the two programs. This includes material on the language used to express theorems, predicate calculus, and the rules of...

Stable convergence and stable limit theorems

CERN Document Server

Häusler, Erich

2015-01-01

The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level...

Theorems of Tarski's Undefinability and Godel's Second Incompleteness - Computationally

OpenAIRE

Salehi, Saeed

2015-01-01

We present a version of Godel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions (first discussed by M. Detlefsen 2001). We also argue that Tarski's theorem on the Undefinability of Truth is Godel's First Incompleteness Theorem relativized to definable oracles; here a unification of these two theorems is given.

Power spectrum weighted edge analysis for straight edge detection in images

Science.gov (United States)

Karvir, Hrishikesh V.; Skipper, Julie A.

2007-04-01

Most man-made objects provide characteristic straight line edges and, therefore, edge extraction is a commonly used target detection tool. However, noisy images often yield broken edges that lead to missed detections, and extraneous edges that may contribute to false target detections. We present a sliding-block approach for target detection using weighted power spectral analysis. In general, straight line edges appearing at a given frequency are represented as a peak in the Fourier domain at a radius corresponding to that frequency, and a direction corresponding to the orientation of the edges in the spatial domain. Knowing the edge width and spacing between the edges, a band-pass filter is designed to extract the Fourier peaks corresponding to the target edges and suppress image noise. These peaks are then detected by amplitude thresholding. The frequency band width and the subsequent spatial filter mask size are variable parameters to facilitate detection of target objects of different sizes under known imaging geometries. Many military objects, such as trucks, tanks and missile launchers, produce definite signatures with parallel lines and the algorithm proves to be ideal for detecting such objects. Moreover, shadow-casting objects generally provide sharp edges and are readily detected. The block operation procedure offers advantages of significant reduction in noise influence, improved edge detection, faster processing speed and versatility to detect diverse objects of different sizes in the image. With Scud missile launcher replicas as target objects, the method has been successfully tested on terrain board test images under different backgrounds, illumination and imaging geometries with cameras of differing spatial resolution and bit-depth.

The origins of cosmic rays and quantum effects on gravity

Science.gov (United States)

Tomozawa, Y.

1985-01-01

The energy spectrum of primary cosmic rays is explained by particles emitted during a thermal expansion of explosive objects inside and near the galaxy, remnants of which may be supernova and/or active talaxies, or even stars or galaxies that disappeared from our sight after the explosion. A power law energy spectrum for cosmic rays, E to the (-alpha -1, is obtained from an expansion rate T is proportional to R to the alpha. Using the solution of the Einstein equation, we obtain a spectrum which agrees very well with experimental data. The implication of an inflationary early universe on the cosmic ray spectrum is also discussed. It is also suggested that the conflict between this model and the singularity theorem in classical general relativity may be eliminated by quantum effects.

New versions of the Fan-Browder fixed point theorem and existence of economic equilibria

Directory of Open Access Journals (Sweden)

Park Sehie

2004-01-01

Full Text Available We introduce a generalized form of the Fan-Browder fixed point theorem and apply to game-theoretic and economic equilibrium existence problem under the more generous restrictions. Consequently, we state some of recent results of Urai (2000 in more general and efficient forms.

X-ray absorption near-edge structure of GaN with high Mn concentration grown on SiC

Energy Technology Data Exchange (ETDEWEB)

Sancho-Juan, O; Cantarero, A; Garro, N; Cros, A [Materials Science Institute, University of Valencia, PO Box 22085, E46071 Valencia (Spain); Martinez-Criado, G; Salome, M; Susini, J [European Synchrotron Radiation Facility, 6 rue Jules Horowitz, 38043 Grenoble (France); Olguin, D [Dept. de Fisica, CINVESTAV-IPN, 07300 Mexico D F (Mexico); Dhar, S [Experimentalphysik, Universitaet Duisburg-Essen, Lotharstrasse 1, 47057 Duisburg (Germany)

2009-07-22

By means of x-ray absorption near-edge structure (XANES) several Ga{sub 1-x}Mn{sub x}N (0.03edges. All samples studied present a similar Mn ionization state, very close to 2+, and tetrahedral coordination. In order to interpret the near-edge structure, we have performed ab initio calculations using the full potential linear augmented plane wave method as implemented in the Wien2k code. The calculations show the appearance of a Mn bonding t{sub 2}arrow up band localized in the gap region, and the corresponding anti-bonding state t{sub 2}arrow down, which seem to be responsible for the double structure which appears at the pre-edge absorption region. The shoulders and main absorption peak of the XANES spectra are attributed to transitions from the Mn(1s) band to the conduction bands, which are partially dipole allowed because of the Mn(4p) contribution to these bands.

Fermat's last theorem and Catalan's conjecture in weak exponential arithmetics

Czech Academy of Sciences Publication Activity Database

Glivický, Petr; Kala, V.

2017-01-01

Roč. 63, 3-4 (2017), s. 162-174 ISSN 0942-5616 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : Fermat's last theorem * Catalan's conjecture Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.250, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/malq.201500069/full

Kohn's theorem in a superfluid Fermi gas with a Feshbach resonance

International Nuclear Information System (INIS)

Ohashi, Y.

2004-01-01

We investigate the dipole mode in a superfluid gas of Fermi atoms trapped in a harmonic potential. According to Kohn's theorem, the frequency of this collective mode is not affected by an interaction between the atoms and is always equal to the trap frequency. This remarkable property, however, does not necessarily hold in an approximate theory. We explicitly prove that the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA), including a coupling between fluctuations in the density and Cooper channels, is consistent with both Kohn's theorem as well as Goldstone's theorem. This proof can be immediately extended to the strong-coupling superfluid theory developed by Nozieres and Schmitt-Rink (NSR), where the effect of superfluid fluctuations is included within the Gaussian level. As a result, the NSR-GRPA formalism can be used to study collective modes in the BCS-BEC crossover region in a manner which is consistent with Kohn's theorem. We also include the effect of a Feshbach resonance and a condensate of the associated molecular bound states. A detailed discussion is given of the unusual nature of the Kohn mode eigenfunctions in a Fermi superfluid, in the presence and absence of a Feshbach resonance. When the molecular bosons feel a different trap frequency from the Fermi atoms, the dipole frequency is shown to depend on the strength of effective interaction associated with the Feshbach resonance

Logical and historical determination of the Arrow and Sen impossibility theorems