Brillouin scattering at high pressures
International Nuclear Information System (INIS)
Grimsditch, M.; Polian, A.
1988-02-01
Technical advances which have made Brillouin scattering a useful tool in high pressure diamond anvil cell (DAC) studies, viz. multipassing and tandem operation of Fabry-Perot interferometers, are reviewed. Experimental aspects, such as allowed scattering geometries, are outlined and the data analysis required to transform Brillouin spectra into sound velocities and elastic constants is presented. Experimental results on H 2 , N 2 , Ar, and He are presented, and the close relationship between the Brillouin scattering results and equations of state is highlighted
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
Brillouin Spectroscopy Data Base for Biological Threats
National Research Council Canada - National Science Library
Rubel, Glenn
2003-01-01
.... Brillouin scattering from DNA, ovalbumen, the Bacillus spores globigii and thuringiensis were measured to determine the feasibility of biological material discrimination using Brillouin scattering...
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
Stimulated Brillouin scattering experiments
International Nuclear Information System (INIS)
Slater, D.C.; Berger, R.L.; Busch, G.; Kinzer, C.M.; Mayer, F.J.; Powers, L.V.; Tanner, D.J.
1981-01-01
This report describes two experiments in which SBS would be expected to play an important role. In the first experiment, we find a clear signature of the Brillouin backscatter of a short (100 psec) pulse from a long (approx. 50 μm) gradient length gas target plasma. The second experiment used much longer (approx. 1 nsec) pulses on spherical glass shell targets. These experiments were done with both narrow ( 30A) bandwidth laser light. Using one-dimensional, spherically symmetric fluid simulations, we have attempted to model many of the laser-plasma interaction processes which combine to determine the amount of absorbed energy in the long-pulse experiments. These simulations indicate that modest laser bandwidths are successful in reducing the level of SBS at the irradiances ( 15 W/cm 2 ) used in these experiments
Fiber-integrated Brillouin microspectroscopy: Towards Brillouin endoscopy
Directory of Open Access Journals (Sweden)
Irina V. Kabakova
2017-11-01
Full Text Available Brillouin imaging (BI for micromechanical characterization of tissues and biomaterials is a fast-developing field of research with a strong potential for medical diagnosis of disease-modified tissues and cells. Although the principles of BI imply its compatibility with in vivo and in situ measurements, the integration of BI with a flexible catheter, capable of reaching the region of interest within the body, is yet to be reported. Here, for the first time, we experimentally investigate integration of the Brillouin spectroscope with standard optical fiber components to achieve a Brillouin endoscope. The performance of single-fiber and dual-fiber endoscopes are demonstrated and analyzed. We show that a major challenge in construction of Brillouin endoscopes is the strong backward Brillouin scattering in the optical fiber and we present a dual-fiber geometry as a possible solution. Measurements of Brillouin spectra in test liquids (water, ethanol and glycerol are demonstrated using the dual-fiber endoscope and its performance is analyzed numerically with the help of a beam propagation model.
Debattista, Josephine
2000-01-01
Pythagoras 580 BC was a Greek mathematician who became famous for formulating Pythagoras Theorem but its principles were known earlier. The ancient Egyptians wanted to layout square (90°) corners to their fields. To solve this problem about 2000 BC they discovered the 'magic' of the 3-4-5 triangle.
International Nuclear Information System (INIS)
Palmer, R.
1994-06-01
Electromagnetic fields can be separated into near and far components. Near fields are extensions of static fields. They do not radiate, and they fall off more rapidly from a source than far fields. Near fields can accelerate particles, but the ratio of acceleration to source fields at a distance R, is always less than R/λ or 1, whichever is smaller. Far fields can be represented as sums of plane parallel, transversely polarized waves that travel at the velocity of light. A single such wave in a vacuum cannot give continuous acceleration, and it is shown that no sums of such waves can give net first order acceleration. This theorem is proven in three different ways; each method showing a different aspect of the situation
The quantitative Morse theorem
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.
Bursting behaviours in cascaded stimulated Brillouin scattering
International Nuclear Information System (INIS)
Liu Zhan-Jun; He Xian-Tu; Zheng Chun-Yang; Wang Yu-Gang
2012-01-01
Stimulated Brillouin scattering is studied by numerically solving the Vlasov—Maxwell system. A cascade of stimulated Brillouin scattering can occur when a linearly polarized laser pulse propagates in a plasma. It is found that a stimulated Brillouin scattering cascade can reduce the scattering and increase the transmission of light, as well as introduce a bursting behaviour in the evolution of the laser-plasma interaction. The bursting time in the reflectivity is found to be less than half the ion acoustic period. The ion temperature can affect the stimulated Brillouin scattering cascade, which can repeat several times at low ion temperatures and can be completely eliminated at high ion temperatures. For stimulated Brillouin scattering saturation, higher-harmonic generation and wave—wave interaction of the excited ion acoustic waves can restrict the amplitude of the latter. In addition, stimulated Brillouin scattering cascade can restrict the amplitude of the scattered light. (physics of gases, plasmas, and electric discharges)
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)
Magnetic compression into Brillouin flow
International Nuclear Information System (INIS)
Becker, R.
1977-01-01
The trajectories of beam edge electrons are calculated in the transition region between an electrostatic gun and an increasing magnetic field for various field shapes, transition length, and cathode fluxes, assuming that the resultant beam is of Brillouin flow type. The results give a good physical interpretation to the axial gradient of the magnetic field being responsible for the amount of magnetic compression and also for the proper injection conditions. Therefore it becomes possible to predict from the known characteristics of any fairly laminary electrostatic gun the necessary axial gradient of the magnetic field and the axial position of the gun with respect to the field build-up. (orig.) [de
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 ...
Stimulated Brillouin processes in crystals and glasses
International Nuclear Information System (INIS)
Faris, G.W.; Hickman, A.P.
1992-02-01
The basic physics and material properties needed to describe and predict the Brillouin gain for a variety of materials have been investigated. Lawrence Livermore National Laboratory (LLNL) has identified transverse stimulated Brillouin scattering (SBS) as an important limiting mechanism in high power laser fusion systems. At sufficiently high laser intensities, SBS drives acoustic vibrations that can damage optical components. SRI has performed measurements and developed the corresponding theory for stimulated Brillouin gain spectroscopy in anisotropic crystals. Absolute Brillouin steady-state gain coefficients, linewidths, and frequency shifts have been determined at 532 nm for a number of optical materials of interest to LLNL. This knowledge can be used to select optical materials and devise suppression schemes that will allow much higher laser fluences to be used in laser fusion
Brillouin scatter in laser-produced plasmas
International Nuclear Information System (INIS)
Phillion, D.W.; Kruer, W.L.; Rupert, V.C.
1977-01-01
The absorption of intense laser light is found to be reduced when targets are irradiated by 1.06 μm light with long pulse widths (150-400 psec) and large focal spots (100-250 μm). Estimates of Brillouin scatter which account for the finite heat capacity of the underdense plasma predict this reduction. Spectra of the back reflected light show red shifts indicative of Brillouin scattering
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
The Patchwork Divergence Theorem
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...
Brillouin microscopy: assessing ocular tissue biomechanics.
Yun, Seok Hyun; Chernyak, Dimitri
2018-07-01
Assessment of corneal biomechanics has been an unmet clinical need in ophthalmology for many years. Many researchers and clinicians have identified corneal biomechanics as source of variability in refractive procedures and one of the main factors in keratoconus. However, it has been difficult to accurately characterize corneal biomechanics in patients. The recent development of Brillouin light scattering microscopy heightens the promise of bringing biomechanics into the clinic. The aim of this review is to overview the progress and discuss prospective applications of this new technology. Brillouin microscopy uses a low-power near-infrared laser beam to determine longitudinal modulus or mechanical compressibility of tissue by analyzing the return signal spectrum. Human clinical studies have demonstrated significant difference in the elastic properties of normal corneas versus corneas diagnosed with mild and severe keratoconus. Clinical data have also shown biomechanical changes after corneal cross-linking treatment of keratoconus patients. Brillouin measurements of the crystalline lens and sclera have also been demonstrated. Brillouin microscopy is a promising technology under commercial development at present. The technique enables physicians to characterize the biomechanical properties of ocular tissues.
Multiwavelength ytterbium-Brillouin random Rayleigh feedback fiber laser
Wu, Han; Wang, Zinan; Fan, Mengqiu; Li, Jiaqi; Meng, Qingyang; Xu, Dangpeng; Rao, Yunjiang
2018-03-01
In this letter, we experimentally demonstrate the multiwavelength ytterbium-Brillouin random fiber laser for the first time, in the half-open cavity formed by a fiber loop mirror and randomly distributed Rayleigh mirrors. With a cladding-pumped ytterbium-doped fiber and a long TrueWave fiber, the narrow linewidth Brillouin pump can generate multiple Brillouin Stokes lines with hybrid ytterbium-Brillouin gain. Up to six stable channels with a spacing of about 0.06 nm are obtained. This work extends the operation wavelength of the multiwavelength Brillouin random fiber laser to the 1 µm band, and has potential in various applications.
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)
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 ...
Nonextensive Pythagoras' Theorem
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...
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 ...
Stimulated Brillouin scattering threshold in fiber amplifiers
International Nuclear Information System (INIS)
Liang Liping; Chang Liping
2011-01-01
Based on the wave coupling theory and the evolution model of the critical pump power (or Brillouin threshold) for stimulated Brillouin scattering (SBS) in double-clad fiber amplifiers, the influence of signal bandwidth, fiber-core diameter and amplifier gain on SBS threshold is simulated theoretically. And experimental measurements of SBS are presented in ytterbium-doped double-clad fiber amplifiers with single-frequency hundred nanosecond pulse amplification. Under different input signal pulses, the forward amplified pulse distortion is observed when the pulse energy is up to 660 nJ and the peak power is up to 3.3 W in the pulse amplification with pulse duration of 200 ns and repetition rate of 1 Hz. And the backward SBS narrow pulse appears. The pulse peak power equals to SBS threshold. Good agreement is shown between the modeled and experimental data. (authors)
Neutron Brillouin scattering in dense fluids
Energy Technology Data Exchange (ETDEWEB)
Verkerk, P [Technische Univ. Delft (Netherlands); FINGO Collaboration
1997-04-01
Thermal neutron scattering is a typical microscopic probe for investigating dynamics and structure in condensed matter. In contrast, light (Brillouin) scattering with its three orders of magnitude larger wavelength is a typical macroscopic probe. In a series of experiments using the improved small-angle facility of IN5 a significant step forward is made towards reducing the gap between the two. For the first time the transition from the conventional single line in the neutron spectrum scattered by a fluid to the Rayleigh-Brillouin triplet known from light-scattering experiments is clearly and unambiguously observed in the raw neutron data without applying any corrections. Results of these experiments are presented. (author).
Brillouin gain enhancement in nano-scale photonic waveguide
Nouri Jouybari, Soodabeh
2018-05-01
The enhancement of stimulated Brillouin scattering in nano-scale waveguides has a great contribution in the improvement of the photonic devices technology. The key factors in Brillouin gain are the electrostriction force and radiation pressure generated by optical waves in the waveguide. In this article, we have proposed a new scheme of nano-scale waveguide in which the Brillouin gain is considerably improved compared to the previously-reported schemes. The role of radiation pressure in the Brillouin gain was much higher than the role of the electrostriction force. The Brillouin gain strongly depends on the structural parameters of the waveguide and the maximum value of 12127 W-1 m-1 is obtained for the Brillouin gain.
Brillouin micro-spectroscopy through aberrations via sensorless adaptive optics
Edrei, Eitan; Scarcelli, Giuliano
2018-04-01
Brillouin spectroscopy is a powerful optical technique for non-contact viscoelastic characterizations which has recently found applications in three-dimensional mapping of biological samples. Brillouin spectroscopy performances are rapidly degraded by optical aberrations and have therefore been limited to homogenous transparent samples. In this work, we developed an adaptive optics (AO) configuration designed for Brillouin scattering spectroscopy to engineer the incident wavefront and correct for aberrations. Our configuration does not require direct wavefront sensing and the injection of a "guide-star"; hence, it can be implemented without the need for sample pre-treatment. We used our AO-Brillouin spectrometer in aberrated phantoms and biological samples and obtained improved precision and resolution of Brillouin spectral analysis; we demonstrated 2.5-fold enhancement in Brillouin signal strength and 1.4-fold improvement in axial resolution because of the correction of optical aberrations.
Complex proofs of real theorems
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 ...
Observation of narrowband intrinsic spectra of Brillouin dynamic gratings.
Song, Kwang Yong; Yoon, Hyuk Jin
2010-09-01
We experimentally demonstrate that the reflection spectrum of a Brillouin dynamic grating in a polarization-maintaining fiber can be much narrower than the intrinsic linewidth of the stimulated Brillouin scattering, matching well with the theory of a fiber Bragg grating in terms of the linewidth and the reflectivity. A 3 dB bandwidth as narrow as 10.5 MHz is observed with the Brillouin dynamic grating generated in a 9 m uniform fiber.
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....
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...
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.
Dalen, D. van
The following pages make form a new chapter for the book Logic and Structure. This chapter deals with the incompleteness theorem, and contains enough basic material for the treatment of the required notions of computability, representability and the like. This chapter will appear in the next
Indian Academy of Sciences (India)
eralizing the method of proof of the well known. Cantor's ... Godel's first incompleteness theorem is proved. ... that the number of elements in any finite set is a natural number. ..... proof also has a Godel number; of course, you have to fix.
Saikia, Manjil P.
2013-01-01
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \\cite{thales}, \\cite{wiki} and \\cite{wiki2} for the historical comments and sources.
Converse Barrier Certificate Theorems
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer
2016-01-01
This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither...
International Nuclear Information System (INIS)
Cahill, K.
1975-11-01
Local field theory is used to derive formulas that express certain boundary values of the N-point function as sums of products of scattering amplitudes. These formulas constitute a generalization of the optical theorem and facilitate the analysis of multiparticle scattering functions [fr
Signatures of chaos in the Brillouin zone.
Barr, Aaron; Barr, Ariel; Porter, Max D; Reichl, Linda E
2017-10-01
When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.
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)
Discovering the Theorem of Pythagoras
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.
MCSCF optimization through combined use of natural orbitals and the Brillouin-Levy-Berthier theorem
International Nuclear Information System (INIS)
Ruedenberg, K.; Cheung, L.M.; Elbert, S.T.
1979-01-01
A novel approach is developed for optimizing molecular orbitals within the context of a multiconfiguration self-consistent-field problem. The MCSCF wave function is determined through a sequence of eigenvalue problems in the multiconfiguration space and the single-excitation space. They are used iteratively to improve the natural orbitals, which in turn are related, by successively improved transformations, to the MCSCF orbitals. The mathematical problems arising out of this general concept are solved and the computational implementation is discussed. In many applications the method has proven itself as a powerful approach in forcing rapid convergence. Adaptation to spin and spatial symmetry is maintained throughout, and the procedure is applicable to excited states as well as to ground states. 3 figures, 2 tables
Effect of the stimulated Brillouin backscattering on selffocusing threshold
International Nuclear Information System (INIS)
Rubenchik, A.M.; Shapiro, E.G.; Turitsyn, S.K.
1994-03-01
In many physical problems stimulated Brillouin scattering (SBS) and selffocusing are manifested simultaneously. We consider effect of the stimulated Brillouin backscattering (SBS) on self-focusing of laser radiation in plasmas. It was found that the self-focusing may be supressed substantionally by the SBS effect
Acoustic profilometry within polymers as performed by Brillouin microscopy
Energy Technology Data Exchange (ETDEWEB)
Sanctuary, R [Laboratoire Europeen de Recherche Universitaire Saarland-Lorraine (LERUSL) at the Centre Universitaire de Luxembourg, Departement des Sciences, Laboratoire 1.19, 162a avenue de la Faiencerie, L-1511 Luxembourg (Luxembourg); Bactavatchalou, Ravi [Universitaet des Saarlandes, Fakultaet fuer Physik und Elektrotechnik 7.2, Gebaeude 38, D-66041 Saarbruecken (Germany); Mueller, Ulrich [Universitaet des Saarlandes, Fakultaet fuer Physik und Elektrotechnik 7.2, Gebaeude 38, D-66041 Saarbruecken (Germany); Possart, W [Universitaet des Saarlandes, Fakultaet fuer Chemie, Pharmazie und Werkstoffwissenschaften 8.15, Gebaeude 22, D-66041 Saarbruecken (Germany); Alnot, P [Laboratoire de Physique des Milieux Ionises et Applications (LPMIA), UMR 7040-C.N.R.S, Universite de Nancy I, Bd des Aiguillettes, B.P. 239 F-54506 Vandoeuvre les Nancy (France); Krueger, J K [Universitaet des Saarlandes, Fakultaet fuer Physik und Elektrotechnik 7.2, Gebaeude 38, D-66041 Saarbruecken (Germany)
2003-11-07
Using high performance Brillouin spectroscopy we present a new technique, which enables us to perform acoustic microscopy with a spatial resolution of about 1 {mu}m. This technique, called Brillouin microscopy, is tested on several bulk- and film-like polymer samples.
The electromagnetic Brillouin precursor in one-dimensional photonic crystals
Uitham, R.; Hoenders, B. J.
2008-01-01
We have calculated the electromagnetic Brillouin precursor that arises in a one-dimensional photonic crystal that consists of two homogeneous slabs which each have a single electron resonance. This forerunner is compared with the Brillouin precursor that arises in a homogeneous double-electron
International Nuclear Information System (INIS)
Veltman, H.
1990-01-01
The equivalence theorem states that, at an energy E much larger than the vector-boson mass M, the leading order of the amplitude with longitudinally polarized vector bosons on mass shell is given by the amplitude in which these vector bosons are replaced by the corresponding Higgs ghosts. We prove the equivalence theorem and show its validity in every order in perturbation theory. We first derive the renormalized Ward identities by using the diagrammatic method. Only the Feynman-- 't Hooft gauge is discussed. The last step of the proof includes the power-counting method evaluated in the large-Higgs-boson-mass limit, needed to estimate the leading energy behavior of the amplitudes involved. We derive expressions for the amplitudes involving longitudinally polarized vector bosons for all orders in perturbation theory. The fermion mass has not been neglected and everything is evaluated in the region m f ∼M much-lt E much-lt m Higgs
Fully Quantum Fluctuation Theorems
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.
Multivariable Chinese Remainder Theorem
Indian Academy of Sciences (India)
IAS Admin
to sleep. The 3rd thief wakes up and finds the rest of the coins make 7 equal piles excepting a coin which he pockets. If the total number of coins they stole is not more than 200, what is the exact number? With a bit of hit and miss, one can find that 157 is a possible number. The Chinese remainder theorem gives a systematic ...
Temporal evolution of stimulated Brillouin backscatter
International Nuclear Information System (INIS)
Hinkel, D.E.; Williams, E.A.; Berger, R.L.
1994-01-01
A qualitative understanding of the time dependence of stimulated Brillouin scattering (SBS) provides estimates of the amount of temporal growth that occurs in current inertial confinement fusion and short laser pulse interaction experiments when the growth is limited by the length of the experiment or by motion of the ''hot spots'' of the laser intensity pattern induced by beam smoothing. In the weak coupling limit, the instantaneous growth rate depends upon the plasma initial conditions early in time, is proportional to t -1/2 later in time, and asymptotically approaches the absolute growth rate (in the absence of damping). When the instability is strongly coupled, the growth rate depends upon the plasma initial conditions early in time but is proportional to t -1/3 later in time. When the growth rate drops to a value comparable to that of the ion acoustic frequency, the instability becomes effectively weakly coupled. The effects of damping are also discussed
International Nuclear Information System (INIS)
Lloyd, Mark Anthony
1999-01-01
We in the nuclear power industry consider ourselves to be at the forefront of civilised progress. Yet, all too often, even we ourselves don't believe our public relations statements about nuclear power. Why is this? Let us approach the question by considering Godel's Theorem. Godel's Theorem is extremely complicated mathematically, but for our purposes can be simplified to the maxim that one cannot validate a system from within that system. Scientists, especially those in the fields of astronomy and nuclear physics, have long realised the implications of Godel's Theorem. The people to whom we must communicate look to us, who officially know everything about our industry, to comfort and reassure them. And we forget that we can only comfort them by addressing their emotional needs, not by demonstrating our chilling o bjectivity . Let us try something completely new in communication. Instead of looking for incremental rules which will help us marginally differentiate the way we communicate about minor or major incidents, let us leapfrog across 'objectivity' to meaning and relevance. If we truly believe that nuclear energy is a good thing, this leap should not be difficult. Finally, if we as communicators are not prepared to be meaningful and relevant - not prepared to leapfrog beyond weasel terms like 'minor incident' - what does that say about the kinds of people we believe the nuclear community to be? Are nuclear people a group apart, divisible from the rest of the human race by their evil? In fact the nuclear community is a living, laughing, normal part of a whole society; and is moreover a good contributor to the technological progress that society demands. When we ourselves recognise this, we will start to communicate nuclear issues in the same language as the rest of society. We will start to speak plainly and convincingly, and our conviction will leapfrog our audience into being able to believe us
Topological interpretation of Luttinger theorem
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...
Bertrand's theorem and virial theorem in fractional classical mechanics
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.
Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides.
Shin, Heedeuk; Qiu, Wenjun; Jarecki, Robert; Cox, Jonathan A; Olsson, Roy H; Starbuck, Andrew; Wang, Zheng; Rakich, Peter T
2013-01-01
Nanoscale modal confinement is known to radically enhance the effect of intrinsic Kerr and Raman nonlinearities within nanophotonic silicon waveguides. By contrast, stimulated Brillouin-scattering nonlinearities, which involve coherent coupling between guided photon and phonon modes, are stifled in conventional nanophotonics, preventing the realization of a host of Brillouin-based signal-processing technologies in silicon. Here we demonstrate stimulated Brillouin scattering in silicon waveguides, for the first time, through a new class of hybrid photonic-phononic waveguides. Tailorable travelling-wave forward-stimulated Brillouin scattering is realized-with over 1,000 times larger nonlinearity than reported in previous systems-yielding strong Brillouin coupling to phonons from 1 to 18 GHz. Experiments show that radiation pressures, produced by subwavelength modal confinement, yield enhancement of Brillouin nonlinearity beyond those of material nonlinearity alone. In addition, such enhanced and wideband coherent phonon emission paves the way towards the hybridization of silicon photonics, microelectromechanical systems and CMOS signal-processing technologies on chip.
Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides
Shin, Heedeuk; Qiu, Wenjun; Jarecki, Robert; Cox, Jonathan A.; Olsson, Roy H.; Starbuck, Andrew; Wang, Zheng; Rakich, Peter T.
2013-01-01
Nanoscale modal confinement is known to radically enhance the effect of intrinsic Kerr and Raman nonlinearities within nanophotonic silicon waveguides. By contrast, stimulated Brillouin-scattering nonlinearities, which involve coherent coupling between guided photon and phonon modes, are stifled in conventional nanophotonics, preventing the realization of a host of Brillouin-based signal-processing technologies in silicon. Here we demonstrate stimulated Brillouin scattering in silicon waveguides, for the first time, through a new class of hybrid photonic–phononic waveguides. Tailorable travelling-wave forward-stimulated Brillouin scattering is realized—with over 1,000 times larger nonlinearity than reported in previous systems—yielding strong Brillouin coupling to phonons from 1 to 18 GHz. Experiments show that radiation pressures, produced by subwavelength modal confinement, yield enhancement of Brillouin nonlinearity beyond those of material nonlinearity alone. In addition, such enhanced and wideband coherent phonon emission paves the way towards the hybridization of silicon photonics, microelectromechanical systems and CMOS signal-processing technologies on chip. PMID:23739586
The Non-Signalling theorem in generalizations of Bell's theorem
Walleczek, J.; Grössing, G.
2014-04-01
Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational
Directory of Open Access Journals (Sweden)
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].
Geometry of the Adiabatic Theorem
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.…
A Decomposition Theorem for Finite Automata.
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)
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...
Guney, Veli Ugur
In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible
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
Green's theorem and Gorenstein sequences
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...
-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.
Complex integration and Cauchy's theorem
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
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
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 Levy sections theorem revisited
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.
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
Generalized Dandelin’s Theorem
Kheyfets, A. L.
2017-11-01
The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.
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.
Factor and Remainder Theorems: An Appreciation
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…
Stability of Brillouin flow in planar, conventional, and inverted magnetrons
International Nuclear Information System (INIS)
Simon, D. H.; Lau, Y. Y.; Greening, G.; Wong, P.; Gilgenbach, R. M.; Hoff, B. W.
2015-01-01
The Brillouin flow is the prevalent flow in crossed-field devices. We systematically study its stability in the conventional, planar, and inverted magnetron geometry. To investigate the intrinsic negative mass effect in Brillouin flow, we consider electrostatic modes in a nonrelativistic, smooth bore magnetron. We found that the Brillouin flow in the inverted magnetron is more unstable than that in a planar magnetron, which in turn is more unstable than that in the conventional magnetron. Thus, oscillations in the inverted magnetron may startup faster than the conventional magnetron. This result is consistent with simulations, and with the negative mass property in the inverted magnetron configuration. Inclusion of relativistic effects and electromagnetic effects does not qualitatively change these conclusions
Modes of spheroidal ion plasmas at the Brillouin limit
International Nuclear Information System (INIS)
Tinkle, M. D.; Greaves, R. G.; Surko, C. M.
1995-01-01
Brillouin-density pure ion plasmas have been generated in a quadrupole Penning tray by electron-beam ionization of a low-pressure gas. Large, spheroidal, steady-state plasmas are produced that extend to one of the trap electrodes. With the density fixed at the Brillouin limit by the high ion production rate, the electrode potentials determine the plasma shape. The frequencies of azimuthally propagating cyclotron and diocotron modes are found to vary significantly with the plasma aspect ratio. For oblate plasmas, we are able to test theoretical predictions of a simple fluid model, and the frequencies are in good agreement
Self-pulsation threshold of Raman amplified Brillouin fiber cavities
DEFF Research Database (Denmark)
Ott, Johan Raunkjær; Pedersen, Martin Erland Vestergaard; Rottwitt, Karsten
2009-01-01
An implicit equation for the oscillation threshold of stimulated Brillouin scattering from Raman amplified signals in fibers with external feedback is derived under the assumption of no depletion. This is compared to numerical investigations of Raman amplification schemes showing good agreement...
