Bell's Theorem from Moore's Theorem
Fields, Chris
2012-01-01
It is shown that the restrictions of what can be inferred from classically-recorded observational outcomes that are imposed by the no-cloning theorem, the Kochen-Specker theorem and Bell's theorem also follow from restrictions on inferences from observations formulated within classical automata theory. Similarities between the assumptions underlying classical automata theory and those underlying universally-unitary quantum theory are discussed.
Schleimer, Saul
2009-01-01
This note is an exposition of Waldhausen's proof of Waldhausen's Theorem: the three-sphere has a single Heegaard splitting, up to isotopy, in every genus. As a necessary step we also give a sketch of the Reidemeister-Singer Theorem.
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
International Nuclear Information System (INIS)
Noether's theorem attains its maximum simplicity and depth when formulated in curved space-time, gravitation being included. Extension to curved space-times is here made simple by the use of a formulation, for the flat case, due to Jackiw. The exposition purports to be pedagogical. (Author)
SELECTION OF BRILLOUIN SHIFT DISCRIMINATOR FOR BRILLOUIN LIDAR
Institute of Scientific and Technical Information of China (English)
吴东; 刘智深
2002-01-01
For the measurement of vertical profiles of sound speed in the sea using laser excited Brillouin scattering, a high-resolution measurement of Brillouin frequency shift is required. In this work, a molecular absorption cell was selec ted as the frequency shift discriminator and several kinds of absorption gases were tri ed. It was found that the strong line (#1095) of 127I2 at 18783.3297 cm-1 and two absorption lines of 129I2 located at the two sides of the #1095 line of 127 I2 could be used as frequency shift discriminator to detect the changes of the Brillouin frequency s hift. This selection is the best one within the range from 532.0131 nm to 532.5154 nm. But it is not perfect and there is a lot of work to do before its practical application.
SELECTION OF BRILLOUIN SHIFT DISCRIMINATOR FOR BRILLOUIN LIDAR
Institute of Scientific and Technical Information of China (English)
吴东; 刘智深
2002-01-01
For the measurement of vertical profiles of sound speed in the sea using laser excited Brillouin scattering, a high-resolution measurement of Brillouin frequency shift is required. In this work, a molecular absorption cell was selected as the frequency shift discriminator and several kinds of absorption gases were tried. It was found that the strong line ( # 1095) of 127 I2 at 18783. 3297 cm-1 and two absorption lines of 129 I2 located at the two sides of the # 1095 line of 127 I2 could be used as frequency shift discriminator to detect the changes of the Brillouin frequency shift. This selection is the best one within the range from 532.0131 run to 532.5154 nm. But it is not perfect and there is a lot of work to do before its practical application.
Shear Brillouin light scattering microscope.
Kim, Moonseok; Besner, Sebastien; Ramier, Antoine; Kwok, Sheldon J J; An, Jeesoo; Scarcelli, Giuliano; Yun, Seok Hyun
2016-01-11
Brillouin spectroscopy has been used to characterize shear acoustic phonons in materials. However, conventional instruments had slow acquisition times over 10 min per 1 mW of input optical power, and they required two objective lenses to form a 90° scattering geometry necessary for polarization coupling by shear phonons. Here, we demonstrate a confocal Brillouin microscope capable of detecting both shear and longitudinal phonons with improved speeds and with a single objective lens. Brillouin scattering spectra were measured from polycarbonate, fused quartz, and borosilicate in 1-10 s at an optical power level of 10 mW. The elastic constants, phonon mean free path and the ratio of the Pockels coefficients were determined at microscopic resolution. PMID:26832263
Brillouin scattering self-cancellation
Florez, O.; Jarschel, P. F.; Espinel, Y. A. V.; Cordeiro, C. M. B.; Mayer Alegre, T. P.; Wiederhecker, G. S.; Dainese, P.
2016-06-01
The interaction between light and acoustic phonons is strongly modified in sub-wavelength confinement, and has led to the demonstration and control of Brillouin scattering in photonic structures such as nano-scale optical waveguides and cavities. Besides the small optical mode volume, two physical mechanisms come into play simultaneously: a volume effect caused by the strain-induced refractive index perturbation (known as photo-elasticity), and a surface effect caused by the shift of the optical boundaries due to mechanical vibrations. As a result, proper material and structure engineering allows one to control each contribution individually. Here, we experimentally demonstrate the perfect cancellation of Brillouin scattering arising from Rayleigh acoustic waves by engineering a silica nanowire with exactly opposing photo-elastic and moving-boundary effects. This demonstration provides clear experimental evidence that the interplay between the two mechanisms is a promising tool to precisely control the photon-phonon interaction, enhancing or suppressing it.
Brillouin Scattering Self-Cancellation
Florez, Omar; Espinel, Yovanny A V; Cordeiro, Cristiano M B; Alegre, Thiago P Mayer; Wiederhecker, Gustavo S; Dainese, Paulo
2016-01-01
The interaction between light and acoustic phonons is strongly modified in sub-wavelength confinement, and has led to the demonstration and control of Brillouin scattering in photonic structures such as nano-scale optical waveguides and cavities. Besides the small optical mode volume, two physical mechanisms come into play simultaneously: a volume effect caused by the strain induced refractive index perturbation (known as photo-elasticity), and a surface effect caused by the shift of the optical boundaries due to mechanical vibrations. As a result proper material and structure engineering allows one to control each contribution individually. In this paper, we experimentally demonstrate the perfect cancellation of Brillouin scattering by engineering a silica nanowire with exactly opposing photo-elastic and moving-boundary effects. This demonstration provides clear experimental evidence that the interplay between the two mechanisms is a promising tool to precisely control the photon-phonon interaction, enhancin...
Asano, Motoki; Özdemir, Şahin Kaya; Ikuta, Rikizo; Yang, Lan; Imoto, Nobuyuki; Yamamoto, Takashi
2016-01-01
We report the first observation of stimulated Brillouin scattering (SBS) with Brillouin lasing, and Brillouin-coupled four-wave-mixing (FWM) in an ultra-high-Q silica microbottle resonator. The Brillouin lasing was observed at the frequency of $\\Omega_B=2\\pi\\times10.4$ GHz with a threshold power of $0.45$ mW. Coupling between Brillouin and FWM was observed in both backward and forward scattering directions with separations of $2\\Omega_B$. At a pump power of $10$ mW, FWM spacing reached to 7th and 9th order anti-Stokes and Stokes, respectively.
Stimulated Brillouin scattering in metamaterials
Smith, M J A; de Sterke, C Martijn; Wolff, C; Lapine, M; Poulton, C G
2016-01-01
We compute the SBS gain for a metamaterial comprising a cubic lattice of dielectric spheres suspended in a background dielectric material. Theoretical methods are presented to calculate the optical, acoustic, and opto-acoustic parameters that describe the SBS properties of the material at long wavelengths. Using the electromagnetic and strain energy densities we accurately characterise the optical and acoustic properties of the metamaterial. From a combination of energy density methods and perturbation theory, we recover the appropriate terms of the photoelastic tensor for the metamaterial. We demonstrate that electrostriction is not necessarily the dominant mechanism in the enhancement and suppression of the SBS gain coefficient in a metamaterial, and that other parameters, such as the Brillouin linewidth, can dominate instead. Examples are presented that exhibit an order of magnitude enhancement in the SBS gain as well as perfect suppression.
Tunable multiwavelength Brillouin-Erbium fiber laser with intra-cavity pre-amplified Brillouin pump
International Nuclear Information System (INIS)
We have demonstrated a new configuration of Brillouin-Erbium fiber laser, in which the Brillouin pump is pre-amplified within the laser cavity before entering the single-mode fiber. By using this simple scheme, a lower external Brillouin pump power is required to create the Brillouin gain and suppresses the laser cavity modes. The proposed laser structure exhibits a wide tuning range of 13 nm from 1597 nm to 1610 nm with 1480 nm pump power of 100 mW. The number of channels obtained within this wavelength range is 14 channels with 0.089 nm spacing
Unifying Brillouin scattering and cavity optomechanics
Van Laer, Raphaël; Baets, Roel; Van Thourhout, Dries
2015-01-01
So far, Brillouin scattering and cavity optomechanics were mostly disconnected branches of research. Both deal with photon-phonon coupling, but a number of differences impeded their unambiguous fusion. Here, we reveal a close connection between two parameters of central importance in these fields: the Brillouin gain coefficient $\\tilde{\\mathcal{G}}$ and the zero-point optomechanical coupling rate $g_{0}$. In addition, we derive the dynamical cavity equations from the coupled-mode description of a Brillouin waveguide. This explicit transition shows the unity of optomechanical phenomena, such as stimulated Brillouin scattering and electromagnetically induced transparency, regardless of whether they occur in waveguides or in resonators. Therefore, the fields can no longer be disentangled. We propose an experimental manifestation of the link in silicon photonic nanowires.
Brillouin Cooling in a Linear Waveguide
Chen, Yin-Chung; Bahl, Gaurav
2016-01-01
Brillouin scattering is rarely considered as a mechanism that can cause cooling of a material due to the thermodynamic dominance of Stokes scattering in most practical systems. However, it has been shown in experiments on resonators that net phonon annihilation through anti-Stokes Brillouin scattering can be enabled by means of a suitable set of optical and acoustic states. The cooling of traveling phonons in a linear waveguide, on the other hand, could lead to the exciting future prospect of manipulating unidirectional heat fluxes and even the nonreciprocal transport of quantum information via phonons. In this work, we present the first analysis of the conditions under which Brillouin cooling may be achieved in a linear waveguide. We analyze the three-wave mixing interaction between the optical and acoustic modes that participate in forward Brillouin scattering, and reveal the key regimes of operation for the process. Our calculations indicate that measurable cooling may occur in state-of-the-art systems whe...
Stimulated Brillouin processes in crystals and glasses
International Nuclear Information System (INIS)
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
Guided-wave Brillouin scattering in air
Renninger, William H; Rakich, Peter T
2016-01-01
Here we identify a new form of optomechanical coupling in gas-filled hollow-core fibers. Stimulated forward Brillouin scattering is observed in air in the core of a photonic bandgap fiber. A single resonance is observed at 35 MHz, which corresponds to the first excited axial-radial acoustic mode in the air-filled core. The linewidth and coupling strengths are determined by the acoustic loss and electrostrictive coupling in air, respectively. A simple analytical model, refined by numerical simulations, is developed that accurately predicts the Brillouin coupling strength and frequency from the gas and fiber parameters. Since this form of Brillouin coupling depends strongly on both the acoustic and dispersive optical properties of the gas within the fiber, this new type of optomechanical interaction is highly tailorable. These results allow for forward Brillouin spectroscopy in dilute gases, could be useful for sensing and will present a power and noise limitation for certain applications.
Noise and dynamics in forward Brillouin interactions
Kharel, Prashanta; Renninger, William; Rakich, Peter
2015-01-01
In this paper, we explore the spatio-temporal dynamics of spontaneous and stimulated forward Brillouin scattering. This general treatment incorporates the optomechanical coupling produced by boundary-induced radiation pressures (boundary motion) and material-induced electrostrictive forces (photo-elastic effects), permitting straightforward application to a range of emerging micro- and nano-scale optomechanical systems. Through a self-consistent fully coupled nonlinear treatment, developed within a general Hamiltonian framework, we establish the connection between the power spectral density of spontaneously scattered light in forward Brillouin interactions and the nonlinear coupling strength. We show that, in sharp contrast to backward Brillouin scattering, noise-initiated stimulated forward Brillouin scattering is forbidden in the majority of experimental systems. In fact, the single-pass gain, which characterizes the threshold for energy transfer in back-scattering processes, is negative for a large class o...
Noise and dynamics in forward Brillouin interactions
Kharel, P.; Behunin, R. O.; Renninger, W. H.; Rakich, P. T.
2016-06-01
In this paper, we explore the spatiotemporal dynamics of spontaneous and stimulated forward Brillouin scattering. This general treatment incorporates the optomechanical coupling produced by boundary-induced radiation pressures (boundary motion) and material-induced electrostrictive forces (photoelastic effects), permitting straightforward application to a range of emerging micro- and nanoscale optomechanical systems. Through a self-consistent fully coupled nonlinear treatment, developed within a general Hamiltonian framework, we establish the connection between the power spectral density of spontaneously scattered light in forward Brillouin interactions and the nonlinear coupling strength. We show that, in sharp contrast to backward Brillouin scattering, noise-initiated stimulated forward Brillouin scattering is forbidden in the majority of experimental systems. In fact, the single-pass gain, which characterizes the threshold for energy transfer in back-scattering processes, is negative for a large class of forward Brillouin devices. Beyond this frequent experimental case, we explore mechanisms for dispersive symmetry breaking that lead to amplification and dynamics reminiscent of backward Brillouin scattering.
Loh, K. K.; Yeo, K. S.; Shee, Y. G.
2015-04-01
A microwave photonic filter based on double-Brillouin-frequency spaced multiwavelength Brillouin-erbium fiber laser (BEFL) is experimentally demonstrated. The filter selectivity can be easily adjusted by tuning and apodizing the optical taps generated from the multiwavelength BEFL. Reconfiguration of different frequency responses are demonstrated.
Energy Technology Data Exchange (ETDEWEB)
Loh, K. K.; Yeo, K. S.; Shee, Y. G. [Integrated Lightwave Research Group, Department of Electrical Engineering, University of Malaya, 50603 Kuala Lumpur (Malaysia)
2015-04-24
A microwave photonic filter based on double-Brillouin-frequency spaced multiwavelength Brillouin-erbium fiber laser (BEFL) is experimentally demonstrated. The filter selectivity can be easily adjusted by tuning and apodizing the optical taps generated from the multiwavelength BEFL. Reconfiguration of different frequency responses are demonstrated.
International Nuclear Information System (INIS)
A microwave photonic filter based on double-Brillouin-frequency spaced multiwavelength Brillouin-erbium fiber laser (BEFL) is experimentally demonstrated. The filter selectivity can be easily adjusted by tuning and apodizing the optical taps generated from the multiwavelength BEFL. Reconfiguration of different frequency responses are demonstrated
International Nuclear Information System (INIS)
We examine a soft scalar theorem which has proved useful in the evaluation of certain Feynman graphs. The use of this theorem is described in connection with the determination of the Λnphi coupling in a unified model of weak and electromagnetic interactions. (author)
Smith, Michael D.
2016-01-01
The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…
Saa, Diego
2005-01-01
Goedel's results have had a great impact in diverse fields such as philosophy, computer sciences and fundamentals of mathematics. The fact that the rule of mathematical induction is contradictory with the rest of clauses used by Goedel to prove his undecidability and incompleteness theorems is proved in this paper. This means that those theorems are invalid.
Kreutzer, Stephan
2009-01-01
Algorithmic meta-theorems are general algorithmic results applying to a whole range of problems, rather than just to a single problem alone. They often have a "logical" and a "structural" component, that is they are results of the form: every computational problem that can be formalised in a given logic L can be solved efficiently on every class C of structures satisfying certain conditions. This paper gives a survey of algorithmic meta-theorems obtained in recent years and the methods used to prove them. As many meta-theorems use results from graph minor theory, we give a brief introduction to the theory developed by Robertson and Seymour for their proof of the graph minor theorem and state the main algorithmic consequences of this theory as far as they are needed in the theory of algorithmic meta-theorems.
Genova, Alessandro; Pavanello, Michele
2015-12-16
In order to approximately satisfy the Bloch theorem, simulations of complex materials involving periodic systems are made n(k) times more complex by the need to sample the first Brillouin zone at n(k) points. By combining ideas from Kohn-Sham density-functional theory (DFT) and orbital-free DFT, for which no sampling is needed due to the absence of waves, subsystem DFT offers an interesting middle ground capable of sizable theoretical speedups against Kohn-Sham DFT. By splitting the supersystem into interacting subsystems, and mapping their quantum problem onto separate auxiliary Kohn-Sham systems, subsystem DFT allows an optimal topical sampling of the Brillouin zone. We elucidate this concept with two proof of principle simulations: a water bilayer on Pt[1 1 1]; and a complex system relevant to catalysis-a thiophene molecule physisorbed on a molybdenum sulfide monolayer deposited on top of an α-alumina support. For the latter system, a speedup of 300% is achieved against the subsystem DTF reference by using an optimized Brillouin zone sampling (600% against KS-DFT). PMID:26596499
Intersection homology Kunneth theorems
Friedman, Greg
2008-01-01
Cohen, Goresky and Ji showed that there is a Kunneth theorem relating the intersection homology groups $I^{\\bar p}H_*(X\\times Y)$ to $I^{\\bar p}H_*(X)$ and $I^{\\bar p}H_*(Y)$, provided that the perversity $\\bar p$ satisfies rather strict conditions. We consider biperversities and prove that there is a K\\"unneth theorem relating $I^{\\bar p,\\bar q}H_*(X\\times Y)$ to $I^{\\bar p}H_*(X)$ and $I^{\\bar q}H_*(Y)$ for all choices of $\\bar p$ and $\\bar q$. Furthermore, we prove that the Kunneth theorem...
To string together six theorems of physics by Pythagoras theorem
Cui, H. Y.
2002-01-01
In this paper, we point out that there are at lest six theorems in physics sharing common virtue of Pythagoras theorem, so that it is possible to string these theorems together with the Pythagoras theorem for physics teaching, the six theorems are Newton's three laws of motion, universal gravitational force, Coulomb's law, and the formula of relativistic dynamics. Knowing the internal relationships between them, which have never been clearly revealed by other author, will benefit the logic of...
Virial Theorem and Hypervirial Theorem in a spherical geometry
Li, Yan; Zhang, Fu-Lin; Chen, Jing-Ling
2010-01-01
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 \\emph{perturbation theorem without wave functions}, corresponding to the Hypervirial-Hellmann-Feynman Theorem perturbation theorem of Euclidean geometry. The o...
Zapletal, Jindrich
2005-01-01
I prove preservation theorems for countable support iteration of proper forcing concerning certain classes of capacities and submeasures. New examples of forcing notions and connections with measure theory are included.
Unifying Brillouin scattering and cavity optomechanics
Van Laer, Raphaël; Baets, Roel; Van Thourhout, Dries
2016-05-01
So far, Brillouin scattering and cavity optomechanics have been mostly disconnected branches of research, although both deal with photon-phonon coupling. This begs for the development of a broader theory that contains both fields. Here, we derive the dynamics of optomechanical cavities from that of Brillouin-active waveguides. This explicit transition elucidates the link between phenomena such as Brillouin amplification and electromagnetically induced transparency. It proves that effects familiar from cavity optomechanics all have traveling-wave partners, but not vice versa. We reveal a close connection between two parameters of central importance in these fields: the Brillouin gain coefficient and the zero-point optomechanical coupling rate. This enables comparisons between systems as diverse as ultracold atom clouds, plasmonic Raman cavities, and nanoscale silicon waveguides. In addition, back-of-the-envelope calculations show that unobserved effects, such as photon-assisted amplification of traveling phonons, are now accessible in existing systems. Finally, we formulate both circuit- and cavity-oriented optomechanics in terms of vacuum coupling rates, cooperativities, and gain coefficients, thus reflecting the similarities in the underlying physics.
D'Agostini, G
2005-01-01
It is curious to learn that Enrico Fermi knew how to base probabilistic inference on Bayes theorem, and that some influential notes on statistics for physicists stem from what the author calls elsewhere, but never in these notes, {\\it the Bayes Theorem of Fermi}. The fact is curious because the large majority of living physicists, educated in the second half of last century -- a kind of middle age in the statistical reasoning -- never heard of Bayes theorem during their studies, though they have been constantly using an intuitive reasoning quite Bayesian in spirit. This paper is based on recollections and notes by Jay Orear and on Gauss' ``Theoria motus corporum coelestium'', being the {\\it Princeps mathematicorum} remembered by Orear as source of Fermi's Bayesian reasoning.
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).
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 by...
Poutiainen, H. (Hayley)
2015-01-01
Group theory is a mathematical domain where groups and their properties are studied. The evolution of group theory as an area of study is said to be the result of the parallel development of a variety of different studies in mathematics. Sylow’s Theorems were a set of theorems proved around the same time the concept of group theory was being established, in the 1870s. Sylow used permutation groups in his proofs which were then later generalized and shown to hold true for all finite groups....