High-speed stimulated Brillouin scattering spectroscopy at 780 nm
Directory of Open Access Journals (Sweden)
Itay Remer
2016-09-01
Full Text Available We demonstrate a high-speed stimulated Brillouin scattering (SBS spectroscopy system that is able to acquire stimulated Brillouin gain point-spectra in water samples and Intralipid tissue phantoms over 2 GHz within 10 ms and 100 ms, respectively, showing a 10-100 fold increase in acquisition rates over current frequency-domain SBS spectrometers. This improvement was accomplished by integrating an ultra-narrowband hot rubidium-85 vapor notch filter in a simplified frequency-domain SBS spectrometer comprising nearly counter-propagating continuous-wave pump-probe light at 780 nm and conventional single-modulation lock-in detection. The optical notch filter significantly suppressed stray pump light, enabling detection of stimulated Brillouin gain spectra with substantially improved acquisition times at adequate signal-to-noise ratios (∼25 dB in water samples and ∼15 dB in tissue phantoms. These results represent an important step towards the use of SBS spectroscopy for high-speed measurements of Brillouin gain resonances in scattering and non-scattering samples.
Preservation theorems on finite structures
International Nuclear Information System (INIS)
Hebert, M.
1994-09-01
This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ''homomorphism into'' case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs
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...
Scale symmetry and virial theorem
International Nuclear Information System (INIS)
Westenholz, C. von
1978-01-01
Scale symmetry (or dilatation invariance) is discussed in terms of Noether's Theorem expressed in terms of a symmetry group action on phase space endowed with a symplectic structure. The conventional conceptual approach expressing invariance of some Hamiltonian under scale transformations is re-expressed in alternate form by infinitesimal automorphisms of the given symplectic structure. That is, the vector field representing scale transformations leaves the symplectic structure invariant. In this model, the conserved quantity or constant of motion related to scale symmetry is the virial. It is shown that the conventional virial theorem can be derived within this framework
Nonperturbative Adler-Bardeen theorem
International Nuclear Information System (INIS)
Mastropietro, Vieri
2007-01-01
The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions
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 ...
Dynamic Newton-Puiseux Theorem
DEFF Research Database (Denmark)
Mannaa, Bassel; Coquand, Thierry
2013-01-01
A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization...
Opechowski's theorem and commutator groups
International Nuclear Information System (INIS)
Caride, A.O.; Zanette, S.I.
1985-01-01
It is shown that the conditions of application of Opechowski's theorem for double groups of subgroups of O(3) are directly associated to the structure of their commutator groups. Some characteristics of the structure of classes are also discussed. (Author) [pt
Shell theorem for spontaneous emission
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Mortensen, Jakob Egeberg; Lodahl, Peter
2013-01-01
and therefore is given exactly by the dipole approximation theory. This surprising result is a spontaneous emission counterpart to the shell theorems of classical mechanics and electrostatics and provides insights into the physics of mesoscopic emitters as well as great simplifications in practical calculations....
KLN theorem and infinite statistics
International Nuclear Information System (INIS)
Grandou, T.
1992-01-01
The possible extension of the Kinoshita-Lee-Nauenberg (KLN) theorem to the case of infinite statistics is examined. It is shown that it appears as a stable structure in a quantum field theory context. The extension is provided by working out the Fock space realization of a 'quantum algebra'. (author) 2 refs
The Geometric Mean Value Theorem
de Camargo, André Pierro
2018-01-01
In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…
Fermion fractionization and index theorem
International Nuclear Information System (INIS)
Hirayama, Minoru; Torii, Tatsuo
1982-01-01
The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)
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 ...
Angle Defect and Descartes' Theorem
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
Optical theorem and its history
International Nuclear Information System (INIS)
Newton, R.G.
1978-01-01
A translation is presented of a paper submitted to the symposium ''Concepts and methods in microscopic physics'' held at Washington University in 1974. A detailed description is given of the history of the optical theorem, its various formulations and derivations and its use in the scattering theory. (Z.J.)
On the Fourier integral theorem
Koekoek, J.
1987-01-01
Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the
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...
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 note on generalized Weyl's theorem
Zguitti, H.
2006-04-01
We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.
A definability theorem for first order logic
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
Extreme temperature sensing using brillouin scattering in optical fibers
Fellay, Alexandre
Stimulated Brillouin scattering in silica-based optical fibers may be considered from two different and complementary standpoints. For a physicist, this interaction of light and pressure wave in a material, or equivalently in quantum theory terms between photons and phonons, gives some glimpses of the atomic structure of the solid and of its vibration modes. For an applied engineer, the same phenomenon may be put to good use as a sensing mechanism for distributed measurements, thanks to the dependence of the scattered light on external parameters such as the temperature, the pressure or the strain applied to the fiber. As far as temperature measurements are concerned, Brillouin-based distributed sensors have progressively gained wide recognition as efficient systems, even if their rather high cost still restricts the number of their applications. Yet they are generally used in a relatively narrow temperature range around the usual ambient temperature; in this domain, the frequency of the scattered light incre...
Brillouin optical correlation domain analysis in composite material beams
DEFF Research Database (Denmark)
Stern, Yonatan; London, Yosef; Preter, Eyal
2017-01-01
Structural health monitoring is a critical requirement in many composites. Numerous monitoring strategies rely on measurements of temperature or strain (or both), however these are often restricted to point-sensing or to the coverage of small areas. Spatially-continuous data can be obtained...... with optical fiber sensors. In this work, we report high-resolution distributed Brillouin sensing over standard fibers that are embedded in composite structures. A phase-coded, Brillouin optical correlation domain analysis (B-OCDA) protocol was employed, with spatial resolution of 2 cm and sensitivity of 1 °K...... or 20 micro-strain. A portable measurement setup was designed and assembled on the premises of a composite structures manufacturer. The setup was successfully utilized in several structural health monitoring scenarios: (a) monitoring the production and curing of a composite beam over 60 h; (b...
Modes of spheroidal ion plasmas at the Brillouin limit
International Nuclear Information System (INIS)
Tinkle, M.D.; Greaves, R.G.; Surko, C.M.
1996-01-01
The confinement properties and collective modes of single-component plasmas are investigated in a quadrupole Penning trap. Brillouin-density pure ion plasmas are generated by electron-beam ionization of a low-pressure gas. Large, spheroidal, steady-state plasmas are produced, extending out to contact one or more of the trap electrodes. With the density fixed at the Brillouin limit by the high ion production rate, the electrode potentials determine the plasma shape. The frequencies of azimuthally propagating cyclotron and diocotron modes are found to vary significantly with the plasma aspect ratio. For oblate plasmas, the frequencies are in good agreement with a simple fluid model. copyright 1996 American Institute of Physics
Tight closure and vanishing theorems
International Nuclear Information System (INIS)
Smith, K.E.
2001-01-01
Tight closure has become a thriving branch of commutative algebra since it was first introduced by Mel Hochster and Craig Huneke in 1986. Over the past few years, it has become increasingly clear that tight closure has deep connections with complex algebraic geometry as well, especially with those areas of algebraic geometry where vanishing theorems play a starring role. The purpose of these lectures is to introduce tight closure and to explain some of these connections with algebraic geometry. Tight closure is basically a technique for harnessing the power of the Frobenius map. The use of the Frobenius map to prove theorems about complex algebraic varieties is a familiar technique in algebraic geometry, so it should perhaps come as no surprise that tight closure is applicable to algebraic geometry. On the other hand, it seems that so far we are only seeing the tip of a large and very beautiful iceberg in terms of tight closure's interpretation and applications to algebraic geometry. Interestingly, although tight closure is a 'characteristic p' tool, many of the problems where tight closure has proved useful have also yielded to analytic (L2) techniques. Despite some striking parallels, there had been no specific result directly linking tight closure and L∼ techniques. Recently, however, the equivalence of an ideal central to the theory of tight closure was shown to be equivalent to a certain 'multiplier ideal' first defined using L2 methods. Presumably, deeper connections will continue to emerge. There are two main types of problems for which tight closure has been helpful: in identifying nice structure and in establishing uniform behavior. The original algebraic applications of tight closure include, for example, a quick proof of the Hochster-Roberts theorem on the Cohen-Macaulayness of rings of invariants, and also a refined version of the Brianqon-Skoda theorem on the uniform behaviour of integral closures of powers of ideals. More recent, geometric
SBS [stimulated Brillouin scattering] pulse distortion in multimode optical fibers
International Nuclear Information System (INIS)
Smith, J.R.; Hawkins, R.J.; Laumann, C.W.; Hatch, J.
1989-01-01
We have observed sever temporal-pulse-shape distortion due to stimulated Brillouin scattering (SBS) in multimode optical fibers used to diagnose 351 m laser pulses on the Nova laser system. Our measurements can be fit by a basic model of SBS and provide a clear indication of the intensity and temporal regimes where significant SBS-induced temporal-pulse-shape distortion can be avoided. 15 refs., 3 figs., 1 tab
Brillouin Optical Correlation Domain Analysis in Composite Material Beams
Directory of Open Access Journals (Sweden)
Yonatan Stern
2017-10-01
Full Text Available Structural health monitoring is a critical requirement in many composites. Numerous monitoring strategies rely on measurements of temperature or strain (or both, however these are often restricted to point-sensing or to the coverage of small areas. Spatially-continuous data can be obtained with optical fiber sensors. In this work, we report high-resolution distributed Brillouin sensing over standard fibers that are embedded in composite structures. A phase-coded, Brillouin optical correlation domain analysis (B-OCDA protocol was employed, with spatial resolution of 2 cm and sensitivity of 1 °K or 20 micro-strain. A portable measurement setup was designed and assembled on the premises of a composite structures manufacturer. The setup was successfully utilized in several structural health monitoring scenarios: (a monitoring the production and curing of a composite beam over 60 h; (b estimating the stiffness and Young’s modulus of a composite beam; and (c distributed strain measurements across the surfaces of a model wing of an unmanned aerial vehicle. The measurements are supported by the predictions of structural analysis calculations. The results illustrate the potential added values of high-resolution, distributed Brillouin sensing in the structural health monitoring of composites.
Time-domain Brillouin scattering assisted by diffraction gratings
Matsuda, Osamu; Pezeril, Thomas; Chaban, Ievgeniia; Fujita, Kentaro; Gusev, Vitalyi
2018-02-01
Absorption of ultrashort laser pulses in a metallic grating deposited on a transparent sample launches coherent compression/dilatation acoustic pulses in directions of different orders of acoustic diffraction. Their propagation is detected by delayed laser pulses, which are also diffracted by the metallic grating, through the measurement of the transient intensity change of the first-order diffracted light. The obtained data contain multiple frequency components, which are interpreted by considering all possible angles for the Brillouin scattering of light achieved through multiplexing of the propagation directions of light and coherent sound by the metallic grating. The emitted acoustic field can be equivalently presented as a superposition of plane inhomogeneous acoustic waves, which constitute an acoustic diffraction grating for the probe light. Thus the obtained results can also be interpreted as a consequence of probe light diffraction by both metallic and acoustic gratings. The realized scheme of time-domain Brillouin scattering with metallic gratings operating in reflection mode provides access to wide range of acoustic frequencies from minimal to maximal possible values in a single experimental optical configuration for the directions of probe light incidence and scattered light detection. This is achieved by monitoring the backward and forward Brillouin scattering processes in parallel. Potential applications include measurements of the acoustic dispersion, simultaneous determination of sound velocity and optical refractive index, and evaluation of samples with a single direction of possible optical access.
Brillouin Optical Correlation Domain Analysis in Composite Material Beams.
Stern, Yonatan; London, Yosef; Preter, Eyal; Antman, Yair; Diamandi, Hilel Hagai; Silbiger, Maayan; Adler, Gadi; Levenberg, Eyal; Shalev, Doron; Zadok, Avi
2017-10-02
Structural health monitoring is a critical requirement in many composites. Numerous monitoring strategies rely on measurements of temperature or strain (or both), however these are often restricted to point-sensing or to the coverage of small areas. Spatially-continuous data can be obtained with optical fiber sensors. In this work, we report high-resolution distributed Brillouin sensing over standard fibers that are embedded in composite structures. A phase-coded, Brillouin optical correlation domain analysis (B-OCDA) protocol was employed, with spatial resolution of 2 cm and sensitivity of 1 °K or 20 micro-strain. A portable measurement setup was designed and assembled on the premises of a composite structures manufacturer. The setup was successfully utilized in several structural health monitoring scenarios: (a) monitoring the production and curing of a composite beam over 60 h; (b) estimating the stiffness and Young's modulus of a composite beam; and (c) distributed strain measurements across the surfaces of a model wing of an unmanned aerial vehicle. The measurements are supported by the predictions of structural analysis calculations. The results illustrate the potential added values of high-resolution, distributed Brillouin sensing in the structural health monitoring of composites.
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.
A Randomized Central Limit Theorem
International Nuclear Information System (INIS)
Eliazar, Iddo; Klafter, Joseph
2010-01-01
The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√(n)), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √(n). This Letter considers scaling schemes which are stochastic and non-uniform, and presents a 'Randomized Central Limit Theorem' (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Levy laws.
Bell's theorem, accountability and nonlocality
International Nuclear Information System (INIS)
Vona, Nicola; Liang, Yeong-Cherng
2014-01-01
Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner (2011 Nature Commun. 2 411), we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)
Fluctuation theorems and atypical trajectories
International Nuclear Information System (INIS)
Sahoo, M; Lahiri, S; Jayannavar, A M
2011-01-01
In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work (W c ), thermodynamic work (W), total entropy (Δs tot ) and dissipated heat (Q), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at the macroscale. The distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit a peak in the regime of typical behaviour only.
Lectures on Fermat's last theorem
International Nuclear Information System (INIS)
Sury, B.
1993-09-01
The report presents the main ideas involved in the approach towards the so-called Fermat's last theorem (FLT). The discussion leads to the point where recent work of A. Wiles starts and his work is not discussed. After a short history of the FLT and of the present approach, are discussed the elliptic curves and the modular forms with their relations, the Taniyama-Shimura-Well conjecture and the FLT
Pythagoras Theorem and Relativistic Kinematics
Mulaj, Zenun; Dhoqina, Polikron
2010-01-01
In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.
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
Brillouin Scattering Spectrum Analysis Based on Auto-Regressive Spectral Estimation
Huang, Mengyun; Li, Wei; Liu, Zhangyun; Cheng, Linghao; Guan, Bai-Ou
2018-06-01
Auto-regressive (AR) spectral estimation technology is proposed to analyze the Brillouin scattering spectrum in Brillouin optical time-domain refelectometry. It shows that AR based method can reliably estimate the Brillouin frequency shift with an accuracy much better than fast Fourier transform (FFT) based methods provided the data length is not too short. It enables about 3 times improvement over FFT at a moderate spatial resolution.
Brillouin Scattering Spectrum Analysis Based on Auto-Regressive Spectral Estimation
Huang, Mengyun; Li, Wei; Liu, Zhangyun; Cheng, Linghao; Guan, Bai-Ou
2018-03-01
Auto-regressive (AR) spectral estimation technology is proposed to analyze the Brillouin scattering spectrum in Brillouin optical time-domain refelectometry. It shows that AR based method can reliably estimate the Brillouin frequency shift with an accuracy much better than fast Fourier transform (FFT) based methods provided the data length is not too short. It enables about 3 times improvement over FFT at a moderate spatial resolution.
Large On-Chip Amplification in Silicon via Forward Stimulated Brillouin Scattering
Energy Technology Data Exchange (ETDEWEB)
Kittlaus, Eric [Yale Univ., New Haven, CT (United States); Shin, Heedeuk [Yale Univ., New Haven, CT (United States); Rakich, Peter [Yale Univ., New Haven, CT (United States)
2015-10-15
Strong Brillouin coupling has only recently been realized in silicon using a new class of op- tomechanical waveguides that yield both optical and phononic con nement. Despite these major advances, appreciable Brillouin ampli cation has yet to be observed in silicon. Using new membrane- suspended silicon waveguide we report large Brillouin ampli cation for the rst time, reaching levels greater than 5 dB for modest pump powers, and demonstrate a record low (5 mW) threshold for net ampli cation. This work represents a crucial advance necessary to realize high-performance Brillouin lasers and ampli ers in silicon.
Expanding the Interaction Equivalency Theorem
Directory of Open Access Journals (Sweden)
Brenda Cecilia Padilla Rodriguez
2015-06-01
Full Text Available Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner is present at a high level. This study sought to apply this theorem to the corporate sector, and to expand it to include other indicators of course effectiveness: satisfaction, knowledge transfer, business results and return on expectations. A large Mexican organisation participated in this research, with 146 learners, 30 teachers and 3 academic assistants. Three versions of an online course were designed, each emphasising a different type of interaction. Data were collected through surveys, exams, observations, activity logs, think aloud protocols and sales records. All course versions yielded high levels of effectiveness, in terms of satisfaction, learning and return on expectations. Yet, course design did not dictate the types of interactions in which students engaged within the courses. Findings suggest that the interaction equivalency theorem can be reformulated as follows: In corporate settings, an online course can be effective in terms of satisfaction, learning, knowledge transfer, business results and return on expectations, as long as (a at least one of three types of interaction (learner-content, learner-teacher or learner-learner features prominently in the design of the course, and (b course delivery is consistent with the chosen type of interaction. Focusing on only one type of interaction carries a high risk of confusion, disengagement or missed learning opportunities, which can be managed by incorporating other forms of interactions.
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.
Confinement, diquarks and goldstone's theorem
International Nuclear Information System (INIS)
Roberts, C.D.
1996-01-01
Determinations of the gluon propagator in the continuum and in lattice simulations are compared. A systematic truncation procedure for the quark Dyson-Schwinger and bound state Bethe-Salpeter equations is described. The procedure ensures the flavor-octet axial- vector Ward identity is satisfied order-by-order, thereby guaranteeing the preservation of Goldstone's theorem; and identifies a mechanism that simultaneously ensures the absence of diquarks in QCD and their presence in QCD N c =2 , where the color singlet diquark is the ''baryon'' of the theory
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
Bernstein Lethargy Theorem and Reflexivity
Aksoy, Asuman Güven; Peng, Qidi
2018-01-01
In this paper, we prove the equivalence of reflexive Banach spaces and those Banach spaces which satisfy the following form of Bernstein's Lethargy Theorem. Let $X$ be an arbitrary infinite-dimensional Banach space, and let the real-valued sequence $\\{d_n\\}_{n\\ge1}$ decrease to $0$. Suppose that $\\{Y_n\\}_{n\\ge1}$ is a system of strictly nested subspaces of $X$ such that $\\overline Y_n \\subset Y_{n+1}$ for all $n\\ge1$ and for each $n\\ge1$, there exists $y_n\\in Y_{n+1}\\backslash Y_n$ such that ...
Cyclic graphs and Apery's theorem
International Nuclear Information System (INIS)
Sorokin, V N
2002-01-01
This is a survey of results about the behaviour of Hermite-Pade approximants for graphs of Markov functions, and a survey of interpolation problems leading to Apery's result about the irrationality of the value ζ(3) of the Riemann zeta function. The first example is given of a cyclic graph for which the Hermite-Pade problem leads to Apery's theorem. Explicit formulae for solutions are obtained, namely, Rodrigues' formulae and integral representations. The asymptotic behaviour of the approximants is studied, and recurrence formulae are found
Abstract decomposition theorem and applications
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).
Symbolic logic and mechanical theorem proving
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.
Tunable Stimulated Brillouin Scattering in Planar Optical Circuits
2012-11-01
J. Gauthier, R. W. Boyd, and A. L. Gaeta, Phys. Rev. Lett. 94, 153902 (2005). 4. R. Pant, M. D. Stenner , M. A. Neifeld, and D. J. Gauthier, Opt...Express 16, 2764 (2008). 5. Z. Shi, R. Pant, Z. Zhu, M. D. Stenner , M. A. Neifeld, D. J. Gauthier, and R. W. Boyd, Opt. Lett. 32, 1986 (2007). 6. K. Y...stimulated Brillouin scattering,” Opt. Express 19(9), 8285–8290 (2011). 25. R. Pant, M. D. Stenner , M. A. Neifeld, Z. M. Shi, R. W. Boyd, and D. J
Biomechanics of subcellular structures by non-invasive Brillouin microscopy
Antonacci, Giuseppe; Braakman, Sietse
2016-11-01
Cellular biomechanics play a pivotal role in the pathophysiology of several diseases. Unfortunately, current methods to measure biomechanical properties are invasive and mostly limited to the surface of a cell. As a result, the mechanical behaviour of subcellular structures and organelles remains poorly characterised. Here, we show three-dimensional biomechanical images of single cells obtained with non-invasive, non-destructive Brillouin microscopy with an unprecedented spatial resolution. Our results quantify the longitudinal elastic modulus of subcellular structures. In particular, we found the nucleoli to be stiffer than both the nuclear envelope (p biomechanics and its role in pathophysiology.
Optimization of the Brillouin operator on the KNL architecture
Dürr, Stephan
2018-03-01
Experiences with optimizing the matrix-times-vector application of the Brillouin operator on the Intel KNL processor are reported. Without adjustments to the memory layout, performance figures of 360 Gflop/s in single and 270 Gflop/s in double precision are observed. This is with Nc = 3 colors, Nv = 12 right-hand-sides, Nthr = 256 threads, on lattices of size 323 × 64, using exclusively OMP pragmas. Interestingly, the same routine performs quite well on Intel Core i7 architectures, too. Some observations on the much harderWilson fermion matrix-times-vector optimization problem are added.
Reduction of stimulated Brillouin backscattering with plasma beam smoothing
Energy Technology Data Exchange (ETDEWEB)
Yahia, V.; Loisel, G.; Baccou, C.; Labaune, C. [Laboratoire pour l' Utilisation des Lasers Intenses, Ecole Polytechnique, Palaiseau (France); Masson-Laborde, P.-E.; Depierreux, S.; Goyon, C.; Teychenné, D. [CEA, DAM, DIF, F-91297 Arpajon (France); Borisenko, N. G.; Orekhov, A. [P.N. Lebedev Physical Institute, Russian Academy of Science, Moscow (Russian Federation); Rienecker, T.; Rosmej, O. [GSI Helmhotzzentrum fur Schwerionenforschung, 64291 Darmstadt (Germany)
2015-04-15
Plasma induced incoherence (PII) can strongly modify the growth rates of stimulated scattering instabilities. A special double-target design was used to quantify the effect of PII on stimulated Brillouin scattering (SBS). Successive shots using all or part of these targets led to the characterization of temporal and spatial incoherence of a laser pulse after propagation through a foam plasma and to the quantification of the reduction of SBS from the second target. Numerical simulations were used to identify the main physical mechanisms in play.
Rayleigh-Brillouin spectrum in special relativistic hydrodynamics
International Nuclear Information System (INIS)
Garcia-Perciante, A. L.; Garcia-Colin, L. S.; Sandoval-Villalbazo, A.
2009-01-01
In this paper we calculate the Rayleigh-Brillouin spectrum for a relativistic simple fluid according to three different versions available for a relativistic approach to nonequilibrium thermodynamics. An outcome of these calculations is that Eckart's version predicts that such spectrum does not exist. This provides an argument to question its validity. The remaining two results, which differ one from another, do provide a finite form for such spectrum. This raises the rather intriguing question as to which of the two theories is a better candidate to be taken as a possible version of relativistic nonequilibrium thermodynamics. The answer will clearly require deeper examination of this problem.
Equivalent conserved currents and generalized Noether's theorem
International Nuclear Information System (INIS)
Gordon, T.J.
1984-01-01
A generalized Noether theorem is presented, relating symmetries and equivalence classes of local) conservation laws in classical field theories; this is contrasted with the standard theorem. The concept of a ''Noether'' field theory is introduced, being a theory for which the generalized theorem applies; not only does this include the cases of Lagrangian and Hamiltonian field theories, these structures are ''derived'' from the Noether property in a natural way. The generalized theorem applies to currents and symmetries that contain derivatives of the fields up to an arbitrarily high order
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.
Al-Asadi, H A; Al-Mansoori, M H; Ajiya, M; Hitam, S; Saripan, M I; Mahdi, M A
2010-10-11
We develop a theoretical model that can be used to predict stimulated Brillouin scattering (SBS) threshold in optical fibers that arises through the effect of Brillouin pump recycling technique. Obtained simulation results from our model are in close agreement with our experimental results. The developed model utilizes single mode optical fiber of different lengths as the Brillouin gain media. For 5-km long single mode fiber, the calculated threshold power for SBS is about 16 mW for conventional technique. This value is reduced to about 8 mW when the residual Brillouin pump is recycled at the end of the fiber. The decrement of SBS threshold is due to longer interaction lengths between Brillouin pump and Stokes wave.
Phase-detected Brillouin optical correlation-domain reflectometry
Mizuno, Yosuke; Hayashi, Neisei; Fukuda, Hideyuki; Nakamura, Kentaro
2018-05-01
Optical fiber sensing techniques based on Brillouin scattering have been extensively studied for structural health monitoring owing to their capability of distributed strain and temperature measurement. Although a higher signal-to-noise ratio (leading to high spatial resolution and high-speed measurement) is generally obtained for two-end-access systems, they reduce the degree of freedom in embedding the sensors into structures, and render the measurement no longer feasible when extremely high loss or breakage occurs at a point of the sensing fiber. To overcome these drawbacks, a one-end-access sensing technique called Brillouin optical correlation-domain reflectometry (BOCDR) has been developed. BOCDR has a high spatial resolution and cost efficiency, but its conventional configuration suffered from relatively low-speed operation. In this paper, we review the recently developed high-speed configurations of BOCDR, including phase-detected BOCDR, with which we demonstrate real-time distributed measurement by tracking a propagating mechanical wave. We also demonstrate breakage detection with a wide strain dynamic range.
Brillouin-zone database on the Bilbao Crystallographic Server.
Aroyo, Mois I; Orobengoa, Danel; de la Flor, Gemma; Tasci, Emre S; Perez-Mato, J Manuel; Wondratschek, Hans
2014-03-01
The Brillouin-zone database of the Bilbao Crystallographic Server (http://www.cryst.ehu.es) offers k-vector tables and figures which form the background of a classification of the irreducible representations of all 230 space groups. The symmetry properties of the wavevectors are described by the so-called reciprocal-space groups and this classification scheme is compared with the classification of Cracknell et al. [Kronecker Product Tables, Vol. 1, General Introduction and Tables of Irreducible Representations of Space Groups (1979). New York: IFI/Plenum]. The compilation provides a solution to the problems of uniqueness and completeness of space-group representations by specifying the independent parameter ranges of general and special k vectors. Guides to the k-vector tables and figures explain the content and arrangement of the data. Recent improvements and modifications of the Brillouin-zone database, including new tables and figures for the trigonal, hexagonal and monoclinic space groups, are discussed in detail and illustrated by several examples.
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 ...
Howell, Russell W.; Schrohe, Elmar
2017-01-01
Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…
Other trigonometric proofs of Pythagoras theorem
Luzia, Nuno
2015-01-01
Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \\cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing, geometrically, the half-angle formula $\\cos\\theta=1-2\\sin^2 \\frac{\\theta}{2}$.
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.
Theorems of low energy in Compton scattering
International Nuclear Information System (INIS)
Chahine, J.
1984-01-01
We have obtained the low energy theorems in Compton scattering to third and fouth order in the frequency of the incident photon. Next we calculated the polarized cross section to third order and the unpolarized to fourth order in terms of partial amplitudes not covered by the low energy theorems, what will permit the experimental determination of these partial amplitudes. (Author) [pt
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
Visualizing the Central Limit Theorem through Simulation
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
The Classical Version of Stokes' Theorem Revisited
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
The divergence theorem for unbounded vector fields
De Pauw, Thierry; Pfeffer, Washek F.
2007-01-01
In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector. elds that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is. nite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions.
The Pomeranchuk theorem and its modifications
International Nuclear Information System (INIS)
Fischer, J.; Saly, R.
1980-01-01
A review of the various modifications and improvements of the Pomeranchuk theorem and also of related statements is given. The present status of the Pomeranchuk relation based on dispersion relation is discussed. Numerous problems related to the Pomeranchuk theorem and some answers to these problems are collected in a clear table
Coalgebraic Lindström Theorems
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,
A Metrized Duality Theorem for Markov Processes
DEFF Research Database (Denmark)
Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash
2014-01-01
We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...
Uniqueness theorems in linear elasticity
Knops, Robin John
1971-01-01
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...
Riemannian and Lorentzian flow-cut theorems
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.
OTTER, Resolution Style Theorem Prover
International Nuclear Information System (INIS)
McCune, W.W.
2001-01-01
1 - Description of program or function: OTTER (Other Techniques for Theorem-proving and Effective Research) is a resolution-style theorem-proving program for first-order logic with equality. OTTER includes the inference rules binary resolution, hyper-resolution, UR-resolution, and binary para-modulation. These inference rules take as small set of clauses and infer a clause. If the inferred clause is new and useful, it is stored and may become available for subsequent inferences. Other capabilities are conversion from first-order formulas to clauses, forward and back subsumption, factoring, weighting, answer literals, term ordering, forward and back demodulation, and evaluable functions and predicates. 2 - Method of solution: For its inference process OTTER uses the given-clause algorithm, which can be viewed as a simple implementation of the set of support strategy. OTTER maintains three lists of clauses: axioms, sos (set of support), and demodulators. OTTER is not automatic. Even after the user has encoded a problem into first-order logic or into clauses, the user must choose inference rules, set options to control the processing of inferred clauses, and decide which input formulae or clauses are to be in the initial set of support and which, if any, equalities are to be demodulators. If OTTER fails to find a proof, the user may try again different initial conditions. 3 - Restrictions on the complexity of the problem - Maxima of: 5000 characters in an input string, 64 distinct variables in a clause, 51 characters in any symbol. The maxima can be changed by finding the appropriate definition in the header.h file, increasing the limit, and recompiling OTTER. There are a few constraints on the order of commands
Stimulated brillouin scattering of electromagnetic waves in a dusty plasma
International Nuclear Information System (INIS)
Salimullah, M.; Sen, A.
1991-08-01
The stimulated Brilluoin scattering of electromagnetic waves in a homogeneous, unmagnetized and collisionless dusty plasma has been investigated theoretically. The Vlasov equation has been solved perturbatively to find the nonlinear response of the plasma particles. The presence of the dust particles introduces a background inhomogeneous electric field which significantly influences the dispersive properties of the plasma. At the ion acoustic branch we find the usual scattering slightly modified by the charged dust grains. However, at the frequency lower than the ion acoustic branch we find a new mode of the plasma arising from the oscillations of the ions in the static structure of the dust distribution. This low frequency branch causes enhanced stimulated Brillouin scattering of electromagnetic waves in a dusty plasma. (author). 15 refs
Time gated phase-correlation distributed Brillouin fibre sensor
Denisov, Andrey; Soto, Marcelo A.; Thévenaz, Luc
2013-05-01
A random access distributed Brillouin fibre sensor is presented, based on phase modulation using a pseudo-random bit sequence (PRBS) together with time gating. The standard phase-correlation technique is known to show a noise level increasing linearly with the number of measured points due to weak gratings generated randomly along the whole sensing fibre. Here we show how intensity modulated pump and time gated detection significantly improve the signal-tonoise ratio (SNR) of the system with no impact on the spatial resolution. A measurement with 1.1 cm spatial resolution over 3.3 km is demonstrated, representing 300'000 equivalent points. The limitations of the proposed technique are discussed through the paper.
Stimulated brillouin backscatter of a short-pulse laser
International Nuclear Information System (INIS)
Hinkel, D.E.; Williams, E.A.; Berger, R.L.
1994-01-01
Stimulated Brillouin backscattering (SBBS) from a short-pulse laser, where the pulse length is short compared to the plasma length, is found to be qualitatively different than in the long pulse regime, where the pulse length is long compared to the plasma length. We find that after an initial transient of order the laser pulse length transit time, the instability reaches a steady state in the variables x' = x - V g t, t' = t, where V g is the pulse group velocity. In contrast, SBBS in a long pulse can be absolutely unstable and grows indefinitely, or until nonlinearities intervene. We find that the motion of the laser pulse induces Doppler related effects that substantially modify the backscattered spectrum at higher intensities, where the instability is strongly coupled (i.e. , has a growth rate large compared to the ion acoustic frequency)
Optimized chaotic Brillouin dynamic grating with filtered optical feedback.
Zhang, Jianzhong; Li, Zhuping; Wu, Yuan; Zhang, Mingjiang; Liu, Yi; Li, Mengwen
2018-01-16
Chaotic Brillouin dynamic gratings (BDGs) have special advantages such as the creation of single, permanent and localized BDG. However, the periodic signals induced by conventional optical feedback (COF) in chaotic semiconductor lasers can lead to the generation of spurious BDGs, which will limit the application of chaotic BDGs. In this paper, filtered optical feedback (FOF) is proposed to eliminate spurious BDGs. By controlling the spectral width of the optical filter and its detuning from the laser frequency, semiconductor lasers with FOF operate in the suppression region of the time-delay signature, and chaotic outputs serving as pump waves are then utilized to generate the chaotic BDG in a polarization maintaining fiber. Through comparative analysis of the COF and FOF schemes, it has been demonstrated that spurious BDGs are effectively eliminated and that the reflection characterization of the chaotic BDG is improved. The influence of FOF on the reflection and gain spectra of the chaotic BDG is analyzed as well.
Correct Brillouin zone and electronic structure of BiPd
Yaresko, Alexander; Schnyder, Andreas P.; Benia, Hadj M.; Yim, Chi-Ming; Levy, Giorgio; Damascelli, Andrea; Ast, Christian R.; Peets, Darren C.; Wahl, Peter
2018-02-01
A promising route to the realization of Majorana fermions is in noncentrosymmetric superconductors, in which spin-orbit coupling lifts the spin degeneracy of both bulk and surface bands. A detailed assessment of the electronic structure is critical to evaluate their suitability for this through establishing the topological properties of the electronic structure. This requires correct identification of the time-reversal-invariant momenta. One such material is BiPd, a recently rediscovered noncentrosymmetric superconductor which can be grown in large, high-quality single crystals and has been studied by several groups using angular resolved photoemission to establish its surface electronic structure. Many of the published electronic structure studies on this material are based on a reciprocal unit cell which is not the actual Brillouin zone of the material. We show here the consequences of this for the electronic structures and show how the inferred topological nature of the material is affected.
Wavelength dependence of the Brillouin spectral width of boron doped germanosilicate optical fibers.
Law, Pi-Cheng; Dragic, Peter D
2010-08-30
Boron co-doped germanosilicate fibers are investigated via the Brillouin light scattering technique using two wavelengths, 1534 nm and 1064 nm. Several fibers are investigated, including four drawn from the same preform but at different draw temperatures. The Stokes' shifts and the Brillouin spectral widths are found to increase with increasing fiber draw temperature. A frequency-squared law has adequately described the wavelength dependence of the Brillouin spectral width of conventional Ge-doped fibers. However, it is found that unlike conventional Ge-doped fibers these fibers do not follow the frequency-squared law. This is explained through a frequency-dependent dynamic viscosity that modifies this law.
The classical version of Stokes' Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we show how 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...... 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 with a 'fattening' technique for surfaces and the inverse function theorem....
Security Theorems via Model Theory
Directory of Open Access Journals (Sweden)
Joshua Guttman
2009-11-01
Full Text Available A model-theoretic approach can establish security theorems for cryptographic protocols. Formulas expressing authentication and non-disclosure properties of protocols have a special form. They are quantified implications for all xs . (phi implies for some ys . psi. Models (interpretations for these formulas are *skeletons*, partially ordered structures consisting of a number of local protocol behaviors. *Realized* skeletons contain enough local sessions to explain all the behavior, when combined with some possible adversary behaviors. We show two results. (1 If phi is the antecedent of a security goal, then there is a skeleton A_phi such that, for every skeleton B, phi is satisfied in B iff there is a homomorphism from A_phi to B. (2 A protocol enforces for all xs . (phi implies for some ys . psi iff every realized homomorphic image of A_phi satisfies psi. Hence, to verify a security goal, one can use the Cryptographic Protocol Shapes Analyzer CPSA (TACAS, 2007 to identify minimal realized skeletons, or "shapes," that are homomorphic images of A_phi. If psi holds in each of these shapes, then the goal holds.
Energy Technology Data Exchange (ETDEWEB)
Escane, J.M. [Ecole Superieure d' Electricite, 91 - Gif-sur-Yvette (France)
2005-04-01
The first part of this article defines the different elements of an electrical network and the models to represent them. Each model involves the current and the voltage as a function of time. Models involving time functions are simple but their use is not always easy. The Laplace transformation leads to a more convenient form where the variable is no more directly the time. This transformation leads also to the notion of transfer function which is the object of the second part. The third part aims at defining the fundamental operation rules of linear networks, commonly named 'general theorems': linearity principle and superimposition theorem, duality principle, Thevenin theorem, Norton theorem, Millman theorem, triangle-star and star-triangle transformations. These theorems allow to study complex power networks and to simplify the calculations. They are based on hypotheses, the first one is that all networks considered in this article are linear. (J.S.)
Dimensional analysis beyond the Pi theorem
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 ...
Stable convergence and stable limit theorems
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...
Theorem on axially symmetric gravitational vacuum configurations
Energy Technology Data Exchange (ETDEWEB)
Papadopoulos, A; Le Denmat, G [Paris-6 Univ., 75 (France). Inst. Henri Poincare
1977-01-24
A theorem is proved which asserts the non-existence of axially symmetric gravitational vacuum configurations with non-stationary rotation only. The eventual consequences in black-hole physics are suggested.
Non-renormalisation theorems in string theory
International Nuclear Information System (INIS)
Vanhove, P.
2007-10-01
In this thesis we describe various non renormalisation theorems for the string effective action. These results are derived in the context of the M theory conjecture allowing to connect the four gravitons string theory S matrix elements with that of eleven dimensional supergravity. These theorems imply that N = 8 supergravity theory has the same UV behaviour as the N = 4 supersymmetric Yang Mills theory at least up to three loops, and could be UV finite in four dimensions. (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
Singularity theorems from weakened energy conditions
International Nuclear Information System (INIS)
Fewster, Christopher J; Galloway, Gregory J
2011-01-01
We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.
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
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)
Liouville's theorem and phase-space cooling
International Nuclear Information System (INIS)
Mills, R.L.; Sessler, A.M.
1993-01-01
A discussion is presented of Liouville's theorem and its consequences for conservative dynamical systems. A formal proof of Liouville's theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur
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
Double soft theorem for perturbative gravity
Saha, Arnab
2016-01-01
Following up on the recent work of Cachazo, He and Yuan \\cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.
A Converse of Fermat's Little Theorem
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
The large deviations theorem and ergodicity
International Nuclear Information System (INIS)
Gu Rongbao
2007-01-01
In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions
Multi-wavelength Brillouin Raman erbium-doped fiber laser generation in a linear cavity
International Nuclear Information System (INIS)
Shirazi, M R; Harun, S W; Ahmad, H
2014-01-01
A multi-wavelength Brillouin Raman erbium-doped fiber laser is proposed and demonstrated. The setup uses a 7.7 km dispersion compensating fiber simultaneously as the Brillouin and Raman nonlinear gain media and operates in conjunction with a 3 m erbium-doped fiber as the linear gain medium. At a Brillouin pump (BP) wavelength of 1530 nm, where Raman and erbium gains overlap each other, 34 Brillouin Stokes lines having line spacing of 0.075 nm are created by using a Raman pump power of only 24.1 dBm, an erbium pump power of about 22.1 dBm, and a BP power of 6.5 dBm in the proposed linear cavity. The system is highly efficient and is able to generate many comparable peak-power lines at a low pump power. (paper)
Measurement of sound velocity on metal surfaces by impulsive stimulated Brillouin scattering
International Nuclear Information System (INIS)
Shimada, Yukihiro; Murakami, Hiroshi; Nishimura, Akihiko
2005-01-01
Impulsive stimulated Brillouin Scattering (ISBS) experiment was performed in order to measure acoustic waves on metal surfaces. The ISBS technique offers robust method of obtaining acoustic velocities without physical contact. The generation and detection mechanism were discussed. (author)
International Nuclear Information System (INIS)
Yu, Yin; Ma, Yong; Li, Hao; Huang, Jun; Fang, Yu; Liang, Kun; Zhou, Bo
2014-01-01
A method for simultaneously obtaining the ocean temperature and salinity based on dual-wavelength Brillouin lidar is proposed in this letter. On the basis of the relationships between the temperature and salinity and the Brillouin shifts, a retrieval model for retrieving the temperature and salinity is established. By using the retrieval model, the ocean temperature and salinity can be simultaneously obtained through the Brillouin shifts. Simulation based on dual-wavelength Brillouin lidar is also carried out for verification of the accuracy of the retrieval model. Results show that the errors of the retrieval model for temperature and salinity are ±0.27 °C and ±0.33‰. (letter)
Steelman, Zachary; Meng, Zhaokai; Traverso, Andrew J; Yakovlev, Vladislav V
2015-05-01
Bacterial meningitis is a disease of pronounced clinical significance, especially in the developing world. Immediate treatment with antibiotics is essential, and no single test can provide a conclusive diagnosis. It is well established that elevated total protein in cerebrospinal fluid (CSF) is associated with bacterial meningitis. Brillouin spectroscopy is a widely used optical technique for noninvasive determination of the elastic moduli of materials. We found that elevated protein levels in CSF alter the fluid elasticity sufficiently to be measurable by Brillouin spectroscopy, with model healthy and diseased fluids distinguishable to marked significance (P = 0.014), which increases with sample concentration by dialysis. Typical raw output of a 2-stage VIPA Brillouin spectrometer: inelastically scattered Brillouin peaks (arrows) and elastically scattered incident radiation (center cross). © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
High-resolution stimulated Brillouin gain spectroscopy in glasses and crystals
International Nuclear Information System (INIS)
Faris, G.W.; Jusinski, L.E.; Hickman, A.P.
1993-01-01
Theory and measurements are presented for stimulated Brillouin gain spectroscopy in anisotropic media. The coupling between arbitrary pump and Stokes waves and the corresponding acoustic wave is formulated in terms of the elastic displacement vector and the photoelastic tensor. A propagation equation that fully includes transient effects is obtained for the Stokes wave. In the limit of small-signal gains this propagation equation can be solved analytically, yielding expressions that relate experimentally accessible quantities to material properties. Absolute Brillouin steady-state gain coefficients, linewidths, and frequency shifts are thereby determined in a number of optical materials at 532 nm. The Brillouin gain coefficient for fused silica is measured by three techniques, providing the reference for absolute gain measurements. Quantitative agreement is found between theory and experiment for transient effects on stimulated Brillouin scattering
Bi-Directional Brillouin Optical Time Domain Analyzer System for Long Range Distributed Sensing.
Guo, Nan; Wang, Liang; Wang, Jie; Jin, Chao; Tam, Hwa-Yaw; Zhang, A Ping; Lu, Chao
2016-12-16
We propose and experimentally demonstrate a novel scheme of bi-directional Brillouin time domain analyzer (BD-BOTDA) to extend the sensing range. By deploying two pump-probe pairs at two different wavelengths, the Brillouin frequency shift (BFS) distribution over each half of the whole fiber can be obtained with the simultaneous detection of Brillouin signals in both channels. Compared to the conventional unidirectional BOTDA system of the same sensing range, the proposed BD-BOTDA scheme enables distributed sensing with a performance level comparable to the conventional one with half of the sensing range and a spatial resolution of 2 m, while maintaining the Brillouin signal-to-noise ratio (SNR) and the BFS uncertainty. Based on this technique, we have achieved distributed temperature sensing with a measurement range of 81.9 km fiber at a spatial resolution of 2 m and BFS uncertainty of ~0.44 MHz without introducing any complicated components or schemes.
Stimulated Brillouin scattering of laser in semiconductor plasma embedded with nano-sized grains
Energy Technology Data Exchange (ETDEWEB)
Sharma, Giriraj, E-mail: grsharma@gmail.com [SRJ Government Girls’ College, Neemuch (M P) (India); Dad, R. C. [Government P G College, Mandsaur (M P) (India); Ghosh, S. [School of Studies in Physics, Vikram University, Ujjain, (M P) (India)
2015-07-31
A high power laser propagating through semiconductor plasma undergoes Stimulated Brillouin scattering (SBS) from the electrostrictively generated acoustic perturbations. We have considered that nano-sized grains (NSGs) ions are embedded in semiconductor plasma by means of ion implantation. The NSGs are bombarded by the surrounding plasma particles and collect electrons. By considering a negative charge on the NSGs, we present an analytically study on the effects of NSGs on threshold field for the onset of SBS and Brillouin gain of generated Brillouin scattered mode. It is found that as the charge on the NSGs builds up, the Brillouin gain is significantly raised and the threshold pump field for the onset of SBS process is lowered.
Highly localized distributed Brillouin scattering response in a photonic integrated circuit
Zarifi, Atiyeh; Stiller, Birgit; Merklein, Moritz; Li, Neuton; Vu, Khu; Choi, Duk-Yong; Ma, Pan; Madden, Stephen J.; Eggleton, Benjamin J.
2018-03-01
The interaction of optical and acoustic waves via stimulated Brillouin scattering (SBS) has recently reached on-chip platforms, which has opened new fields of applications ranging from integrated microwave photonics and on-chip narrow-linewidth lasers, to phonon-based optical delay and signal processing schemes. Since SBS is an effect that scales exponentially with interaction length, on-chip implementation on a short length scale is challenging, requiring carefully designed waveguides with optimized opto-acoustic overlap. In this work, we use the principle of Brillouin optical correlation domain analysis to locally measure the SBS spectrum with high spatial resolution of 800 μm and perform a distributed measurement of the Brillouin spectrum along a spiral waveguide in a photonic integrated circuit. This approach gives access to local opto-acoustic properties of the waveguides, including the Brillouin frequency shift and linewidth, essential information for the further development of high quality photonic-phononic waveguides for SBS applications.
Bi-Directional Brillouin Optical Time Domain Analyzer System for Long Range Distributed Sensing
Guo, Nan; Wang, Liang; Wang, Jie; Jin, Chao; Tam, Hwa-Yaw; Zhang, A. Ping; Lu, Chao
2016-01-01
We propose and experimentally demonstrate a novel scheme of bi-directional Brillouin time domain analyzer (BD-BOTDA) to extend the sensing range. By deploying two pump-probe pairs at two different wavelengths, the Brillouin frequency shift (BFS) distribution over each half of the whole fiber can be obtained with the simultaneous detection of Brillouin signals in both channels. Compared to the conventional unidirectional BOTDA system of the same sensing range, the proposed BD-BOTDA scheme enables distributed sensing with a performance level comparable to the conventional one with half of the sensing range and a spatial resolution of 2 m, while maintaining the Brillouin signal-to-noise ratio (SNR) and the BFS uncertainty. Based on this technique, we have achieved distributed temperature sensing with a measurement range of 81.9 km fiber at a spatial resolution of 2 m and BFS uncertainty of ~0.44 MHz without introducing any complicated components or schemes. PMID:27999250
Pascal’s Theorem in Real Projective Plane
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.
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.
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered...... we apply the key instrumental concepts and verify the various steps towards this alternative proof of the divergence theorem....
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 ...
Illustrating the Central Limit Theorem through Microsoft Excel Simulations
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…
Controlling Stimulated Brillouin/Raman Scattering in High Power Fiber Lasers
2017-08-09
AFRL-RD-PS- AFRL-RD-PS- TR-2017-0043 TR-2017-0043 CONTROLLING STIMULATED BRILLOUIN/RAMAN SCATTERING IN HIGH POWER FIBER LASERS Cody Mart Ben...average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed...unlimited. 13. SUPPLEMENTARY NOTES 14. ABSTRACT This research addressed suppression of stimulated Brillouin/Raman scattering in high power fiber lasers
DEFF Research Database (Denmark)
Lorenzen, Michael Rodas; Noordegraaf, Danny; Nielsen, Carsten Vandel
2008-01-01
We demonstrate an increased gain in optical parametric amplier through suppression of stimulated Brillouin scattering by applying a temperature distribution along the fiber resulting in a reduction of the required phase modulation.......We demonstrate an increased gain in optical parametric amplier through suppression of stimulated Brillouin scattering by applying a temperature distribution along the fiber resulting in a reduction of the required phase modulation....
Al-Taiy, Hassanain Majeed
2017-01-01
Stimulated Brillouin scattering is a third order non-linear effect with the lowest power threshold in standard single mode optical fiber, by which an interaction between optical and acoustic modes takes place. During the Brillouin scattering process, part of the pump wave power will be transferred to a counter propagating wave (Stokes), with a frequency shift of about 11 GHz for a telecommunication wavelength of 1550 nm in a standard single mode fiber. The frequency shift effective parameters...
Theorem on magnet fringe field
International Nuclear Information System (INIS)
Wei, Jie; Talman, R.
1995-01-01
Transverse particle motion in particle accelerators is governed almost totally by non-solenoidal magnets for which the body magnetic field can be expressed as a series expansion of the normal (b n ) and skew (a n ) multipoles, B y + iB x = summation(b n + ia n )(x + iy) n , where x, y, and z denote horizontal, vertical, and longitudinal (along the magnet) coordinates. Since the magnet length L is necessarily finite, deflections are actually proportional to ''field integrals'' such as bar BL ≡ ∫ B(x,y,z)dz where the integration range starts well before the magnet and ends well after it. For bar a n , bar b n , bar B x , and bar B y defined this way, the same expansion Eq. 1 is valid and the ''standard'' approximation is to neglect any deflections not described by this expansion, in spite of the fact that Maxwell's equations demand the presence of longitudinal field components at the magnet ends. The purpose of this note is to provide a semi-quantitative estimate of the importance of |Δp ∝ |, the transverse deflection produced by the ion-gitudinal component of the fringe field at one magnet end relative to |Δp 0 |, the total deflection produced by passage through the whole magnet. To emphasize the generality and simplicity of the result it is given in the form of a theorem. The essence of the proof is an evaluation of the contribution of the longitudinal field B x from the vicinity of one magnet end since, along a path parallel to the magnet axis such as path BC
Li, Q.; Jia, Z. X.; Weng, H. Z.; Li, Z. R.; Yang, Y. D.; Xiao, J. L.; Chen, S. W.; Huang, Y. Z.; Qin, W. P.; Qin, G. S.
2018-05-01
We demonstrate broadband multi-wavelength Brillouin lasers with an operating wavelength range of 1500–1600 nm and a frequency separation of ~9.28 GHz generated by four-wave mixing in a dual wavelength Brillouin fiber laser cavity. By using one continuous-wave laser as the pump source, multi-wavelength Brillouin lasers with an operating wavelength range of 1554–1574 nm were generated via cascaded Brillouin scattering and four-wave mixing. Interestingly, when pumped by two continuous-wave lasers with an appropriate frequency separation, the operating wavelength range of the multi-wavelength Brillouin lasers was increased to 1500–1600 nm due to cavity-enhanced cascaded four-wave mixing among the frequency components generated by two pump lasers in the dual wavelength Brillouin laser cavity.
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.
Phase transition in lead titanate thin films: a Brillouin study
International Nuclear Information System (INIS)
Kuzel, P; Dugautier, C; Moch, P; Marrec, F Le; Karkut, M G
2002-01-01
The elastic properties of both polycrystalline and epitaxial PbTiO 3 (PTO) thin films are studied using Brillouin scattering spectroscopy. The epitaxial PTO films were prepared by pulsed laser ablation on (1) a [0 0 1] single crystal of SrTiO 3 (STO) doped with Nb and (2) a [0 0 1] STO buffered with a layer of YBa 2 Cu 3 O 7 . The polycrystalline PTO films were prepared by sol-gel on a Si substrate buffered with TiO 2 and Pt layers. The data analysis takes into account the ripple and the elasto-optic contributions. The latter significantly affects the measured spectra since it gives rise to a Love mode in the p-s scattering geometry. At room temperature, the spectra of the epitaxially grown samples are interpreted using previously published elastic constants of PTO single crystals. Sol-gel samples exhibit appreciable softening of the effective elastic properties compared to PTO single crystals: this result is explained by taking into account the random orientation of the microscopic PTO grains. For both the polycrystalline and the epitaxial films we have determined that the piezoelectric terms do not contribute to the spectra. The temperature dependence of the spectra shows strong anomalies of the elastic properties near the ferroelectric phase transition. Compared to the bulk, T C is higher in the sol-gel films, while in the epitaxial films the sign of the T C shift depends on the underlying material
The Non-Signalling theorem in generalizations of Bell's theorem
International Nuclear Information System (INIS)
Walleczek, J; Grössing, G
2014-01-01
Does 'epistemic non-signalling' ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the
Gleason-Busch theorem for sequential measurements
Flatt, Kieran; Barnett, Stephen M.; Croke, Sarah
2017-12-01
Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957), 10.1512/iumj.1957.6.56050]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003), 10.1103/PhysRevLett.91.120403], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.
Adiabatic Theorem for Quantum Spin Systems
Bachmann, S.; De Roeck, W.; Fraas, M.
2017-08-01
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
A uniform Tauberian theorem in dynamic games
Khlopin, D. V.
2018-01-01
Antagonistic dynamic games including games represented in normal form are considered. The asymptotic behaviour of value in these games is investigated as the game horizon tends to infinity (Cesàro mean) and as the discounting parameter tends to zero (Abel mean). The corresponding Abelian-Tauberian theorem is established: it is demonstrated that in both families the game value uniformly converges to the same limit, provided that at least one of the limits exists. Analogues of one-sided Tauberian theorems are obtained. An example shows that the requirements are essential even for control problems. Bibliography: 31 titles.
The aftermath of the intermediate value theorem
Directory of Open Access Journals (Sweden)
Morales Claudio H
2004-01-01
Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (17811848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.
Pauli and the spin-statistics theorem
Duck, Ian M
1997-01-01
This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties. Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that
Elastic hadron scattering and optical theorem
Lokajicek, Milos V.; Prochazka, Jiri
2014-01-01
In principle all contemporary phenomenological models of elastic hadronic scattering have been based on the assumption of optical theorem validity that has been overtaken from optics. It will be shown that the given theorem which has not been actually proved cannot be applied to short-ranged strong interactions in any case. The actual progress in description of collision processes might then exist only if the initial states are specified on the basis of impact parameter values of colliding particles and probability dependence on this parameter is established.