Kartavtsev, Alexander
2014-01-01
According to the Goldstone theorem a scalar theory with a spontaneously broken global symmetry contains strictly massless states. In this letter we identify a loophole in the current-algebra proof of the theorem. Therefore, the question whether in models with Mexican hat potential the tangential excitations are strictly massless or are just almost massless as compared to the radial ones remains open. We also argue that mass of the tangential excitations approaches zero even if the symmetry is not spontaneously broken but a combination of the field components invariant under the symmetry transformations acquires a large vacuum expectation value.
DEFF Research Database (Denmark)
Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard;
2015-01-01
The main result of the present paper is an analogue of Kontsevich formality theorem in the context of the deformation theory of gerbes. We construct an L∞L∞ deformation of the Schouten algebra of multi-vectors which controls the deformation theory of a gerbe.......The main result of the present paper is an analogue of Kontsevich formality theorem in the context of the deformation theory of gerbes. We construct an L∞L∞ deformation of the Schouten algebra of multi-vectors which controls the deformation theory of a gerbe....
Virial Theorem and Scale Transformations.
Kleban, Peter
1979-01-01
Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)
Bandwidth reconfigurable microwave photonic filter based on stimulated Brillouin scattering
Xiao, Yongchuan; Wang, Xin; Zhang, Youdi; Dong, Wei; Zhang, Xindong; Liu, Caixia; Ruan, Shengping; Chen, Weiyou
2015-01-01
A bandwidth reconfigurable microwave photonic filter is proposed and numerically analyzed employing Brillouin gain spectrum narrowing and broadening. The stimulated Brillouin scattering (SBS) process is used to convert the phase modulation to intensity modulation to generate filter passband. Due to the fact that the passband is formed by mapping the Brillouin gain spectrum, bandwidth reconfiguration can be implemented by changing Brillouin gain linewidth. In this paper, both bandwidth reduction and increase are included in a single system and the details of gain spectrum narrowing and broadening are demonstrated. Theoretically, nearly 60% bandwidth reduction and hundreds times of bandwidth increase are achieved as compared to the case without gain spectrum process.
Dalen, D. van
2008-01-01
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 edition of Logic and Structure. Comments are welcome.
Dalen, D. van
2008-01-01
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 edition
An Improved Subadditive Ergodic Theorem
Liggett, Thomas M.
1985-01-01
A new version of Kingman's subadditive ergodic theorem is presented, in which the subadditivity and stationarity assumptions are relaxed without weakening the conclusions. This result applies to a number of situations that were not covered by Kingman's original theorem. The proof involves a rather simple reduction to the additive case, where Birkhoff's ergodic theorem can be applied.
Abramovitz, Buma; Berezina, Miryam; Berman, Abraham; Shvartsman, Ludmila
2009-01-01
In this article we describe the process of studying the assumptions and the conclusion of a theorem. We tried to provide the students with exercises and problems where we discuss the following questions: What are the assumptions of a theorem and what are the conclusions? What is the geometrical meaning of a theorem? What happens when one or more…
Virial theorem and hypervirial theorem in a spherical geometry
Energy Technology Data Exchange (ETDEWEB)
Li Yan; Chen Jingling [Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Zhang Fulin, E-mail: flzhang@tju.edu.cn, E-mail: chenjl@nankai.edu.cn [Physics Department, School of Science, Tianjin University, Tianjin 300072 (China)
2011-09-09
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)
Fixed points, intersection theorems, variational inequalities, and equilibrium theorems
Directory of Open Access Journals (Sweden)
Sehie Park
2000-07-01
Full Text Available From a fixed point theorem for compact acyclic maps defined on admissible convex sets in the sense of Klee, we first deduce collectively fixed point theorems, intersection theorems for sets with convex sections, and quasi-equilibrium theorems. These quasi-equilibrium theorems are applied to give simple and unified proofs of the known variational inequalities of the Hartman-Stampacchia-Browder type. Moreover, from our new fixed point theorem, we deduce new variational inequalities which can be used to obtain fixed point results for convex-valued maps. Finally, various general economic equilibrium theorems are deduced in the forms of the Nash type, the Tarafdar type, and the Yannelis-Prabhakar type. Our results are stated for not-necessarily locally convex topological vector spaces and for abstract economies with arbitrary number of commodities and agents. Our new results extend a lot of known works with much simpler proofs.
International Nuclear Information System (INIS)
Noether's theorem relates symmetries and conservation laws of Hamiltonians systems. Arnol'd's theorem uses those integrals of motion for the construction of sufficient stability conditions of hydrodynamical problems, which are Hamiltonian with a singular Poisson bracket. Finally, Andrews' theorem imposes restriction on the existence of Arnol'd stable solutions of symmetric systems. It is shown that denial of Andrews'theorem implies the divergence of the velocity component normal to the symmetric coordinate. This proof by reductio ad absurdum may be used to determine the strength of the symmetry breaking elements, necessary to overcome the limitations imposed by this theorem (Author)
Rayleigh-Brillouin scattering of carbon dioxide
Gu, Ziyu; van de Water, Willem
2014-01-01
The spectral lineshape of spontaneous Rayleigh-Brillouin scattering in CO2 is studied in a range of pressures. The spectrum is influenced by the bulk viscosity, which is a relaxation phenomenon involving the internal degrees of freedom of the molecule. The associated relaxation rates can be compared to the frequency shift of the scattered light, which demands precise measurements of the spectral lineshape. We find the value of the bulk viscosity around 5.7 X 10^{-6} kg/(ms) for the range of pressures p= 2-4 bar and for conditions of room temperature.
Taylor, Marika
2016-01-01
The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension $3/2 < \\Delta < 5/2$. Therefore the strongest version of the F theorem is in general violated.
Indian Academy of Sciences (India)
N V Rao
2003-02-01
The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose is a compact set in the complex plane and 0 belongs to the boundary . Let $\\mathcal{A}(K)$ denote the space of all functions on such that is holomorphic in a neighborhood of and (0) = 0. Also for any given positive integer , let $\\mathcal{A}(m, K)$ denote the space of all such that is holomorphic in a neighborhood of and $f(0) = f'(0) = \\cdots = f^{(m)}(0) = 0$. Then $\\mathcal{A}(m, K)$ is dense in $\\mathcal{A}(K)$ under the supremum norm on provided that there exists a sector $W = \\{re^{i}; 0 ≤ r ≤ , ≤ ≤ \\}$ such that $W \\cap K = \\{0\\}$. (This is the well-known Poincare's external cone condition).} We present various generalizations of this result in the context of higher dimensions replacing holomorphic with harmonic.
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 reson
Short-Pulse Amplification by Strongly-Coupled Brillouin Scattering
Edwards, Matthew R; Mikhailova, Julia M; Fisch, Nathaniel J
2016-01-01
We examine the feasibility of strongly-coupled stimulated Brillouin scattering as a mechanism for the plasma-based amplification of sub-picosecond pulses. In particular, we use fluid theory and particle-in-cell simulations to compare the relative advantages of Raman and Brillouin amplification over a broad range of achievable parameters.
Stephen A. Ross
2011-01-01
We can only estimate the distribution of stock returns but we observe the distribution of risk neutral state prices. Risk neutral state prices are the product of risk aversion - the pricing kernel - and the natural probability distribution. The Recovery Theorem enables us to separate these and to determine the market's forecast of returns and the market's risk aversion from state prices alone. Among other things, this allows us to determine the pricing kernel, the market risk premium, the pro...
Vela Velupillai, K.
2011-01-01
Takashi Negishi's remarkable youthful contribution to welfare economics, general equilibrium theory and, with the benefit of hindsight, also to one strand of computable general equilibrium theory, all within the span of six pages in one article, has become one of the modern classics of general equilibrium theory and mathematical economics. Negishi's celebrated theorem and what has been called Negishi's Method have formed one foundation for computable general equilibrium theory. In this paper ...
Coevolution. Extending Prigogine Theorem
Leon, Antonio
2006-01-01
The formal consideration of the concept of interaction in thermodynamic analysis makes it possible to deduce, in the broadest terms, new results related to the coevolution of interacting systems, irrespective of their distance from thermodynamic equilibrium. In this paper I prove the existence of privileged coevolution trajectories characterized by the minimum joint production of internal entropy, a conclusion that extends Prigogine theorem to systems evolving far from thermodynamic equilibri...
Bourgain's discretization theorem
Giladi, Ohad; Schechtman, Gideon
2011-01-01
Bourgain's discretization theorem asserts that there exists a universal constant $C\\in (0,\\infty)$ with the following property. Let $X,Y$ be Banach spaces with $\\dim X=n$. Fix $D\\in (1,\\infty)$ and set $\\d= e^{-n^{Cn}}$. Assume that $\\mathcal N$ is a $\\d$-net in the unit ball of $X$ and that $\\mathcal N$ admits a bi-Lipschitz embedding into $Y$ with distortion at most $D$. Then the entire space $X$ admits a bi-Lipschitz embedding into $Y$ with distortion at most $CD$. This mostly expository article is devoted to a detailed presentation of a proof of Bourgain's theorem. We also obtain an improvement of Bourgain's theorem in the important case when $Y=L_p$ for some $p\\in [1,\\infty)$: in this case it suffices to take $\\delta= C^{-1}n^{-5/2}$ for the same conclusion to hold true. The case $p=1$ of this improved discretization result has the following consequence. For arbitrarily large $n\\in \\N$ there exists a family $\\mathscr Y$ of $n$-point subsets of ${1,...,n}^2\\subseteq \\R^2$ such that if we write $|\\mathscr ...
Tailorable Stimulated Brillouin Scattering in Nanoscale Silicon Waveguides
Shin, Heedeuk; Jarecki, Robert; Cox, Jonathan A; Olsson, Roy H; Starbuck, Andrew; Wang, Zheng; Rakich, Peter T
2013-01-01
While nanoscale modal confinement radically enhances a variety of nonlinear light-matter interactions within silicon waveguides, traveling-wave stimulated Brillouin scattering nonlinearities have never been observed in silicon nanophotonics. Through a new class of hybrid photonic-phononic waveguides, we demonstrate tailorable traveling-wave forward stimulated Brillouin scattering in nanophotonic silicon waveguides for the first time, yielding 3000 times stronger forward SBS responses than any previous waveguide system. Simulations reveal that a coherent combination of electrostrictive forces and radiation pressures are responsible for greatly enhanced photon-phonon coupling at nano-scales. Highly tailorable Brillouin nonlinearities are produced by engineering the structure of a membrane-suspended waveguide to yield Brillouin resonances from 1 to 18 GHz through high quality-factor (>1000) phonon modes. Such wideband and tailorable stimulated Brillouin scattering in silicon photonics could enable practical real...
The Non-Signalling theorem in generalizations of Bell's theorem
Walleczek, Jan; Groessing, Gerhard
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 even nonlocal hidden...
Arrow's Theorem in Judgement Aggregation
Franz Dietrich; Christian List
2005-01-01
In response to recent work on the aggregation of individual judgements on logically connected propositions into collective judgements, it is often asked whether judgement aggregation is a special case of Arrowian preference aggregation. We argue the opposite. After proving a general impossibility theorem, we construct an embedding of preference aggregation into judgement aggregation and prove Arrow's theorem as a corollary of our result. Although we provide a new proof of Arrow's theorem, our...
Perspectives on the CAP Theorem
Gilbert, Seth; Lynch, Nancy Ann
2012-01-01
Almost twelve years ago, in 2000, Eric Brewer introduced the idea that there is a fundamental trade-off between consistency, availability, and partition tolerance. This trade-off, which has become known as the CAP Theorem, has been widely discussed ever since. In this paper, we review the CAP Theorem and situate it within the broader context of distributed computing theory. We then discuss the practical implications of the CAP Theorem, and explore some general techniques for coping with the i...
A theorem in relativistic electronics
Yongjian, Yu
1990-04-01
This paper presents a theorem that connects the dispersion relation of the Electron Cyclotron Maser' and the oscillation equation of the Gyromonotron. This theorem gives us a simple way of obtaining the osscillating characteristics of the Gyromonotron provided that dispersion relation of the ECRM is given. Though the theorem is proved only with the case of ECRM and Gyromonotron, it holds for other kinds of Electron Masers, FEL4etc. and corresponding osscillators.
International Nuclear Information System (INIS)
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 objectivity. 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
Cobham's theorem for substitutions
Durand, Fabien
2010-01-01
The seminal theorem of Cobham has given rise during the last 40 years to a lot of works around non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let $\\alpha$ and $\\beta$ be two multiplicatively independent Perron numbers. Then, a sequence $x\\in A^\\mathbb{N}$, where $A$ is a finite alphabet, is both $\\alpha$-substitutive and $\\beta$-substitutive if and only if $x$ is ultimately periodic.
Fluctuation theorem in spintronics
International Nuclear Information System (INIS)
Microscopic reversibility is a key in deriving the Onsager relation. It even leads a new exact relationship that would be valid far from equilibrium, called fluctuation theorem (FT). The FT provides a precise statement for the second law of thermodynamics; and remarkably, reproduces the linear response theory. We consider the FT in the spin-dependent transport and derive universal relations among nonlinear spin and charge transport coefficients. We apply the relations to a quantum dot embedded in a two-terminal Aharonov-Bohm interferometer and check that the relations are satisfied.
Reiher, Christian
2012-01-01
Tur\\'{a}n's theorem is a cornerstone of extremal graph theory. It asserts that for any integer $r \\geq 2$ every graph on $n$ vertices with more than ${\\tfrac{r-2}{2(r-1)}\\cdot n^2}$ edges contains a clique of size $r$, i.e., $r$ mutually adjacent vertices. The corresponding extremal graphs are balanced $(r-1)$-partite graphs. The question as to how many such $r$-cliques appear at least in any $n$-vertex graph with $\\gamma n^2$ edges has been intensively studied in the literature. In particula...
Abelian theorems for Whittaker transforms
Directory of Open Access Journals (Sweden)
Richard D. Carmichael
1987-01-01
Full Text Available Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches 0 or ∞ in absolute value inside a wedge region in the right half plane.
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.…
Andreev's Theorem on hyperbolic polyhedra
Roeder, R K W; Dunbar, W D; Roeder, Roland K. W.; Hubbard, John H.; Dunbar, William D.
2004-01-01
In 1970, E. M. Andreev published a classification of all three-dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, $C$, Andreev's Theorem provides five classes of linear inequalities, depending on $C$, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing $C$ with the assigned dihedral angles. Andreev's Theorem also shows that the resulting polyhedron is unique, up to hyperbolic isometry. Andreev's Theorem is both an interesting statement about the geometry of hyperbolic 3-dimensional space, as well as a fundamental tool used in the proof for Thurston's Hyperbolization Theorem for 3-dimensional Haken manifolds. It is also remarkable to what level the proof of Andreev's Theorem resembles (in a simpler way) the proof of Thurston. We correct a fundamental error in Andreev's proof of existence and also provide a readable new proof of the other parts of the proof of And...
Cascaded forward Brillouin scattering to all Stokes orders
Wolff, Christian; Eggleton, Benjamin J; Steel, Michael J; Poulton, Christopher G
2016-01-01
Inelastic scattering processes such as Brillouin scattering can often function in cascaded regimes and this is likely to occur in certain integrated opto-acoustic devices. We develop a Hamiltonian formalism for cascaded Brillouin scattering valid for both quantum and classical regimes. By regarding Brillouin scattering as the interaction of a single acoustic envelope and a single optical envelope that covers all Stokes and anti-Stokes orders, we obtain a compact model that is well suited for numerical implementation, extension to include other optical nonlinearities or short pulses, and application in the quantum-optics domain. We then theoretically analyze intra-mode forward Brillouin scattering (FBS) for arbitrary waveguides with and without optical dispersion. In the absence of optical dispersion, we find an exact analytical solution. With a perturbative approach, we furthermore solve the case of weak optical dispersion. Our work leads to several key results on intra-mode FBS. For negligible dispersion, we...
Stimulated Raman-Brillouin scattering processes in magnetoactive semiconductor plasma
International Nuclear Information System (INIS)
A simple analytical treatment based on hydrodynamic model of plasma is developed to study both steady-state and transient stimulated Raman and Brillouin scattering processes (SRS and SBS) in centrosymmetric or weakly non centrosymmetric semiconductors. Gain constants, threshold-pump intensities, and optimum-pulse durations for the onset of Raman and Brillouin instabilities are estimated. Authors have also addressed themselves to the question of behaviour of the transient gain factors (Raman and Brillouin) as function of different physical parameters such as external magnetic field, pump pulse durations etc. The quantitative behaviour of transient gain factors is found to be in agreement with the experimental and other theoretical observations. The analysis explain satisfactorily the competition between stimulated Raman and Brillouin processes in the short and long pulse duration regimes. The highlight of present theory is that both SRS and SBS (steady-state as well as transient) can be studied in centrosymmetric or weakly non centrosymmetric dielectrics using simple classical treatment. (author)
Some Theorems on Generalized Basic Hypergeometric Series
Directory of Open Access Journals (Sweden)
A. D. Wadhwa
1972-07-01
Full Text Available In an earlier paper the author has established two theorems on generalized hypergeometric functions. In each theorem a numerator differs from a denominator by a positive integer. These theorems were further used to prove some theorems on the sums of Kampe de Feriet functions. Here, we have established the theorems which are the basic analogues of the theorems proved in the earlier paper.
Herbrand's Fundamental Theorem - an encyclopedia article
Wirth, Claus-Peter
2015-01-01
Herbrand's Fundamental Theorem provides a constructive characterization of derivability in first-order predicate logic by means of sentential logic. Sometimes it is simply called "Herbrand's Theorem", but the longer name is preferable as there are other important "Herbrand theorems" and Herbrand himself called it "Th\\'eor\\`eme fondamental". It was ranked by Bernays [1957] as follows: "In its proof-theoretic form, Herbrand's Theorem can be seen as the central theorem of predicate logic. It exp...
Combinatorial Reciprocity Theorems
Beck, Matthias
2012-01-01
A common theme of enumerative combinatorics is formed by counting functions that are polynomials evaluated at positive integers. In this expository paper, we focus on four families of such counting functions connected to hyperplane arrangements, lattice points in polyhedra, proper colorings of graphs, and $P$-partitions. We will see that in each instance we get interesting information out of a counting function when we evaluate it at a \\emph{negative} integer (and so, a priori the counting function does not make sense at this number). Our goals are to convey some of the charm these "alternative" evaluations of counting functions exhibit, and to weave a unifying thread through various combinatorial reciprocity theorems by looking at them through the lens of geometry, which will include some scenic detours through other combinatorial concepts.
Variable delay using stationary and localized Brillouin dynamic gratings
Antman, Yair; Primerov, Nikolay; Sancho Dura, Juan; Thévenaz, Luc; Zadok, Avinoam
2012-01-01
Reflections from movable, dynamic acoustic gratings in polarization maintaining (PM) fibers are employed in the long variable delay of periodic, isolated pulses. The gratings are introduced by stimulated Brillouin scattering (SBS) interaction between two counter-propagating pump waves, which are spectrally detuned by the Brillouin frequency shift of the PM fiber and are both polarized along one of its principal axes. The gratings are interrogated by the reflections of read-out signals that ar...
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
While nanoscale modal confinement radically enhances a variety of nonlinear light-matter interactions within silicon waveguides, traveling-wave stimulated Brillouin scattering nonlinearities have never been observed in silicon nanophotonics. Through a new class of hybrid photonic-phononic waveguides, we demonstrate tailorable traveling-wave forward stimulated Brillouin scattering in nanophotonic silicon waveguides for the first time, yielding 3000 times stronger forward SBS responses than any...
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
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
-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.
Cascaded Brillouin lasing in monolithic barium fluoride whispering gallery mode resonators
International Nuclear Information System (INIS)
We report the observation of stimulated Brillouin scattering and lasing at 1550 nm in barium fluoride (BaF2) crystal. Brillouin lasing was achieved with ultra-high quality (Q) factor monolithic whispering gallery mode mm-size disk resonators. Overmoded resonators were specifically used to provide cavity resonances for both the pump and all Brillouin Stokes waves. Single and multiple Brillouin Stokes radiations with frequency shift ranging from 8.2 GHz up to 49 GHz have been generated through cascaded Brillouin lasing. BaF2 resonator-based Brillouin lasing can find potential applications for high-coherence lasers and microwave photonics
Cascaded Brillouin lasing in monolithic barium fluoride whispering gallery mode resonators
Lin, Guoping; Saleh, Khaldoun; Martinenghi, Romain; Beugnot, Jean-Charles; Sylvestre, Thibaut; Chembo, Yanne K
2015-01-01
We report the observation of stimulated Brillouin scattering and lasing at 1550~nm in barium fluoride (BaF$_2$) crystal. Brillouin lasing was achieved with ultra-high quality ($Q$) factor monolithic whispering gallery mode (WGM) mm-size disk resonators. Overmoded resonators were specifically used to provide cavity resonances for both the pump and all Brillouin Stokes waves. Single and multiple Brillouin Stokes radiations with frequency shift ranging from $8.2$ GHz up to $49$ GHz have been generated through cascaded Brillouin lasing. BaF$_2$ resonator-based Brillouin lasing can find potential applications for high-coherence lasers and microwave photonics.