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.
Determination of the elastic constants of portlandite by Brillouin spectroscopy
Speziale, S.; Reichmann, H.J.; Schilling, F.R.; Wenk, H.R.; Monteiro, P.J.M.
2008-01-01
The single crystal elastic constants Cij and the shear and adiabatic bulk modulus of a natural portlandite (Ca(OH)2) crystal were determined by Brillouin spectroscopy at ambient conditions. The elastic constants, expressed in GPa, are: C11 = 102.0(± 2.0), C12 = 32.1(± 1.0), C13 = 8.4(± 0.4), C14 = 4.5(± 0.2), C33 = 33.6(± 0.7), C44 = 12.0(± 0.3), C66 = (C11-C12)/2 = 35.0(± 1.1), where the numbers in parentheses are 1σ standard deviations. The Reuss bounds of the adiabatic bulk and shear moduli are K0S = 26.0(± 0.3) GPa and G0 = 17.5(± 0.4) GPa, respectively, while the Voigt bounds of these moduli are K0S = 37.3(± 0.4) GPa and G0 = 24.4(± 0.3) GPa. The Reuss and Voigt bounds for the aggregate Young's modulus are 42.8(± 1.0) GPa and 60.0(± 0.8) GPa respectively, while the aggregate Poisson's ratio is equal to 0.23(± 0.01). Portlandite exhibits both large compressional elastic anisotropy with C11/C33 = 3.03(± 0.09) equivalent to that of the isostructural hydroxide brucite (Mg(OH)2), and large shear anisotropy with C66/C44 = 2.92(± 0.12) which is 11% larger than brucite. The comparison between the bulk modulus of portlandite and that of lime (CaO) confirms a systematic linear relationship between the bulk moduli of brucite-type simple hydroxides and the corresponding NaCl-type oxides. © 2008 Elsevier Ltd. All rights reserved.
Brillouin scattering, piezobirefringence, and dispersion of photoelastic coefficients of CdS and ZnO
DEFF Research Database (Denmark)
Berkowicz, R.; Skettrup, Torben
1975-01-01
We have measured the dispersion of the Brillouin scattering from acoustoelectrical domains in CdS and ZnO. These spectra are compared with the birefringence spectra obtained by applying uniaxial stress. The resonant cancellation of the Brillouin scattering occurs at the spectral position of the i......We have measured the dispersion of the Brillouin scattering from acoustoelectrical domains in CdS and ZnO. These spectra are compared with the birefringence spectra obtained by applying uniaxial stress. The resonant cancellation of the Brillouin scattering occurs at the spectral position...... of the isotropic point of the stress-induced birefringence. From these spectra it is concluded that the Brillouin scattering in CdS and ZnO is determined by elasto-optic effects alone. The spectra of some of the photoelastic coefficients have been determined. A model dielectric constant is derived where both....... It is found that the exchange interaction between the excitons may change the values of the photoelastic coefficients in ZnO about 10%....
Influence of core diameter and length of polymer optical fiber on Brillouin scattering properties
Mizuno, Yosuke; Ishigure, Takaaki; Nakamura, Kentaro
2012-02-01
Brillouin scattering in perfluorinated graded-index polymer optical fibers (PFGI-POFs) is potentially useful in developing high-accuracy distributed temperature sensors with reduced strain sensitivity. In this study, we investigate, both experimentally and theoretically, the influence of the fiber core diameter and length on the Brillouin gain spectra (BGS) in PFGI-POFs. First, we show that smaller core diameter drastically enhances the Stokes power using PFGI-POFs with 62.5-μm and 120-μm core diameters, and discuss the Brillouin threshold power. Then, we demonstrate that the PFGI-POF length has little influence on the BGS when the length is longer than 50 m. We also predict that, at 1.55-μm wavelength, it is difficult to reduce the Brillouin threshold power of PFGI-POFs below that of long silica single-mode fibers even if their core diameter is sufficiently reduced to satisfy the single-mode condition. Finally, making use of the enhanced Stokes signal, we confirm the Brillouin linewidth narrowing effect.
Non-local effect in Brillouin optical time-domain analyzer based on Raman amplification
International Nuclear Information System (INIS)
Jia Xinhong; Rao Yunjiang; Wang Zinan; Zhang Weili; Ran Zengling; Deng Kun; Yang Zixin
2012-01-01
Compared with conventional Brillouin optical time-domain analyzer (BOTDA), the BOTDA based on Raman amplification allows longer sensing range, higher signal-to-noise ratio and higher measurement accuracy. However, the non-local effect induced by pump depletion significantly restricts the probe optical power injected to sensing fiber, thereby limiting the further extension for sensing distance. In this paper, the coupled equations including the interaction of probe light, Brillouin and Raman pumps are applied to the study on the non-local characteristics of BOTDA based on Raman amplification. The results show that, the system error induced by non-local effect worsens with increased powers of probe wave and Raman pump. The frequency-division-multiplexing (cascading the fibers with various Brillouin frequency shifts) and time-division-multiplexing (modulating both of the Brillouin pump and probe lights) technologies are efficient approaches to suppress the non-local effect, through shortening the effective interaction range between Brillouin pump and probe lights. (authors)
The effect of pressure on spontaneous Rayleigh-Brillouin scattering spectrum in nitrogen
Yang, Chuanyin; Wu, Tao; Shang, Jingcheng; Zhang, Xinyi; Hu, Rongjing; He, XingDao
2018-05-01
In order to study the effect of gas pressure on spontaneous Rayleigh-Brillouin scattering spectrum and verify the validity of Tenti S6 model at pressures up to 8 atm, the spontaneous Rayleigh-Brillouin scattering experiment in nitrogen was performed for a wavelength of 532 nm at the constant room temperature of 296 K and a 90° scattering angle. By comparing the experimental spectrum with the theoretical spectrum, the normalized root mean square deviation was calculated and found less than 2.2%. It is verified that Tenti S6 model can be applied to the spontaneous Rayleigh-Brillion scattering of nitrogen under higher pressures. The results of the experimental data analysis demonstrate that pressure has more effect on Brillouin peak intensity and has negligible effect on Brillouin frequency shift, and pressure retrieval based on spontaneous Rayleigh-Brillouin scattering profile is a promising method for remote of pressure, such as harsh environment applications. Some factors that caused experiment deviations are also discussed.
Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime
International Nuclear Information System (INIS)
Lehmann, G.; Spatschek, K. H.
2013-01-01
Parametric plasma processes received renewed interest in the context of generating ultra-intense and ultra-short laser pulses up to the exawatt-zetawatt regime. Both Raman as well as Brillouin amplifications of seed pulses were proposed. Here, we investigate Brillouin processes in the one-dimensional (1D) backscattering geometry with the help of numerical simulations. For optimal seed amplification, Brillouin scattering is considered in the so called strong coupling (sc) regime. Special emphasis lies on the dependence of the amplification process on the finite duration of the initial seed pulses. First, the standard plane-wave instability predictions are generalized to pulse models, and the changes of initial seed pulse forms due to parametric instabilities are investigated. Three-wave-interaction results are compared to predictions by a new (kinetic) Vlasov code. The calculations are then extended to the nonlinear region with pump depletion. Generation of different seed layers is interpreted by self-similar solutions of the three-wave interaction model. Similar to Raman amplification, shadowing of the rear layers by the leading layers of the seed occurs. The shadowing is more pronounced for initially broad seed pulses. The effect is quantified for Brillouin amplification. Kinetic Vlasov simulations agree with the three-wave interaction predictions and thereby affirm the universal validity of self-similar layer formation during Brillouin seed amplification in the strong coupling regime
A note on the Pfaffian integration theorem
International Nuclear Information System (INIS)
Borodin, Alexei; Kanzieper, Eugene
2007-01-01
Two alternative, fairly compact proofs are presented of the Pfaffian integration theorem that surfaced in the recent studies of spectral properties of Ginibre's Orthogonal Ensemble. The first proof is based on a concept of the Fredholm Pfaffian; the second proof is purely linear algebraic. (fast track communication)
Mean value theorem in topological vector spaces
International Nuclear Information System (INIS)
Khan, L.A.
1994-08-01
The aim of this note is to give shorter proofs of the mean value theorem, the mean value inequality, and the mean value inclusion for the class of Gateaux differentiable functions having values in a topological vector space. (author). 6 refs
1/4-pinched contact sphere theorem
DEFF Research Database (Denmark)
Ge, Jian; Huang, Yang
2016-01-01
Given a closed contact 3-manifold with a compatible Riemannian metric, we show that if the sectional curvature is 1/4-pinched, then the contact structure is universally tight. This result improves the Contact Sphere Theorem in [EKM12], where a 4/9-pinching constant was imposed. Some tightness...
Generalized Friedland's theorem for C0-semigroups
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.
Automated theorem proving theory and practice
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...
Answering Junior Ant's "Why" for Pythagoras' Theorem
Pask, Colin
2002-01-01
A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…
On Callan's proof of the BPHZ theorem
International Nuclear Information System (INIS)
Lesniewski, A.
1984-01-01
The author gives an elementary proof of the BPHZ theorem in the case of the Euclidean lambdaphi 4 theory. The method of proof relies on a detailed analysis of the skeleton structure of graphs and estimates based on the Callan-Symanzik equations. (Auth.)
A Short Proof of Klee's Theorem
Zanazzi, John J.
2013-01-01
In 1959, Klee proved that a convex body $K$ is a polyhedron if and only if all of its projections are polygons. In this paper, a new proof of this theorem is given for convex bodies in $\\mathbb{R}^3$.
On Noethers theorem in quantum field theory
International Nuclear Information System (INIS)
Buchholz, D.; Doplicher, S.; Longo, R.
1985-03-01
Extending an earlier construction of local generators of symmetries in (S. Doplicher, 1982) to space-time and supersymmetries, we establish a weak form of Noethers theorem in quantum field theory. We also comment on the physical significance of the 'split property', underlying our analysis, and discuss some local aspects of superselection rules following from our results. (orig./HSI)
Green-Tao theorem in function fields
Le, Thai Hoang
2009-01-01
We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every $k$, the irreducible polynomials in $\\mathbf{F}_q[t]$ contain configurations of the form $\\{f+ Pg : \\d(P)
Pauli and The Spin-Statistics Theorem
International Nuclear Information System (INIS)
Duck, Ian; Sudarshan, E.C.G.
1998-03-01
This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties.Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that 'everyone knows the spin-statistics theorem, but no one understands it'. This book simplifies and clarifies the formal statements of the theorem, and also corrects the invariably flawed intuitive explanations which are frequently put forward. The book will be of interest to many practising physicists in all fields who have long been frustrated by the impenetrable discussions on the subject which have been available until now.It will also be accessible to students at an advanced undergraduate level as an introduction to modern physics based directly on the classical writings of the founders, including Pauli, Dirac, Heisenberg, Einstein and many others
Central Limit Theorem for Coloured Hard Dimers
Directory of Open Access Journals (Sweden)
Maria Simonetta Bernabei
2010-01-01
Full Text Available We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs. The techniques used at arriving this result comprise combinatorics, generating functions, and conditional expectations.
Reciprocity theorem in high-temperature superconductors
Czech Academy of Sciences Publication Activity Database
Janeček, I.; Vašek, Petr
2003-01-01
Roč. 390, - (2003), s. 330-340 ISSN 0921-4534 R&D Projects: GA ČR GA202/00/1602; GA AV ČR IAA1010919 Institutional research plan: CEZ:AV0Z1010914 Keywords : transport properties * reciprocity theorem Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.192, year: 2003
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.
Limit theorems for functionals of Gaussian vectors
Institute of Scientific and Technical Information of China (English)
Hongshuai DAI; Guangjun SHEN; Lingtao KONG
2017-01-01
Operator self-similar processes,as an extension of self-similar processes,have been studied extensively.In this work,we study limit theorems for functionals of Gaussian vectors.Under some conditions,we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process.
Bell's theorem and the nature of reality
International Nuclear Information System (INIS)
Bertlmann, R.A.
1988-01-01
We rediscuss the Einstein-Podolsky-Rosen paradox in Bohm's spin version and oppose to it Bohr's controversial point of view. Then we explain Bell's theorem, Bell inequalities and its consequences. We describe the experiment of Aspect, Dalibard and Roger in detail. Finally we draw attention to the nonlocal structure of the underlying theory. 61 refs., 8 tabs. (Author)
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
journal of. July 2007 physics pp. 31–47. A singularity theorem based on spatial ... In this paper I would like to present a result which confirms – at least partially – ... A detailed analysis of how the model fits in with the .... Further, the statement that the spatial average ...... Financial support under grants FIS2004-01626 and no.
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
H-theorems from macroscopic autonomous equations
Czech Academy of Sciences Publication Activity Database
De Roeck, W.; Maes, C.; Netočný, Karel
2006-01-01
Roč. 123, č. 3 (2006), s. 571-583 ISSN 0022-4715 Institutional research plan: CEZ:AV0Z10100520 Keywords : H-theorem, entropy * irreversible equations Subject RIV: BE - Theoretical Physics Impact factor: 1.437, year: 2006
Student Research Project: Goursat's Other Theorem
Petrillo, Joseph
2009-01-01
In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…
On Viviani's Theorem and Its Extensions
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
The Embedding Theorems of Whitney and Nash
Indian Academy of Sciences (India)
We begin by briefly motivating the idea of amanifold and then discuss the embedding theorems of Whitney and Nash that allow us toview these objects inside appropriately large Euclidean spaces. Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 4. Current Issue Volume 23 | Issue 4. April 2018.
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...
General Correlation Theorem for Trinion Fourier Transform
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.
Directory of Open Access Journals (Sweden)
SEVER ANGEL POPESCU
2015-03-01
Full Text Available In this note we make some remarks on the classical Laguerre’s theorem and extend it and some other old results of Walsh and Gauss-Lucas to the so called trace series associated with transcendental elements of the completion of the algebraic closure of Q in C, with respect to the spectral norm:
Lagrange’s Four-Square Theorem
Directory of Open Access Journals (Sweden)
Watase Yasushige
2015-02-01
Full Text Available This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23].
Anomalous Levinson theorem and supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Boya, L.J.; Casahorran, J.; Esteve, J.G.
1993-01-01
We analyse the symmetry breaking associated to anomalous realization of supersymmetry in the context of SUSY QM. In this case one of the SUSY partners is singular; that leads to peculiar forms of the Levinson theorem relating phase shifts and bound states. Some examples are exhibited; peculiarities include negative energies, incomplete pairing of states and extra phases in scattering. (Author) 8 refs
Another look at the second incompleteness theorem
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
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
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)
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
A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
程立新; 腾岩梅
2003-01-01
This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.
Zaghloul, Mohamed A S; Wang, Mohan; Milione, Giovanni; Li, Ming-Jun; Li, Shenping; Huang, Yue-Kai; Wang, Ting; Chen, Kevin P
2018-04-12
Brillouin optical time domain analysis is the sensing of temperature and strain changes along an optical fiber by measuring the frequency shift changes of Brillouin backscattering. Because frequency shift changes are a linear combination of temperature and strain changes, their discrimination is a challenge. Here, a multicore optical fiber that has two cores is fabricated. The differences between the cores' temperature and strain coefficients are such that temperature (strain) changes can be discriminated with error amplification factors of 4.57 °C/MHz (69.11 μ ϵ /MHz), which is 2.63 (3.67) times lower than previously demonstrated. As proof of principle, using the multicore optical fiber and a commercial Brillouin optical time domain analyzer, the temperature (strain) changes of a thermally expanding metal cylinder are discriminated with an error of 0.24% (3.7%).
Directory of Open Access Journals (Sweden)
Mohamed A. S. Zaghloul
2018-04-01
Full Text Available Brillouin optical time domain analysis is the sensing of temperature and strain changes along an optical fiber by measuring the frequency shift changes of Brillouin backscattering. Because frequency shift changes are a linear combination of temperature and strain changes, their discrimination is a challenge. Here, a multicore optical fiber that has two cores is fabricated. The differences between the cores’ temperature and strain coefficients are such that temperature (strain changes can be discriminated with error amplification factors of 4.57 °C/MHz (69.11 μ ϵ /MHz, which is 2.63 (3.67 times lower than previously demonstrated. As proof of principle, using the multicore optical fiber and a commercial Brillouin optical time domain analyzer, the temperature (strain changes of a thermally expanding metal cylinder are discriminated with an error of 0.24% (3.7%.
Applications of square-related theorems
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.
DISCRETE FIXED POINT THEOREMS AND THEIR APPLICATION TO NASH EQUILIBRIUM
Sato, Junichi; Kawasaki, Hidefumi
2007-01-01
Fixed point theorems are powerful tools in not only mathematics but also economic. In some economic problems, we need not real-valued but integer-valued equilibriums. However, classical fixed point theorems guarantee only real-valued equilibria. So we need discrete fixed point theorems in order to get discrete equilibria. In this paper, we first provide discrete fixed point theorems, next apply them to a non-cooperative game and prove the existence of a Nash equilibrium of pure strategies.
A general comparison theorem for backward stochastic differential equations
Cohen, Samuel N.; Elliott, Robert J.; Pearce, Charles E. M.
2010-01-01
A useful result when dealing with backward stochastic differential equations is the comparison theorem of Peng (1992). When the equations are not based on Brownian motion, the comparison theorem no longer holds in general. In this paper we present a condition for a comparison theorem to hold for backward stochastic differential equations based on arbitrary martingales. This theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectat...
Theorems of Tarski's Undefinability and Godel's Second Incompleteness - Computationally
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.
Determination of the elastic constants of portlandite by Brillouin spectroscopy
Speziale, S.
2008-10-01
The single crystal elastic constants Cij and the shear and adiabatic bulk modulus of a natural portlandite (Ca(OH)2) crystal were determined by Brillouin spectroscopy at ambient conditions. The elastic constants, expressed in GPa, are: C11 = 102.0(± 2.0), C12 = 32.1(± 1.0), C13 = 8.4(± 0.4), C14 = 4.5(± 0.2), C33 = 33.6(± 0.7), C44 = 12.0(± 0.3), C66 = (C11-C12)/2 = 35.0(± 1.1), where the numbers in parentheses are 1σ standard deviations. The Reuss bounds of the adiabatic bulk and shear moduli are K0S = 26.0(± 0.3) GPa and G0 = 17.5(± 0.4) GPa, respectively, while the Voigt bounds of these moduli are K0S = 37.3(± 0.4) GPa and G0 = 24.4(± 0.3) GPa. The Reuss and Voigt bounds for the aggregate Young\\'s modulus are 42.8(± 1.0) GPa and 60.0(± 0.8) GPa respectively, while the aggregate Poisson\\'s ratio is equal to 0.23(± 0.01). Portlandite exhibits both large compressional elastic anisotropy with C11/C33 = 3.03(± 0.09) equivalent to that of the isostructural hydroxide brucite (Mg(OH)2), and large shear anisotropy with C66/C44 = 2.92(± 0.12) which is 11% larger than brucite. The comparison between the bulk modulus of portlandite and that of lime (CaO) confirms a systematic linear relationship between the bulk moduli of brucite-type simple hydroxides and the corresponding NaCl-type oxides. © 2008 Elsevier Ltd. All rights reserved.
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
2014-01-01
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
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.
COMPARISON THEOREMS AND APPLICATIONS OF OSCILLATION OF NEUTRAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
燕居让
1991-01-01
We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equation is reduced to that of nonneutral delay differential equa-tion, from which we give a series of oscillation theorems for neutral delay differentialequation.
A generalization of the virial theorem for strongly singular potentials
International Nuclear Information System (INIS)
Gesztesy, F.; Pittner, L.
1978-09-01
Using scale transformations the authors prove a generalization of the virial theorem for the eigenfunctions of non-relativistic Schroedinger Hamiltonians which are defined as the Friedrichs extension of strongly singular differential operators. The theorem also applies to situations where the ground state has divergent kinetic and potential energy and thus the usual version of the virial theorem becomes meaningless. (Auth.)
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
Search strategy for theorem proving in artificial systems. I
Energy Technology Data Exchange (ETDEWEB)
Lovitskii, V A; Barenboim, M S
1981-01-01
A strategy is contrived, employing the language of finite-order predicate calculus, for finding proofs of theorems. A theorem is formulated, based on 2 known theorems on purity and absorption, and used to determine 5 properties of a set of propositions. 3 references.
Goedel incompleteness theorems and the limits of their applicability. I
International Nuclear Information System (INIS)
Beklemishev, Lev D
2011-01-01
This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.
Guided acoustic and optical waves in silicon-on-insulator for Brillouin scattering and optomechanics
Directory of Open Access Journals (Sweden)
Christopher J. Sarabalis
2016-10-01
Full Text Available We numerically study silicon waveguides on silica showing that it is possible to simultaneously guide optical and acoustic waves in the technologically important silicon on insulator (SOI material system. Thin waveguides, or fins, exhibit geometrically softened mechanical modes at gigahertz frequencies with phase velocities below the Rayleigh velocity in glass, eliminating acoustic radiation losses. We propose slot waveguides on glass with telecom optical frequencies and strong radiation pressure forces resulting in Brillouin gains on the order of 500 and 50 000 W−1m−1 for backward and forward Brillouin scattering, respectively.
Fiber break location technique utilizing stimulated Brillouin scattering effects in optical fiber
International Nuclear Information System (INIS)
Bakar, A A A; Al-Mansoori, M H; Mahdi, M A; Mohd Azau, M A; Zainal Abidin, M S
2009-01-01
A new technique of fiber break detection system in optical communication networks is proposed and experimentally demonstrated in this paper. This technique is based-on continuous wave light source rather than pulsed source that is commonly deployed in existing techniques. The nonlinear effect of stimulated Brillouin scattering is manipulated to locate the fiber-break position in optical communication networks. This technique enables the utilization of a less-sensitive photodetector to detect the Brillouin Stokes line since its intensity increases with the fiber length in the detectable region. The fiber break location can be determined with accuracy of more than 98% for fiber length less than 50 km using this technique
A Meinardus Theorem with Multiple Singularities
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.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
A Geometrical Approach to Bell's Theorem
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
A THEOREM ON CENTRAL VELOCITY DISPERSIONS
International Nuclear Information System (INIS)
An, Jin H.; Evans, N. Wyn
2009-01-01
It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere (SIS), the logarithmic cusp slope γ of the tracers must be given exactly by γ = 2β, where β is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster than that of the SIS, the velocity dispersion of the tracers must diverge at the center too. In particular, if the logarithmic halo cusp slope is larger than two, the diverging velocity dispersion also traces the behavior of the potential. The implication of our theorem on projected quantities is also discussed. We argue that our theorem should be understood as a warning against interpreting results based on simplifying assumptions such as isotropy and spherical symmetry.
Asymptotic twistor theory and the Kerr theorem
International Nuclear Information System (INIS)
Newman, Ezra T
2006-01-01
We first review asymptotic twistor theory with its real subspace of null asymptotic twistors: a five-dimensional CR manifold. This is followed by a description of the Kerr theorem (the identification of shear-free null congruences, in Minkowski space, with the zeros of holomorphic functions of three variables) and an asymptotic version of the Kerr theorem that produces regular asymptotically shear-free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes. A surprising aspect of this work is the role played by analytic curves in H-space, each curve generating an asymptotically flat null geodesic congruence. Also there is a discussion of the physical space realizations of the two associated five- and three-dimensional CR manifolds
Theorem of comparative sensitivity of fibre sensors
Belovolov, M. I.; Paramonov, V. M.; Belovolov, M. M.
2017-12-01
We report an analysis of sensitivity of fibre sensors of physical quantities based on different types of interferometers. We formulate and prove the following theorem: under the time-dependent external physical perturbations at nonzero frequencies (i.e., except the static and low-frequency ones) on the sensitive arms of an interferometer in the form of multiturn elements (coils), there exist such lengths L of the measuring arms of the fibre interferometers at which the sensitivity of sensors based on the Sagnac fibre interferometers can be comparable with the sensitivity of sensors based on Michelson, Mach - Zehnder, or Fabry - Perot fibre interferometers, as well as exceed it under similar other conditions (similar-type perturbations, similar arm lengths and single-mode fibre types). The consequences that follow from the theorem, important for practical implementation of arrays of fibre sensors for measurement purposes and the devices with stable metrological properties, are discussed.
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.
The self-normalized Donsker theorem revisited
Parczewski, Peter
2016-01-01
We extend the Poincar\\'{e}--Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the self-normalized Donsker theorem in Cs\\"{o}rg\\H{o} et al. (2003). Some notes on spheres with respect to $\\ell_p$-norms are given.
The untyped stack calculus and Bohm's theorem
Directory of Open Access Journals (Sweden)
Alberto Carraro
2013-03-01
Full Text Available The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We present a simple extension of stack calculus which is for the stack calculus what Saurin's Lambda-mu is for lambda-mu.
Gauge Invariance and the Goldstone Theorem
Guralnik, Gerald S.
This paper was originally created for and printed in the "Proceedings of seminar on unified theories of elementary particles" held in Feldafing, Germany from July 5 to 16, 1965 under the auspices of the Max-Planck-Institute for Physics and Astrophysics in Munich. It details and expands upon the 1964 Guralnik, Hagen, and Kibble paper demonstrating that the Goldstone theorem does not require physical zero mass particles in gauge theories.
A remark on three-surface theorem
International Nuclear Information System (INIS)
Lu Zhujia
1991-01-01
The three-surface theorem for uniformly elliptic differential inequalities with nonpositive coefficient of zero-order term in some domain D is included in R n becomes trivial if the maximum of u on two separate boundary surface of D is nonpositive. We give a method in this paper for obtaining a nontrivial estimate of the maximum of u on a family of closed surfaces. (author). 2 refs
Asynchronous networks: modularization of dynamics theorem
Bick, Christian; Field, Michael
2017-02-01
Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or dynamical modules. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network: the modularization of dynamics theorem. We give examples to illustrate the main results.
Fractional and integer charges from Levinson's theorem
International Nuclear Information System (INIS)
Farhi, E.; Graham, N.; Jaffe, R.L.; Weigel, H.
2001-01-01
We compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson's theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional regularization in a (1+1)-dimensional gauge theory. We demonstrate that this regularization procedure automatically eliminates the anomaly in the vector current that a naive regulator would produce. We also apply these techniques to bag models in one and three dimensions
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.)
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
Central limit theorem and deformed exponentials
International Nuclear Information System (INIS)
Vignat, C; Plastino, A
2007-01-01
The central limit theorem (CLT) can be ranked among the most important ones in probability theory and statistics and plays an essential role in several basic and applied disciplines, notably in statistical thermodynamics. We show that there exists a natural extension of the CLT from exponentials to so-called deformed exponentials (also denoted as q-Gaussians). Our proposal applies exactly in the usual conditions in which the classical CLT is used. (fast track communication)
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
Optical theorem for heavy-ion scattering
International Nuclear Information System (INIS)
Schwarzschild, A.Z.; Auerbach, E.H.; Fuller, R.C.; Kahana, S.