Brillouin spectroscopy on doped SmS
International Nuclear Information System (INIS)
SmS becomes intermediate valent at an applied pressure of about 6.5 kbar. On the other hand, SmS doped with La or Tm is already intermediate valent at normal pressure and room temperature. The doping atoms (depending on their concentration) create new occupied states in the SmS gap which lead to the typical hybridised 4fi/4fi-1-5d1-states. The La-cation is always trivalent in LaS, whereas the Tm-cation has a valence between 2 and 3. Therefore, we expect to see a difference in the intermediate valent behaviour. A strong evidence of intermediate valence is a negative C12 and a negative Poisson's ratio. Using high-resolution Brillouin-spectroscopy we measured the phase velocity of the surface acoustic waves in the (100)-plane of Sm1-xLaxS and Sm1-xTmxS. Applying a standard fit-algorithm we calculated all three elastic constants (C11, C12 and C44) from the angular dispersion relation. To get more reliable results the compression-moduli also have been determined and linked to the elastic constants C11 and C12 in the fit model. (orig.)
Nonstationary stimulated Brillouin scattering in laser plasma
International Nuclear Information System (INIS)
Stimulated Brillouin scattering (SBS) is a known phenomenon observed in many laser plasma experiments. In spite of enormous amount of experimental and theoretical works there are some properties of SBS that have no ambiguous interpretation yet. Here we try to explain some characteristic features of SBS taking place in the high intensity laser plasma interaction. Here we compare numerical results with experimental data obtained with use of CO2 laser facility TIR-1. Experiments have been performed under the next parameters of the laser system: energy of up to 100 J, pulse length (FWHM) of 3 ns, contrast ratio larger than 107, wavelength of 10.591 mkm. The NaCl aspherical lens was used to focus the laser beam on the plane massive target. Intensity distribution in the focal plate had near Gaussian distribution with diameter (1/e) of 65 mkm, maximum intensity being 5.*1014 W/cm2. One of the most characteristic features of SBS in these experiments is its nonstationarity. (author) 4 refs., 3 figs
Opechowski's theorem and commutator groups
International Nuclear Information System (INIS)
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)
KAM Theorem and Renormalization Group
E. Simone; Kupiainen, A.
2007-01-01
We give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a PDE with quadratic nonlinearity, the so called Polchinski renormalization group equation studied in quantum field theory.
The Kramer sampling theorem revisited
García García, Antonio; Hernandez Medina, Miguel Angel; Muñoz Bouto, María José
2013-01-01
The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. Besides, it has been the cornerstone for a significant mathematical literature on the topic of sampling theorems associated with differential and difference problems. In this work we provide, in an unified way, new and old generalizations of this result corresponding to various different settings; all these generalizations are illustrated with examples. All the different situations along the pa...
Complex extension of Wigner's theorem
Brody, Dorje C
2013-01-01
Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed, we obtain the following complex generalisation of Wigner's theorem: a holomorphically projective (complex geodesic-curves preserving) transformation on a quantum state space must be generated by a Hamiltonian that is not necessarily Hermitian.
Kazhdan's Theorem on Arithmetic Varieties
Milne, J S
2001-01-01
Define an arithmetic variety to be the quotient of a bounded symmetric domain by an arithmetic group. An arithmetic variety is algebraic, and the theorem in question states that when one applies an automorphism of the field of complex numbers to the coefficients of an arithmetic variety the resulting variety is again arithmetic. This article simplifies Kazhdan's proof. In particular, it avoids recourse to the classification theorems. It was originally completed on March 28, 1984, and distribu...
Noether theorems and higher derivatives
Townsend, Paul K.
2016-01-01
A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\\epsilon$ to an arbitrary function of time, the Noether charge $Q$ is then the coefficient of $\\dot\\epsilon$ in the variation of the action. Here we examine the validity of this proof for Lagrangian mechanics with arbitrarily-high time derivatives, in which context "higher-level" analogs of Noether's theorem can be similarly proved, and "Noetherian charges" read off from, e.g. the coefficient of...
Acceptable Complexity Measures of Theorems
Grenet, Bruno
2009-01-01
In 1931, G\\"odel presented in K\\"onigsberg his famous Incompleteness Theorem, stating that some true mathematical statements are unprovable. Yet, this result gives us no idea about those independent (that is, true and unprovable) statements, about their frequency, the reason they are unprovable, and so on. Calude and J\\"urgensen proved in 2005 Chaitin's "heuristic principle" for an appropriate measure: the theorems of a finitely-specified theory cannot be significantly more complex than the t...
Goedel's Incompleteness Theorems hold vacuously
Anand, Bhupinder Singh
2002-01-01
In an earlier paper, "Omega-inconsistency in Goedel's formal system: a constructive proof of the Entscheidungsproblem" (math/0206302), I argued that a constructive interpretation of Goedel's reasoning establishes any formal system of Arithmetic as omega-inconsistent. It follows from this that Goedel's Theorem VI holds vacuously. In this paper I show that Goedel's Theorem XI essentially states that, if we assume there is a P-formula [Con(P)] whose standard interpretation is equivalent to the a...
Local virial and tensor theorems.
Cohen, Leon
2011-11-17
We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem. PMID:21863837
The Heisenberg Uncertainty Principle and the Nyquist-Shannon Sampling Theorem
Directory of Open Access Journals (Sweden)
Millette P. A.
2013-07-01
Full Text Available The derivation of the Heisenberg Uncertainty Principle (HUP from the Uncertainty Theorem of Fourier Transform theory demonstrates that the HUP arises from the dependency of momentum on a wave number that exists at the quantum level. It also establishes that the HUP is purely a relationship between the eﬀective widths of Fourier transform pairs of variables (i.e. conjugate variables. We note that the HUP is not a quantum mechanical measurement principle per se. We introduce the Quantum Mechanical equivalent of the Nyquist-Shannon Sampling Theorem of Fourier Transform theory, and show that it is a better principle to describe the measurement limitations of Quantum Mechanics. We show that Brillouin zones in Solid State Physics are a manifestation of the Nyquist-Shannon Sampling Theorem at the quantum level. By comparison with other ﬁelds where Fourier Transform theory is used, we propose that we need todiscern between measurement limitations and inherent limitations when interpreting the impact of the HUP on the nature of the quantum level. We further propose that while measurement limitations result in our perception of indeterminism at the quantum level, there is no evidence that there are any inherent limitations at the quantum level, based on the Nyquist-Shannon Sampling Theorem
Photonic-phononic orbital angular momentum in Brillouin parametric conversion
Zhu, Zhihan; Mu, Chunyuan; Li, Hongwei
2014-01-01
Orbital angular momentum (OAM) is a fundamental photonic degree of freedom, showed by Allen and co-workers. Its most attractive feature is an inherently infinite dimensionality, which in recent years has obtained several ground-breaking demonstrations for high information-density communication and processing, both in classical and quantum. Here, by seeking the reason for photonic OAM non-conservation in stimulated Brillouin amplification, we report the first demonstration of the evolution law for OAM in Brillouin process. The parameter of OAM can conveniently transfer between the phonons and different polarized photons due to the photonic spin angular momentum conservation. Our results have revealed a parametric conversion mechanism of Brillouin process for Photonic-phononic OAM, demonstrated the role of phononic OAM and the vortex acoustic wave in this process, and suggested this mechanism may find important applications in OAM-based information communication and processing.
Brillouin filtering of optical combs for narrow linewidth frequency synthesis
Galindo-Santos, Juan; Velasco, Aitor V.; Carrasco-Sanz, Ana; Corredera, Pedro
2016-05-01
We report a tunable monochromatic source generation scheme, based on Brillouin filtering of a self-referenced optical frequency comb. The system benefits from the high stability and mode linewidth of the frequency comb, significantly improving the performance of the original laser source used as Brillouin pump. A synthesized frequency with stability under 4×10-11 and a linewidth under 75 kHz was experimentally demonstrated for two separate pump lasers in the C-band. The proposed monochromatic source can be tuned with high precision in a very broad band by combining a coarse control with the pumping source and a fine control with the optical frequency comb references. In our experimental setup, coarse and fine tuning resolutions were 4 MHz and 20 Hz, respectively. Influence of Brillouin pump fluctuations in the synthesized signal stability were also analyzed for observation times up to 104 s.
A new configuration of multi-wavelength Brillouin fiber laser
International Nuclear Information System (INIS)
A multi-wavelength laser is demonstrated using stimulated Brillouin scattering in a single-mode fiber with a feedback loop using two couplers and an optical circulator. This Brillouin fiber laser can operate at any wavelength depending on the Brillouin pump (BP) wavelength used. With a BP of 14 dBm, approximately 8 to 10 BFL lines are obtained in both forward and backward directions respectively with a line spacing of 0.16 nm. The use of the 99/1 coupler and 50/50 coupler gives the highest power and number of lines for the forward and backward outputs respectively. The maximum Stokes power obtained is approximately 8.0 dBm. The anti-Stokes lines are also obtained due to four wave mixing and bidirectional operation. The combination of forward and backward output can generate a larger number of lines with channel spacing of 0.08 nm
Cascaded Brillouin lasing in monolithic barium fluoride whispering gallery mode resonators
Lin, Guoping; Diallo, Souleymane; Saleh, Khaldoun; Martinenghi, Romain; Beugnot, Jean-Charles; Sylvestre, Thibaut; Chembo, Yanne K.
2015-01-01
We report the observation of stimulated Brillouin scattering and lasing at 1550~nm in barium fluoride (BaF$_2$) crystal. Brillouin lasing was achieved with ultra-high quality ($Q$) factor monolithic whispering gallery mode (WGM) mm-size disk resonators. Overmoded resonators were specifically used to provide cavity resonances for both the pump and all Brillouin Stokes waves. Single and multiple Brillouin Stokes radiations with frequency shift ranging from $8.2$ GHz up to $49$ GHz have been gen...
Recent Progress in Brillouin Scattering Based Fiber Sensors
Directory of Open Access Journals (Sweden)
Liang Chen
2011-04-01
Full Text Available Brillouin scattering in optical fiber describes the interaction of an electro-magnetic field (photon with a characteristic density variation of the fiber. When the electric field amplitude of an optical beam (so-called pump wave, and another wave is introduced at the downshifted Brillouin frequency (namely Stokes wave, the beating between the pump and Stokes waves creates a modified density change via the electrostriction effect, resulting in so-called the stimulated Brillouin scattering. The density variation is associated with a mechanical acoustic wave; and it may be affected by local temperature, strain, and vibration which induce changes in the fiber effective refractive index and sound velocity. Through the measurement of the static or dynamic changes in Brillouin frequency along the fiber one can realize a distributed fiber sensor for local temperature, strain and vibration over tens or hundreds of kilometers. This paper reviews the progress on improving sensing performance parameters like spatial resolution, sensing length limitation and simultaneous temperature and strain measurement. These kinds of sensors can be used in civil structural monitoring of pipelines, bridges, dams, and railroads for disaster prevention. Analogous to the static Bragg grating, one can write a moving Brillouin grating in fibers, with the lifetime of the acoustic wave. The length of the Brillouin grating can be controlled by the writing pulses at any position in fibers. Such gratings can be used to measure changes in birefringence, which is an important parameter in fiber communications. Applications for this kind of sensor can be found in aerospace, material processing and fine structures.
Multibeam seeded brillouin sidescatter in inertial confinement fusion experiments.
Turnbull, D; Michel, P; Ralph, J E; Divol, L; Ross, J S; Berzak Hopkins, L F; Kritcher, A L; Hinkel, D E; Moody, J D
2015-03-27
We present the first observations of multibeam weakly seeded Brillouin sidescatter in indirect-drive inertial confinement fusion (ICF) experiments. Two seeding mechanisms have been identified and quantified: specular reflections ("glint") from opposite hemisphere beams, and Brillouin backscatter from neighboring beams with a different angle of incidence. Seeded sidescatter can dominate the overall coupling losses, so understanding this process is crucial for proper accounting of energy deposition and drive symmetry. Glint-seeded scattered light could also be used to probe hydrodynamic conditions inside ICF targets. PMID:25860748
Brillouin amplification and processing of the Rayleigh scattered signal.
Mermelstein, David; Shacham, Eliashiv; Biton, Moran; Sternklar, Shmuel
2015-07-15
Brillouin amplification of Rayleigh scattering is demonstrated using two different configurations. In the first technique, the Rayleigh scattering and amplification occurs simultaneously in the same fiber. In the second technique, the amplification takes place in a second fiber. The differences between the two techniques are delineated. Using the second technique, we demonstrate single-sideband off-resonant Brillouin amplification of the Rayleigh signal. This technique is shown to enhance the SNR of a signal that is due to vibration-induced strain on the fiber. PMID:26176464
Alternative implementation of simplified Brillouin optical correlation-domain reflectometry
Hayashi, Neisei; Nakamura, Kentaro
2014-01-01
We developed an alternative configuration of simplified Brillouin optical correlation-domain reflectometry, which can overcome the drawbacks of the original configuration. This system uses, as reference light, the light that is Fresnel reflected at a partial reflection point artificially produced near an optical circulator. We show that the influence of the 0th correlation peak fixed at the partial reflection point can be suppressed by replacing the nearby fibers with other fibers having different Brillouin frequency shift values (here, multi-mode fibers are used). Finally, we demonstrate a distributed measurement for detecting a 1.46-m-long strained section with a high signal-to-noise ratio.
Soft theorems from anomalous symmetries
Huang, Yu-tin
2015-01-01
We discuss constraints imposed by soft limits for effective field theories arising from symmetry breaking. In particular, we consider those associated with anomalous conformal symmetry as well as duality symmetries in supergravity. We verify these soft theorems for the dilaton effective action relevant for the a-theorem, as well as the one-loop effective action for N=4 supergravity. Using the universality of leading transcendental coefficients in the alpha' expansion of string theory amplitudes, we study the matrix elements of operator R^4 with half maximal supersymmetry. We construct the non-linear completion of R^4 that satisfies both single and double soft theorems up to seven points. This supports the existence of duality invariant completion of R^4.
Fluctuation theorems for quantum processes
Albash, Tameem; Marvian, Milad; Zanardi, Paolo
2013-01-01
We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that unitality replaces micro-reversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.
Nonperturbative Adler-Bardeen theorem
International Nuclear Information System (INIS)
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
Two extensions of Ramsey's theorem
Conlon, David; Fox, Jacob; Sudakov, Benny
2011-01-01
Ramsey’s theorem, in the version of Erdős and Szekeres, states that every $2$ -coloring of the edges of the complete graph on $\\{1,2,\\ldots,n\\}$ contains a monochromatic clique of order $({1}/{2})\\log n$ . In this article, we consider two well-studied extensions of Ramsey’s theorem. Improving a result of Rödl, we show that there is a constant $c\\gt 0$ such that every $2$ -coloring of the edges of the complete graph on $\\{2,3,\\ldots,n\\}$ contains a monochromatic clique $S$ for which the sum of...
Noether theorems and higher derivatives
Townsend, Paul K
2016-01-01
A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\\epsilon$ to an arbitrary function of time; the Noether charge $Q$ is then the coefficient of $\\dot\\epsilon$ in the variation of the action. Here we examine the validity of this proof for Lagrangian mechanics with arbitrarily-high time derivatives, in which context "higher-level" analogs of Noether's theorem can be similarly proved, and "Noetherian charges" read off from, e.g. the coefficient of $\\ddot \\epsilon$ in the variation of the action. While $Q=0$ implies a restricted gauge invariance, an unrestricted gauge invariance requires zero Noetherian charges too. Some illustrative examples are considered.
Relativistic Brillouin flow in the high ν/γ diode
International Nuclear Information System (INIS)
Relativistic Brillouin solutions have been derived for electron flow in crossed electric and magnetic fields. The application of these solutions to the high ν/γ diode is discussed and an approximate analytical expression for the anode current is derived. Measurements of diode current are compared to the theoretical and empirical expressions for diode current which have been developed
Nonlinear stimulated Brillouin scattering based photonic signal processors
Energy Technology Data Exchange (ETDEWEB)
Minasian, Robert A. [School of Electrical and Information Engineering, Institute of Photonics and Optical Science, University of Sydney, NSW, Sydney, 2006 (Australia)
2014-10-06
Recent new methods in photonic signal processing based on stimulated Brillouin scattering, that enable the realization of photonic mixers with high conversion efficiency, ultra-wide continuously tunable high-resolution microwave photonic filters and programmable switchable microwave photonic tunable filters, are presented. These processors provide new capabilities for the realisation of high-performance and high-resolution signal processing.
Nonlinear stimulated Brillouin scattering based photonic signal processors
International Nuclear Information System (INIS)
Recent new methods in photonic signal processing based on stimulated Brillouin scattering, that enable the realization of photonic mixers with high conversion efficiency, ultra-wide continuously tunable high-resolution microwave photonic filters and programmable switchable microwave photonic tunable filters, are presented. These processors provide new capabilities for the realisation of high-performance and high-resolution signal processing
Directory of Open Access Journals (Sweden)
Yin Chen
2004-01-01
Full Text Available We extend the Putnam-Fuglede theorem and the second-degree Putnam-Fuglede theorem to the nonnormal operators and to an elementary operator under perturbation by quasinilpotents. Some asymptotic results are also given.
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.)
Kruglikov, Boris
2011-01-01
We prove a global algebraic version of the Lie-Tresse theorem which states that the algebra of differential invariants of an algebraic pseudogroup action on a differential equation is generated by a finite number of polynomial-rational differential invariants and invariant derivations.
Birkhoff Theorems in General Relativity
Torre, Charles G.
2014-01-01
In the following Maple worksheet I demonstrate three versions of Birkhoff's theorem, which is a characterization of spherically symmetric solutions of the Einstein equations. The three versions considered here correspond to taking the "Einstein equations" to be: (1) the vacuum Einstein equations; (2) the Einstein equations with a cosmological constant (3) the Einstein-Maxwell equations.
Microwave electronics Slater's perturbation theorem
International Nuclear Information System (INIS)
Slater's perturbation theorem is one of the most useful for both experiments and theories of microwave electronics. In particular, this is applied to measurements of the field strengths in standing-wave systems. Since a traveling wave can be represented by a linear combination of two standing waves, the field measurement is also possible in a traveling-wave system. The theorem tells us the amount of the shift in a resonant frequency arising from a metallic body. Since the amount is dependent upon the square of the electric and magnetic field strengths at the metallic body, one can obtain the field strengths at the metallic body from the measured frequency shift. First the theorem is derived in Sec. 2. We then discuss the implications of the theorem by deriving it intuitively in Sec. 3. The perturbation of the field due to a metallic body is described in Sec. 4, where the frequency shift is actually related to the field strengths. In Sec. 5, we describe how to determine the impedance by using the data thus measured. Examples of field measurement are shown in Sec. 6 together with the impedance measurement. (author)
JACKSON'S THEOREM FOR COMPACT GROUPS
Institute of Scientific and Technical Information of China (English)
H. Vaezi; S. F. Rzaev
2002-01-01
In this article we consider the generalized shift operator defined by(Sh.f)(g) = ∫Gf (tut-1g)dton compact group G and by help of this operator we define "Spherical" modulus of continuity. So we proveStechkin and Jackson type theorems.
Illustrating the Central Limit Theorem
Corcoran, Mimi
2016-01-01
Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…
Discovering the Inscribed Angle Theorem
Roscoe, Matt B.
2012-01-01
Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…
Almost Subadditive Extensions of Kingman's Ergodic Theorem
Schurger, Klaus
1991-01-01
Based on two notions of almost subadditivity which were introduced by Derriennic and Schurger, two a.s. limit theorems are proved which both generalize Kingman's subadditive ergodic theorem. These results, being valid under weak moment conditions, are obtained by short proofs. One of these proofs is completely elementary and does not even make use of Birkhoff's ergodic theorem which, instead, is obtained as a by-product. Finally, an improvement of Liggett's a.s. limit theorem is given.
On Brayton and Moser's missing stability theorem
Jeltsema, D.; Scherpen, J. M. A.
2005-01-01
In the early 1960s, Brayton and Moser proved three theorems concerning the stability of nonlinear electrical circuits. The applicability of each theorem depends on three different conditions on the type of admissible nonlinearities in circuit. Roughly speaking, this means that the theorems apply to
Pythagorean Theorem Proofs: Connecting Interactive Websites
Lin, Cheng-Yao
2007-01-01
There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)
An Algebraic Identity Leading to Wilson Theorem
Ruiz, Sebastian Martin
2004-01-01
In most text books on number theory Wilson Theorem is proved by applying Lagrange theorem concerning polynomial congruences.Hardy and Wright also give a proof using cuadratic residues. In this article Wilson theorem is derived as a corollary to an algebraic identity.
A generalized no-broadcasting theorem
Barnum, H.; Barrett, J; Leifer, M.; Wilce, A.
2007-01-01
We prove a generalized version of the no-broadcasting theorem, applicable to essentially \\emph{any} nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with ``super-quantum'' correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
Tight closure and vanishing theorems
International Nuclear Information System (INIS)
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
The Classical Version of Stokes' Theorem Revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2005-01-01
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......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...... general version of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly that this latter fact usually does not get within reach for students in first year calculus courses and secondly that calculus textbooks in general only just hint at the...
The relativistic virial theorem and scale invariance
Gaite, Jose
2013-01-01
The virial theorem is related to the dilatation properties of bound states. This is realized, in particular, by the Landau-Lifshitz formulation of the relativistic virial theorem, in terms of the trace of the energy-momentum tensor. We construct a Hamiltonian formulation of dilatations in which the relativistic virial theorem naturally arises as the condition of stability against dilatations. A bound state becomes scale invariant in the ultrarelativistic limit, in which its energy vanishes. However, for very relativistic bound states, scale invariance is broken by quantum effects and the virial theorem must include the energy-momentum tensor trace anomaly. This quantum field theory virial theorem is directly related to the Callan-Symanzik equations. The virial theorem is applied to QED and then to QCD, focusing on the bag model of hadrons. In massless QCD, according to the virial theorem, 3/4 of a hadron mass corresponds to quarks and gluons and 1/4 to the trace anomaly.
Navier Stokes Theorem in Hydrology
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
A Randomized Central Limit Theorem
Eliazar, Iddo; Klafter, Joseph
2010-05-01
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 Lévy laws.
A Randomized Central Limit Theorem
International Nuclear Information System (INIS)
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)
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)
Lectures on Fermat's last theorem
International Nuclear Information System (INIS)
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
Expectation Value in Bell's Theorem
Wang, Zheng-Chuan
2006-01-01
We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell's inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experiments to show the violation of Bell's inequality and then further deny the local hidden-variables theor...
Dynamic Newton-Puiseux Theorem
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 algorithm of polynomials over the base field is not needed. The extensions obtained are a type of regular algebras over the base field and the expansions are given as formal power series over these algebras.
Khesin, B.; Rosly, A.; Thomas, R. P.
2003-01-01
We prove an analogue of the de Rham theorem for polar homology; that the polar homology $HP_q(X)$ of a smooth projective variety $X$ is isomorphic to its $H^{n,n-q}$ Dolbeault cohomology group. This analogue can be regarded as a geometric complexification where arbitrary (sub)manifolds are replaced by complex (sub)manifolds and de Rham's operator $d$ is replaced by Dolbeault's $\\bar\\partial$.
International Nuclear Information System (INIS)
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
On Harnack's theorem and extensions
Costa, Antonio F.; Parlier, Hugo
Harnack's theorem states that the fixed points of an orientation reversing involution of a compact orientable surface of genus g are a set of k disjoint simple closed geodesic where 0≤ k≤ g+1 . The first goal of this article is to give a purely geometric, complete and self-contained proof of this fact. In the case where the fixed curves of the involution do not separate the surface, we prove an extension of this theorem, by exhibiting the existence of auxiliary invariant curves with interesting properties. Although this type of extension is well known (see, for instance, Comment. Math. Helv. 57(4): 603-626 (1982) and Transl. Math. Monogr., vol. 225, Amer. Math. Soc., Providence, RI, 2004), our method also extends the theorem in the case where the surface has boundary. As a byproduct, we obtain a geometric method on how to obtain these auxiliary curves. As a consequence of these constructions, we obtain results concerning presentations of Non-Euclidean crystallographic groups and a new proof of a result on the set of points corresponding to real algebraic curves in the compactification of the Moduli space of complex curves of genus g , overline{M_{g}} . More concretely, we establish that given two real curves there is a path in overline{M_{g}} which passes through at most two singular curves, a result of M. Seppaelae (Ann. Sci. Ecole Norm. Sup. (4), 24(5), 519-544 (1991)).
Stimulated Brillouin scatter in a magnetized ionospheric plasma.
Bernhardt, P A; Selcher, C A; Lehmberg, R H; Rodriguez, S P; Thomason, J F; Groves, K M; McCarrick, M J; Frazer, G J
2010-04-23
High power electromagnetic waves transmitted from the HAARP facility in Alaska can excite low-frequency electrostatic waves by magnetized stimulated Brillouin scatter. Either an ion-acoustic wave with a frequency less than the ion cyclotron frequency (f(CI)) or an electrostatic ion cyclotron (EIC) wave just above f(CI) can be produced. The coupled equations describing the magnetized stimulated Brillouin scatter instability show that the production of both ion-acoustic and EIC waves is strongly influenced by the wave propagation relative to the background magnetic field. Experimental observations of stimulated electromagnetic emissions using the HAARP transmitter have confirmed that only ion-acoustic waves are excited for propagation along the magnetic zenith and that EIC waves can only be detected with oblique propagation angles. The ion composition can be obtained from the measured EIC frequency. PMID:20482059
Stimulated Brillouin Scatter in a Magnetized Ionospheric Plasma
International Nuclear Information System (INIS)
High power electromagnetic waves transmitted from the HAARP facility in Alaska can excite low-frequency electrostatic waves by magnetized stimulated Brillouin scatter. Either an ion-acoustic wave with a frequency less than the ion cyclotron frequency (fCI) or an electrostatic ion cyclotron (EIC) wave just above fCI can be produced. The coupled equations describing the magnetized stimulated Brillouin scatter instability show that the production of both ion-acoustic and EIC waves is strongly influenced by the wave propagation relative to the background magnetic field. Experimental observations of stimulated electromagnetic emissions using the HAARP transmitter have confirmed that only ion-acoustic waves are excited for propagation along the magnetic zenith and that EIC waves can only be detected with oblique propagation angles. The ion composition can be obtained from the measured EIC frequency.
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...
A Rayleigh-Brillouin scattering spectrometer for ultraviolet wavelengths
Gu, Ziyu; van Duijn, Eric-Jan; Ubachs, Wim; 10.1063/1.4721272
2012-01-01
A spectrometer for the measurement of spontaneous Rayleigh-Brillouin scattering line profiles at ultraviolet wavelengths from gas phase molecules has been developed, employing a high-power frequency-stabilized UV laser with narrow bandwidth (2 MHz). The UV light from a frequency-doubled titanium:sapphire laser is further amplified in an enhancement cavity, delivering a 5 Watt UV-beam propagating through the interaction region inside a scattering cell. The design of the RB-scattering cell allows for measurements at gas pressures in the range 0-4 bar and at stably controlled temperatures from -30 to 70 degree Celsius. A scannable Fabry-Perot analyzer with instrument resolution of 232 MHz probes the Rayleigh-Brillouin profiles. Measurements on N2 and SF6 gases demonstrate the high signal-to-noise ratio achievable with the instrument, at the 1% level at the peak amplitude of the scattering profile.
A New Approach to Cascaded Stimulated Brillouin Scattering
Dong, Mark
2015-01-01
We present a novel approach to cascaded stimulated Brillouin scattering and frequency comb generation in which the multitude of interacting pump, Stokes, and anti-Stokes optical fields are described by a single forward wave and a single backward wave at a single carrier frequency. The envelopes of these two waves are modulated through coupling to a single acoustic oscillation and through four-wave mixing. Starting from a single pump field, we observe the emergence of a comb of frequencies as the intensity is increased. The set of three differential equations derived here are sufficient to describe the generation of any number of Brillouin sidebands in oscillator systems that would have required hundreds of coupled equations in the standard approach. We test the new approach on some published experiments and find excellent agreement with the results.
Brillouin scattering induced transparency and non-reciprocal light storage
Dong, Chun-Hua; Zou, Chang-Ling; Zhang, Yan-Lei; Fu, Wei; Guo, Guang-Can
2014-01-01
Stimulated Brillouin scattering (SBS) is a very fundamental interaction between light and travelling acoustic waves, which is mainly attributed to the electrostriction and photoelastic effects with the interaction strength being orders of magnitude larger than other nonlinearities. Although various photonic applications for all-optical light controlling based on SBS have been achieved in optical fiber and waveguides, the coherent light-acoustic interaction remains a challenge. Here, we experimentally demonstrated the Brillouin scattering induced transparency (BSIT) in a high quality optical microresonantor. Benefited from the triple-resonance in the whispering gallery cavity, the photon-phonon interaction is enhanced, and enables the light storage to the phonon, which has lifetime up to 10us. In addition, due to the phase matching condition, the stored circulating acoustic phonon can only interact with certain direction light, which leads to non-reciprocal light storage and retrieval. Our work paves the way t...
Realistic model for the stimulated Brillouin scattering instability
International Nuclear Information System (INIS)
The purpose of this work is to present a new model describing the stimulated Brillouin scattering instability in an inhomogeneous plasma. This model, called the harmonic decomposition method is based on the decomposition of plasma characteristics like density and speed into their short and long wavelengths components. This model describes: the propagation of the incident and reflected laser wave, the evolution of the sound wave and the hydrodynamic evolution of the plasma on a large scale. The first chapter recalls theoretical concepts concerning the stimulated Brillouin scattering, the filamentation and auto-focusing and introduces the harmonic decomposition method. The second chapter deals with the validation of this method through a comparison with an exact hydrodynamics model. The third chapter presents the interpretation of laser-plasma experiments with this new method. The fourth chapter presents different ways of improving the description by taking into account kinetics effects or a better decomposition of the sound wave. (A.C.)
Meng, Zhaokai; Jaiswal, Manish K.; Chitrakar, Chandani; Thakur, Teena; Gaharwar, Akhilesh K.; Yakovlev, Vladislav V.
2016-03-01
Developing new biomaterials is essential for the next-generation of materials for bioenergy, bioelectronics, basic biology, medical diagnostics, cancer research, and regenerative medicine. Specifically, recent progress in nanotechnology has stimulated the development of multifunctional biomaterials for tissue engineering applications. The physical properties of nanocomposite biomaterials, including elasticity and viscosity, play key roles in controlling cell fate, which underlines therapeutic success. Conventional mechanical tests, including uniaxial compression and tension, dynamic mechanical analysis and shear rheology, require mechanical forces to be directly exerted onto the sample and therefore may not be suitable for in situ measurements or continuous monitoring of mechanical stiffness. In this study, we employ spontaneous Brillouin spectroscopy as a viscoelasticity-specific probing technique. We utilized a Brillouin spectrometer to characterize biomaterial's microscopic elasticity and correlated those with conventional mechanical tests (e.g., rheology).
Quasi distributed hybrid Brillouin fiber laser sensor system
International Nuclear Information System (INIS)
A hybrid quasi distributed sensing system combining point fiber Bragg gratings and long integral Brillouin scattering transducers is presented. It is able to measure global temperature changes along the sensing line as well as punctual changes at the critical locations of the structure. A 20 km proof-of-concept system has been experimentally demonstrated with a temperature resolution of 0.47 °C. (paper)
Brillouin-Wigner perturbation theory in open electromagnetic systems
Muljarov, E. A.; Langbein, W; R. Zimmermann(Physikalisches Institut, University of Bonn, Bonn, Germany)
2012-01-01
A Brillouin-Wigner perturbation theory is developed for open electromagnetic systems which are characterised by discrete resonant states with complex eigenenergies. Since these states are exponentially growing at large distances, a modified normalisation is introduced that allows a simple spectral representation of the Green's function. The perturbed modes are found by solving a linear eigenvalue problem in matrix form. The method is illustrated on exactly solvable one- and three-dimensional ...
Brillouin distributed sensing using localized and stationary dynamic gratings
Primerov, Nikolay; Antman, Yair; Sancho Dura, Juan; Zadok, Avinoam; Thévenaz, Luc
2012-01-01
In this work, we apply a recent technique for the generation of stimulated Brillouin scattering (SBS) dynamic gratings that are both localized and stationary to realize high-resolution distributed temperature sensing. The gratings generation method relies on the phase modulation of two pump waves by a common pseudo-random bit sequence (PRBS), with a symbol duration that is much shorter than the acoustic lifetime. This way the acoustic wave can efficiently build up in the medium at discrete lo...
Distributed sensing employing stimulated Brillouin scattering in optical fibers
Antman, Yair; Thévenaz, Luc; Zadok, Avinoam
2012-01-01
Disclosed are methods and devices for distributed sensing of a measurable parameter employing stimulated Brillouin scattering in an optical fiber. A frequency-modulated or phase-modulated light wave is transmitted into the optical fiber. A scattered light wave in the optical fiber is monitored for sensing a measurable parameter. In some embodiments, the calculating step may include calculating a distance of a sensed location along the optical fiber using the monitored time of arrival.
All-optical signal processing using dynamic Brillouin gratings
Santagiustina, Marco; Chin, Sanghoon; Primerov, Nicolay; Ursini, Leonora; Thévenaz, Luc
2013-01-01
The manipulation of dynamic Brillouin gratings in optical fibers is demonstrated to be an extremely flexible technique to achieve, with a single experimental setup, several all-optical signal processing functions. In particular, all-optical time differentiation, time integration and true time reversal are theoretically predicted, and then numerically and experimentally demonstrated. The technique can be exploited to process both photonic and ultra-wide band microwave signals, so enabling many applications in photonics and in radio science. PMID:23549159
Brillouin-Wigner perturbation theory in open electromagnetic systems
Muljarov, E A; Zimmermann, R; 10.1209/0295-5075/92/50010
2012-01-01
A Brillouin-Wigner perturbation theory is developed for open electromagnetic systems which are characterised by discrete resonant states with complex eigenenergies. Since these states are exponentially growing at large distances, a modified normalisation is introduced that allows a simple spectral representation of the Green's function. The perturbed modes are found by solving a linear eigenvalue problem in matrix form. The method is illustrated on exactly solvable one- and three-dimensional examples being, respectively, a dielectric slab and a microsphere.
Stimulated Brillouin scattering enhancement in silicon inverse opal waveguides
Smith, M. J. A.; Wolff, C; Sterke, C. Martijn de; Lapine, M.; Kuhlmey, B. T.; Poulton, C. G.
2016-01-01
Silicon is an ideal material for on-chip applications, however its poor acoustic properties limit its performance for important optoacoustic applications, particularly for Stimulated Brillouin Scattering (SBS). We theoretically show that silicon inverse opals exhibit a strongly improved acoustic performance that enhances the bulk SBS gain coefficient by more than two orders of magnitude. We also design a waveguide that incorporates silicon inverse opals and which has SBS gain values that are ...
What is the Brillouin Zone of an Anisotropic Photonic Crystal?
Sivarajah, P; Ofori-Okai, B K; Nelson, K A
2015-01-01
The concept of the Brillouin zone (BZ) in relation to a photonic crystal fabricated in an optically anisotropic material is explored both experimentally and theoretically. In experiment, we used femtosecond laser pulses to excite THz polaritons and image their propagation in lithium niobate and lithium tantalate photonic crystal (PhC) slabs. We directly measured the dispersion relation inside PhCs and observed that the lowest bandgap expected to form at the BZ boundary forms inside the BZ in the anisotropic lithium niobate PhC. Our analysis shows that in an anisotropic material the BZ - defined as the Wigner-Seitz cell in the reciprocal lattice - is no longer bounded by Bragg planes and thus does not conform to the original definition of the BZ by Brillouin. We construct an alternative Brillouin zone defined by Bragg planes and show its utility in identifying features of the dispersion bands. We show that for an anisotropic 2D PhC without dispersion, the Bragg plane BZ can be constructed by applying the Wigne...
Fiore, Antonio; Zhang, Jitao; Shao, Peng; Yun, Seok Hyun; Scarcelli, Giuliano
2016-05-01
Brillouin microscopy has recently emerged as a powerful technique to characterize the mechanical properties of biological tissue, cell, and biomaterials. However, the potential of Brillouin microscopy is currently limited to transparent samples, because Brillouin spectrometers do not have sufficient spectral extinction to reject the predominant non-Brillouin scattered light of turbid media. To overcome this issue, we combined a multi-pass Fabry-Perot interferometer with a two-stage virtually imaged phased array spectrometer. The Fabry-Perot etalon acts as an ultra-narrow band-pass filter for Brillouin light with high spectral extinction and low loss. We report background-free Brillouin spectra from Intralipid solutions and up to 100 μm deep within chicken muscle tissue.
High-extinction VIPA-based Brillouin spectroscopy of turbid biological media
Fiore, Antonio; Shao, Peng; Yun, Seok Hyun; Scarcelli, Giuliano
2016-01-01
Brillouin microscopy has recently emerged as powerful technique to characterize the mechanical properties of biological tissue, cell and biomaterials. However, the potential of Brillouin microscopy is currently limited to transparent samples, because Brillouin spectrometers do not have sufficient spectral extinction to reject the predominant non-Brillouin scattered light of turbid media. To overcome this issue, we developed a spectrometer composed of a two VIPA stages and a multi-pass Fabry-Perot interferometer. The Fabry-Perot etalon acts as an ultra-narrow band-pass filter for Brillouin light with high spectral extinction and low loss. We report background-free Brillouin spectra from Intralipid solutions and up to 100 microns deep within chicken muscle tissue.
Cascaded Brillouin lasing in monolithic barium fluoride whispering gallery mode resonators
Energy Technology Data Exchange (ETDEWEB)
Lin, Guoping, E-mail: guoping.lin@femto-st.fr; Diallo, Souleymane; Saleh, Khaldoun; Martinenghi, Romain; Beugnot, Jean-Charles; Sylvestre, Thibaut; Chembo, Yanne K. [Optics Department, FEMTO-ST Institute (CNRS UMR6174), 25030 Besançon (France)
2014-12-08
We report the observation of stimulated Brillouin scattering and lasing at 1550 nm in barium fluoride (BaF{sub 2}) crystal. Brillouin lasing was achieved with ultra-high quality (Q) factor monolithic whispering gallery mode mm-size disk resonators. Overmoded resonators were specifically used to provide cavity resonances for both the pump and all Brillouin Stokes waves. Single and multiple Brillouin Stokes radiations with frequency shift ranging from 8.2 GHz up to 49 GHz have been generated through cascaded Brillouin lasing. BaF{sub 2} resonator-based Brillouin lasing can find potential applications for high-coherence lasers and microwave photonics.
Measurement error analysis of Brillouin lidar system using F-P etalon and ICCD
Yao, Yuan; Niu, Qunjie; Liang, Kun
2016-09-01
Brillouin lidar system using Fabry-Pérot (F-P) etalon and Intensified Charge Coupled Device (ICCD) is capable of real time remote measuring of properties like temperature of seawater. The measurement accuracy is determined by two key parameters, Brillouin frequency shift and Brillouin linewidth. Three major errors, namely the laser frequency instability, the calibration error of F-P etalon and the random shot noise are discussed. Theoretical analysis combined with simulation results showed that the laser and F-P etalon will cause about 4 MHz error to both Brillouin shift and linewidth, and random noise bring more error to linewidth than frequency shift. A comprehensive and comparative analysis of the overall errors under various conditions proved that colder ocean(10 °C) is more accurately measured with Brillouin linewidth, and warmer ocean (30 °C) is better measured with Brillouin shift.