1976-01-01
An heuristic derivation is given of an equivalent of the optical theorem stated in the charged situation with the remainder or nuclear elastic scattering amplitude defined as a difference of elastic and Coulomb amplitudes. To test the detailed behavior of this elastic scattering amplitude and the cross section, calculations were performed for elastic scattering of 18 O + 58 Ni, 136 Xe + 209 Bi, 84 Kr + 208 Pb, and 11 B + 26 Mg at 63.42 to 114 MeV
Applications of Wck's theorem, ch. 17
International Nuclear Information System (INIS)
Brussaard, P.J.; Glaudemans, P.W.M.
1977-01-01
Wick's theorem is introduced and used to write the many-body Hamiltonian in a selfconsistent basis. The terms of a perturbation expansion are evaluated with the use of the second-quantization formalism.The correspondence with Feyman diagrams is demonstrated. For some nuclei a description in terms of particle-hole configurations is quite convenient. The simplest case, i.e. one-particle, one-hole states, is treated
Theorem Proving In Higher Order Logics
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
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)
Soft theorems from conformal field theory
International Nuclear Information System (INIS)
Lipstein, Arthur E.
2015-01-01
Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambtwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.
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
KrF laser amplifier with phase-conjugate Brillouin retroreflectors.
Gower, M C
1982-09-01
We have demonstrated the use of phase-conjugate stimulated Brillouin scattering mirrors to produce high-quality, short-pulse KrF laser beams from angular multiplexed and regenerative amplifiers. The mirror was also shown to isolate systems optically from amplifier spontaneous emission. Automatic alignment of targets using this mirror as a retroreflector was also demonstrated.
Choi, Bo-Hun; Kwon, Il-Bum
2015-03-09
We propose a distributed residual strain sensor that uses an Al-packaged optical fiber for the first time. The residual strain which causes Brillouin frequency shifts in the optical fiber was measured using Brillouin optical correlation domain analysis with 2 cm spatial resolution. We quantified the Brillouin frequency shifts in the Al-packaged optical fiber by the tensile stress and compared them for a varying number of Al layers in the optical fiber. The Brillouin frequency shift of an optical fiber with one Al layer had a slope of 0.038 MHz/με with respect to tensile stress, which corresponds to 78% of that for an optical fiber without Al layers. After removal of the stress, 87% of the strain remained as residual strain. When different tensile stresses were randomly applied, the strain caused by the highest stress was the only one detected as residual strain. The residual strain was repeatedly measured for a time span of nine months for the purpose of reliability testing, and there was no change in the strain except for a 4% reduction, which is within the error tolerance of the experiment. A composite material plate equipped with our proposed Al-packaged optical fiber sensor was hammered for impact experiment and the residual strain in the plate was successfully detected. We suggest that the Al-packaged optical fiber can be adapted as a distributed strain sensor for smart structures, including aerospace structures.
All solid-state diode pumped Nd:YAG MOPA with stimulated Brillouin phase conjugate mirror
Offerhaus, Herman L.; Godfried, Herman; Godfried, H.P; Witteman, W.J.
1996-01-01
At the Nederlands Centrum voor Laser Research (NCLR) a 1 kHz diode-pumped Nd:YAG Master Oscillator Power Amplifier (MOPA) chain with a Stimulated Brillouin Scattering (SBS) Phase Conjugate mirror is designed and operated. A small Brewster angle Nd:YAG slab (2 by 2 by 20 mm) is side pumped with 200
Dual Raman-Brillouin spectroscopic investigation of plant stress response and development
Coker, Zachary; Troyanova-Wood, Maria; Marble, Kassie; Yakovlev, Vladislav
2018-03-01
Raman and Brillouin spectroscopy are powerful tools for non-invasive and non-destructive investigations of material chemical and mechanical properties. In this study, we use a newly developed custom-built dual Raman-Brillouin microspectroscopy instrument to build on previous works studying in-vivo stress response of live plants using only a Raman spectroscopy system. This dual Raman-Brillouin spectroscopy system is capable of fast simultaneous spectra acquisition from single-point locations. Shifts and changes in a samples Brillouin spectrum indicate a change in the physical characteristics of the sample, namely mechano-elasticity; in measuring this change, we can establish a relationship between the mechanical properties of a sample and known stress response agents, such as reactive oxygen species and other chemical constituents as indicated by peaks in the Raman spectra of the same acquisition point. Simultaneous application of these spectroscopic techniques offers great promise for future development and applications in agricultural and biological studies and can help to improve our understanding of mechanochemical changes of plants and other biological samples in response to environmental and chemically induced stresses at microscopic or cellular level.
Highly localized distributed Brillouin scattering response in a photonic integrated circuit
Directory of Open Access Journals (Sweden)
Atiyeh Zarifi
2018-03-01
Full Text Available The interaction of optical and acoustic waves via stimulated Brillouin scattering (SBS has recently reached on-chip platforms, which has opened new fields of applications ranging from integrated microwave photonics and on-chip narrow-linewidth lasers, to phonon-based optical delay and signal processing schemes. Since SBS is an effect that scales exponentially with interaction length, on-chip implementation on a short length scale is challenging, requiring carefully designed waveguides with optimized opto-acoustic overlap. In this work, we use the principle of Brillouin optical correlation domain analysis to locally measure the SBS spectrum with high spatial resolution of 800 μm and perform a distributed measurement of the Brillouin spectrum along a spiral waveguide in a photonic integrated circuit. This approach gives access to local opto-acoustic properties of the waveguides, including the Brillouin frequency shift and linewidth, essential information for the further development of high quality photonic-phononic waveguides for SBS applications.
Spontaneous Rayleigh-Brillouin scattering of ultraviolet light in nitrogen, dry air and moist air,
Witschas, B.; Vieitez, M.O.; Duijn, van E.-J.; Reitebuch, O.; Water, van de W.; Ubachs, W.
2010-01-01
Atmospheric lidar techniques for the measurement of wind, temperature, and optical properties of aerosols rely on the exact knowledge of the spectral line shape of the scattered laser light on molecules. We report on spontaneous Rayleigh–Brillouin scattering measurements in the ultraviolet at a
Four theorems on the psychometric function.
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
Stochastic thermodynamics, fluctuation theorems and molecular machines
International Nuclear Information System (INIS)
Seifert, Udo
2012-01-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (review article)
The implicit function theorem history, theory, and applications
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...
Some fixed point theorems in fuzzy reflexive Banach spaces
International Nuclear Information System (INIS)
Sadeqi, I.; Solaty kia, F.
2009-01-01
In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.
On the inverse of the Pomeranchuk theorem
International Nuclear Information System (INIS)
Nagy, E.
1977-04-01
The Pomeranchuk theorem is valid only for bounded total cross sections at infinite energies, and for arbitrarily rising cross sections one cannot prove the zero asymptotic limit of the difference of the particle and antiparticle total cross sections. In the paper the problem is considered from the inverse point of view. It is proved using dispersion relations that if the total cross sections rise with some power of logarithm and the difference of the particle and antiparticle total cross sections remain finite, then the real to imaginary ratios of both the particle and antiparticle forward scattering amplitudes are bounded. (Sz.N.Z.)
Noncommutative gauge theories and Kontsevich's formality theorem
International Nuclear Information System (INIS)
Jurco, B.; Schupp, P.; Wess, J.
2001-01-01
The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a 'Mini Seiberg-Witten map' that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor
The Invariance and the General CCT Theorems
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...
No-cloning theorem on quantum logics
International Nuclear Information System (INIS)
Miyadera, Takayuki; Imai, Hideki
2009-01-01
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem
Directory of Open Access Journals (Sweden)
Juliana Bueno-Soler
2016-09-01
Full Text Available This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs. We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes’ theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.
Stone's representation theorem in fuzzy topology
Institute of Scientific and Technical Information of China (English)
刘应明; 张德学
2003-01-01
In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0 ∈ L is a prime or 1 ∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L-locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L-topological spaces.
Soft theorems for shift-symmetric cosmologies
Finelli, Bernardo; Goon, Garrett; Pajer, Enrico; Santoni, Luca
2018-03-01
We derive soft theorems for single-clock cosmologies that enjoy a shift symmetry. These so-called consistency conditions arise from a combination of a large diffeomorphism and the internal shift symmetry and fix the squeezed limit of all correlators with a soft scalar mode. As an application, we show that our results reproduce the squeezed bispectrum for ultra-slow-roll inflation, a particular shift-symmetric, nonattractor model which is known to violate Maldacena's consistency relation. Similar results have been previously obtained by Mooij and Palma using background-wave methods. Our results shed new light on the infrared structure of single-clock cosmological spacetimes.
Central limit theorems under special relativity.
McKeague, Ian W
2015-04-01
Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.
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.
Logic for computer science foundations of automatic theorem proving
Gallier, Jean H
2015-01-01
This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in fir
On Pythagoras Theorem for Products of Spectral Triples
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...
A remark on the energy conditions for Hawking's area theorem
Lesourd, Martin
2018-06-01
Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
Markvorsen, Steen
2006-01-01
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered only much later in more advanced math courses - is comprehensible with only a little extension of the first year curriculum. Moreover, it is more intuitive than the static proof. We support this intuit...
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 ...
The Surprise Examination Paradox and the Second Incompleteness Theorem
Kritchman, Shira; Raz, Ran
2010-01-01
We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest that the second incompleteness theorem gives a possible resolution of the surprise examination paradox. Roughly speaking, we argue that the flaw in the derivation of the paradox is that it contains a hidden assumption that one can prove the consistency of the...
Goedel incompleteness theorems and the limits of their applicability. I
Energy Technology Data Exchange (ETDEWEB)
Beklemishev, Lev D [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2011-01-25
This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.
From Einstein's theorem to Bell's theorem: a history of quantum non-locality
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.
2012-07-01
Brillouin-scattering Optical Time Domain Reflectometry (BOTDR) is a viable technology for simultaneous, distributed : strain and temperature measurements for miles-long transportation structures. It is a promising tool to ensure the smooth : operatio...
Generalizations of the Nash Equilibrium Theorem in the KKM Theory
Directory of Open Access Journals (Sweden)
Sehie Park
2010-01-01
Full Text Available The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minimax theorem, the von Neumann-Fan intersection theorem, the Fan-type analytic alternative, and the Nash equilibrium theorem for abstract convex spaces satisfying the partial KKM principle. These results are compared with previously known cases for G-convex spaces. Consequently, our results unify and generalize most of previously known particular cases of the same nature. Finally, we add some detailed historical remarks on related topics.
International Nuclear Information System (INIS)
Spirin, V V; Lopez-Mercado, C A; Megret, P; Fotiadi, A A
2012-01-01
We demonstrate a single-mode Brillouin fiber ring laser, which is passively stabilized at pump resonance frequency by using self-injection locking of semiconductor pump laser. Resonance condition for Stokes radiation is achieved by length fitting of Brillouin laser cavity. The laser generate single-frequency Stokes wave with linewidth less than 0.5 kHz using approximately 17-m length cavity
Energy Technology Data Exchange (ETDEWEB)
Vincent, B [Lab. Europeen de Recherche Univ.: Saarland-Lorraine, Univ. des Saarlandes, D-66041 Saarbruecken (Germany)]|[Lab. de Physique des Milieux Ionises et Applications, CNRS-UMR 7040, Univ. H. Poincare, Nancy I, F-54506 (France); Krueger, J K [Lab. Europeen de Recherche Univ.: Saarland-Lorraine, Univ. des Saarlandes, D-66041 Saarbruecken (Germany)]|[Fachrichtung 7.2, Experimentalphysik, Univ. des Saarlandes, Bau 38, D-66041 Saarbruecken (Germany); Elmazria, O [Laboratoire Europeen de Recherche Universitaire: Saarland-Lorraine, Universitaet des Saarlandes, D-66041 Saarbruecken (Germany)]|[Laboratoire de Physique des Milieux Ionises et Applications, CNRS-UMR 7040, Universite H. Poincare, Nancy I, F-54506 (France); Bouvot, L [Laboratoire Europeen de Recherche Universitaire: Saarland-Lorraine, Universitaet des Saarlandes, D-66041 Saarbruecken (Germany)]|[Laboratoire de Physique des Milieux Ionises et Applications, CNRS-UMR 7040, Universite H. Poincare, Nancy I, F-54506 (France); Mainka, J [Laboratoire Europeen de Recherche Universitaire: Saarland-Lorraine, Universitaet des Saarlandes, D-66041 Saarbruecken (Germany)]|[Fachrichtung 7.2, Experimentalphysik, Universitaet des Saarlandes, Bau 38, D-66041 Saarbruecken (Germany); Sanctuary, R [Laboratoire Europeen de Recherche Universitaire: Saarland-Lorraine, Universitaet des Saarlandes, D-66041 Saarbruecken (Germany)]|[Laboratoire de Physique des Materiaux, Campus Luxembourg-Limpertsberg, L-1511 Luxembourg (Luxembourg); Rouxel, D [Lab. Europeen de Recherche Univ.: Saarland-Lorraine, Univ. des Saarlandes, D-66041 Saarbruecken (Germany)]|[Lab. de Physique des Milieux Ionises et Applications, CNRS-UMR 7040, Univ. H. Poincare, Nancy I, F-54506 (France); Alnot, P [Lab. Europeen de Recherche Univ.: Saarland-Lorraine, Univ. des Saarlandes, D-66041 Saarbruecken (Germany)]|[Lab. de Physique des Milieux Ionises et Applications, CNRS-UMR 7040, Univ. H. Poincare, Nancy I, F-54506 (France)
2005-06-21
High performance Brillouin microscopy (BM) has been used to characterize the spatial distribution of piezoelectrically induced acoustic fields excited at microwave frequencies in a LiNbO{sub 3} single crystal. It is demonstrated that under suitable conditions BM is able to detect microwave-induced bulk as well as surface acoustic waves. Brillouin spectroscopy is able to probe sound wave intensities of induced phonons, which are as small as those of thermal phonons.
Randomized central limit theorems: A unified theory.
Eliazar, Iddo; Klafter, Joseph
2010-08-01
The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.
Birth of a theorem a mathematical adventure
Villani, Cédric
2015-01-01
This man could plainly do for mathematics what Brian Cox has done for physics" (Sunday Times). What goes on inside the mind of a rock-star mathematician? Where does inspiration come from? With a storyteller's gift, Cedric Villani takes us on a mesmerising journey as he wrestles with a new theorem that will win him the most coveted prize in mathematics. Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, doubt and anxiety, elation and despair. We discover how it feels to be obsessed by a theorem during your child's cello practise and throughout your dreams, why appreciating maths is a bit like watching an episode of Columbo, and how sometimes inspiration only comes from locking yourself away in a dark room to think. Blending science with history, biography with myth, Villani conjures up an inimitable cast of characters including the omnipresent Einstein, mad genius Kurt Godel, and Villani's personal hero, John Nash. Bir...
Electrically tunable Brillouin fiber laser based on a metal-coated single-mode optical fiber
Directory of Open Access Journals (Sweden)
S.M. Popov
Full Text Available We explore tunability of the Brillouin fiber laser employing Joule heating. For this purpose, 10-m-length of a metal-coated single-mode optical cavity fiber has been directly included into an electrical circuit, like a conductor wire. With the current up to â¼3.5Â A the laser tuning is demonstrated over a spectrum range of â¼400Â MHz. The observed laser line broadening up to â¼2Â MHz is explained by frequency drift and mode-hoping in the laser caused by thermal noise. Keywords: Brillouin fiber laser, Metal-coated optical fiber, Laser tuning, Fiber sensors
Brillouin scattering on TbAsO4 and GdVO4
International Nuclear Information System (INIS)
Wehrle, H.
1975-01-01
Using a two-pass interferometer the set of elastic constants in TbAsO 4 was determined. On the basis of these constants the Debye temperature was evaluated for T→0. The crystallographic phase transition could not be demonstrated in either case (TbAsO 4 and TmAsO 4 ) because of small Brillouin-line intensity in the low-temperature region. The frequency shifts of the Brillouin lines detected in the case of GdVO 4 show an increase of 5% for the temperature change from room temperature to helium temperature. Assuming this dependence for TbAsO 4 , too, the Debye temperature is changed by 5%. (HPOE) [de
Directory of Open Access Journals (Sweden)
Xiaoyi Bao
2013-01-01
Full Text Available A distributed optical fiber sensor with the capability of simultaneously measuring temperature and strain is proposed using a large effective area non-zero dispersion shifted fiber (LEAF with sub-meter spatial resolution. The Brillouin frequency shift is measured using Brillouin optical time-domain analysis (BOTDA with differential pulse-width pair technique, while the spectrum shift of the Rayleigh backscatter is measured using optical frequency-domain reflectometry (OFDR. These shifts are the functions of both temperature and strain, and can be used as two independent parameters for the discrimination of temperature and strain. A 92 m measurable range with the spatial resolution of 50 cm is demonstrated experimentally, and accuracies of ±1.2 °C in temperature and ±15 με in strain could be achieved.
Battistoni, Andrea; Bencivenga, Filippo; Fioretto, Daniele; Masciovecchio, Claudio
2014-10-15
In this Letter, we present a simple method to avoid the well-known spurious contributions in the Brillouin light scattering (BLS) spectrum arising from the finite aperture of collection optics. The method relies on the use of special spatial filters able to select the scattered light with arbitrary precision around a given value of the momentum transfer (Q). We demonstrate the effectiveness of such filters by analyzing the BLS spectra of a reference sample as a function of scattering angle. This practical and inexpensive method could be an extremely useful tool to fully exploit the potentiality of Brillouin acoustic spectroscopy, as it will easily allow for effective Q-variable experiments with unparalleled luminosity and resolution.
Rayleigh-Brillouin scattering in NH4Cl under hydrostatic pressure
International Nuclear Information System (INIS)
Hikita, Tomoyuki; Kitabatake, Makoto; Ikeda, Takuro
1981-01-01
Rayleigh-Brillouin scattering in NH 4 Cl has been studied under hydrostatic pressure. Brillouin shifts of the longitudinal phonons propagating along the and directions and of the transverse phonons propagating along the direction are measured as a function of temperature at four fixed pressures up to 2.3 kbar. All components increase almost linearly with decreasing temperature in the disordered phase and show incremental increases similar to the temperature dependence of the long range order parameter in the ordered phase. It was found that the longitudinal modes exhibit large despersion effect even at high pressures. On the other hand, the transverse mode appears to give no dispersion effect. The intensity of the Rayleigh component in the VV polarization condition increases as the temperature approaches the transition point, while that in the VH polarization does not show such anomalous increase. (author)
Directory of Open Access Journals (Sweden)
Yongqian Li
2017-03-01
Full Text Available A useful method for eliminating the detrimental effect of laser frequency instability on Brillouin signals by employing the self-heterodyne detection of Rayleigh and Brillouin scattering is presented. From the analysis of Brillouin scattering spectra from fibers with different lengths measured by heterodyne detection, the maximum usable pulse width immune to laser frequency instability is obtained to be about 4 µs in a self-heterodyne detection Brillouin optical time domain reflectometer (BOTDR system using a broad-band laser with low frequency stability. Applying the self-heterodyne detection of Rayleigh and Brillouin scattering in BOTDR system, we successfully demonstrate that the detrimental effect of laser frequency instability on Brillouin signals can be eliminated effectively. Employing the broad-band laser modulated by a 130-ns wide pulse driven electro-optic modulator, the observed maximum errors in temperatures measured by the local heterodyne and self-heterodyne detection BOTDR systems are 7.9 °C and 1.2 °C, respectively.
Guided Acoustic and Optical Waves in Silicon-on-Insulator for Brillouin Scattering and Optomechanics
2016-08-01
APL PHOTONICS 1, 071301 (2016) Guided acoustic and optical waves in silicon-on- insulator for Brillouin scattering and optomechanics Christopher J...is possible to simultaneously guide optical and acoustic waves in the technologically important silicon on insulator (SOI) material system. Thin...high sound velocity — makes guiding acoustic waves difficult, motivating the use of soft chalcogenide glasses and partial or complete releases (removal
Stimulated Brillouin backscattering losses in weakly inhomogeneous laser-produced plasmas
International Nuclear Information System (INIS)
Eidmann, K.; Brederlow, G.; Brodmann, R.; Petsch, R.; Sigel, R.; Tsarkiris, G.; Volk, R.; Witkowski, S.
1979-02-01
Studies of the reflection from a plane solid target plasma produced with a 1TW iodine laser (lambda = 1.3μm) at pulse durations of 300 ps are presented. The specularly reflected and the backscattered light was observed separately at different angles of incidence, intensities and spot sizes (up to 400 μm). Stimulated Brillouin scattering was identified as the main mechanism for backscattering with saturation at 20 - 30% reflection. (orig.) [de
Development of a Brillouin scattering based distributed fibre optic strain sensor
Brown, Anthony Wayne
2001-07-01
The parameters of the Brillouin spectrum of an optical fibre depend upon the strain and temperature conditions of the fibre. As a result, fibre optic distributed sensors based on Brillouin scattering can measure strain and temperature in arbitrary regions of a sensing fibre. In the past, such sensors have often been demonstrated under laboratory conditions, demonstrating the principle of operation. Although some field tests of temperature sensing have been reported, the actual deployment of such sensors in the field for strain measurements has been limited by poor spatial resolution (typically 1 m or more) and poor strain accuracy (+/-100 muepsilon). Also, cross-sensitivity of the Brillouin spectrum to temperature further reduces the accuracy of strain measurement while long acquisition times hinders field use. The high level of user knowledge and lack of automation required to operate the equipment is another limiting factor of the only commercially available unit. The potential benefits of distributed measurements are great for instrumentation of civil structures provided that the above limitations are overcome. However, before this system is used with confidence by practitioners, it is essential that it can be effectively operated in field conditions. In light of this, the fibre optics group at the University of New Brunswick has been developing an automated system for field measurement of strain in civil structures, particularly in reinforced concrete. The development of the sensing system hardware and software was the main focus of this thesis. This has been made possible, in part, by observation of the Brillouin spectrum for the case of using very short light pulses (performance to measure strain to an accuracy of 10 muepsilon; and allow the simultaneous measurement of strain and temperature to an accuracy of 204 muepsilon and 3°C are presented. Finally, the results of field measurement of strain on a concrete structure are presented.
Rayleigh-Brillouin scattering in SF6 in the kinetic regime
Wang, Yuanqing; Yu, Yin; Liang, Kun; Marques, Wilson; van de Water, Willem; Ubachs, Wim
2017-01-01
Rayleigh-Brillouin spectral profiles are measured with a laser-based scatterometry setup for a 90° scattering angle at a high signal-to-noise ratio (r.m.s. noise below 0.15% w.r.t. peak intensity) in sulfur-hexafluoride gas for pressures in the range 0.2–5 bar and for a wavelength of λ=403.0 nm. The
Directory of Open Access Journals (Sweden)
Xingjun Lv
2011-11-01
Full Text Available In this paper, a novel kind of method to monitor corrosion expansion of steel rebars in steel reinforced concrete structures named fiber optic coil winding method is proposed, discussed and tested. It is based on the fiber optical Brillouin sensing technique. Firstly, a strain calibration experiment is designed and conducted to obtain the strain coefficient of single mode fiber optics. Results have shown that there is a good linear relationship between Brillouin frequency and applied strain. Then, three kinds of novel fiber optical Brillouin corrosion expansion sensors with different fiber optic coil winding packaging schemes are designed. Sensors were embedded into concrete specimens to monitor expansion strain caused by steel rebar corrosion, and their performance was studied in a designed electrochemical corrosion acceleration experiment. Experimental results have shown that expansion strain along the fiber optic coil winding area can be detected and measured by the three kinds of sensors with different measurement range during development the corrosion. With the assumption of uniform corrosion, diameters of corrosion steel rebars were obtained using calculated average strains. A maximum expansion strain of 6,738 με was monitored. Furthermore, the uniform corrosion analysis model was established and the evaluation formula to evaluate mass loss rate of steel rebar under a given corrosion rust expansion rate was derived. The research has shown that three kinds of Brillouin sensors can be used to monitor the steel rebar corrosion expansion of reinforced concrete structures with good sensitivity, accuracy and monitoring range, and can be applied to monitor different levels of corrosion. By means of this kind of monitoring technique, quantitative corrosion expansion monitoring can be carried out, with the virtues of long durability, real-time monitoring and quasi-distribution monitoring.
Zhao, Xuefeng; Gong, Peng; Qiao, Guofu; Lu, Jie; Lv, Xingjun; Ou, Jinping
2011-01-01
In this paper, a novel kind of method to monitor corrosion expansion of steel rebars in steel reinforced concrete structures named fiber optic coil winding method is proposed, discussed and tested. It is based on the fiber optical Brillouin sensing technique. Firstly, a strain calibration experiment is designed and conducted to obtain the strain coefficient of single mode fiber optics. Results have shown that there is a good linear relationship between Brillouin frequency and applied strain. Then, three kinds of novel fiber optical Brillouin corrosion expansion sensors with different fiber optic coil winding packaging schemes are designed. Sensors were embedded into concrete specimens to monitor expansion strain caused by steel rebar corrosion, and their performance was studied in a designed electrochemical corrosion acceleration experiment. Experimental results have shown that expansion strain along the fiber optic coil winding area can be detected and measured by the three kinds of sensors with different measurement range during development the corrosion. With the assumption of uniform corrosion, diameters of corrosion steel rebars were obtained using calculated average strains. A maximum expansion strain of 6,738 με was monitored. Furthermore, the uniform corrosion analysis model was established and the evaluation formula to evaluate mass loss rate of steel rebar under a given corrosion rust expansion rate was derived. The research has shown that three kinds of Brillouin sensors can be used to monitor the steel rebar corrosion expansion of reinforced concrete structures with good sensitivity, accuracy and monitoring range, and can be applied to monitor different levels of corrosion. By means of this kind of monitoring technique, quantitative corrosion expansion monitoring can be carried out, with the virtues of long durability, real-time monitoring and quasi-distribution monitoring.
Shao, Liyang; Zhang, Yunpeng; Li, Zonglei; Zhang, Zhiyong; Zou, Xihua; Luo, Bin; Pan, Wei; Yan, Lianshan
2016-11-01
Logarithmic detectors (LogDs) have been used in coherent Brillouin optical time-domain analysis (BOTDA) sensors to reduce the effect of phase fluctuation, demodulation complexities, and measurement time. However, because of the inherent properties of LogDs, a DC component at the level of hundreds of millivolts that prohibits high-gain signal amplification (SA) could be generated, resulting in unacceptable data acquisition (DAQ) inaccuracies and decoding errors in the process of prototype integration. By generating a reference light at a level similar to the probe light, differential detection can be applied to remove the DC component automatically using a differential amplifier before the DAQ process. Therefore, high-gain SA can be employed to reduce quantization errors. The signal-to-noise ratio of the weak Brillouin gain signal is improved from ˜11.5 to ˜21.8 dB. A BOTDA prototype is implemented based on the proposed scheme. The experimental results show that the measurement accuracy of the Brillouin frequency shift (BFS) is improved from ±1.9 to ±0.8 MHz at the end of a 40-km sensing fiber.