Effect of collisions on amplification of laser beams by Brillouin scattering in plasmas
Humphrey, K. A.; Trines, R. M. G. M.; Fiuza, F.; Speirs, D. C.; Norreys, P.; Cairns, R. A.; Silva, L. O.; R. Bingham
2013-01-01
We report on particle in cell simulations of energy transfer between a laser pump beam and a counter-propagating seed beam using the Brillouin scattering process in uniform plasma including collisions. The results presented show that the ion acoustic waves excited through naturally occurring Brillouin scattering of the pump field are preferentially damped without affecting the driven Brillouin scattering process resulting from the beating of the pump and seed fields together. We find that col...
Signal Processing for Fibre-optic Distributed Sensing Techniques Employing Brillouin Scattering
Institute of Scientific and Technical Information of China (English)
XIAO Shang-hui; LI Li
2009-01-01
As fibre optic distributed scattering sensing systems are providing innovative solutions for the monitoring of large structures, Brillouin-based distributed scattering sensing techniques represent a new physical approach for structures health monitoring, which seems extremely promising and is receiving most attentions. This paper comprehensively presents some methods of signal interrogation for fibre optic Brillouin-based distributed scattering sensing technology, especially establishes an accurate Pseudo-Voigt model of Brillouin gain spectrum and gives some results on spectrum analysis and data processing.
Carnot's theorem as Noether's theorem for thermoacoustic engines
International Nuclear Information System (INIS)
Onset in thermoacoustic engines, the transition to spontaneous self-generation of oscillations, is studied here as both a dynamical critical transition and a limiting heat engine behavior. The critical transition is interesting because it occurs for both dissipative and conservative systems, with common scaling properties. When conservative, the stable oscillations above the critical point also implement a reversible engine cycle satisfying Carnot's theorem, a universal conservation law for entropy flux. While criticality in equilibrium systems is naturally associated with symmetries and universal conservation laws, these are usually exploited with global minimization principles, which dynamical critical systems may not have if dissipation is essential to their criticality. Acoustic heat engines furnish an example connecting equilibrium methods with dynamical and possibly even dissipative critical transitions: A reversible engine is shown to map, by a change of variables, to an equivalent system in apparent thermal equilibrium; a Noether symmetry in the equilibrium field theory implies Carnot's theorem for the engine. Under the same association, onset is shown to be a process of spontaneous symmetry breaking and the scaling of the quality factor predicted for both the reversible and irreversible engines is shown to arise from the Ginzburg-Landau description of the broken phase. copyright 1998 The American Physical Society
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.
Bringing Theorem Proving to the (sonic) Masses
Gallego Arias, Emilio Jesús; Pin, Benoît; Jouvelot, Pierre,
2015-01-01
We explore the intersection of interactive theorem proving and digital signal processing through the use of web-based, rich interfaces. Traditionally, the barrier to entry to interactive theorem proving has been high.Provers are complex systems using obscure programming languages, and libraries may be underdocumented and use formalisms and notations far from the standard domain-specific practice. Thus, it doesn't come at a surprise that interactive theorem proving has seldom been explored in ...
The relativistic virial theorem and scale invariance
Gaite, Jose
2013-01-01
The virial theorem is related to the dilatation properties of bound states. This is realized, in particular, by the Landau-Lifshitz formulation of the relativistic virial theorem, in terms of the trace of the energy-momentum tensor. We construct a Hamiltonian formulation of dilatations in which the relativistic virial theorem naturally arises as the condition of stability against dilatations. A bound state becomes scale invariant in the ultrarelativistic limit, in which its energy vanishes. H...
The Equivalence Theorem and Effective Lagrangians
Grosse-Knetter, Carsten; Kuss, Ingolf
1994-01-01
We point out that the equivalence theorem, which relates the amplitude for a process with external longitudinally polarized vector bosons to the amplitude in which the longitudinal vector bosons are replaced by the corresponding pseudo-Goldstone bosons, is not valid for effective Lagrangians. However, a more general formulation of this theorem also holds for effective interactions. The generalized theorem can be utilized to determine the high-energy behaviour of scattering processes just by p...
The exchange fluctuation theorem in quantum mechanics
Akagawa, Shiho; Hatano, Naomichi
2009-01-01
We study the heat transfer between two finite quantum systems initially at different temperatures. We find that a recently proposed fluctuation theorem for heat exchange, namely the exchange fluctuation theorem [C. Jarzynski and D. K. Wojcik, Phys. Rev. Lett. 92, 230602 (2004)], does not generally hold in the presence of a finite heat transfer as in the original form proved for weak coupling. As the coupling is weakened, the deviation from the theorem and the heat transfer vanish in the same ...
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.
Shell theorem for spontaneous emission
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Mortensen, Jakob Egeberg; Lodahl, Peter; Stobbe, Søren
2013-01-01
We investigate spontaneous emission from excitons beyond the point source dipole approximation and show how the symmetry of the exciton wave function plays a crucial role. We find that for spherically symmetric wave functions, the Purcell effect is independent of the wave function size 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....
Herbrand Theorems for Substructural Logics
Czech Academy of Sciences Publication Activity Database
Cintula, Petr; Metcalfe, G.
Berlin: Springer, 2013 - (McMillan, K.; Middeldorp, A.; Voronkov, A.), s. 584-600. (Lecture Notes in Computer Science. Advanced Research in Computing and Software Science. 8312). ISBN 978-3-642-45221-5. ISSN 0302-9743. [LPAR-19. International Conference /19./. Stellenbosch (ZA), 14.12.2013-19.12.2013] R&D Projects: GA ČR GAP202/10/1826 Institutional support: RVO:67985807 Keywords : substructural logics * residuated lattices * Herbrand theorem * Skolemization * predicate logics Subject RIV: BA - General Mathematics
The inverse Fueter mapping theorem
Colombo, Fabrizio; Sabadini, Irene; Sommen, Franciscus
2011-01-01
In a recent paper the authors have shown how to give an integral representation of the Fueter mapping theorem using the Cauchy formula for slice monogenic functions. Specifically, given a slice monogenic function f of the form f = alpha + (omega) under bar beta (where alpha, beta satisfy the Cauchy-Riemann equations) we represent in integral form the axially monogenic function f = A + (omega) under barB (where A, B satisfy the Vekua's system) given by f(x) = Delta n-1/2 f (x) where Delta is t...
A generalized preimage theorem in global analysis
Institute of Scientific and Technical Information of China (English)
MA; Jipu
2001-01-01
［1］Ma Jipu, (1.2) inverses of operators between Banach spaces and conjugacy theorem, Chinese Annals of Math., B, 1999, 20(1): 57.［2］Ma Jipu, Rank theorem of operators between Banach spaces, Science in China, Ser. A, 2000, 43(1): 1.［3］Ma Jipu, Local conjugacy theorem, rank theorems in advenced calculus and a generalized principle constructing Banach manifolds, Science in China, Ser. A, 2000, 43(12): 1233.［4］Zeidler, A. E., Nonlinear Function Analysis and Its Applications, IV: Applications to Mathematical Physics, New York: Springer-Verlag, 1988.
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.
Cosmological Perturbations and the Weinberg Theorem
Akhshik, Mohammad; Jazayeri, Sadra
2015-01-01
The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.
Vela Velupillai, K.
2014-01-01
The Hahn-Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using nonconstructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn-Banach theorems in mathematical economics and advanced general equilibrium theory. The suggested modification would make applied and policy-oriented...
An elementary derivation of the quantum virial theorem from Hellmann–Feynman theorem
İpekoğlu, Y.; Turgut, S.
2016-07-01
A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann–Feynman theorem produces the final statement of the virial theorem.
Two extensions of Ramsey's theorem
Conlon, David; Sudakov, Benny
2011-01-01
Ramsey's theorem, in the version of Erd\\H{o}s and Szekeres, states that every 2-coloring of the edges of the complete graph on {1, 2,...,n} contains a monochromatic clique of order 1/2\\log n. In this paper, we consider two well-studied extensions of Ramsey's theorem. Improving a result of R\\"odl, we show that there is a constant $c>0$ such that every 2-coloring of the edges of the complete graph on \\{2, 3,...,n\\} contains a monochromatic clique S for which the sum of 1/\\log i over all vertices i \\in S is at least c\\log\\log\\log n. This is tight up to the constant factor c and answers a question of Erd\\H{o}s from 1981. Motivated by a problem in model theory, V\\"a\\"an\\"anen asked whether for every k there is an n such that the following holds. For every permutation \\pi of 1,...,k-1, every 2-coloring of the edges of the complete graph on {1, 2, ..., n} contains a monochromatic clique a_1a_{\\pi(2)+1}-a_{\\pi(2)}>...>a_{\\pi(k-1)+1}-a_{\\pi(k-1)}. That is, not only do we want a monochromatic clique, but the difference...
Zonas de Brillouin de los grupos de capa
García Santos, Laura
2016-01-01
La base de datos de las zonas de Brillouin de los grupos de capa del Bilbao Crystallographic Server incluye tablas de vectores de onda y figuras que forman la base para la clasificación de las representaciones de los grupos de capa. Las propiedades de simetría de los vectores de onda se determinan por los llamados grupos del espacio recíproco y esta clasificación se compara con la que recoge el libro “Character Tables and Compatibility Relations of The Eighty Layer Groups and Seventeen Plane ...
Stimulated Brillouin scattering enhancement in silicon inverse opal waveguides
Smith, M J A; de Sterke, C Martijn; Lapine, M; Kuhlmey, B T; Poulton, C G
2016-01-01
Silicon is an ideal material for on-chip applications, however its poor acoustic properties limit its performance for important optoacoustic applications, particularly for Stimulated Brillouin Scattering (SBS). We theoretically show that silicon inverse opals exhibit a strongly improved acoustic performance that enhances the bulk SBS gain coefficient by more than two orders of magnitude. We also design a waveguide that incorporates silicon inverse opals and which has SBS gain values that are comparable with chalcogenide glass waveguides. This research opens new directions for opto-acoustic applications in on-chip material systems.
Atherosclerotic plaque detection by confocal Brillouin and Raman microscopies
Meng, Zhaokai; Basagaoglu, Berkay; Yakovlev, Vladislav V.
2015-02-01
Atherosclerosis, the development of intraluminal plaque, is a fundamental pathology of cardiovascular system and remains the leading cause of morbidity and mortality worldwide. Biomechanical in nature, plaque rupture occurs when the mechanical properties of the plaque, related to the morphology and viscoelastic properties, are compromised, resulting in intraluminal thrombosis and reduction of coronary blood flow. In this report, we describe the first simultaneous application of confocal Brillouin and Raman microscopies to ex-vivo aortic wall samples. Such a non-invasive, high specific approach allows revealing a direct relationship between the biochemical and mechanical properties of atherosclerotic tissue.
Brillouin scattering from collective spin waves in magnetic superlattices (invited)
Energy Technology Data Exchange (ETDEWEB)
Hillebrands, B.; Boufelfel, A.; Falco, C.M.; Baumgart, P.; Guentherodt, G.; Zirngiebl, E.; Thompson, J.D.
1988-04-15
We report on the observation and the analysis of collective magnetostatic spin-wave excitations in magnetic superlattices. The influence of interface anisotropies, which can become dominant for small modulation wavelengths, is discussed. For the system Fe/Pd we show that Brillouin spectroscopy experiments in combination with the measurement of the saturation magnetization by a SQUID magnetometer give evidence for a magnetic polarization of the Pd spacer layers, as well as for a small negative out-of-plane interface anisotropy constant of K/sub s/ = -0.15 erg/cm/sup 2/.
Brillouin scattering from collective spin waves in magnetic superlattices
Energy Technology Data Exchange (ETDEWEB)
Hillebrands, B.; Boufelfel, A.; Falco, C.M.; Baumgart, P.; Guentherodt, G.; Zirngiebl, E.; Thompson, J.D.
1987-01-01
We report on the observation and the analysis of collective magnetostatic spin-wave excitations in magnetic superlattices. The influence of interface anisotropies, which can become dominant for small modulation wavelengths, is discussed. For the system Fe/Pd we show that Brillouin spectroscopy experiments in combination with the measurement of the saturation magnetization by a SQUID magnetometer give evidence for a magnetic polarization of the Pd spacer layers, as well as for a small negative out-of-plane interface anisotropy constant of K/sub s/ = -0.15 erg/cm/sup 2/. 22 refs., 5 figs., 1 tab.
Magnetostatic wave device characterization by Brillouin light scattering
Patton, Carl E.; Srinivasan, Gopalan
1989-02-01
This final report summarizes the important results of the Brillouin light scattering investigations of magnetic excitations in magnetostatic wave (MSW) devices which were carried out under the RADC contract. The key accomplishments were the observation and characterization of surface waves, forward volume waves, backward volume waves, parametric spin waves, and a new type of evanescent surface wave in yttrium iron garnet film MSW devices. The propagation characteristics for surface wave in Fe, Co-Cr, and Ni-Fe films were also examined, in order to investigate the possible use of such films in MSW devices. Details on technical publications and participating personnel during this contract period are also provided.
Sancho J.; Chin S.; Sagues M.; Loayssa A.; Lloret J.; Gasulla I.; Sales S.; Thevenaz L.; Capmany J.
2010-01-01
Dynamic reconfiguration of a microwave photonic filter by tuning its basic delay based on stimulated Brillouin scattering-induced slow light and optical phase shift of the optical carrier is experimentally implemented. The measurements confirm that the free spectral range of the filter changes when a Brillouin pump is applied. These results demonstrate the potential of the separate carrier technique in microwave photonics applications.
Abel's Theorem in the Noncommutative Case
Leitenberger, Frank
2005-01-01
We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic differentials of the first kind. Following Abel we prove Abel's Theorem.
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...
Anisotropic weak Hardy spaces and interpolation theorems
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper, the authors establish the anisotropic weak Hardy spaces associated with very general discrete groups of dilations. Moreover, the atomic decomposition theorem of the anisotropic weak Hardy spaces is also given. As some applications of the above results, the authors prove some interpolation theorems and obtain the boundedness of the singular integral operators on these Hardy spaces.
Convergence theorems for intermediate problems. II
Beattie, C. A.; Greenlee, W. M.
2002-01-01
Convergence theorems for the practical eigenvector free methods of Gay and Goerisch are obtained under a variety of hypotheses, so that our theorems apply to both traditional boundary-value problems and atomic problems. In addition, we prove convergence of the T*T method of Bazley and Fox without an alignment of projections hypothesis required in previous literature.
Interpolation theorems on weighted Lorentz martingale spaces
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation theorems,we obtain some inequalities on martingale transform operator.
AN ABSTRACT ORLICS: PETTIS THEOREM AND APPLICATIONS
Directory of Open Access Journals (Sweden)
LI RONGLU
2008-08-01
Full Text Available In this paper we establish two abstract versions of the classical Orlicz-Pettis Theorem for multiplier convergent series. We show that these abstract results yield known versions of the Orlicz-Pettis Theorem for locally convex spaces as well as versions for operator valued series. We also give applications to vector valued measures and spaces of continuous functions.
The Ahlfors lemma and Picard's theorems
Simonič, Aleksander
2015-01-01
The article introduces Ahlfors' generalization of the Schwarz lemma. With this powerful geometric tool of complex functions in one variable, we are able to prove some theorems concerning the size of images under holomorphic mappings, including the celebrated Picard's theorems. The article concludes with a brief insight into the theory of Kobayashi hyperbolic complex manifolds.
Generalized Fibonacci Numbers and Blackwell's Renewal Theorem
Christensen, Sören
2010-01-01
We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers. With the help of error estimates in the renewal theorem we figure out an explicit representation.
Szemeredi's theorem and problems on arithmetic progressions
International Nuclear Information System (INIS)
Szemeredi's famous theorem on arithmetic progressions asserts that every subset of integers of positive asymptotic density contains arithmetic progressions of arbitrary length. His remarkable theorem has been developed into a major new area of combinatorial number theory. This is the topic of the present survey.
No-cloning theorem in thermofield dynamics
Prudencio, Thiago
2011-01-01
Here we apply the no-cloning theorem from quantum information in the thermofield dynamics (TFD) scenario, relating the doubling procedure of TFD to a cloning machine process. As a consequence we use the no-cloning theorem to demonstrate that the thermal vaccuum state defined in TFD is necessarilly a mixed state.
No-cloning theorem in thermofield dynamics
Prudencio, Thiago
2011-01-01
We discuss the relation between the no-cloning theorem from quantum information and the doubling procedure used in the formalism of thermofield dynamics (TFD). We also discuss how to apply the no-cloning theorem in the context of thermofield states defined in TFD. Consequences associated to mixed states, von Neumann entropy and thermofield vacuum are also addressed.
A New Fixed Point Theorem and Applications
Directory of Open Access Journals (Sweden)
Min Fang
2013-01-01
Full Text Available A new fixed point theorem is established under the setting of a generalized finitely continuous topological space (GFC-space without the convexity structure. As applications, a weak KKM theorem and a minimax inequalities of Ky Fan type are also obtained under suitable conditions. Our results are different from known results in the literature.
Non perturbative Adler-Bardeen Theorem
Mastropietro, Vieri
2006-01-01
The Adler-Bardeen theorem has been proved 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 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…
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...
A Generalization of the Prime Number Theorem
Bruckman, Paul S.
2008-01-01
In this article, the author begins with the prime number theorem (PNT), and then develops this into a more general theorem, of which many well-known number theoretic results are special cases, including PNT. He arrives at an asymptotic relation that allows the replacement of certain discrete sums involving primes into corresponding differentiable…
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…
Boundary contributions to the hypervirial theorem
Esteve, J. G.; Falceto, F.; Giri, Pulak Ranjan
2012-01-01
It is shown that under certain boundary conditions the virial theorem has to be modified. We analyze the origin of the extra term and compute it in particular examples. The Coulomb and harmonic oscillator with point interaction have been studied in the light of this generalization of the virial theorem.
A Simple Vector Proof of Feuerbach's Theorem
Scheer, Michael
2011-01-01
The celebrated theorem of Feuerbach states that the nine-point circle of a nonequilateral triangle is tangent to both its incircle and its three excircles. In this note, we give a simple proof of Feuerbach's Theorem using straightforward vector computations. All required preliminaries are proven here for the sake of completeness.
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: 0.765, year: 2014 http://cms.math.ca/10.4153/CJM-2014-030-6
New proofs of basic theorems in calculus
Reem, Daniel
2007-01-01
In this note we present new proofs of three basic theorems in calculus. Although these theorems are well-known, in each proof we obtain something which seems to be unknown. We start with the Heine-Cantor theorem about uniform continuity and obtain explicitly the optimal delta for the given epsilon. We then proceed with the Weierstrass extreme value theorem and present two proofs of it: the ``envelope proof'' in which the largest possible maximal point is found using an envelope function, and the ``programmer proof'', which does not use the costume argument of proving boundedness first, and in which an explicit sequence is shown to converge monotonically to the maximal value. We finish with the intermediate value theorem, which is generalized to a class of discontinuous functions and in which the meaning of the intermediate value property is re-examined. In the end we discuss in which sense the proofs are constructive.
Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre.
Beugnot, Jean-Charles; Lebrun, Sylvie; Pauliat, Gilles; Maillotte, Hervé; Laude, Vincent; Sylvestre, Thibaut
2014-01-01
Brillouin scattering in optical fibres is a fundamental interaction between light and sound with important implications ranging from optical sensors to slow and fast light. In usual optical fibres, light both excites and feels shear and longitudinal bulk elastic waves, giving rise to forward-guided acoustic wave Brillouin scattering and backward-stimulated Brillouin scattering. In a subwavelength-diameter optical fibre, the situation changes dramatically, as we here report with the first experimental observation of Brillouin light scattering from surface acoustic waves. These Rayleigh-type surface waves travel the wire surface at a specific velocity of 3,400 m s(-1) and backscatter the light with a Doppler shift of about 6 GHz. As these acoustic resonances are sensitive to surface defects or features, surface acoustic wave Brillouin scattering opens new opportunities for various sensing applications, but also in other domains such as microwave photonics and nonlinear plasmonics. PMID:25341638
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...
Dirac's theorem for random graphs
Lee, Choongbum
2011-01-01
A classical theorem of Dirac from 1952 asserts that every graph on $n$ vertices with minimum degree at least $\\lceil n/2 \\rceil$ is Hamiltonian. In this paper we extend this result to random graphs. Motivated by the study of resilience of random graph properties we prove that if $p \\gg \\log n /n$, then a.a.s. every subgraph of $G(n,p)$ with minimum degree at least $(1/2+o(1))np$ is Hamiltonian. Our result improves on previously known bounds, and answers an open problem of Sudakov and Vu. Both, the range of edge probability $p$ and the value of the constant 1/2 are asymptotically best possible.