Directory of Open Access Journals (Sweden)
Sara Mattana
2017-11-01
Full Text Available Amyloidopathy is one of the most prominent hallmarks of Alzheimer’s disease (AD, the leading cause of dementia worldwide, and is characterized by the accumulation of amyloid plaques in the brain parenchyma. The plaques consist of abnormal deposits mainly composed of an aggregation-prone protein fragment, β-amyloid 1-40/1-42, into the extracellular matrix. Brillouin microspectroscopy is an all-optical contactless technique that is based on the interaction between visible light and longitudinal acoustic waves or phonons, giving access to the viscoelasticity of a sample on a subcellular scale. Here, we describe the first application of micromechanical mapping based on Brillouin scattering spectroscopy to probe the stiffness of individual amyloid plaques in the hippocampal part of the brain of a β-amyloid overexpressing transgenic mouse. Correlative analysis based on Brillouin and Raman microspectroscopy showed that amyloid plaques have a complex structure with a rigid core of β-pleated sheet conformation (β-amyloid protein surrounded by a softer ring-shaped region richer in lipids and other protein conformations. These preliminary results give a new insight into the plaque biophysics and biomechanics, and a valuable contrast mechanism for the study and diagnosis of amyloidopathy.
Influence of chirp on laser-pulse amplification in Brillouin backscattering schemes
Lehmann, Goetz; Schluck, Friedrich; Spatschek, Karl-Heinz
2015-11-01
Plasma-based amplification of laser pulses is currently discussed as a key component for the next generation of high-intensity laser systems, possibly enabling the generation of ultra-short pulses in the exawatt-zetawatt regime. In these scenarios the energy of a long pump pulse (several ps to ns of duration) is transferred to a short seed pulse via a plasma oscillation. Weakly- and strongly-coupled (sc) Brillouin backscattering have been identified as potential candidates for robust amplification scenarios. With the help of three-wave interaction models, we investigate the influence of a chirp of the pump beam on the seed amplification. We show that chirp can mitigate deleterious spontaneous Raman backscattering of the pump off noise and that at the same time the amplification dynamics due to Brillouin scattering is still intact. For the experimentally very interesting case of sc-Brillouin we find a dependence of the efficiency on the sign of the chirp. Funding provided by project B10 of SFB TR18 of the Deutsche Forschungsgemeinschaft (DFG).
Spontaneous Rayleigh-Brillouin scattering spectral analysis based on the Wiener filter
Directory of Open Access Journals (Sweden)
Tao Wu
2018-01-01
Full Text Available In this paper, a spontaneous Rayleigh-Brillouin scattering spectrometer is developed to measure the gaseous spontaneous Rayleigh-Brillouin scattering profiles over the pressure range from 1 to 5 atm for a wavelength of 532nm at a constant room temperature of 296K and a 90o scattering angle. In order to make a direct comparison between the experimentally obtained spectrum and the theoretical spectrum calculated from the Tenti S6 model, the measured spontaneous Rayleigh-Brillouin scattering signal is deconvolved by the Wiener filtering. The purpose is to remove the effect on the spectrum by the transmission function of the Fabry-Perrot scanning interferometer. The results of the comparison show that the deconvolved spectra are consistent with the theoretical spectra calculated from the Tenti S6 model, and thus confirm that the deconvolution based on the Wiener filter is able to process the measured spectra and improve the spectral resolution. Some factors that influence the accuracy of deconvolution are analyzed and discussed. At the same time, another comparison between the raw experimentally obtained spectra and the theoretical spectra calculated by convolving the Tenti S6 model with instrument function of the measurement system is performed in the same experimental condition. The results of the two comparisons show that, compared with the raw experimentally obtained spectrum, the deconvolved spectrum matches the theoretically calculated spectrum more accurately under lower pressure (≤2atm than under relative higher pressure (>2atm.
Single-crystal Brillouin spectroscopy with CO{sub 2} laser heating and variable q
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jin S.; Bass, Jay D. [Department of Geology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States); Zhu, Gaohua [Materials Research Department, Toyota Research Institute of North America, Ann Arbor, Michigan 48105 (United States)
2015-06-15
We describe a Brillouin spectroscopy system integrated with CO{sub 2} laser-heating and Raman spectroscopic capabilities. Temperature is determined by measurements of the grey-body thermal radiation emitted by the hot sample, with the system response calibrated relative to a standard tungsten ribbon lamp. High-pressure laser-heating Brillouin scattering measurements of acoustic velocities on liquid water and ice compressed in a diamond-anvil cell were performed at temperatures up to 2500 ± 150 K at high pressure. Single-crystal laser-heating Brillouin measurements were made on the (111) plane of San Carlos olivine at ∼13 GPa, 1300 ± 200 K. The pressure as measured by ruby fluorescence is shown to be within ±0.5 GPa of the pressure on the olivine sample during laser heating when KCl and KBr are used as pressure-transmitting media. In addition, the system is designed for continuously variable scattering angles from forward scattering (near 0° scattering angle) up to near back scattering (∼141°). This novel setup allows us to probe a wide range of wave vectors q for investigation of phonon dispersion on, for example, crystals with large unit cells (on the scale of hundreds of nm)
A perceptron network theorem prover for the propositional calculus
Drossaers, M.F.J.
In this paper a short introduction to neural networks and a design for a perceptron network theorem prover for the propositional calculus are presented. The theorem prover is a representation of a variant of the semantic tableau method, called the parallel tableau method, by a network of
Leaning on Socrates to Derive the Pythagorean Theorem
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…
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.)
COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It-Kunita integral. By the application of this theorem, we give an existence result of the solutions to these equations with continuous coefficients.
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.
K S Krishnan's 1948 Perception of the Sampling Theorem
Indian Academy of Sciences (India)
K S Krishnan's 1948 Perception of the. Sampling Theorem. Raiiah Simon is a. Professor at the Institute of Mathematical. Sciences, Chennai. His primary interests are in classical and quantum optics, geometric phases, group theoretical techniques and quantum information science. Keywords. Sompling theorem, K S ...
On Frobenius, Mazur, and Gelfand-Mazur theorems on division ...
African Journals Online (AJOL)
... R of real numbers, the field C of complex numbers, or the non-commutative algebra Q of quaternions. Gelfand [15] proved that every normed division algebra over the field C is isomorphic to C. He named this theorem, which is fundamental for the development of the theory of Banach Algebras, the Gelfand-Mazur theorem.
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
A general conservative extension theorem in process algebras with inequalities
d' Argenio, P.R.; Verhoef, Chris
1997-01-01
We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to
A power counting theorem for Feynman integrals on the lattice
International Nuclear Information System (INIS)
Reisz, T.
1988-01-01
A convergence theorem is proved, which states sufficient conditions for the existence of the continuum limit for a wide class of Feynman integrals on a space-time lattice. A new kind of a UV-divergence degree is introduced, which allows the formulation of the theorem in terms of power counting conditions. (orig.)
A Hohenberg-Kohn theorem for non-local potentials
International Nuclear Information System (INIS)
Meron, E.; Katriel, J.
1977-01-01
It is shown that within any class of commuting one-body potentials a Hohenberg-Kohn type theorem is satisfied with respect to an appropriately defined density. The Hohenberg-Kohn theorem for local potentials follows as a special case. (Auth.)
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.
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 ...
Bell's "Theorem": loopholes vs. conceptual flaws
Kracklauer, A. F.
2017-12-01
An historical overview and detailed explication of a critical analysis of what has become known as Bell's Theorem to the effect that, it should be impossible to extend Quantum Theory with the addition of local, real variables so as to obtain a version free of the ambiguous and preternatural features of the currently accepted interpretations is presented. The central point on which this critical analysis, due originally to Edwin Jaynes, is that Bell incorrectly applied probabilistic formulas involving conditional probabilities. In addition, mathematical technicalities that have complicated the understanding of the logical or mathematical setting in which current theory and experimentation are embedded, are discussed. Finally, some historical speculations on the sociological environment, in particular misleading aspects, in which recent generations of physicists lived and worked are mentioned.
A Theorem on Grid Access Control
Institute of Scientific and Technical Information of China (English)
XU ZhiWei(徐志伟); BU GuanYing(卜冠英)
2003-01-01
The current grid security research is mainly focused on the authentication of grid systems. A problem to be solved by grid systems is to ensure consistent access control. This problem is complicated because the hosts in a grid computing environment usually span multiple autonomous administrative domains. This paper presents a grid access control model, based on asynchronous automata theory and the classic Bell-LaPadula model. This model is useful to formally study the confidentiality and integrity problems in a grid computing environment. A theorem is proved, which gives the necessary and sufficient conditions to a grid to maintain confidentiality.These conditions are the formalized descriptions of local (node) relations or relationship between grid subjects and node subjects.
Theorem Proving in Intel Hardware Design
O'Leary, John
2009-01-01
For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.
Virial Theorem in Nonlocal Newtonian Gravity
Directory of Open Access Journals (Sweden)
Bahram Mashhoon
2016-05-01
Full Text Available Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for “isolated” astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy’s baryonic diameter D 0 —namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time—is predicted to be larger than the effective dark matter fraction f D M times a universal length that is the basic nonlocality length scale λ 0 ≈ 3 ± 2 kpc.
On a curvature-statistics theorem
International Nuclear Information System (INIS)
Calixto, M; Aldaya, V
2008-01-01
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature (κ = ±1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.
On a curvature-statistics theorem
Energy Technology Data Exchange (ETDEWEB)
Calixto, M [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de Astrofisica de Andalucia, Apartado Postal 3004, 18080 Granada (Spain)], E-mail: Manuel.Calixto@upct.es
2008-08-15
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature ({kappa} = {+-}1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.
An interlacing theorem for reversible Markov chains
International Nuclear Information System (INIS)
Grone, Robert; Salamon, Peter; Hoffmann, Karl Heinz
2008-01-01
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
An interlacing theorem for reversible Markov chains
Energy Technology Data Exchange (ETDEWEB)
Grone, Robert; Salamon, Peter [Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720 (United States); Hoffmann, Karl Heinz [Institut fuer Physik, Technische Universitaet Chemnitz, D-09107 Chemnitz (Germany)
2008-05-30
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
Asset management using an extended Markowitz theorem
Directory of Open Access Journals (Sweden)
Paria Karimi
2014-06-01
Full Text Available Markowitz theorem is one of the most popular techniques for asset management. The method has been widely used to solve many applications, successfully. In this paper, we present a multi objective Markowitz model to determine asset allocation by considering cardinality constraints. The resulted model is an NP-Hard problem and the proposed study uses two metaheuristics, namely genetic algorithm (GA and particle swarm optimization (PSO to find efficient solutions. The proposed study has been applied on some data collected from Tehran Stock Exchange over the period 2009-2011. The study considers four objectives including cash return, 12-month return, 36-month return and Lower Partial Moment (LPM. The results indicate that there was no statistical difference between the implementation of PSO and GA methods.
On Pythagoras Theorem for Products of Spectral Triples
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
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.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
International Nuclear Information System (INIS)
Stenlund, Mikko
2016-01-01
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
A note on the weighted Khintchine-Groshev Theorem
DEFF Research Database (Denmark)
Hussain, Mumtaz; Yusupova, Tatiana
Let W(m,n;ψ−−) denote the set of ψ1,…,ψn-approximable points in Rmn. The classical Khintchine-Groshev theorem assumes a monotonicity condition on the approximating functions ψ−−. Removing monotonicity from the Khintchine-Groshev theorem is attributed to different authors for different cases of m...... and n. It can not be removed for m=n=1 as Duffin-Shcaeffer provided the counter example. We deal with the only remaining case m=2 and thereby remove all unnecessary conditions from the Khintchine-Groshev theorem....
Quantum voting and violation of Arrow's impossibility theorem
Bao, Ning; Yunger Halpern, Nicole
2017-06-01
We propose a quantum voting system in the spirit of quantum games such as the quantum prisoner's dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's impossibility theorem. Arrow's theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's theorem. A quantum version of majority rule, we show, violates this quantum Arrow conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.
Convergence theorems for certain classes of nonlinear mappings
International Nuclear Information System (INIS)
Chidume, C.E.
1992-01-01
Recently, Xinlong Weng announced a convergence theorem for the iterative approximation of fixed points of local strictly pseudo-contractive mappings in uniformly smooth Banach spaces, (Proc. Amer. Math. Soc. Vol.113, No.3 (1991) 727-731). An example is presented which shows that this theorem of Weng is false. Then, a convergence theorem is proved, in certain real Banach spaces, for approximation a solution of the inclusion f is an element of x + Tx, where T is a set-valued monotone operator. An explicit error estimate is also presented. (author). 26 refs
Direct and converse theorems the elements of symbolic logic
Gradshtein, I S; Stark, M; Ulam, S
1963-01-01
Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chap
A primer on Higgs boson low-energy theorems
International Nuclear Information System (INIS)
Dawson, S.; Haber, H.E.; California Univ., Santa Cruz, CA
1989-05-01
We give a pedagogical review of Higgs boson low-energy theorems and their applications in the study of light Higgs boson interactions with mesons and baryons. In particular, it is shown how to combine the chiral Lagrangian method with the Higgs low-energy theorems to obtain predictions for the interaction of Higgs bosons and pseudoscalar mesons. Finally, we discuss the relation between the low-energy theorems and a technique which makes use of the trace of the QCD energy-momentum tensor. 35 refs
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
Energy Technology Data Exchange (ETDEWEB)
Stenlund, Mikko, E-mail: mikko.stenlund@helsinki.fi [University of Helsinki, Department of Mathematics and Statistics (Finland)
2016-09-15
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
Markov's theorem and algorithmically non-recognizable combinatorial manifolds
International Nuclear Information System (INIS)
Shtan'ko, M A
2004-01-01
We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem
International Nuclear Information System (INIS)
Bohidar, H.; Berland, T.; Boger, F.; Joessang, T.; Feder, J.
1987-01-01
The development of a Multipass Fabry-Perot interforometer assembly for use in Rayleigh-Brillouin scattering experiments is reported. The optical alignment and the scattered signal data acquisition have been completely computerized. Digital scanning and alignment strategies of the Fabry-Perot resonator have been incorporated, which makes this instrument quite unique in this respect. The high contrast (∼10 10 ) and finesse (∼50) offered by this instrument makes it possible to detect Brillouin peaks from samples that have a small Brillouin scattering cross-section. As part of this system a compatible and precision sample chamber has been constructed, which has been designed to operate in the pressure and temperature ranges of 1-1000B and 20-150 o C, respectively. The cell has been constructed to be small and compact, but it still has a large heat capacity (∼250J/K) which ensures easy and stable temperature control of the liquid sample volume which has a size of 40 mm 3 . The achievable temperature stability is +-1mK and +-2mK for operating temperatures below and above 100 o C, respectively. The pressure stability is in the range of +-0.05B of the set pressure for pressures below 100B and it is +-0.05% for higher pressures up to 1000B. Both pressure and temperature are remotely monitored and controlled by a ND/100 computer. Special care has been taken in designing the optics of the pressure cell to ensure that both the primary and secondary reflections from the entrance window, as well as the main beam, go out of the scattering region in order to achieve higher signal-to-noise ratio in actual experiments
Flat deformation theorem and symmetries in spacetime
International Nuclear Information System (INIS)
Llosa, Josep; Carot, Jaume
2009-01-01
The flat deformation theorem states that given a semi-Riemannian analytic metric g on a manifold, locally there always exists a two-form F, a scalar function c, and an arbitrarily prescribed scalar constraint depending on the point x of the manifold and on F and c, say Ψ(c, F, x) = 0, such that the deformed metric η = cg - εF 2 is semi-Riemannian and flat. In this paper we first show that the above result implies that every (Lorentzian analytic) metric g may be written in the extended Kerr-Schild form, namely η ab := ag ab - 2bk (a l b) where η is flat and k a , l a are two null covectors such that k a l a = -1; next we show how the symmetries of g are connected to those of η, more precisely; we show that if the original metric g admits a conformal Killing vector (including Killing vectors and homotheties), then the deformation may be carried out in a way such that the flat deformed metric η 'inherits' that symmetry.
The Michaelis-Menten-Stueckelberg Theorem
Directory of Open Access Journals (Sweden)
Alexander N. Gorban
2011-05-01
Full Text Available We study chemical reactions with complex mechanisms under two assumptions: (i intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS and (ii they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE. Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events. This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.
Low energy theorems of hidden local symmetries
International Nuclear Information System (INIS)
Harada, Masayasu; Kugo, Taichiro; Yamawaki, Koichi.
1994-01-01
We prove to all orders of the loop expansion the low energy theorems of hidden local symmetries in four-dimensional nonlinear sigma models based on the coset space G/H, with G and H being arbitrary compact groups. Although the models are non-renormalizable, the proof is done in an analogous manner to the renormalization proof of gauge theories and two-dimensional nonlinear sigma models by restricting ourselves to the operators with two derivatives (counting a hidden gauge boson field as one derivative), i.e., with dimension 2, which are the only operators relevant to the low energy limit. Through loop-wise mathematical induction based on the Ward-Takahashi identity for the BRS symmetry, we solve renormalization equation for the effective action up to dimension-2 terms plus terms with the relevant BRS sources. We then show that all the quantum corrections to the dimension-2 operators, including the finite parts as well as the divergent ones, can be entirely absorbed into a re-definition (renormalization) of the parameters and the fields in the dimension-2 part of the tree-level Lagrangian. (author)
Quantum fluctuation theorems and power measurements
International Nuclear Information System (INIS)
Prasanna Venkatesh, B; Watanabe, Gentaro; Talkner, Peter
2015-01-01
Work in the paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system’s dynamics is frozen in the power measurement basis due to the quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics. (paper)
Subexponential estimates in Shirshov's theorem on height
International Nuclear Information System (INIS)
Belov, Aleksei Ya; Kharitonov, Mikhail I
2012-01-01
Suppose that F 2,m is a free 2-generated associative ring with the identity x m =0. In 1993 Zelmanov put the following question: is it true that the nilpotency degree of F 2,m has exponential growth? We give the definitive answer to Zelmanov's question by showing that the nilpotency class of an l-generated associative algebra with the identity x d =0 is smaller than Ψ(d,d,l), where Ψ(n,d,l)=2 18 l(nd) 3log 3 (nd)+13 d 2 . This result is a consequence of the following fact based on combinatorics of words. Let l, n and d≥n be positive integers. Then all words over an alphabet of cardinality l whose length is not less than Ψ(n,d,l) are either n-divisible or contain x d ; a word W is n-divisible if it can be represented in the form W=W 0 W 1 …W n so that W 1 ,...,W n are placed in lexicographically decreasing order. Our proof uses Dilworth's theorem (according to V.N. Latyshev's idea). We show that the set of not n-divisible words over an alphabet of cardinality l has height h 87 l·n 12log 3 n+48 . Bibliography: 40 titles.
Parsons, L. C.; Andrews, G. T.
2012-09-01
Pseudo-reflection geometry Brillouin spectroscopy can be used to probe acoustic wave dispersion approximately along the surface normal of a material system while avoiding the difficulties associated with specularly reflected light encountered in an ideal reflection configuration. As an example of its application, we show analytically that it can be used to determine both the refractive index and bulk acoustic mode velocities of optically-isotropic non-metallic materials and confirm the utility of the approach via a series of experiments on fused quartz, gallium phosphide, water, and porous silicon films.
Ko, Jae-Hyeon; Lee, Kwang-Sei; Ike, Yuji; Kojima, Seiji
2008-11-01
The acoustic waves propagating along the direction perpendicular to the (1 0 0) cleavage plane of aspirin crystal were investigated using micro-Brillouin spectroscopy from which C11, C55 and C66 were obtained. The temperature dependence of the longitudinal acoustic waves could be explained by normal anharmonic lattice models, while the transverse acoustic waves showed an abnormal increase in the hypersonic attenuation at low temperatures indicating their coupling to local remnant dynamics. The sound velocity as well as the attenuation of the longitudinal acoustic waves of glassy aspirin showed a substantial change at ˜235 K confirming a transition from glassy to supercooled liquid state in vitreous aspirin.
Brillouin lasing in single-mode tapered optical fiber with inscribed fiber Bragg grating array
Directory of Open Access Journals (Sweden)
S.M. Popov
2018-06-01
Full Text Available A tapered optical fiber has been manufactured with an array of fiber Bragg gratings (FBG inscribed during the drawing process. The total fiber peak reflectivity is 5% and the reflection bandwidth is ∼3.5 nm. A coherent frequency domain reflectometry has been applied for precise profiling of the fiber core diameter and grating reflectivity both distributed along the whole fiber length. These measurements are in a good agreement with the specific features of Brillouin lasing achieved in the semi-open fiber cavity configuration. Keywords: Tapered optical fibers, Fiber Bragg gratings, Random lasers
Directory of Open Access Journals (Sweden)
Romeo Bernini
2011-01-01
Full Text Available The structural strain measurement of tension and compression in a 4 m long concrete beam was demonstrated with a distributed fiber-optic sensor portable system based on Brillouin scattering. Strain measurements provided by the fiber-optic sensor permitted to detect the formation of a crack in the beam resulting from the external applied load. The sensor system is valuable for structural monitoring applications, enabling the long-term performance and health of structures to be efficiently monitored.
Observation of spin-wave dispersion in Nd-Fe-B magnets using neutron Brillouin scattering
International Nuclear Information System (INIS)
Ono, K.; Inami, N.; Saito, K.; Takeichi, Y.; Kawana, D.; Yokoo, T.; Itoh, S.; Yano, M.; Shoji, T.; Manabe, A.; Kato, A.; Kaneko, Y.
2014-01-01
The low-energy spin-wave dispersion in polycrystalline Nd-Fe-B magnets was observed using neutron Brillouin scattering (NBS). Low-energy spin-wave excitations for the lowest acoustic spin-wave mode were clearly observed. From the spin-wave dispersion, we were able to determine the spin-wave stiffness constant D sw (100.0 ± 4.9 meV.Å 2 ) and the exchange stiffness constant A (6.6 ± 0.3 pJ/m)
Barashkov, M. S.; Bel'dyugin, Igor'M.; Zolotarev, M. V.; Krymskiĭ, M. I.; Oshkin, S. P.; Umnov, A. F.; Kharchenko, M. A.
1990-06-01
The results are presented of an experimental investigation of a solid-state ring laser with a stimulated Brillouin scattering mirror and lasing initiated by a series of ~ 200-300 ns pulses of 1.06 μm wavelength. It is shown that this laser may be useful for the development of a source with radiation parameters controlled by an external signal (energy, transverse and time structure) and also of a low-threshold mirror for phase self-conjugation of radiation.
Brillouin lasing in single-mode tapered optical fiber with inscribed fiber Bragg grating array
Popov, S. M.; Butov, O. V.; Chamorovskiy, Y. K.; Isaev, V. A.; Kolosovskiy, A. O.; Voloshin, V. V.; Vorob'ev, I. L.; Vyatkin, M. Yu.; Mégret, P.; Odnoblyudov, M.; Korobko, D. A.; Zolotovskii, I. O.; Fotiadi, A. A.
2018-06-01
A tapered optical fiber has been manufactured with an array of fiber Bragg gratings (FBG) inscribed during the drawing process. The total fiber peak reflectivity is 5% and the reflection bandwidth is ∼3.5 nm. A coherent frequency domain reflectometry has been applied for precise profiling of the fiber core diameter and grating reflectivity both distributed along the whole fiber length. These measurements are in a good agreement with the specific features of Brillouin lasing achieved in the semi-open fiber cavity configuration.
A non linear ergodic theorem and application to a theorem of A. Pazy
International Nuclear Information System (INIS)
Djafari Rouhani, B.
1989-07-01
We prove that if (y n )n≥1 is a sequence in a real Hilbert space H such that for every non negative integer m the sequence (parallelΣ l =0 m y i +l parallel) i≥1 is non increasing, then: s n = 1/n Σ i=1 n y i converges strongly in H to the element of minimum norm in the closed convex hull of the sequence (y n ) n≥1 . We deduce a direct proof of a result containing a theorem of A. Pazy. (author). 27 refs
International Nuclear Information System (INIS)
Bolognini, Gabriele; Soto, Marcelo A; Di Pasquale, Fabrizio
2010-01-01
An investigation is performed of the possibility of achieving simultaneous distributed strain and temperature sensing based on hybrid Raman–Brillouin scattering with the use of multi-wavelength optical sources such as common Fabry–Perot (FP) lasers. By employing a self-heterodyne detection scheme based on a multi-wavelength optical local oscillator, the benefits of FP lasers are fully exploited, allowing for high-power Raman intensity measurements and a simultaneous high-accuracy detection of the Brillouin frequency shift parameter for each FP longitudinal mode. Experimental results point out a significant reduction of coherent Rayleigh noise, and highlight the enhanced performance in hybrid Raman–Brillouin sensing when using FP lasers; in particular using standard FP lasers at 1550 nm results in about 12 dB (7 dB) temperature (strain) accuracy improvement at 25 km sensing distance with respect to the use of standard distributed feedback lasers
International Nuclear Information System (INIS)
Halliwell, J.J.
2014-01-01
Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH inequalities are well-known to be necessary conditions, but Fine's theorem is the striking result that they are also sufficient conditions. Here two transparent and self-contained proofs of Fine's theorem are presented. The first is a physically motivated proof using an explicit local hidden variables model. The second is an algebraic proof which uses a representation of the probabilities in terms of correlation functions. - Highlights: • A discussion of the various approaches to proving Fine's theorem. • A new physically-motivated proof using a local hidden variables model. • A new algebraic proof. • A new form of the CHSH inequalities
A Coordinate-Based Proof of the Scallop Theorem
Ishimoto, Kenta; Yamada, Michio
2012-01-01
We reconsider fluid dynamics for a self-propulsive swimmer in Stokes flow. With an exact definition of deformation of a swimmer, a coordinate-based proof is first given to Purcell's scallop theorem including the body rotation.
Forest Carbon Uptake and the Fundamental Theorem of Calculus
Zobitz, John
2013-01-01
Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.
The power counting theorem for Feynman integrals with massless propagators
International Nuclear Information System (INIS)
Lowenstein, J.H.
2000-01-01
Dyson's power counting theorem is extended to the case where some of the mass parameters vanish. Weinberg's ultraviolet convergence conditions are supplemented by infrared convergence conditions which combined are sufficient for the convergence of Feynman integrals. (orig.)
The power counting theorem for Feynman integrals with massless propagators
International Nuclear Information System (INIS)
Lowenstein, J.H.
1975-01-01
Dyson's power counting theorem is extended to the case where some of the mass parameters vanish. Weinberg's ultraviolet convergence conditions are supplemented by infrared convergence conditions which combined are sufficient for the convergence of Feynman integrals. (orig.) [de
A divergence theorem for pseudo-Finsler spaces
Minguzzi, E.