Ehrenfest Theorem in Precanonical Quantization
Kanatchikov, I V
2015-01-01
We discuss the precanonical quantization of fields, which is based on the De Donder-Weyl (DW) Hamiltonian formulation and does not distinguish between the space and time variables. Classical field equations in DW Hamiltonian form are derived as the equations on the expectation values of the corresponding precanonical quantum operators. This field-theoretic generalization of the quantum mechanical Ehrenfest theorem demonstrates the consistency of three aspects of precanonical field quantization: the precanonical representation of operators in terms of the Clifford (Dirac) algebra valued partial differential operators, the Dirac-like precanonical generalization of the Schr\\"odinger equation without the distinguished time dimension, and the prescription of calculating the expectation values of operators using the Clifford-valued precanonical wave functions.
Singlet and triplet instability theorems
Energy Technology Data Exchange (ETDEWEB)
Yamada, Tomonori; Hirata, So, E-mail: sohirata@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan)
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree–Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree–Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree–Fock-theory-based explanations of Hund’s rule, a singlet instability in Jahn–Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Magnetohydrodynamic stability comparison theorems revisited
International Nuclear Information System (INIS)
Magnetohydrodynamic (MHD) stability comparison theorems are presented for several different plasma models, each one corresponding to a different level of collisionality: a collisional fluid model (ideal MHD), a collisionless kinetic model (kinetic MHD), and two intermediate collisionality hybrid models (Vlasov-fluid and kinetic MHD-fluid). Of particular interest is the re-examination of the often quoted statement that ideal MHD makes the most conservative predictions with respect to stability boundaries for ideal modes. Some of the models have already been investigated in the literature and we clarify and generalize these results. Other models are essentially new and for them we derive new comparison theorems. Three main conclusions can be drawn: (1) it is crucial to distinguish between ergodic and closed field line systems; (2) in the case of ergodic systems, ideal MHD does indeed make conservative predictions compared to the other models; (3) in closed line systems undergoing perturbations that maintain the closed line symmetry this is no longer true. Specifically, when the ions are collisionless and their gyroradius is finite, as in the Vlasov-fluid model, there is no compressibility stabilization. The Vlasov-fluid model is more unstable than ideal MHD. The reason for this is related to the wave-particle resonance associated with the perpendicular precession drift motion of the particles (i.e., the ExB drift and magnetic drifts), combined with the absence of any truly toroidally trapped particles. The overall conclusion is that to determine macroscopic stability boundaries for ideal modes for any magnetic geometry using a simple conservative approach, one should analyze the ideal MHD energy principle for incompressible displacements.
Singlet and triplet instability theorems
International Nuclear Information System (INIS)
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree–Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree–Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree–Fock-theory-based explanations of Hund’s rule, a singlet instability in Jahn–Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions
OTTER, Resolution Style Theorem Prover
International Nuclear Information System (INIS)
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
Spectral shape of stimulated Brillouin scattering in crystals
Ohno, S.; Sonehara, T.; Tatsu, E.; Koreeda, A.; Saikan, S.
2015-12-01
We derived a formula to describe the stimulated Brillouin spectral shape in crystals for various temperatures ranging from room temperature to liquid-helium temperature. We modeled a sample as a one-dimensional system with a finite thickness in which the optically induced phonon propagates, partly interacting with the pump and probe laser beams. When the sample length is shorter than the propagation distance (i.e., the mean free path) of phonons, the spectral shape becomes multipeaked due to the multiple phonon reflections in the sample. Such a situation can be realized in a thin film or a bulk sample at low temperatures. We experimentally measured the Brillouin gain spectra with a multipeak structure in TeO2 and PbMoO4 crystals at low temperatures. We found that these spectra were reproduced by our formula for both the coaxial and off-axis phonon propagations with respect to the laser beams. It was revealed that our formula is very useful in estimating the phonon attenuation coefficient from the observed spectra, which gradually change from Lorentzian shape to a multipeak spectrum with decreasing temperature.
Brillouin distributed sensing using localized and stationary dynamic gratings
Primerov, Nikolay; Antman, Yair; Sancho, Juan; Zadok, Avi; Thevenaz, Luc
2012-04-01
In this work, we apply a recent technique for the generation of stimulated Brillouin scattering (SBS) dynamic gratings that are both localized and stationary to realize high-resolution distributed temperature sensing. The gratings generation method relies on the phase modulation of two pump waves by a common pseudo-random bit sequence (PRBS), with a symbol duration that is much shorter than the acoustic lifetime. This way the acoustic wave can efficiently build up in the medium at discrete locations only, where the phase difference between the two waves does not temporarily vary. The separation between neighboring correlation peaks can be made arbitrarily long. Using the proposed method, we experimentally demonstrate distributed temperature sensing with 5 cm resolution, based on modifications to both the local birefringence and the local Brillouin frequency shift in polarization maintaining fibers. The localization method does not require wideband detection and can generate the grating at any random position along the fiber, with complete flexibility. The phase-coding method is equally applicable to high-resolution SBS distributed sensing over standard fibers.
Brillouin scattering of light by spin waves in ferromagnetic nanorods
International Nuclear Information System (INIS)
We report the investigations of spin wave modes of arrays of Ni and Co nanorods using Brillouin light scattering. We have revealed the significant influence of spin wave modes along the nanorod axis in contrast to infinite magnetic nanowires. Unusual optical properties featuring an inverted Stokes/anti-Stokes asymmetry of the Brillouin scattering spectra have been observed. The spectrum of spin wave modes in the nanorod array has been calculated and compared with the experiment. Experimental observations are explained in terms of a combined numerical–analytical approach taking into account both the low aspect ratio of individual magnetic nanorods and dipolar magnetic coupling between the nanorods in the array. The optical studies of spin-wave modes in nanorod metamaterials with low aspect ratio nanorods have revealed new magnetic and magneto-optical properties compared to continuous magnetic films or infinite magnetic nanowires. Such magnetic artificial materials are important class of active metamaterials needed for prospective data storage and signal processing applications.
The pointwise Hellmann-Feynman theorem
Directory of Open Access Journals (Sweden)
David Carfì
2010-02-01
Full Text Available In this paper we study from a topological point of view the Hellmann-Feynman theorem of Quantum Mechanics. The goal of the paper is twofold: On one hand we emphasize the role of the strong topology in the classic version of the theorem in Hilbert spaces, for what concerns the kind of convergence required on the space of continuous linear endomorphisms, which contains the space of (continuous observables.On the other hand we state and prove a new pointwise version of the classic Hellmann-Feynman theorem. This new version is not yet present in the literature and follows the idea of A. Bohm concerning the topology which is desiderable to use in Quantum Mechanics. It is indeed out of question that this non-trivial new version of the Hellmann-Feynman theorem is the ideal one - for what concerns the continuous observables on Hilbert spaces, both from a theoretical point of view, since it is the strongest version obtainable in this context - we recall that the pointwise topology is the coarsest one compatible with the linear structure of the space of continuous observables -, and from a practical point of view, because the pointwise topology is the easiest to use among topologies: it brings back the problems to the Hilbert space topology. Moreover, we desire to remark that this basic theorem of Quantum Mechanics, in his most desiderable form, is deeply interlaced with two cornerstones of Functional Analysis: the Banach-Steinhaus theorem and the Baire theorem.
An algebraic spin and statistics theorem
Guido, I D
1994-01-01
Abstract. A spin-statistics theorem and a PCT theorem are obtained in the context of the superselection sectors in Quantum Field Theory on a 4-dimensional space-time. Our main assumption is the requirement that the modular groups of the von Neumann algebras of local observables associated with wedge regions act geometrically as pure Lorentz transformations. Such a property, satisfied by the local algebras generated by Wightman fields because of the Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.
A Generalization of Chaplygin's Reducibility Theorem
Fernandez, O E; Bloch, A M
2009-01-01
In this paper we study Chaplygin's Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton-Poincare-d'Alembert equations in arbitrary degrees of freedom. As special cases we extract the extension of the Theorem to nonholonomic Chaplygin systems with nonabelian symmetry groups as well as Euler-Poincare-Suslov systems in arbitrary degrees of freedom. In the latter case, we also extend the Hamiltonization Theorem to nonholonomic systems which do not possess an invariant measure. Lastly, we extend previous work on conditionally variational systems using the results above. We illustrate the results through various examples of well-known nonholonomic systems.
Existence theorems for ordinary differential equations
Murray, Francis J
2007-01-01
Theorems stating the existence of an object-such as the solution to a problem or equation-are known as existence theorems. This text examines fundamental and general existence theorems, along with the Picard iterants, and applies them to properties of solutions and linear differential equations.The authors assume a basic knowledge of real function theory, and for certain specialized results, of elementary functions of a complex variable. They do not consider the elementary methods for solving certain special differential equations, nor advanced specialized topics; within these restrictions, th
Limit theorems for 2D invasion percolation
Damron, Michael
2010-01-01
We prove limit theorems and variance estimates for quantities related to ponds and outlets for 2D invasion percolation. We first exhibit several properties of a sequence (O(n)) of outlet variables, the n-th of which gives the number of outlets in the box centered at the origin of side length 2^n. The most important of these properties describe the sequence's renewal structure and exponentially fast mixing behavior. We use these to prove a central limit theorem and strong law of large numbers for (O(n)). We then show consequences of these limit theorems for the pond radii and outlet weights.
Quadratic Goldreich-Levin Theorems
Tulsiani, Madhur
2011-01-01
Decomposition theorems in classical Fourier analysis enable us to express a bounded function in terms of few linear phases with large Fourier coefficients plus a part that is pseudorandom with respect to linear phases. The Goldreich-Levin algorithm can be viewed as an algorithmic analogue of such a decomposition as it gives a way to efficiently find the linear phases associated with large Fourier coefficients. In the study of "quadratic Fourier analysis", higher-degree analogues of such decompositions have been developed in which the pseudorandomness property is stronger but the structured part correspondingly weaker. For example, it has previously been shown that it is possible to express a bounded function as a sum of a few quadratic phases plus a part that is small in the $U^3$ norm, defined by Gowers for the purpose of counting arithmetic progressions of length 4. We give a polynomial time algorithm for computing such a decomposition. A key part of the algorithm is a local self-correction procedure for Re...
Lorentz violating kinematics: threshold theorems
Baccetti, Valentina; Tate, Kyle; Visser, Matt
2012-03-01
Recent tentative experimental indications, and the subsequent theoretical speculations, regarding possible violations of Lorentz invariance have attracted a vast amount of attention. An important technical issue that considerably complicates detailed calculations in any such scenario, is that once one violates Lorentz invariance the analysis of thresholds in both scattering and decay processes becomes extremely subtle, with many new and naively unexpected effects. In the current article we develop several extremely general threshold theorems that depend only on the existence of some energy momentum relation E(p), eschewing even assumptions of isotropy or monotonicity. We shall argue that there are physically interesting situations where such a level of generality is called for, and that existing (partial) results in the literature make unnecessary technical assumptions. Even in this most general of settings, we show that at threshold all final state particles move with the same 3-velocity, while initial state particles must have 3-velocities parallel/anti-parallel to the final state particles. In contrast the various 3-momenta can behave in a complicatedand counter-intuitive manner.
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.
TRANSVERSAL SPACES AND FIXED POINT THEOREMS
Sinia N. Ješić; Milan R. Tasković; Nataša Babačev
2007-01-01
In this paper we define Transversal functional probabilistic spaces (upper and lower) as a natural extension of Metric spaces, Probabilistic metric spaces and Fuzzy metric spaces. Also, we formulate and prove some fixed and common fixed point theorems.
Remarks on the Cayley-Hamilton Theorem
Gatto, Letterio; Scherbak, Inna
2015-01-01
We revisit the classical theorem by Cayley and Hamilton, "{\\em each endomorphism is a root of its own characteristic polynomial}", from the point of view of {\\em Hasse--Schmidt derivations on an exterior algebra}
Yet another proof of Szemeredi's theorem
Green, Ben
2010-01-01
Using the density-increment strategy of Roth and Gowers, we derive Szemeredi's theorem on arithmetic progressions from the inverse conjectures GI(s) for the Gowers norms, recently established by the authors and Ziegler.
Limit Theorems in Free Probability Theory I
Chistyakov, G. P.; Götze, F.
2006-01-01
Based on a new analytical approach to the definition of additive free convolution on probability measures on the real line we prove free analogs of limit theorems for sums for non-identically distributed random variables in classical Probability Theory.
Two No-Go Theorems on Superconductivity
Tada, Yasuhiro
2016-01-01
We study lattice superconductors such as attractive Hubbard models. As is well known, Bloch's theorem asserts absence of persistent current in ground states and equilibrium states for general fermion systems. While the statement of the theorem is true, we can show that the theorem cannot exclude possibility of a surface persistent current. Such a current can be stabilized by boundary magnetic fields which do not penetrate into the bulk region of a superconductor, provided emergence of massive photons, i.e., Meissner effect. Therefore, we can expect that a surface persistent current is realized for a ground/equilibrium state in the sense of stability against local perturbations. We also apply Elitzur's theorem to superconductors at finite temperatures. As a result, we prove absence of symmetry breaking of the global U(1) phase of electrons for almost all gauge fixings. These observations suggest that the nature of superconductivity is the emergence of massive photons rather than the symmetry breaking of the U(...
A generalized preimage theorem in global analysis
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The concept of locally fine point and generalized regular valueof a C1 map between Banach spaces were carried over C1 map between Banach manifolds. Hence the preimage theorem, a principle constructing Banach manifolds in global analysis, is generalized.
Interval logic. Proof theory and theorem proving
DEFF Research Database (Denmark)
Rasmussen, Thomas Marthedal
2002-01-01
Real-time systems are computer systems which have to meet real-time constraints. To increase the confidence in such systems, formal methods and formal verification are utilized. The class of logics known as interval logics can be used for expressing properties and requirements of real-time systems...... labelled natural deduction system. We conduct theoretical investigations of the systems with respect to subformula properties, proof search, etc. The generic theorem proving system Isabelle is used as a framework for encoding both proof theoretical systems. We consider a number of examples/small case....... By theorem proving we understand the activity of proving theorems of a logic with the assistance of a computer. The goal of this thesis is to improve theorem proving support for interval logics such that larger and more realistic case-studies of real-time systems can be conducted using these...
Lambda-mu-calculus and Bohm's theorem
David, René; Py, Walter
2001-01-01
The lambda mu-calculus is an extension of the lambda-calculus that has been introduced by M. Parigot to give an algorithmic content to classical proofs. We show that Bohm's theorem fails in this calculus.
Transformation groups and the virial theorem
Kampen, N.G. van
1972-01-01
A generalization of Noether's result for classical mechanics is given, which shows that the virial theorem is related to an invariance property of the Lagrange function. Two examples are discussed in detail.
Lie Algebras and the Four Color Theorem
Bar-Natan, Dror
1996-01-01
We present a ``reasonable'' statement about Lie algebras that is equivalent to the Four Color Theorem. The notions appearing in the statement also appear in the theory of finite-type invariants of knots (Vassiliev invariants) and 3-manifolds.
On the failure of Bell's theorem
Bene, Gyula
1997-01-01
Using a new approach to quantum mechanics we revisit Hardy's proof for Bell's theorem and point out a loophole in it. We also demonstrate on this example that quantum mechanics is a local realistic theory.
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...
Protein dynamics in Brillouin light scattering: Termal denaturation of hen egg white lysozyme
Svanidze, A. V.; Lushnikov, S. G.; Kojima, S.
2009-09-01
Thermal denaturation of hen egg white lysozyme has been investigated by Brillouin light scattering in the temperature range from 297 to 350 K. Anomalies in the temperature dependences of velocity and damping of hypersound and also in the behavior of the intensity of Brillouin components for the lysozyme solution at thermal denaturation have been revealed. These anomalies are attributable to phase transformations of the protein in the high-temperature region. It has been shown that Brillouin light scattering is a suitable tool for studying the structural evolution of proteins.
ESTIMATION OF SOUNDING ABILITY OF A BRILLOUIN LIDAR IN THE EAST CHINA SEA
Institute of Scientific and Technical Information of China (English)
吴东; 宋小全; 刘智深
2001-01-01
Vertical profiles of sound speed in the sea can be measured by using laser excited Brillouin scattering. In this paper the dependence of the accuracy of sound speed measurement on the accuracy of the Brillouin shift measurement is analyzed. We calculated the maximum detecting depths of sound speed to an accuracy of 1 m/s by lidar with different laser pulse energy, platform altitude, telescope aperture and lidar effective attenuation coefficient. The estimation of sounding ability in the East China Sea is made in some stations. These data can be used in the design of Brillouin Lidar for the China Sea.
A tunable multiwavelength Brillouin fiber laser with a semiconductor optical amplifier
International Nuclear Information System (INIS)
A multiwavelength Brillouin fiber laser with wavelength tunability using a semiconductor optical amplifier (SOA) and a birefringence fiber loop mirror has been demonstrated. The inhomogeneous broadening, and flat and broad gain in the SOA make the proposed multiwavelength laser comparatively stable and have the potential to generate a large number of Brillouin lasing wavelengths. A stable multiwavelength output with a spectral spacing of the Brillouin frequency shift of 0.08 nm and a wavelength number of more than 91 has been successfully produced. Moreover, wavelength tuning over a 21 nm wavelength range has been achieved. (paper)
Effect of collisions on amplification of laser beams by Brillouin scattering in plasmas
Humphrey, K. A.; Trines, R. M. G. M.; Fiuza, F.; Speirs, D. C.; Norreys, P.; Cairns, R. A.; Silva, L. O.; Bingham, R.
2013-10-01
We report on particle in cell simulations of energy transfer between a laser pump beam and a counter-propagating seed beam using the Brillouin scattering process in uniform plasma including collisions. The results presented show that the ion acoustic waves excited through naturally occurring Brillouin scattering of the pump field are preferentially damped without affecting the driven Brillouin scattering process resulting from the beating of the pump and seed fields together. We find that collisions, including the effects of Landau damping, allow for a more efficient transfer of energy between the laser beams, and a significant reduction in the amount of seed pre-pulse produced.
Effect of collisions on amplification of laser beams by Brillouin scattering in plasmas
International Nuclear Information System (INIS)
We report on particle in cell simulations of energy transfer between a laser pump beam and a counter-propagating seed beam using the Brillouin scattering process in uniform plasma including collisions. The results presented show that the ion acoustic waves excited through naturally occurring Brillouin scattering of the pump field are preferentially damped without affecting the driven Brillouin scattering process resulting from the beating of the pump and seed fields together. We find that collisions, including the effects of Landau damping, allow for a more efficient transfer of energy between the laser beams, and a significant reduction in the amount of seed pre-pulse produced
Importance of residual stresses in the Brillouin gain spectrum of single mode optical fibers.
Mamdem, Y Sikali; Burov, E; de Montmorillon, L-A; Jaouën, Y; Moreau, G; Gabet, R; Taillade, F
2012-01-16
Residual stresses inside optical fibers can impact significantly on Brillouin spectrum properties. We have analyzed the importance of internal stresses on the Brillouin Gain Spectrum (BGS) for a conventional G.652 fiber and compared modeling results to measurements. Then the residual internal stresses have been investigated for a set of trench-assisted fibers: fibers are coming from a single preform with different draw tensions. Numerical modeling based on measured internal stresses profiles are compared with corresponding BGS experimental results. Clearly, Brillouin spectrum is shifted linearly versus draw tension with a coefficient of -20MHz/100g and its linewidth increases. PMID:22274523
A new approach to measure the ocean temperature using Brillouin lidar
Institute of Scientific and Technical Information of China (English)
Wei Gao; Zhiwei Lü; Yongkang Dong; Weiming He
2006-01-01
@@ An approach of lidar measurements of ocean temperature through measuring the spectral linewidth of the backscattered Brillouin lines is presented. An empirical equation for the temperature as a function of Brillouin linewidth and salinity is derived. Theoretical results are in good agreement with the experimental data. The equation also reveals the dependence of the temperature on the salinity and Brillouin linewidth.It is shown that the uncertainty of the salinity has very little impact on the temperature measurement.The uncertainty of this temperature measurement methodology is approximately 0.02 ℃.
Brillouin lasing in whispering gallery micro-resonators
Sturman, B.; Breunig, I.