2015-01-01
We study the divergence theorem on pseudo-Finsler spaces and obtain a completely Finslerian version for spaces having a vanishing mean Cartan torsion. This result helps to clarify the problem of energy-momentum conservation in Finsler gravity theories.
The Weinberg-Witten theorem on massless particles: an essay
International Nuclear Information System (INIS)
Loebbert, F.
2008-01-01
In this essay we deal with the Weinberg-Witten theorem which imposes limitations on massless particles. First we motivate a classification of massless particles given by the Poincare group as the symmetry group of Minkowski spacetime. We then use the fundamental structure of the background in the form of Poincare covariance to derive restrictions on charged massless particles known as the Weinberg-Witten theorem. We address possible misunderstandings in the proof of this theorem motivated by several papers on this topic. In the last section the consequences of the theorem are discussed. We treat it in the context of known particles and as a constraint for emergent theories. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
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.
Generalized Optical Theorem Detection in Random and Complex Media
Tu, Jing
The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar
A priori knowledge and the Kochen-Specker theorem
International Nuclear Information System (INIS)
Brunet, Olivier
2007-01-01
We introduce and formalize a notion of 'a priori knowledge' about a quantum system, and show some properties about this form of knowledge. Finally, we show that the Kochen-Specker theorem follows directly from this study
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.)
An Elementary Proof of the Polynomial Matrix Spectral Factorization Theorem
Ephremidze, Lasha
2010-01-01
A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.
Perron–Frobenius theorem for nonnegative multilinear forms and extensions
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.
Analogy to Derive an Extended Pythagorean Theorem to ''N'' Dimensions
Directory of Open Access Journals (Sweden)
Acosta-Robledo J.U.
2012-01-01
Full Text Available This article demonstrates that it is possible to extend the Pythagorean Theorem to ''N'' dimensions. This demonstration is mainly done based on linear algebra, especially in the vector product of ''N'' dimensions.
Quantum nonlocality and reality 50 years of Bell's theorem
Gao, Shan
2016-01-01
Description Contents Resources Courses About the Authors Combining twenty-six original essays written by an impressive line-up of distinguished physicists and philosophers of physics, this anthology reflects some of the latest thoughts by leading experts on the influence of Bell's theorem on quantum physics. Essays progress from John Bell's character and background, through studies of his main work, and on to more speculative ideas, addressing the controversies surrounding the theorem, and investigating the theorem's meaning and its deep implications for the nature of physical reality. Combined, they present a powerful comment on the undeniable significance of Bell's theorem for the development of ideas in quantum physics over the past 50 years. Questions surrounding the assumptions and significance of Bell's work still inspire discussion in the field of quantum physics. Adding to this with a theoretical and philosophical perspective, this balanced anthology is an indispensable volume for students and researc...
An imbedding theorem and its applications in degenerate elliptic equations
International Nuclear Information System (INIS)
Duong Minh Duc.
1988-06-01
We improve the Rellich-Kondrachov theorem and apply it to study strongly degenerate and singular elliptic equations. We obtain the maximum principle, Harnacks's inequality and global regularity for solutions of those equations. (author). 11 refs
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.
Probability densities and the radon variable transformation theorem
International Nuclear Information System (INIS)
Ramshaw, J.D.
1985-01-01
D. T. Gillespie recently derived a random variable transformation theorem relating to the joint probability densities of functionally dependent sets of random variables. The present author points out that the theorem can be derived as an immediate corollary of a simpler and more fundamental relation. In this relation the probability density is represented as a delta function averaged over an unspecified distribution of unspecified internal random variables. The random variable transformation is derived from this relation
A short list color proof of Grotzsch's theorem
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable.......We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable....
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
Metrical theorems on systems of small inhomogeneous linear forms
DEFF Research Database (Denmark)
Hussain, Mumtaz; Kristensen, Simon
In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed.......In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed....
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
A New Simple Approach for Entropy and Carnot Theorem
International Nuclear Information System (INIS)
Veliev, E. V.
2004-01-01
Entropy and Carnot theorem occupy central place in the typical Thermodynamics courses at the university level. In this work, we suggest a new simple approach for introducing the concept of entropy. Using simple procedure in TV plane, we proved that for reversible processes ∫dQ/T=0 and it is sufficient to define entropy. And also, using reversible processes in TS plane, we give an alternative simple proof for Carnot theorem
On the c-theorem in higher genus
International Nuclear Information System (INIS)
Espriu, D.; Mavromatos, N.E.
1990-01-01
We study the extension of the c-therorem to arbitrary genus Riemann surfaces. We analyze the breakdown of conformal invariance caused by the need of cutting off regions of moduli space to regulate divergences and argue how these can be absorbed in the bare couplings on the sphere. An extension of the c-theorem then follows. We also discuss the relationship between the c-theorem and the effective action when corrections from higher genera are accounted for. (orig.)
Some functional limit theorems for compound Cox processes
Energy Technology Data Exchange (ETDEWEB)
Korolev, Victor Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Institute of Informatics Problems FRC CSC RAS (Russian Federation); Chertok, A. V. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Euphoria Group LLC (Russian Federation); Korchagin, A. Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Kossova, E. V. [Higher School of Economics National Research University, Moscow (Russian Federation); Zeifman, Alexander I. [Vologda State University, S.Orlova, 6, Vologda (Russian Federation); Institute of Informatics Problems FRC CSC RAS, ISEDT RAS (Russian Federation)
2016-06-08
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
Some functional limit theorems for compound Cox processes
International Nuclear Information System (INIS)
Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.
2016-01-01
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
Cosmological constant, inflation and no-cloning theorem
Energy Technology Data Exchange (ETDEWEB)
Huang Qingguo, E-mail: huangqg@itp.ac.cn [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Science, Beijing 100190 (China); Lin Fengli, E-mail: linfengli@phy.ntnu.edu.tw [Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Department of Physics, National Taiwan Normal University, Taipei, 116, Taiwan (China)
2012-05-30
From the viewpoint of no-cloning theorem we postulate a relation between the current accelerated expansion of our universe and the inflationary expansion in the very early universe. It implies that the fate of our universe should be in a state with accelerated expansion. Quantitatively we find that the no-cloning theorem leads to a lower bound on the cosmological constant which is compatible with observations.
The Hellman-Feynman theorem at finite temperature
International Nuclear Information System (INIS)
Cabrera, A.; Calles, A.
1990-01-01
The possibility of a kind of Hellman-Feynman theorem at finite temperature is discussed. Using the cannonical ensembles, the derivative of the internal energy is obtained when it depends explicitly on a parameter. It is found that under the low temperature regime the derivative of the energy can be obtained as the statistical average of the derivative of the hamiltonian operator. The result allows to speak of the existence of the Hellman-Feynman theorem at finite temperatures (Author)
Generalized Perron--Frobenius Theorem for Nonsquare Matrices
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...
Generalized Panofsky-Wenzel theorem and hybrid coupling
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.
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
Factorization theorems in perturbative quantum field theory
International Nuclear Information System (INIS)
Date, G.D.
1982-01-01
This dissertation deals with factorization properties of Green functions and cross-sections in perturbation theory. It consists of two parts. Part I deals with the factorization theorem for the Drell-Yan cross-section. The new approach developed for this purpose is based upon a renormalization group equation with a generalized anomalous dimension. Using an alternate form of factorization for the Drell-Yan cross-section, derived in perturbation theory, a corresponding generalized anomalous dimension is defined, and explicit Feynman rules for its calculation are given. The resultant renormalization group equation is solved by a formal solution which is exhibited explicitly. Simple, explicit calculations are performed which verify Mueller's conjecture for the recovery of the usual parton model results for the Drell-Yan cross-section. The approach developed in this work offers a general framework to analyze the role played by the group factors in the cancellation of the soft divergences, and study their influence on the asymptotic behavior. Part II deals with factorization properties of the Green functions in position space. In this part, a Landau equation analysis is carried out for the singularities of the position space Green fucntions, in perturbation theory with the theta 4 interaction Lagrangian. A physical picture interpretation is given for the corresponding Landau equations. It is used to suggest a light-cone expansion. Using a power counting method, a formal derivation of the light-cone expansion for the two point function, the three point function and a product of two currents, is given without assuming a short distance expansion. Possible extensions to other theories is also considered
Physics of the ion acoustic wave driven by the stimulated Brillouin scattering instability
International Nuclear Information System (INIS)
Clayton, C.E.
1984-01-01
The ion acoustic wave excited in the stimulated Brillouin scattering (SBS) instability is probed via collective ruby-laser Thomson scattering in order to understand the low saturation level observed in the instability. Many of the features observed in the Brillouin backscattered CO 2 laser light from the underdense gas-target plasma are also observed in the Thomson scattered ruby light - from which it is learned that the ion acoustic wave grows exponentially and then saturates as the CO 2 pump power is increased. The primary advantage of the ruby Thomson scattering diagnostic is in its capability of providing simultaneous space and time resolved measurements of the ion wave amplitude. From these first such detailed measurements, it was found that the ion wave grows exponentially in space at a rate that agrees with the linear convective SBS theory. However, at higher pump powers, the ion wave saturates at an inferred amplitude of anti-n/n 0 approx. = 5 to 10%. Further increases in the pump power appear to result in an increase in the length over which the ion wave is saturated. A nearly constant SBS reflectivity in this saturated regime, however, suggests that the saturated ion wave does not contribute as much to the scattered power as would be expected from Bragg scattering theory. This apparent contradiction can be resolved if ion trapping is responsible for the saturation of the ion wave
Zhou, Wei; Sooryakumar, R.; King, Sean
2010-03-01
Low K dielectrics have predominantly replaced silicon dioxide as the interlayer dielectric material for interconnects in state of the art integrated circuits. To further reduce interconnect resistance-capacitance (RC) delays, additional reductions in the K for these low-K materials is being pursued by the introduction of controlled levels of porosity. The main challenge for porous low-K dielectrics is the substantial reduction in mechanical properties that is accompanied by the increased pore volume content needed to reduce K. We report on the application of the nondestructive Brillouin light scattering technique to monitor and characterize the mechanical properties of these porous films at thicknesses well below 200 nm that are pertinent to present applications. Observation of longitudinal and transverse standing wave acoustic resonances and the dispersion that accompany their transformation into traveling waves with finite in-plane wave vectors provides for the principal elastic constants that completely characterize the mechanical properties of these porous films. The mode amplitudes of the standing waves, their variation within the film, and the calculated Brillouin intensities account for most aspects of the spectra. The resulting elastic constants are compared with corresponding values obtained from other experimental techniques.
Brillouin light scattering studies of the mechanical properties of ultrathin low-k dielectric films
Link, A.; Sooryakumar, R.; Bandhu, R. S.; Antonelli, G. A.
2006-07-01
In an effort to reduce RC time delays that accompany decreasing feature sizes, low-k dielectric films are rapidly emerging as potential replacements for silicon dioxide (SiO2) at the interconnect level in integrated circuits. The main challenge in low-k materials is their substantially weaker mechanical properties that accompany the increasing pore volume content needed to reduce k. We show that Brillouin light scattering is an excellent nondestructive technique to monitor and characterize the mechanical properties of these porous films at thicknesses well below 200nm that are pertinent to present applications. Observation of longitudinal and transverse standing wave acoustic resonances and the dispersion that accompany their transformation into traveling waves with finite in-plane wave vectors provides for a direct measure of the principal elastic constants that completely characterize the mechanical properties of these ultrathin films. The mode amplitudes of the standing waves, their variation within the film, and the calculated Brillouin intensities account for most aspects of the spectra. We further show that the values obtained by this method agree well with other experimental techniques such as nanoindentation and picosecond laser ultrasonics.
Brillouin-Mandelstam spectroscopy of standing spin waves in a ferrite waveguide
Balinskiy, Michael; Kargar, Fariborz; Chiang, Howard; Balandin, Alexander A.; Khitun, Alexander G.
2018-05-01
This article reports results of experimental investigation of the spin wave interference over large distances in the Y3Fe2(FeO4)3 waveguide using Brillouin-Mandelstam spectroscopy. Two coherent spin waves are excited by the micro-antennas fabricated at the edges of the waveguide. The amplitudes of the input spin waves are adjusted to provide approximately the same intensity in the central region of the waveguide. The relative phase between the excited spin waves is controlled by the phase shifter. The change of the local intensity distribution in the standing spin wave is monitored using Brillouin-Mandelstam light scattering spectroscopy. Experimental data demonstrate the oscillation of the scattered light intensity depending on the relative phase of the interfering spin waves. The oscillations of the intensity, tunable via the relative phase shift, are observed as far as 7.5 mm away from the spin-wave generating antennas at room temperature. The obtained results are important for developing techniques for remote control of spin currents, with potential applications in spin-based memory and logic devices.
Virtual continuity of the measurable functions of several variables, and Sobolev embedding theorems
Vershik, Anatoly; Zatitskiy, Pavel; Petrov, Fedor
2013-01-01
Classical Luzin's theorem states that the measurable function of one variable is "almost" continuous. This is not so anymore for functions of several variables. The search of right analogue of the Luzin theorem leads to a notion of virtually continuous functions of several variables. This probably new notion appears implicitly in the statements like embeddings theorems and traces theorems for Sobolev spaces. In fact, it reveals their nature as theorems about virtual continuity. This notion is...
DEFF Research Database (Denmark)
Lorenzen, Michael Rodas; Noordegraaf, Danny; Nielsen, Carsten Vandel
2009-01-01
An increased gain in a fibre-optical parametric amplifier through suppression of stimulated Brillouin scattering is demonstrated by applying a temperature distribution along the fibre for a fixed phase modulation of the pump. The temperature distribution slightly impacts the gain spectrum....
Meijer, A.S.; Wijn, de A.S.; Peters, M.F.E.; Dam, N.J.; Water, van de W.
2010-01-01
We investigate coherent Rayleigh–Brillouin spectroscopy as an efficient process to measure the bulk viscosity of gases at gigahertz frequencies. Scattered spectral distributions are measured using a Fizeau spectrometer. We discuss the statistical error due to the fluctuating mode structure of the
The broad Brillouin doublet and CP of KTaO3, second sound vs. Two-phonon difference scattering
International Nuclear Information System (INIS)
Farhi, E.; Tagantsev, A.K.; Hehlen, B.; Courtens, E.; Boatner, L.A.
1999-01-01
Complete text of publication follows. Low-T Brillouin spectra of the incipient ferroelectric KTaO 3 exhibit a broad central peak (CP) (1), and some additional broad Brillouin doublet (BD) (2), that can both relate to phonon-density fluctuations (3). Starting from extensive new high resolution neutron scattering measurements in pure crystals, low lying phonon sheets were modelled in the central part of Brillouin zone. Such a parameterisation was then used in order to analyse those up-mentioned unusual features in teens of two-phonon mechanisms (4). Numerical evaluations show that transverse acoustic (TA) phonons whose normal damping is faster than the BD frequency (Γ DB > ω DB ) may produce hydrodynamic second sound (propagation of heat). Moreover, two-phonon difference scattering from low damping thermal TA phonons ((Γ DB DB ) can contribute to the spectra with either a sharp or a broader BD, depending on the phonon group velocity and phonon-sheet anisotropy. The position of the doublet is consistent with both mechanisms, but comparing the computed anisotropies with experimental Brillouin and neutron scattering data, one favours the second process. (author)
The design of an electron gun switchable between immersed and Brillouin flowa)
Becker, R.; Kester, O.
2012-02-01
An electron gun, which can be switched from immersed flow to Brillouin flow during operation, may have advantages for charge breeders as well as for electron beam ion sources and traps (EBISTs). For EBISTs this allows to change the current density according to the repetition frequency and charge state, for charge breeders and EBISTs a lower current density in immersed flow provides higher acceptance for injected ions, while the higher current density in Brillouin flow results in shorter breeding times and a lower emittance for the extracted beam. Therefore, we have designed such a gun for an EBIS with 5 T central magnetic field and without the use of iron and moving the gun. The gun was placed in the axial fringing field of the 5 T solenoid in such a position that a gate valve can be placed between the gun and the cryostat to allow for simple maintenance. The field at the cathode surface turned out to be only 0.05 T, which is not enough to focus 50 A/cm2 at a few kV. However, if a small normal conducting solenoid is placed over the vacuum tube in position of the gun, a field of 0.1 T may be obtained. With this the use of LaB6 as cathode material results in a magnetic compression of 44 and therewith in a focused current density in the trap region of more than 2000 A/cm2. By reversing the current in the gun solenoid the cathode field can easily compensated to zero. By proper design of the electrodes and the compression region, the gun will be able to deliver a beam in Brillouin flow. While this is interesting by itself - remember the "super-compression" reported on CRYEBIS-I - any magnetic field between zero and the value for immersed flow will result in an electron beam with a wide range of adjustable high current densities. The design tools used have been INTMAG(C) for the calculation of magnetic fields, EGN2(C) for the simulation of the gun and ANALYSE(C) for detailed analysis of the results (for more information see www.egun-igun.com).
The design of an electron gun switchable between immersed and Brillouin flow.
Becker, R; Kester, O
2012-02-01
An electron gun, which can be switched from immersed flow to Brillouin flow during operation, may have advantages for charge breeders as well as for electron beam ion sources and traps (EBISTs). For EBISTs this allows to change the current density according to the repetition frequency and charge state, for charge breeders and EBISTs a lower current density in immersed flow provides higher acceptance for injected ions, while the higher current density in Brillouin flow results in shorter breeding times and a lower emittance for the extracted beam. Therefore, we have designed such a gun for an EBIS with 5 T central magnetic field and without the use of iron and moving the gun. The gun was placed in the axial fringing field of the 5 T solenoid in such a position that a gate valve can be placed between the gun and the cryostat to allow for simple maintenance. The field at the cathode surface turned out to be only 0.05 T, which is not enough to focus 50 A∕cm(2) at a few kV. However, if a small normal conducting solenoid is placed over the vacuum tube in position of the gun, a field of 0.1 T may be obtained. With this the use of LaB(6) as cathode material results in a magnetic compression of 44 and therewith in a focused current density in the trap region of more than 2000 A∕cm(2). By reversing the current in the gun solenoid the cathode field can easily compensated to zero. By proper design of the electrodes and the compression region, the gun will be able to deliver a beam in Brillouin flow. While this is interesting by itself--remember the "super-compression" reported on CRYEBIS-I--any magnetic field between zero and the value for immersed flow will result in an electron beam with a wide range of adjustable high current densities. The design tools used have been INTMAG(C) for the calculation of magnetic fields, EGN2(C) for the simulation of the gun and ANALYSE(C) for detailed analysis of the results (for more information see www.egun-igun.com).
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.
Formalization of the Integral Calculus in the PVS Theorem Prover
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.
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.
Generalized Fourier slice theorem for cone-beam image reconstruction.
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).
Energy Technology Data Exchange (ETDEWEB)
Gubbiotti, G.; Tacchi, S. [Istituto Officina dei Materiali del Consiglio Nazionale delle Ricerche (IOM-CNR), Sede di Perugia, c/o Dipartimento di Fisica e Geologia, Via A. Pascoli, I-06123 Perugia (Italy); Montoncello, F.; Giovannini, L. [Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via G. Saragat 1, I-44122 Ferrara (Italy); Madami, M.; Carlotti, G. [Dipartimento di Fisica e Geologia, Università di Perugia, Via A. Pascoli, I-06123 Perugia (Italy); Ding, J.; Adeyeye, A. O. [Information Storage Materials Laboratory, Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576 (Singapore)
2015-06-29
The Brillouin light scattering technique has been exploited to study the angle-resolved spin wave band diagrams of squared Permalloy antidot lattice. Frequency dispersion of spin waves has been measured for a set of fixed wave vector magnitudes, while varying the wave vector in-plane orientation with respect to the applied magnetic field. The magnonic band gap between the two most dispersive modes exhibits a minimum value at an angular position, which exclusively depends on the product between the selected wave vector magnitude and the lattice constant of the array. The experimental data are in very good agreement with predictions obtained by dynamical matrix method calculations. The presented results are relevant for magnonic devices where the antidot lattice, acting as a diffraction grating, is exploited to achieve multidirectional spin wave emission.
International Nuclear Information System (INIS)
Hao Yun-Qi; Ye Qing; Pan Zheng-Qing; Cai Hai-Wen; Qu Rong-Hui
2014-01-01
The digital coherent detection technique has been investigated without any frequency-scanning device in the Brillouin optical time domain reflectometry (BOTDR), where the simplex pulse codes are applied in the sensing system. The time domain signal of every code sequence is collected by the data acquisition card (DAQ). A shift-averaging technique is applied in the frequency domain for the reason that the local oscillator (LO) in the coherent detection is fix-frequency deviated from the primary source. With the 31-bit simplex code, the signal-to-noise ratio (SNR) has 3.5-dB enhancement with the same single pulse traces, accordant with the theoretical analysis. The frequency fluctuation for simplex codes is 14.01 MHz less than that for a single pulse as to 4-m spatial resolution. The results are believed to be beneficial for the BOTDR performance improvement. (general)
Effect of diffraction on stimulated Brillouin scattering from a single laser hot spot
International Nuclear Information System (INIS)
Eliseev, V.V.; Rozmus, W.; Tikhonchuk, V.T.; Capjack, C.E.
1996-01-01
A single laser hot spot in an underdense plasma is represented as a focused Gaussian laser beam. Stimulated Brillouin scattering (SBS) from such a Gaussian beam with small f/numbers 2-4 has been studied in a three-dimensional slab geometry. It is shown that the SBS reflectivity from a single laser hot spot is much lower than that predicted by a simple three wave coupling model because of the diffraction of the scattered light from the spatially localized ion acoustic wave. SBS gain per one Rayleigh length of the incident laser beam is proposed as a quantitative measure of this effect. Diffraction-limited SBS from a randomized laser beam is also discussed. copyright 1996 American Institute of Physics
A simple and convenient set-up for high-temperature Brillouin light scattering
International Nuclear Information System (INIS)
Guerette, Michael; Huang Liping
2012-01-01
An emulated platelet geometry (or reflection-induced platelet geometry) is employed to collect photons scattered from both longitudinal and transverse acoustic waves travelling within a bulk transparent sample sitting on a reflective Pt plate. Temperature of the sample was controlled with a Linkam TS1500 optical furnace (maximum temperature of 1500 °C). This simple and convenient set-up allows a full determination of elastic constants of transparent materials in situ as a function of temperature from Brillouin light scattering. Structural information can be gained at the same time by guiding the scattered light into a Raman spectrometer using a flipping mirror or a beam splitter. We will demonstrate the applications of this set-up in transparent inorganic glasses, but it can be easily extended to any other transparent materials, either crystalline or amorphous in nature. (paper)
Brillouin light scattering study of spin waves in NiFe/Co exchange spring bilayer films
Energy Technology Data Exchange (ETDEWEB)
Haldar, Arabinda; Banerjee, Chandrima; Laha, Pinaki; Barman, Anjan, E-mail: abarman@bose.res.in [Thematic Unit of Excellence on Nanodevice Technology, Department of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Kolkata 700098 (India)
2014-04-07
Spin waves are investigated in Permalloy(Ni{sub 80}Fe{sub 20})/Cobalt(Co) exchange spring bilayer thin films using Brillouin light scattering (BLS) experiment. The magnetic hysteresis loops measured by magneto-optical Kerr effect show a monotonic decrease in coercivity of the bilayer films with increasing Py thickness. BLS study shows two distinct modes, which are modelled as Damon-Eshbach and perpendicular standing wave modes. Linewidths of the frequency peaks are found to increase significantly with decreasing Py layer thickness. Interfacial roughness causes to fluctuate exchange coupling at the nanoscale regimes and the effect is stronger for thinner Py films. A quantitative analysis of the magnon linewidths shows the presence of strong local exchange coupling field which is much larger compared to macroscopic exchange field.
Temperature dependence of Brillouin light scattering spectra of acoustic phonons in silicon
International Nuclear Information System (INIS)
Olsson, Kevin S.; Klimovich, Nikita; An, Kyongmo; Sullivan, Sean; Weathers, Annie; Shi, Li; Li, Xiaoqin
2015-01-01
Electrons, optical phonons, and acoustic phonons are often driven out of local equilibrium in electronic devices or during laser-material interaction processes. The need for a better understanding of such non-equilibrium transport processes has motivated the development of Raman spectroscopy as a local temperature sensor of optical phonons and intermediate frequency acoustic phonons, whereas Brillouin light scattering (BLS) has recently been explored as a temperature sensor of low-frequency acoustic phonons. Here, we report the measured BLS spectra of silicon at different temperatures. The origins of the observed temperature dependence of the BLS peak position, linewidth, and intensity are examined in order to evaluate their potential use as temperature sensors for acoustic phonons
Random phase plate hot spots and their effect on stimulated Brillouin backscatter and self-focusing
International Nuclear Information System (INIS)
Rose, H.A.
1995-01-01
Laser hot spots, as determined by Random Phase Plate (RPP) hot spots, control the critical value of the average intensity, I c , at which there is a rapid onset of stimulated scatter in the strongly damped convective regime of three wave parametric instabilities. For the case of stimulated Brillouin backscatter in a long scale length plasma, nascent hot spot ponderomotive self-focusing is shown to reduce the value of I c in the regime of very strongly damped acoustic waves. RPP hot spots have two, intrinsically nonlinear, thresholds for ponderomotive self-focusing. Large intensity amplifications occur in the hot spot neighborhood when the hot spot power exceeds a certain critical power, P c , which is independent of the optic's f number, F. When the second, F-dependent, hot spot power threshold is exceeded, a filament emerges from the far side of the hot spot, whose extent grows erratically in time
Sancho, J; Primerov, N; Chin, S; Antman, Y; Zadok, A; Sales, S; Thévenaz, L
2012-03-12
We propose and experimentally demonstrate new architectures to realize multi-tap microwave photonic filters, based on the generation of a single or multiple dynamic Brillouin gratings in polarization maintaining fibers. The spectral range and selectivity of the proposed periodic filters is extensively tunable, simply by reconfiguring the positions and the number of dynamic gratings along the fiber respectively. In this paper, we present a complete analysis of three different configurations comprising a microwave photonic filter implementation: a simple notch-type Mach-Zehnder approach with a single movable dynamic grating, a multi-tap performance based on multiple dynamic gratings and finally a stationary grating configuration based on the phase modulation of two counter-propagating optical waves by a common pseudo-random bit sequence (PRBS).
Stimulated Brillouin scattering continuous wave phase conjugation in step-index fiber optics.