2015-12-01
Thresholds of stimulated Brillouin scattering (SBS) in solid-state whispering gallery mode (WGM) microresonators are analyzed. It is shown that the SBS interaction is substantially different here from that known in the bulk case and in the case of water droplet resonators. The reason is the absence of pure longitudinal acoustic WGMs owing to strong coupling of the longitudinal (l) and transverse (t) acoustic displacements at the surface of the resonator. As a result, a considerable increase of the SBS thresholds takes place, and the lowest thresholds correspond to the hybrid tl-modes with very large radial indices. Nevertheless, the thresholds lie in the μW range of the pump power. Dependence of the SBS power thresholds on the modal numbers and the possibility of self-tuning to the SBS resonance are analyzed.
Beyond the Brillouin limit with the Penning Fusion Experiment
International Nuclear Information System (INIS)
Several years ago, it was proposed that a dense non-neutral plasma could be produced in a Penning trap. Nonneutral plasmas have excellent confinement, and such a dense plasma might produce simultaneously high density and good confinement. Recently, this theoretical conjecture has been demonstrated in a small (3 mm radius) electron experiment, PFX (Penning Fusion Experiment). Densities up to 35 times the Brillouin density (limiting number density in a static trap) have been inferred from the observed strong (100:1) spherical focusing. Electrons are injected at low energy from a single pole of the sphere. A surprising observation is the self-organization of the system into a spherical state, which occurs precisely when the trap parameters are adjusted to produce a spherical well. This organization is caused by a bootstrapping mechanism which produces a hysteresis. Observations of energy-scattered electrons confirm the existence of a dense spherical focus. copyright 1997 American Institute of Physics
The Einstein-Brillouin Action Quantization for Dirac Fermions
Onorato, P.
The Einstein-Brillouin-Keller semiclassical quantization and the topological Maslov index are used to compute the electronic structure of carbon based nanostructures with or without transverse magnetic field. The calculation is based on the Dirac Fermions approach in the limit of strong coupling for the pseudospin. The electronic bandstructure for carbon nanotubes and graphene nanoribbons are discussed, focusing on the role of the chirality and of the unbonded edges configuration respectively. The effects of a transverse uniform magnetic field are analyzed, the different kinds of classical trajectories are discussed and related to the corresponding energies. The development is concise, transparent, and involves only elementary integral calculus and provides a conceptual and intuitive introduction to the quantum nature of carbon nanostructures.
Bunching of temporal cavity solitons via forward Brillouin scattering
Erkintalo, Miro; Jang, Jae K; Coen, Stéphane; Murdoch, Stuart G
2015-01-01
We report on the experimental observation of bunching dynamics with temporal cavity solitons in a continuously-driven passive fibre resonator. Specifically, we excite a large number of ultrafast cavity solitons with random temporal separations, and observe in real time how the initially random sequence self-organizes into regularly-spaced aggregates. To explain our experimental observations, we develop a simple theoretical model that allows long-range acoustically-induced interactions between a large number of temporal cavity solitons to be simulated. Significantly, results from our simulations are in excellent agreement with our experimental observations, strongly suggesting that the soliton bunching dynamics arise from forward Brillouin scattering. In addition to confirming prior theoretical analyses and unveiling a new cavity soliton self-organization phenomenon, our findings elucidate the manner in which sound interacts with large ensembles of ultrafast pulses of light.
Dual-microcavity narrow-linewidth Brillouin laser
Loh, William; Baynes, Frederick; Cole, Daniel; Quinlan, Franklyn; Lee, Hansuek; Vahala, Kerry; Papp, Scott; Diddams, Scott
2014-01-01
Ultralow noise, yet tunable lasers are a revolutionary tool in precision spectroscopy, displacement measurements at the standard quantum limit, and the development of advanced optical atomic clocks. Further applications include LIDAR, coherent communications, frequency synthesis, and precision sensors of strain, motion, and temperature. While all applications benefit from lower frequency noise, many also require a laser that is robust and compact. Here, we introduce a dual-microcavity laser that leverages one chip-integrable silica microresonator to generate tunable 1550 nm laser light via stimulated Brillouin scattering (SBS) and a second microresonator for frequency stabilization of the SBS light. This configuration reduces the fractional frequency noise to $7.8\\times10^{-14} 1/\\sqrt{Hz}$ at 10 Hz offset, which is a new regime of noise performance for a microresonator-based laser. Our system also features terahertz tunability and the potential for chip-level integration. We demonstrate the utility of our du...
Brillouin resonance broadening due to structural variations in nanoscale waveguides
Wolff, Christian; Steel, Michael J; Eggleton, Benjamin J; Poulton, Christopher G
2015-01-01
We study the impact of structural variations (that is slowly varying geometry aberrations and internal strain fields) on the resonance width and shape of stimulated Brillouin scattering (SBS) in nanoscale waveguides. We find that they lead to an inhomogeneous resonance broadening through two distinct mechanisms: firstly, the acoustic frequency is directly influenced via mechanical nonlinearities; secondly, the optical wave numbers are influenced via the opto-mechanical nonlinearity leading to an additional acoustic frequency shift via the phase-matching condition. We find that this second mechanism is proportional to the opto-mechanical coupling and, hence, related to the SBS-gain itself. It is absent in intra-mode forward SBS, while it plays a significant role in backward scattering. In backward SBS increasing the opto-acoustic overlap beyond a threshold defined by the fabrication tolerances will therefore no longer yield the expected quadratic increase in overall Stokes amplification. Our results can be tra...
Coherent Rayleigh-Brillouin scattering as a flow diagnostic technique
Energy Technology Data Exchange (ETDEWEB)
Graul, J. S.; Lilly, T. C. [Department of Mechanical and Aerospace Engineering, University of Colorado Colorado Springs, 1420 Austin Bluffs Parkway, Colorado Springs, CO 80918 (United States)
2014-12-09
Broadband coherent Rayleigh-Brillouin scattering (CRBS) was used to measure translational gas temperatures for nitrogen at the ambient pressure of 0.8 atm using a purpose-built Fabry-Perot etalon spectrometer. Temperatures derived from the CRBS spectral analysis were compared with experimentally-measured temperatures, and were found to be, on average, within 2% of the experimentally-measured value. Axial flow velocities from a double jet at a pressure ratio of 0.38 were also measured by looking at the Doppler shift of the CRBS line shape. With recent developments in chirped laser technology and the capacity of CRBS to simultaneously provide thermodynamic and bulk flow information, the CRBS line shape acquisition and analysis technique presented here may allow for future time-resolved, characterization of aerospace flows.
Fishman, S.; Soffer, A.
2016-07-01
We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.
The matrix Euler-Fermat theorem
International Nuclear Information System (INIS)
We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem
A Theorem on Combinatorial Group Theory
Institute of Scientific and Technical Information of China (English)
何伯和
2000-01-01
Let F= F(X) be a free group of rand n, A be a finite subset of F(X) and x∈X be a generator. The theorem states that x can be denoted as a rotation-inserting word of A if x is in the normal closure of A in F(X). Finally, an application of the theorem in Heegaard splitting of 3manifolds is given.
International Nuclear Information System (INIS)
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. (letters and comments)
Fluctuation theorems for a molecular refrigerator.
Kim, Kyung Hyuk; Qian, Hong
2007-02-01
We extend fluctuation theorems to a molecular refrigeration system that consists of Brownian particles in a heat bath under feedback control of their velocities. Such control can actively remove heat from the bath due to an entropy-pumping mechanism [Phys. Rev. Lett. 93, 120602 (2004)]. The presence of entropy pumping in an underdamped Brownian system modifies both the Jarzynski equality and the fluctuation theorems. We discover that the entropy pumping has a dual role of work and heat. PMID:17358382
Levi-Civita's Theorem for Noncommutative Tori
Directory of Open Access Journals (Sweden)
Jonathan Rosenberg
2013-11-01
Full Text Available We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need to use two different notions of noncommutative vector field. Levi-Civita's theorem makes it possible to define Riemannian curvature using the usual formulas.
Double Soft Theorem for Perturbative Gravity
Saha, Arnab Priya
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.
Levi-Civita's Theorem for Noncommutative Tori
Jonathan Rosenberg
2013-01-01
We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need to use two different notions of noncommutative vector field. Levi-Civita's theorem makes it possible to define Riemannian curvature using the usual formulas.
The two Bell's theorems of John Bell
International Nuclear Information System (INIS)
Many of the heated arguments about the meaning of ‘Bell's theorem’ arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the dual assumptions of locality and determinism. His 1976 theorem is the incompatibility of quantum phenomena with the unitary property of local causality. This is contrary to Bell's own later assertions, that his 1964 theorem began with that single, and indivisible, assumption of local causality (even if not by that name). While there are other forms of Bell's theorems—which I present to explain the relation between Jarrett-completeness, ‘fragile locality’, and EPR-completeness—I maintain that Bell's two versions are the essential ones. Although the two Bell's theorems are logically equivalent, their assumptions are not, and the different versions of the theorem suggest quite different conclusions, which are embraced by different communities. For realists, the notion of local causality, ruled out by Bell's 1976 theorem, is motivated implicitly by Reichenbach's principle of common cause and explicitly by the principle of relativistic causality, and it is the latter which must be forgone. Operationalists pay no heed to Reichenbach's principle, but wish to keep the principle of relativistic causality, which, bolstered by an implicit ‘principle of agent-causation’, implies their notion of locality. Thus for operationalists, Bell's theorem is the 1964 one, and implies that it is determinism that must be forgone. I discuss why the two ‘camps’ are drawn to these different conclusions, and what can be done to increase mutual understanding. (review article)
A new proof of Goodstein's Theorem
Perez, Juan A.
2009-01-01
Goodstein sequences are numerical sequences in which a natural number m, expressed as the complete normal form to a given base a, is modified by increasing the value of the base a by one unit and subtracting one unit from the resulting expression. As initially defined, the first term of the Goodstein sequence is the complete normal form of m to base 2. Goodstein's Theorem states that, for all natural numbers, the Goodstein sequence eventually terminates at zero. Goodstein's Theorem was origin...
Epistemological Consequences of the Incompleteness Theorems
Raguní, Giuseppe
2016-01-01
After highlighting the cases in which the semantics of a language cannot be mechanically reproduced (in which case it is called inherent), the main epistemological consequences of the first incompleteness Theorem for the two fundamental arithmetical theories are shown: the non-mechanizability for the truths of the first-order arithmetic and the peculiarities for the model of the second-order arithmetic. Finally, the common epistemological interpretation of the second incompleteness Theorem is...
Virial theorems for trapped cold atoms
Werner, Félix
2008-01-01
A few small corrections We present a general virial theorem for quantum particles with arbitrary zero-range or finite-range interactions in an arbitrary external potential. We deduce virial theorems for several situations relevant to trapped cold atoms: zero-range interactions with and without Efimov effect, hard spheres, narrow Feshbach resonances, and finite-range interactions. If the scattering length $a$ is varied adiabatically in the BEC-BCS crossover, we find that the trapping potent...
Virial theorem for radiating accretion discs
Mach, Patryk
2011-01-01
A continuum version of the virial theorem is derived for a radiating self-gravitating accretion disc around a compact object. The central object is point-like, but we can avoid the regularization of its gravitational potential. This is achieved by applying a modified Pohozaev-Rellich identity to the gravitational potential of the disk only. The theorem holds for general stationary configurations, including discontinuous flows (shock waves, contact discontinuities). It is used to test numerica...
Shafranov's virial theorem and magnetic plasma confinement
Faddeev, Ludvig; Freyhult, Lisa; Niemi, Antti J.; Rajan, Peter
2000-01-01
Shafranov's virial theorem implies that nontrivial magnetohydrodynamical equilibrium configurations must be supported by externally supplied currents. Here we extend the virial theorem to field theory, where it relates to Derrick's scaling argument on soliton stability. We then employ virial arguments to investigate a realistic field theory model of a two-component plasma, and conclude that stable localized solitons can exist in the bulk of a finite density plasma. These solitons entail a non...
q-Deformed Dynamics and Virial Theorem
Zhang, Jian-Zu
2002-01-01
In the framework of the q-deformed Heisenberg algebra the investigation of $q$-deformation of Virial theorem explores that q-deformed quantum mechanics possesses better dynamical property. It is clarified that in the case of the zero potential the theoretical framework for the q-deformed Virial theorem is self-consistent. In the selfadjoint states the q-deformed uncertainty relation essentially deviates from the Heisenberg one.
The Fundamental Theorem of Vassiliev Invariants
Bar-Natan, Dror; STOIMENOW, Alexander
1997-01-01
The "fundamental theorem of Vassiliev invariants" says that every weight system can be integrated to a knot invariant. We discuss four different approaches to the proof of this theorem: a topological/combinatorial approach following M. Hutchings, a geometrical approach following Kontsevich, an algebraic approach following Drinfel'd's theory of associators, and a physical approach coming from the Chern-Simons quantum field theory. Each of these approaches is unsatisfactory in one way or anothe...
Has the Goldstone theorem been revisited?
Guerrieri, A
2014-01-01
A recent paper (arXiv:1404.5619) claimed the presence of a loophole in the current-algebra proof of Goldstone Theorem. The enforcing of manifest covariance would lead to contradictory results also in scalar theory. We show that the argument proposed is not in contradiction with covariance, thus not invalidating the theorem. Moreover, the counterexample proposed of a scalar operator with a non-zero vacuum expectation value in an unbroken theory is ill-defined.
Positive energy theorems in General Relativity
Dain, Sergio
2013-01-01
The aim of this chapter is to present an introduction and also an overview of some of the most relevant results concerning positivity energy theorems in General Relativity. These theorems provide the answer to a long standing problem that has been proved remarkably difficult to solve. They constitute one of the major results in classical General Relativity and they uncover a deep self-consistence of the theory.
Integral fluctuation theorem for the housekeeping heat
International Nuclear Information System (INIS)
The housekeeping heat Qhk is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states. By analysing the evolution of its probability distribution, we prove an integral fluctuation theorem (exp[-βQhk]) = 1 valid for arbitrary-driven transitions between steady states. We discuss Gaussian limiting cases and the difference between the new theorem and both the Hatano-Sasa and the Jarzynski relation. (letter to the editor)
Integral fluctuation theorem for the housekeeping heat
Speck, T.; Seifert, U.
2005-01-01
The housekeeping heat $Q\\hk$ is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states. By analyzing the evolution of its probability distribution, we prove an integral fluctuation theorem $\\mean{\\exp[-\\beta Q\\hk]}=1$ valid for arbitrary driven transitions between steady states. We discuss Gaussian limiting cases and the difference between the new theorem and both the Hatano-Sasa and the Jarzynski relation.
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…
Variable delay using stationary and localized Brillouin dynamic gratings
Antman, Yair; Primerov, Nikolay; Sancho, Juan; Thévenaz, Luc; Zadok, Avi
2012-03-01
Reflections from movable, dynamic acoustic gratings in polarization maintaining (PM) fibers are employed in the long variable delay of periodic, isolated pulses. The gratings are introduced by stimulated Brillouin scattering (SBS) interaction between two counter-propagating pump waves, which are spectrally detuned by the Brillouin frequency shift of the PM fiber and are both polarized along one of its principal axes. The gratings are interrogated by the reflections of read-out signals that are polarized along the orthogonal principal axis. High-rate phase modulation of both pump waves by a pseudo-random binary sequence introduces dynamic gratings that are both localized and stationary, at specific locations in which the modulated pumps are correlated. The separation between adjacent correlation peaks can be made arbitrarily long. Long variable delays are readily obtained by scanning the grating along the fiber, via changing either the length or the rate of the modulation sequence. At the same time, the short length of the gratings, on the order of a cm, accommodates the delay of broadband pulses. The technique is therefore free of the delay-times-bandwidth product limitation that undermines the performance of SBS-based 'slow light' delay: we report the delay 1-ns long pulses by as much as 770 ns. In addition, the combined reflections from two dynamic gratings with a variable separation are used to implement radio-frequency photonic filters of tunable free spectral range. At the current stage, the technique is restricted by noise from residual scattering that takes place outside of the correlation peaks. Hence, it is thus far limited to the processing of repetitive signals, for which the noise may be effectively averaged out.
Sperner and KKM-type theorems on trees and cycles
Niedermaier, Andrew; Su, Francis Edward
2009-01-01
In this paper we prove a new combinatorial theorem for labellings of trees, and show that it is equivalent to a KKM-type theorem for finite covers of trees and to discrete and continuous fixed point theorems on finite trees. This is in analogy with the equivalence of the classical Sperner's lemma, KKM lemma, and the Brouwer fixed point theorem on simplices. Furthermore, we use these ideas to develop new KKM and fixed point theorems for infinite covers and infinite trees. Finally, we extend the KKM theorem on trees to an entirely new KKM theorem for cycles, and discuss interesting social consequences, including an application in voting theory.
Combinatorial theorems in sparse random sets
Conlon, D
2010-01-01
We develop a new technique that allows us to show in a unified way that many well-known combinatorial theorems, including Tur\\'an's theorem, Szemer\\'edi's theorem and Ramsey's theorem, hold almost surely inside sparse random sets. For instance, we extend Tur\\'an's theorem to the random setting by showing that for every epsilon > 0 and every positive integer t >= 3 there exists a constant C such that, if G is a random graph on n vertices where each edge is chosen independently with probability at least C n^{-2/(t+1)}, then, with probability tending to 1 as n tends to infinity, every subgraph of G with at least (1 - \\frac{1}{t-1} + epsilon) e(G) edges contains a copy of K_t. This is sharp up to the constant C. We also show how to prove sparse analogues of structural results, giving two main applications, a stability version of the random Tur\\'an theorem stated above and a sparse hypergraph removal lemma. Many similar results have recently been obtained independently in a different way by Schacht and by Friedgut...
Optical theorem detectors for active scatterers
Marengo, Edwin A.; Tu, Jing
2015-10-01
We develop a new theory of the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. It applies to arbitrary lossless backgrounds and quite general probing fields. The derived formulation holds for arbitrary passive scatterers, which can be dissipative, as well as for the more general class of active scatterers which are composed of a (passive) scatterer component and an active, radiating (antenna) component. The generalization of the optical theorem to active scatterers is relevant to many applications such as surveillance of active targets including certain cloaks and invisible scatterers and wireless communications. The derived theoretical framework includes the familiar real power optical theorem describing power extinction due to both dissipation and scattering as well as a novel reactive optical theorem related to the reactive power changes. The developed approach naturally leads to three optical theorem indicators or statistics which can be used to detect changes or targets in unknown complex media. The paper includes numerical simulation results that illustrate the application of the derived optical theorem results to change detection in complex and random media.
A novel sampling theorem on the sphere
McEwen, J D
2011-01-01
We develop a novel sampling theorem on the sphere and corresponding fast algorithms by associating the sphere with the torus through a periodic extension. The fundamental property of any sampling theorem is the number of samples required to represent a band-limited signal. To represent exactly a signal on the sphere band-limited at L, all sampling theorems on the sphere require O(L^2) samples. However, our sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere and an asymptotically identical, but smaller, number of samples than the Gauss-Legendre sampling theorem. The complexity of our algorithms scale as O(L^3), however, the continual use of fast Fourier transforms reduces the constant prefactor associated with the asymptotic scaling considerably, resulting in algorithms that are fast. Furthermore, we do not require any precomputation and our algorithms apply to both scalar and spin functions on the sphere without any change in computational comple...
Mental Constructions for The Group Isomorphism Theorem
Directory of Open Access Journals (Sweden)
Arturo Mena-Lorca
2016-03-01
Full Text Available The group isomorphism theorem is an important subject in any abstract algebra undergraduate course; nevertheless, research shows that it is seldom understood by students. We use APOS theory and propose a genetic decomposition that separates it into two statements: the first one for sets and the second with added structure. We administered a questionnaire to students from top Chilean universities and selected some of these students for interviews to gather information about the viability of our genetic decomposition. The students interviewed were divided in two groups based on their familiarity with equivalence relations and partitions. Students who were able to draw on their intuition of partitions were able to reconstruct the group theorem from the set theorem, while those who stayed on the purely algebraic side could not. Since our approach to learning this theorem was successful, it may be worthwhile to gather data while teaching it the way we propose here in order to check how much the learning of the group isomorphism theorem is improved. This approach could be expanded to other group homomorphism theorems provided further analysis is conducted: going from the general (e.g., sets to the particular (e.g., groups might not always the best strategy, but in some cases we may just be turning to more familiar settings.