Massey, Steven M; Spring, Justin B; Russell, Timothy H
2008-07-21
Continuous wave (CW) stimulated Brillouin scattering (SBS) phase conjugation in step-index optical fibers was studied experimentally and modeled as a function of fiber length. A phase conjugate fidelity over 80% was measured from SBS in a 40 m fiber using a pinhole technique. Fidelity decreases with fiber length, and a fiber with a numerical aperture (NA) of 0.06 was found to generate good phase conjugation fidelity over longer lengths than a fiber with 0.13 NA. Modeling and experiment support previous work showing the maximum interaction length which yields a high fidelity phase conjugate beam is inversely proportional to the fiber NA(2), but find that fidelity remains high over much longer fiber lengths than previous models calculated. Conditions for SBS beam cleanup in step-index fibers are discussed.
Interaction between stimulated Brillouin scattering and the filamentation instability in plasmas
International Nuclear Information System (INIS)
Frycz, P.; Rozmus, W.; Samson, J.; Tikhonchuk, V.T.; Rankin, R.
1992-01-01
The set of equations describing Stimulated Brillouin Scattering (SBS) and the Filamentation Instability (FI) are solved numerically for a spatially periodic system. For short systems (a few wavelengths of the incident light) SBS backscatter modes and the filamentation instability are observed as expected but in addition there are some puzzling features. SBS starts after a significant time delay, is localized, and focuses during its evolution. These features disappear for a long (tens of wavelengths) system for which sidescatter modes are dominant. The energy is dispersed among many non-coherent modes in such a system and none of the modes is strong enough to drive filamentation. The analytic explanation of the ''puzzling features'' is given. (Author)
Inhibition of stimulated Raman scattering due to the excitation of stimulated Brillouin scattering
Zhao, Yao; Yu, Lu-Le; Weng, Su-Ming; Ren, Chuang; Liu, Chuan-Sheng; Sheng, Zheng-Ming
2017-09-01
The nonlinear coupling between stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) of intense laser in underdense plasma is studied theoretically and numerically. Based upon the fluid model, their coupling equations are derived, and a threshold condition of plasma density perturbations due to SBS for the inhibition of SRS is given. Particle-in-cell simulations show that this condition can be achieved easily by SBS in the so-called fluid regime with kLλDDebye length [Kline et al., Phys. Plasmas 13, 055906 (2006)]. SBS can reduce the saturation level of SRS and the temperature of electrons in both homogeneous and inhomogeneous plasma. Numerical simulations also show that this reduced SRS saturation is retained even if the fluid regime condition mentioned above is violated at a later time due to plasma heating.
Temperature Dependence of the Rayleigh Brillouin Spectrum Linewidth in Air and Nitrogen
Directory of Open Access Journals (Sweden)
Kun Liang
2017-06-01
Full Text Available The relation between spontaneous Rayleigh Brillouin (SRB spectrum linewidth, gas temperature, and pressure are analyzed at the temperature range from 220 to 340 K and the pressure range from 0.1 to 1 bar, covering the stratosphere and troposphere relevant for the Earth’s atmosphere and for atmospheric Lidar missions. Based on the analysis, a model retrieving gas temperature from directly measured linewidth is established and the accuracy limitations are estimated. Furthermore, some experimental data of air and nitrogen are used to verify the accuracy of the model. As the results show, the retrieved temperature shows good agreement with the reference temperature, and the absolute difference is less than 3 K, which indicates that this method provides a fruitful tool in satellite retrieval to extract the gaseous properties of atmospheres on-line by directly measuring the SRB spectrum linewidth.
International Nuclear Information System (INIS)
Andreev, N.E.; Gorbunov, L.M.; Tarakanov, S.V.; Zykov, A.I.
1993-01-01
The space--time evolution of ponderomotive self-focusing of electromagnetic beams in a plasma is investigated. The quasineutral, hydrodynamic plasma response to the ponderomotive force is considered. The set of coupled quasioptic and acoustic equations is solved both analytically and numerically for slab and cylindrical beams. It is shown that the transient process of self-focusing has the form of a nonlinear wave propagating along the beam axis from boundary into the interior of a plasma with velocity considerably higher than the ion-sound velocity. Mutual dynamics of self-focusing and stimulated Brillouin backscattering (SBBS) is computed. It is shown that self-focusing results in the high intensity periodical bursts of SBBS. However, the time average level of scattered radiation is quite low
Performance Investigation of Millimeter Wave Generation Reliant on Stimulated Brillouin Scattering
Tickoo, Sheetal; Gupta, Amit
2018-04-01
In this work, photonic method of generating the millimeter waves has been done based on Brillouin scattering effect in optical fiber. Here different approaches are proposed to get maximum frequency shift in mm-wave region using only pumps, radio signals with Mach-Zehnder modulator. Moreover for generated signal validation, signals modulated and send to both wired and wireless medium in optical domain. It is observed that maximum shift of 300 GHz is realized using 60 GHz input sine wave. Basically a frequency doubler is proposed which double shift of input frequency and provide better SNR. For the future generation network system, the generation of millimeter waves makes them well reliable for the transmission of the data.
Energy Technology Data Exchange (ETDEWEB)
Mueller, U; Bactavatchalou, R; Baller, J; Philipp, M; Sanctuary, R; Zielinski, B; Krueger, J K [Laboratoire de Physique des Materiaux, Universite du Luxembourg, 162A, Avenue de la Faiencerie, L-1115 Luxembourg (Luxembourg); Alnot, P; Possart, W [Laboratoire Europeen de Recherche Universitaire Saarland-Lorraine (Germany)], E-mail: mail@tauron.de
2008-02-15
Reactive network forming polymer systems like epoxies are of huge technological interest because of their adhesive properties based on specific interactions with a large variety of materials. These specific interactions alter the morphology of the epoxy within areas determined by the correlation length of these interactions. The changed morphology leads to interphases with altered (mechanical) properties. Besides these surface-induced interphases, bulk interphases do occur due to segregation, crystallization, diffusion, etc. A new experimental technique to characterize such mechanical interphases is {mu}-Brillouin spectroscopy ({mu}-BS). With {mu}-BS, we studied interphases and their formation in epoxies due to segregation of the constituent components and due to selective diffusion of one component. In the latter case, we will demonstrate the influence of changing the boundary conditions of the diffusion process on the shape of the interphase.
Method for pulse control in a laser including a stimulated brillouin scattering mirror system
Dane, C. Brent; Hackel, Lloyd; Harris, Fritz B.
2007-10-23
A laser system, such as a master oscillator/power amplifier system, comprises a gain medium and a stimulated Brillouin scattering SBS mirror system. The SBS mirror system includes an in situ filtered SBS medium that comprises a compound having a small negative non-linear index of refraction, such as a perfluoro compound. An SBS relay telescope having a telescope focal point includes a baffle at the telescope focal point which blocks off angle beams. A beam splitter is placed between the SBS mirror system and the SBS relay telescope, directing a fraction of the beam to an alternate beam path for an alignment fiducial. The SBS mirror system has a collimated SBS cell and a focused SBS cell. An adjustable attenuator is placed between the collimated SBS cell and the focused SBS cell, by which pulse width of the reflected beam can be adjusted.
Surface acoustic waves and elastic constants of InN epilayers determined by Brillouin scattering
Energy Technology Data Exchange (ETDEWEB)
Jimenez-Rioboo, R.J.; Prieto, C. [Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, Madrid (Spain); Cusco, R.; Domenech-Amador, N.; Artus, L. [Institut Jaume Almera, Consell Superior d' Investigacions Cientifiques (CSIC), Lluis Sole i Sabaris s.n., Barcelona, Catalonia (Spain); Yamaguchi, T.; Nanishi, Y. [Faculty of Science and Engineering, Ritsumeikan University, Noji-Higashi, Kusatsu, Shiga (Japan)
2012-06-15
The surface acoustic wave velocity in InN has been experimentally determined by means of Brillouin scattering experiments on c - and m -face epilayers. From simulations based on the Green's function formalism we determine the shear elastic constants c{sub 66} and c{sub 44} and propose a complete set of elastic constants for wurtzite InN. The analysis of the sagittal and azimuthal dependence of the surface acoustic wave velocity indicates a slightly different elastic behavior of the m -face sample that basically affects the c{sub 44} elastic constant. (copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Quantum de Finetti theorem in phase-space representation
International Nuclear Information System (INIS)
Leverrier, Anthony; Cerf, Nicolas J.
2009-01-01
The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
Fourier diffraction theorem for diffusion-based thermal tomography
International Nuclear Information System (INIS)
Baddour, Natalie
2006-01-01
There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging
More on Weinberg's no-go theorem in quantum gravity
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.
Noncommutative gauge field theories: A no-go theorem
International Nuclear Information System (INIS)
Chaichian, M.; Tureanu, A.; Presnajder, P.; Sheikh-Jabbari, M.M.
2001-06-01
Studying the mathematical structure of the noncommutative groups in more detail, we prove a no-go theorem for the noncommutative gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local noncommutative u(n) algebra only admits the irreducible nxn matrix-representation. Hence the gauge fields, as elements of the algebra, are in nxn matrix form, while the matter fields can only be either in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple group factors, the matter fields can transform nontrivially under at most two noncommutative group factors. In other words, the matter fields cannot carry more than two simple noncommutative gauge group charges. This no-go theorem imposes strong restrictions on the construction of the noncommutative version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED. (author)
Deviations from Wick's theorem in the canonical ensemble
Schönhammer, K.
2017-07-01
Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.
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
Out-of-time-order fluctuation-dissipation theorem
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.
Kochen-Specker theorem studied with neutron interferometer.
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.
Limit theorems for multi-indexed sums of random variables
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 ...
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
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.
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.
Hadronic interactions of the J/ψ and Adler's theorem
International Nuclear Information System (INIS)
Bourque, A.; Gale, C.; Haglin, K.L.
2004-01-01
Effective Lagrangian models of charmonium have recently been used to estimate dissociation cross sections with light hadrons. Detailed study of the symmetry properties reveals possible shortcomings relative to chiral symmetry. We therefore propose a new Lagrangian and point out distinguishing features amongst the different approaches. Moreover, we test the models against Adler's theorem, which requires, in the appropriate limit, the decoupling of pions from the theory for the normal parity sector. Using the newly proposed Lagrangian, which exhibits SU L (N f )xSU R (N f ) symmetry and complies with Adler's theorem, we find dissociation cross sections with pions that are reduced in an energy-dependent way, with respect to cases where the theorem is not fulfilled
Zamolodchikov's c-theorem and string effective actions
International Nuclear Information System (INIS)
Mavromatos, N.E.; Miramontes, J.L.
1988-01-01
Zamolodchikov's c-theorem for 2D renormalisable field theories is presented in a way which allows for a straightforward application to the case of bosonic σ-models. As a consistency check in the latter case, the Curci-Paffuti relation is rederived. It is also shown that the 'metric' in coupling constant space in this case is a c-number function of the backgrounds. Attempts to derive off-shell functional relations between the Weyl anomaly coefficients and field variations of string effective actions, compatible with the c-theorem, are discussed by emphasising the necessity of performing explicit perturbative calculations in order to arrive at definite conclusions. Comments concerning the extension of the c-theorem to the case of supersymmetric and heterotic σ-models are also made. (orig.)
Towards a Novel no-hair Theorem for Black Holes
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.
Bayesian approach to the analysis of neutron Brillouin scattering data on liquid metals
De Francesco, A.; Guarini, E.; Bafile, U.; Formisano, F.; Scaccia, L.
2016-08-01
When the dynamics of liquids and disordered systems at mesoscopic level is investigated by means of inelastic scattering (e.g., neutron or x ray), spectra are often characterized by a poor definition of the excitation lines and spectroscopic features in general and one important issue is to establish how many of these lines need to be included in the modeling function and to estimate their parameters. Furthermore, when strongly damped excitations are present, commonly used and widespread fitting algorithms are particularly affected by the choice of initial values of the parameters. An inadequate choice may lead to an inefficient exploration of the parameter space, resulting in the algorithm getting stuck in a local minimum. In this paper, we present a Bayesian approach to the analysis of neutron Brillouin scattering data in which the number of excitation lines is treated as unknown and estimated along with the other model parameters. We propose a joint estimation procedure based on a reversible-jump Markov chain Monte Carlo algorithm, which efficiently explores the parameter space, producing a probabilistic measure to quantify the uncertainty on the number of excitation lines as well as reliable parameter estimates. The method proposed could turn out of great importance in extracting physical information from experimental data, especially when the detection of spectral features is complicated not only because of the properties of the sample, but also because of the limited instrumental resolution and count statistics. The approach is tested on generated data set and then applied to real experimental spectra of neutron Brillouin scattering from a liquid metal, previously analyzed in a more traditional way.
Robust, Brillouin Active Embedded Fiber-Is-The-Sensor System in Smart Composite Structures
Yu, Chung
1996-01-01
Extensive review of our proposed sensing scheme, based mainly on the forward Guided Acoustic Wave Brillouin Scattering (GAWBS) with backward stimulated Brillouin scattering (sBs) as an auxiliary scheme for system fault tolerance has been completed during this project period. This preliminary study is conducted for a number of reasons. The most significant reasons lie in the essential capability of the system to measure temperature and pressure. These two measurands have been proposed to be sensed by sBs in our proposal. Temperature and pressure/strain are important measurands in structural monitoring, so that the effectiveness of sensing by sBs needs to be further examined. It has been pointed out initially that sBs shift will be dependent on temperature and pressure/strain simultaneously. The shift versus temperature or strain is linear. Now, the question is how can these two measurands be separated when sBs is used to sense an environment, in which both temperature and strain are changing simultaneously. Typical sBs shift plotted versus strain and varying temperature is shown in Fig. 1. As is clear, a fiber initially stressed will relax with rising temperature. This is verified by a displacement to the right with rising temperature of the sBs shift vs strain curves in the figure. A way to circumvent this ambiguity is by employing two fibers, one pre-stressed and the other is a free fiber. The latter will measure temperature and subtracting data in the latter fiber from those of the former will give us net strain readings. This is a laborious approach, since it involves the use of two identical fibers, and this is hard to accomplish, especially when many sensors are needed. Additional multiplexing of the data stream for data subtraction becomes a necessity.
Stimulated Brillouin backscattering and magnetic field generation in laser-produced plasmas
International Nuclear Information System (INIS)
Bawa'aneh, M.S.
1999-01-01
This thesis is concerned with aspects of laser-plasma interactions related to fusion reactions; in particular thermoelectric magnetic field generation around a hole dug in plasma by intense laser beams, and stimulated Brillouin back scattering (SBBS) from plasmas containing hot spots. A hole, of the size of the laser focal spot, is dug in the plasma when illuminated by intense laser if the laser pressure exceeds the plasma thermal pressure. This hole is found to have steep, radial density gradients. My first concern arose from the prediction that magnetic fields might be generated around the hole-plasma interface in places where the steep density gradients overlap with the non-aligned temperature gradients. When a high-power laser beam is focused on a solid pellet, plasma is formed at the surface. In order to create conditions for thermonuclear reactions in the interior of the pellet, an effective deposition of the laser energy to thermal energy of the pellet via laser-plasma coupling is necessary. When light irradiates a plasma collective processes occur, which can either enhance or reduce the light absorption. For a better understanding of the fusion problem a knowledge of the nature of these collective processes and of the fraction of light reflected from the plasma modes is required. Local hot spots seen experimentally lead to higher gain levels of scattered light. These local temperature inhomogeneities could lead to non-equilibrium distributions, which result in a free energy leading to some interesting phenomena in plasma. In the second part of the thesis stimulated Brillouin back scattering from an ion acoustic mode in a hot spot is studied. Temperature inhomogeneities lead to an ion acoustic instability, and to higher levels of SBBS gain, which leads to lower thresholds for the same electron to ion temperature ratios. This could be the answer for the observed high levels of scattering from hot spots. (author)
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
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....
Reasoning by analogy as an aid to heuristic theorem proving.
Kling, R. E.
1972-01-01
When heuristic problem-solving programs are faced with large data bases that contain numbers of facts far in excess of those needed to solve any particular problem, their performance rapidly deteriorates. In this paper, the correspondence between a new unsolved problem and a previously solved analogous problem is computed and invoked to tailor large data bases to manageable sizes. This paper outlines the design of an algorithm for generating and exploiting analogies between theorems posed to a resolution-logic system. These algorithms are believed to be the first computationally feasible development of reasoning by analogy to be applied to heuristic theorem proving.
Refinement of Representation Theorems for Context-Free Languages
Fujioka, Kaoru
In this paper, we obtain some refinement of representation theorems for context-free languages by using Dyck languages, insertion systems, strictly locally testable languages, and morphisms. For instance, we improved the Chomsky-Schützenberger representation theorem and show that each context-free language L can be represented in the form L = h (D ∩ R), where D is a Dyck language, R is a strictly 3-testable language, and h is a morphism. A similar representation for context-free languages can be obtained, using insertion systems of weight (3, 0) and strictly 4-testable languages.
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)
Strong limit theorems in noncommutative L2-spaces
Jajte, Ryszard
1991-01-01
The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.
Vanishing theorems and effective results in algebraic geometry
International Nuclear Information System (INIS)
Demailly, J.P.; Goettsche, L.; Lazarsfeld, R.
2001-01-01
The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks
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
Poisson's theorem and integrals of KdV equation
International Nuclear Information System (INIS)
Tasso, H.
1978-01-01
Using Poisson's theorem it is proved that if F = integral sub(-infinity)sup(+infinity) T(u,usub(x),...usub(n,t))dx is an invariant functional of KdV equation, then integral sub(-infinity)sup(+infinity) delta F/delta u dx integral sub(-infinity)sup(+infinity) delta T/delta u dx is also an invariant functional. In the case of a polynomial T, one finds in a simple way the known recursion ΔTr/Δu = Tsub(r-1). This note gives an example of the usefulness of Poisson's theorem. (author)
Testing subleading multiple soft graviton theorem for CHY prescription
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.
A variational proof of Thomson's theorem
Energy Technology Data Exchange (ETDEWEB)
Fiolhais, Miguel C.N., E-mail: miguel.fiolhais@cern.ch [Department of Physics, City College of the City University of New York, 160 Convent Avenue, New York, NY 10031 (United States); Department of Physics, New York City College of Technology, 300 Jay Street, Brooklyn, NY 11201 (United States); LIP, Department of Physics, University of Coimbra, 3004-516 Coimbra (Portugal); Essén, Hanno [Department of Mechanics, Royal Institute of Technology (KTH), Stockholm SE-10044 (Sweden); Gouveia, Tomé M. [Cavendish Laboratory, 19 JJ Thomson Avenue, Cambridge CB3 0HE (United Kingdom)
2016-08-12
Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.
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
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.
A generalized integral fluctuation theorem for general jump processes
International Nuclear Information System (INIS)
Liu Fei; Ouyang Zhongcan; Luo Yupin; Huang Mingchang
2009-01-01
Using the Feynman-Kac and Cameron-Martin-Girsanov formulae, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Unlike the latter approach that has been extensively employed in the existing literature, our approach can naturally bring out the definition of a time reversal of a Markovian stochastic system. Additionally, we find that the robust GIFT usually does not result in a detailed fluctuation theorem. (fast track communication)
Twelve years before the quantum no-cloning theorem
Ortigoso, Juan
2018-03-01
The celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Found. Phys. 1, 23-33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park's demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning.
Two theorems on flat space-time gravitational theories
International Nuclear Information System (INIS)
Castagnino, M.; Chimento, L.
1980-01-01
The first theorem states that all flat space-time gravitational theories must have a Lagrangian with a first term that is an homogeneous (degree-1) function of the 4-velocity usup(i), plus a functional of nsub(ij)usup(i)usup(j). The second theorem states that all gravitational theories that satisfy the strong equivalence principle have a Lagrangian with a first term gsub(ij)(x)usup(i)usup(j) plus an irrelevant term. In both cases the theories must issue from a unique variational principle. Therefore, under this condition it is impossible to find a flat space-time theory that satisfies the strong equivalence principle. (author)
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
Vanishing theorems and effective results in algebraic geometry
Energy Technology Data Exchange (ETDEWEB)
Demailly, J P [Universite de Grenoble (France); Goettsche, L [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Lazarsfeld, R [University of Michigan (United States)
2001-12-15
The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks.
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...
Natural relations and Appelquist-Carazzone decoupling theorem
International Nuclear Information System (INIS)
Grzadkowski, B.; Krawczyk, P.; Pokorski, S.
1984-01-01
It is pointed out that in some cases violation of the Appelquist-Carazzone decoupling theorem in spontaneously broken gauge theories is related to the presence in such theories of the so-called natural zeroth-order relations. In this context heavy-fermion effects in the Glashow-Salam-Weinberg model are discussed
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:
Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos
Boozer, A. D.
2011-01-01
We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…
Quantum golden field theory - Ten theorems and various conjectures
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
Ten theorems and few conjectures related to quantum field theory as applied to high energy physics are presented. The work connects classical quantum field theory with the golden mean renormalization groups of non-linear dynamics and E-Infinity theory
The CAP Theorem Versus Databases with Relaxed ACID properties
DEFF Research Database (Denmark)
Frank, Lars; Pedersen, Rasmus Ulslev; Havnø Frank, Christian
2014-01-01
data from different locations can have at most two of the three desirable CAP properties [5]. The NoSQL movement has applied the CAP theorem as an argument against tradi- tional ACID (atomicity, consistency, isolation, and durabil- ity) databases, which prioritize consistency and partition- tolerance...
An Extension of the Mean Value Theorem for Integrals
Khalili, Parviz; Vasiliu, Daniel
2010-01-01
In this note we present an extension of the mean value theorem for integrals. The extension we consider is motivated by an older result (here referred as Corollary 2), which is quite classical for the literature of Mathematical Analysis or Calculus. We also show an interesting application for computing the sum of a harmonic series.
An Elementary Proof of a Converse Mean-Value Theorem
Almeida, Ricardo
2008-01-01
We present a new converse mean value theorem, with a rather elementary proof. [The work was supported by Centre for Research on Optimization and Control (CEOC) from the "Fundacaopara a Ciencia e a Tecnologia" FCT, co-financed by the European Community Fund FEDER/POCTI.
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
Farmer Brown v. Rancher Wyatt: Teaching the Coase Theorem
Gourley, Patrick
2018-01-01
The Coase Theorem is a fundamental tenet of environmental economics and is taught to thousands of principles of microeconomics students each year. Its counterintuitive conclusion, that a Pareto optimal solution can result between private parties regardless of the initial allocation of property rights over a scarce resource, is difficult for…
A Bayesian perspective on Markovian dynamics and the fluctuation theorem
Virgo, Nathaniel
2013-08-01
One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.
Modified intuitionistic fuzzy metric spaces and some fixed point theorems
International Nuclear Information System (INIS)
Saadati, R.; Sedghi, S.; Shobe, N.
2008-01-01
Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Veereamani P. A note on intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2006;28:902-5]). In this paper, we consider modified intuitionistic fuzzy metric spaces and prove some fixed point theorems in these spaces. All the results presented in this paper are new
The Unforgettable Experience of a Workshop on Pythagoras Theorem
Arwani, Salima Shahzad
2011-01-01
The author conducted a workshop with colleagues in which awareness of Pythagoras' theorem was raised. This workshop was an unforgettable event in the author's life because it was the first time that she had interacted with teachers from a different school system, and it allowed her to develop presentation skills and confidence in her own…
Another proof of Gell-Mann and Low's theorem
Molinari, Luca Guido
2006-01-01
The theorem by Gell-Mann and Low is a cornerstone in QFT and zero-temperature many-body theory. The standard proof is based on Dyson's time-ordered expansion of the propagator; a proof based on exact identities for the time-propagator is here given.
Another proof of Gell-Mann and Low's theorem
International Nuclear Information System (INIS)
Molinari, Luca Guido
2007-01-01
The theorem by Gell-Mann and Low is a cornerstone in quantum field theory and zero-temperature many-body theory. The standard proof is based on Dyson's time-ordered expansion of the propagator; a proof based on exact identities for the time propagator is here given
Virial theorem and Gibbs thermodynamic potential for Coulomb systems
International Nuclear Information System (INIS)
Bobrov, V. B.; Trigger, S. A.
2014-01-01
Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei. This result is valid beyond the perturbation theory with respect to the interparticle interaction
Virial theorem and Gibbs thermodynamic potential for Coulomb systems
Bobrov, V. B.; Trigger, S. A.
2013-01-01
Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei. This result is valid beyond the perturbation theory with respect to the interparticle interaction.
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
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...
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we ...
The Second Fundamental Theorem of Welfare Economics: A Pedagogical Note
Parrinello Sergio
1998-01-01
The author extends the criticism that W. Bryant (1994) levelled against the usual treatment given to the Second Fundamental Theorem of Welfare Economics in many microeconomics textbooks and economic journal literature. He argues that the omission of basic caveats makes the usual interpretation misleading and an obstacle to better economic education.
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
Limits theorems for tail processes with applications tointermediate quantile estimation
Einmahl, J.H.J.
1992-01-01
A description of the weak and strong limiting behaviour of weighted uniform tail empirical and tail quantile processes is given. The results for the tail quantile process are applied to obtain weak and strong functional limit theorems for a weighted non-uniform tail-quantile-type process based on a
Local central limit theorem for a Gibbs random field
Energy Technology Data Exchange (ETDEWEB)
Campanino, M; Capocaccia, D; Tirozzi, B [L' Aquila Univ. (Italy). Istituto di Matematica; Rome Univ. (Italy). Istituto di Matematica)
1979-12-01
The validity of the implication of a local limit theorem is extended from an integral one. The extension eliminates the finite range assumption present in the previous works by using the cluster expansion to analyze the contribution from the tail of the potential.
Hamiltonian Noether theorem for gauge systems and two time physics
International Nuclear Information System (INIS)
Villanueva, V M; Nieto, J A; Ruiz, L; Silvas, J
2005-01-01
The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al model and, with special emphasis, to two time physics
Rigidity theorem for Willmore surfaces in a sphere
Indian Academy of Sciences (India)
(Math. Sci.) Vol. 126, No. 2, May 2016, pp. 253–260. c Indian Academy of Sciences. Rigidity theorem for Willmore surfaces in a sphere. HONGWEI XU1 and DENGYUN YANG2,∗. 1Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027,. People's Republic of China. 2College of Mathematics and ...
Externalities and the Coase Theorem: A Diagrammatic Presentation
Halteman, James
2005-01-01
In intermediate microeconomic textbooks the reciprocal nature of externalities is presented using numerical examples of costs and benefits. This treatment of the Coase theorem obscures the fact that externality costs and benefits are best understood as being on a continuum where costs vary with the degree of intensity of the externality. When…
Liouville's theorem and the method of the inverse problem
International Nuclear Information System (INIS)
Its, A.R.
1985-01-01
An approach to the investigation of the Zakharov-Shabat equations is developed. This approach is based on a classical theorem of Liouville and is the synthesis of ''finite-zone'' integration, the matrix Riemann problem method and the theory of isomonodromy deformations of differential equations. The effectiveness of the proposed scheme is demonstrated by developing ''dressing procedures'' for the Bullough-Dodd equation
Matching factorization theorems with an inverse-error weighting
Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; Pisano, Cristian; Signori, Andrea
2018-06-01
We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.