The modified Poynting theorem and the concept of mutual energy
Zhao, Shuang-ren; Yang, Kang; Yang, Xingang; Yang, Xintie
2015-01-01
The Poynting theorem is generalized to the modified Poynting theorem. In the modified Poynting theorem the electromagnetic field is superimposition of different electromagnetic fields including the field of retarded potential and advanced potential. The media epsilon (permittivity) and mu (permeability) can also be different in the different fields. The concept of mutual energy is introduced which is the difference between the total energy and self-energy. Using the modified Poynting theorem with the concept of the mutual energy the modified mutual energy theorem is derived. Applying time-offset transform and time integral to the modified mutual energy theorem, the time-correlation modified mutual energy theorem is obtained. Assume there are only two fields which are retarded potential, and there is only one media, the modified time-correlation energy theorem becomes the time-correlation energy theorem, which is also referred as the time-correlation reciprocity theorem. Assume there are two electromagnetic fi...
Institute of Scientific and Technical Information of China (English)
Lei DENG; Ming Ge YANG
2006-01-01
Some new coincidence theorems involving admissible set-valued mappings are proved in general noncompact topological spaces. As applications, some new minimax inequalities, section theorem, best approximation theorem, existence theorems of weighted Nash equilibria and Pareto equilibria for multiobjective games are given in general topological spaces.
A Unifying Impossibility Theorem for Compact Metricsocial Alternatives Space
Priscilla Man; Shino Takayama
2013-01-01
In Man and Takayama (2013) (henceforth MT) we show that many classical impossibility theorems follow from three simple and intuitive axioms on the social choice correspondence when the set of social alternatives is finite. This note extends the main theorem (Theorem 1) in MT to the case where the set of social alternatives is a compact metric space. We also qualify how versions of Arrow's Impossibility Theorem and the Muller-Satterthwaite Theorem (Muller and Satterthwaite, 1977) can be obtain...
Stability theorems for multidimensional linear systems with variable parameters
Shrivastava, S. K.
1981-01-01
A Liapunov-type approach is used to derive two equivalent theorems which govern the stability of coupled linear systems with varying multiple parameters. The theorems generalize some of the existing theorems applicable to systems with constant parameters and the Sonin-Polya theorem applicable to a single-degree-of-freedom system with variable coefficients. As an illustration, the proposed theorems are applied to mechanical systems with varying inertia, stiffness, gyroscopic, and damping terms, and velocity and position-dependent forces.
Theorem on magnet fringe field
International Nuclear Information System (INIS)
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 (bn) and skew (an) multipoles, By + iBx = summation(bn + ian)(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 an, bar bn, bar Bx, and bar By 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 |Δp0|, 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 Bx from the vicinity of one magnet end since, along a path parallel to the magnet axis such as path BC
Kharitonov's theorem: Generalizations and algorithms
Rublein, George
1989-01-01
In 1978, the Russian mathematician V. Kharitonov published a remarkably simple necessary and sufficient condition in order that a rectangular parallelpiped of polynomials be a stable set. Here, stable is taken to mean that the polynomials have no roots in the closed right-half of the complex plane. The possibility of generalizing this result was studied by numerous authors. A set, Q, of polynomials is given and a necessary and sufficient condition that the set be stable is sought. Perhaps the most general result is due to Barmish who takes for Q a polytope and proceeds to construct a complicated nonlinear function, H, of the points in Q. With the notion of stability which was adopted, Barmish asks that the boundary of the closed right-half plane be swept, that the set G is considered = to (j(omega)(bar) - infinity is less than omega is less than infinity) and for each j(omega)(sigma)G, require H(delta) is greater than 0. Barmish's scheme has the merit that it describes a true generalization of Kharitonov's theorem. On the other hand, even when Q is a polyhedron, the definition of H requires that one do an optimization over the entire set of vertices, and then a subsequent optimization over an auxiliary parameter. In the present work, only the case where Q is a polyhedron is considered and the standard definition of stability described, is used. There are straightforward generalizations of the method to the case of discrete stability or to cases where certain root positions are deemed desirable. The cases where Q is non-polyhedral are less certain as candidates for the method. Essentially, a method of geometric programming was applied to the problem of finding maximum and minimum angular displacements of points in the Nyquist locus (Q(j x omega)(bar) - infinity is less than omega is less than infinity). There is an obvious connection with the boundary sweeping requirement of Barmish.
Control of Brillouin short-pulse seed amplification by chirping the pump pulse
Energy Technology Data Exchange (ETDEWEB)
Lehmann, G.; Spatschek, K. H. [Institut für Theoretische Physik, Heinrich-Heine-Universität Düsseldorf, D–40225 Düsseldorf (Germany)
2015-04-15
Seed amplification via Brillouin backscattering of a long pump pulse is considered. Similar to Raman amplification, several obstructive effects may occur during short-pulse Brillouin amplification. One is the spontaneous Raman backscattering of the pump before interacting with the seed. Preforming the plasma and/or chirping the pump will reduce unwanted pump backscattering. Optimized regions for low-loss pump propagation were proposed already in conjunction with Raman seed amplification. Hence, the influence of the chirp of the pump during Brillouin interaction with the seed becomes important and will be considered here. Both, the linear as well as the nonlinear evolution phases of the seed caused by Brillouin amplification under the action of a chirped pump are investigated. The amplification rate as well as the seed profiles are presented as function of the chirping rate. Also the dependence of superradiant scaling rates on the chirp parameter is discussed.
Stable and tunable self-seeded multiwavelength Brillouin-erbium fiber laser with higher OSNR
Zou, Hui; Yang, Ruilan; Shen, Xiao; Wei, Wei
2016-07-01
A stable and tunable self-seeded multiwavelength Brillouin-erbium fiber laser (BEFL) is designed and demonstrated based on a Single-Mode-Multimode-Single-Mode (SMS) fiber filter. The SMS filter is fabricated by splicing a 15 cm long multimode fiber between two single mode fibers. The self-excited Brillouin pump is internally achieved by cascaded stimulated Brillouin scattering (SBS) in the single mode fiber. By applying axial strain (from 0 to 466.7 μɛ) to the SMS filter with the same step of 66.7 μɛ , the multiwavelength of the output laser is tuned from 1553.58 to 1559.79 nm correspondingly, and the tunable range is 6.21 nm. The generation of up to 16 Brillouin Stokes wavelengths with 30 dB optical signal to noise ratio (OSNR) are obtained.
Antman, Yair; Primerov, Nikolay; Sancho Dura, Juan; Thévenaz, Luc; Zadok, Avinoam
2012-01-01
Stationary and localized Brillouin dynamic gratings are generated using phase modulation of both pump waves by a pseudo-random bit sequence. The gratings are applied to long variable delay of pulses and to cm-level distributed sensing
Sancho J.; Chin S.; Sagues M.; Loayssa A.; Lloret J.; Gasulla I.; Sales S.; Thevenaz L.; Capmany J.
2010-01-01
A dynamically reconfigurable Microwave Photonic Filter based on True Time Delay generated by Stimulated Brillouin Scattering in optical fibers and separate phase shift of the optical carrier has been experimentally demonstrated, resulting in a flexible tunable Free Spectral Range.
International Nuclear Information System (INIS)
In this letter, we demonstrate a single longitudinal mode (SLM) Brillouin fiber laser by using highly nonlinear fiber (HNLF) as the nonlinear medium in which the stimulated Brillouin scattering effect takes place. The first Stokes line is generated at a threshold power of 18 dBm with a wavelength shift 0.08 nm from the Brillouin pump. The signal-to-noise ratio of the first Stokes line is measured to be ∼58 dB. To the best of the authors’ knowledge, this is the first report of a 0.7 kHz ultra-narrow linewidth of an SLM Brillouin fiber laser, using HNLF as the nonlinear medium, which features a simple cavity configuration. (letter)
Brillouin shifted third harmonic generation of a laser in a plasma
International Nuclear Information System (INIS)
The process of Brillouin shifted resonant third harmonic generation of an intense laser of finite spot size in a plasma is investigated. The laser of frequency ω0 and wave number k-vector0 excites an ion acoustic wave of frequency ω≅kcs and wave number k-vector≅2k-vector0, where cs is the ion acoustic speed, in the primary stimulated Brillouin scattering process. The laser also exerts a second harmonic ponderomotive force on electrons. This imparts them an oscillatory velocity v2ω0,2k0. This velocity beats with the electron density perturbation associated with the ion acoustic wave to produce a density perturbation at Brillouin shifted second harmonic. This perturbation couples with the oscillatory velocity vω0,k0 due to the laser to produce Brillouin shifted third harmonic current density and the radiation field. The phase matching is satisfied when plasma density is two third critical.
Self-Advanced Propagation of Light Pulse in an Optical Fiber Based on Brillouin Scattering
Chin, Sanghoon; Gonzalez-Herraez, Miguel; Thévenaz, Luc
2007-01-01
We propose a novel method to realize self-induced fast light and signal advancement with no distinct pump source in optical fibers, based on stimulated Brillouin scattering. This scheme will be helpful for real application systems.
Stimulated Brillouin scattering of laser in semiconductor plasma embedded with nano-sized grains
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
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)
Indian Academy of Sciences (India)
Sourabh Bal; M Bose
2009-10-01
We have investigated analytically the stimulated Brillouin scattering (SBS) of an electromagnetic wave in non-dissipative weakly magnetized plasma in the presence of dust particles with variable charge.
All-optical calculus based on dynamic Brillouin grating reflectors in optical fibers
Primerov, Nikolay; Chin, Sang Hoon; Thévenaz, Luc; Ursini, Leonora; Santagiustina, Marco
2011-01-01
We experimentally demonstrate that all-optical signal calculus can be realized based on dynamic Brillouin gratings in optical fibers. Temporal integration and first-order differentiation were performed for optical pulse with various waveforms.
Suppression of stimulated Brillouin scattering in high power fibre lasers and amplifiers
Hernandez-Solis, Vladimir
2009-01-01
Fibre sources in high power devices have significant advantages over conventional gas and solid state lasers. However, for applications that require the so-called singlefrequency sources with narrow linewidths, the output power is low mainly because of the problem of the stimulated Brillouin scattering (SBS). A model that accounts for the SBS in dual-clad fibre lasers and amplifiers is presented. This was carried out in order to study the key parameters that affect the Brillouin threshold...
Multi-zone temperature sensor using a multi-wavelength Brillouin fiber ring laser
Galíndez Jamioy, Carlos Augusto; Madruga Saavedra, Francisco Javier; Ullán Nieto, Ángel; López Amo, Manuel; López Higuera, José Miguel
2009-01-01
A simple system for sensing temperature in multiple zones based on a multi-wavelength Brillouin fiber laser ring is presented. Optical fiber reels are serially concatenated and divided in zones (one per sensing area). Setting the Brillouin lasing in each spool of fiber generates a characteristic wavelength that depends on the fiber properties and the temperature in the zone. Thus, it is possible to measure temperature independently and accurately through heterodyne detection between two narro...
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....
Antman, Yair; Primerov, Nikolay; Sancho Dura, Juan; Thévenaz, Luc; Zadok, Avinoam
2012-01-01
A novel technique for the localization of stimulated Brillouin scattering (SBS) interaction is proposed, analyzed and demonstrated experimentally. The method relies on the phase modulation of two counter-propagating optical waves by a common pseudo-random bit sequence (PRBS), these waves being spectrally detuned by the Brillouin frequency shift. The PRBS symbol duration is much shorter than the acoustic lifetime. The interference between the two modulated waves gives rise to an acoustic grati...
High-resolution Brillouin analysis in a carbon-fiber-composite unmanned aerial vehicle model wing
Stern, Yonatan; London, Yosef; Preter, Eyal; Antman, Yair; Shlomi, Orel; Silbiger, Maayan; Adler, Gadi; Zadok, Avi
2016-05-01
Standard optical fibers are successfully embedded within a model wing of an unmanned aerial vehicle, constructed of carbon fiber and epoxy, during its production. Time-gated Brillouin optical correlation domain analysis along the embedded optical fibers is performed with a spatial resolution of 4 cm. Tests were carried out using a portable measurement setup prototype. The results represent an important step towards applications of high-resolution Brillouin analysis outside the research laboratory.
Soto, M. A.; Bolognini, G.; Di Pasquale, F.
2009-01-01
In this work, we propose the use of optical pulse coding techniques for simultaneous strain and temperature sensing based on spontaneous Brillouin scattering. Optical pulse coding provides a significant receiver signal-to-noise ratio enhancement, allowing for accurate Brillouin intensity and frequency shift measurements at low peak power levels. Due to the cross-sensitivity of these two parameters on both temperature and strain, optical pulse coding improves the temperature and strain resolut...
The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory
Claude Semay
2015-01-01
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.
Detection of cracks in a reinforced concrete beam using distributed Brillouin fibre sensors
International Nuclear Information System (INIS)
This paper presents the results of using distributed Brillouin fibre sensors to detect crack formation in a simply supported reinforced concrete beam subjected to four-point loading. A Brillouin multiple-peak fitting method was used to enhance the spatial and strain resolutions of the measurements. By doing this, the distributed strain profile along the beam was determined with a 5 cm read-out resolution in comparison with the 15 cm spatial resolution of the fibres. The location of the cracks was identified by locating the positions in the strain profile where the strain suddenly changes, by searching for the maximum compressive or tensile peaks in the Brillouin frequency spectrum, as opposed to conventional strain reading, which focuses solely on the maximum Brillouin peak. The amplitude of the Brillouin peak for the suddenly changed strain (crack) was found to be smaller than half of the amplitude of the maximum Brillouin peak at the maximum strain location corresponding to the average strain of the material, which would have been neglected by standard peak or area fitting methods, especially for fine cracks or the initial crack build-up period
Widely tunable linear-cavity multiwavelength fiber laser with distributed Brillouin scattering
Institute of Scientific and Technical Information of China (English)
M. Ajiya; M. H. Al-Mansoori; M. A. Mahdi
2011-01-01
We demonstrate a multiple wavelength Brillouin/erbium fiber laser in a linear cavity configuration. The laser cavity is made up of a fiber loop mirror on one end of the resonator and a virtual mirror generated from the distributed stimulated Brillouin scattering effect on the other end. Due to the weak reflectivity provided by the virtual mirror, self-lasing cavity modes are completely suppressed from the laser cavity. At Brillouin pump and 1480-nm pump powers of 2 and 130 mW, respectively, 11 channels of the demonstrated laser with an average total power of 7.13 dBm can freely be tuned over a span of 37-nm wavelength from 1530 to 1567 nm.%@@ We demonstrate a multiple wavelength Brillouin/erbium fiber laser in a linear cavity configuration.The laser cavity is made up of a fiber loop mirror on one end of the resonator and a virtual mirror generated from the distributed stimulated Brillouin scattering effect on the other end.Due to the weak reflectivity provided by the virtual mirror, self-lasing cavity modes are completely suppressed from the laser cavity.At Brillouin pump and 1480-nm pump powers of 2 and 130 mW, respectively, 11 channels of the demonstrated laser with an average total power of 7.13 dBm can freely be tuned over a span of 37-nm wavelength from 1530 to 1567 nm.
Ergodic theorem, ergodic theory, and statistical mechanics.
Moore, Calvin C
2015-02-17
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject--namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697
Anti-Bell - Refutation of Bell's theorem
Barukčić, Ilija
2012-12-01
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
The Non-Signalling theorem in generalizations of Bell's theorem
International Nuclear Information System (INIS)
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
Institute of Scientific and Technical Information of China (English)
DONG Wu-qin; JIA Zhen-hong
2008-01-01
The relation between the power of the Brillouin signal and the swain is one of the bases of the distributed fiber sensors of temperature and strain. The coefficient of the Brillouin gain can be changed by the temperature and the strain that will affect the power of the Brillouin scattering. The relation between the change of the Brillouin gain coefficient and the strain is thought to be linear by many researchers. However, it is not always linear based on the theoretical analysis and numerical simulation. Therefore, errors will be caused if the relation between the change of the Brillouin gain coefficient and the strain is regarded as to be linear approximately for measuring the temperature and the strain. For this reason, the influence of thep arameters on the Brillouin gain coefficient is proposed through theoretical analysis and numerical simulation.
Equilibrium fluctuation theorems compatible with anomalous response
Velazquez, L.; Curilef, S.
2010-12-01
Previously, we have derived a generalization of the canonical fluctuation relation between heat capacity and energy fluctuations C = β2langδU2rang, which is able to describe the existence of macrostates with negative heat capacities C < 0. In this work, we extend our previous results for an equilibrium situation with several control parameters to account for the existence of states with anomalous values in other response functions. Our analysis leads to the derivation of three different equilibrium fluctuation theorems: the fundamental and the complementary fluctuation theorems, which represent the generalization of two fluctuation identities already obtained in previous works, and the associated fluctuation theorem, a result that has no counterpart in the framework of Boltzmann-Gibbs distributions. These results are applied to study the anomalous susceptibility of a ferromagnetic system, in particular, the case of the 2D Ising model.
On Bayes' theorem for improper mixtures
McCullagh, Peter; 10.1214/11-AOS892
2011-01-01
Although Bayes's theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes's theorem sometimes generates sensible procedures from improper priors, Pitman's estimator being a good example. However, improper priors may also lead to Bayes procedures that are paradoxical or otherwise unsatisfactory, prompting some authors to insist that all priors be proper. This paper begins with the observation that an improper measure on Theta satisfying Kingman's countability condition is in fact a probability distribution on the power set. We show how to extend a model in such a way that the extended parameter space is the power set. Under an additional finiteness condition, which is needed for the existence of a sampling region, the conditions for Bayes's theorem are satisfied by the extension. Lack of interference ensures that the posterior distribution in the extended space is compatible with the original parameter space. Provided that the key finiteness conditio...
Bayes' theorem: scientific assessment of experience
Directory of Open Access Journals (Sweden)
Lex Rutten
2010-10-01
Full Text Available Homeopathy is based on experience and this is a scientific procedure if we follow Bayes' theorem. Unfortunately this is not the case at the moment. Symptoms are added to our materia medica based on absolute occurrence, while Bayes theorem tells us that this should be based on relative occurrence. Bayes theorem can be applied on prospective research, but also on retrospective research and consensus based on a large number of cases. Confirmation bias is an important source of false data in experience based systems like homeopathy. Homeopathic doctors should become more aware of this and longer follow-up of cases could remedy this. The existing system of adding symptoms to our materia medica is obsolete.
Spectral mapping theorems a bluffer's guide
Harte, Robin
2014-01-01
Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several and many variables. The basic algebraic systems – semigroups, rings and linear algebras – are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Spectral Mapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory.
Asymptotic symmetries and subleading soft graviton theorem
Campiglia, Miguel; Laddha, Alok
2014-12-01
Motivated by the equivalence between the soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the Bondi, van der Burg, Metzner and Sachs (BMS) group, we propose a new extension (different from the so-called extended BMS) of the BMS group that is a semidirect product of supertranslations and Diff(S2) . We propose a definition for the canonical generators associated with the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger.
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
Jarzynski's theorem for lattice gauge theory
Caselle, Michele; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-01-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium states. In this article, we extend Jarzynski's theorem to lattice gauge theory, and present examples of applications for two challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schroedinger functional and for simulations at finite density using reweighting techniques.
Generalizations of the Abstract Boundary singularity theorem
Whale, Ben E; Scott, Susan M
2015-01-01
The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from $C^1$ curves to locally Lipschitz curves.
GENERALIZATIONS OF THE ORLICZ-PETTIS THEOREM
Directory of Open Access Journals (Sweden)
CHRISTOPHER STUART
2005-05-01
Full Text Available The Orlicz-Pettis Theorem for locally convex spaces asserts that a series in the space which is subseries convergent in the weak topology is actually subseries convergent in the original topology of the space. A subseries convergent series can be viewed as a multiplier convergent series where the terms of the series are multiplied by elements of the scalar sequence space m0 of sequences with finite range. In this paper we show that the conclusion of the Orlicz-Pettis Theorem holds (and can be strengthened if the multiplier space m0 is replaced by a sequence space with the signed weak gliding hump property
Two extensions of Ramsey’s theorem
Conlon, David; Fox, Jacob; Sudakov, Benny
2013-01-01
Ramsey’s theorem, in the version of Erdos and Szekeres, states that every 2-coloring of the edges of the complete graph on {1,2,…,n} contains a monochromatic clique of order (1/2)logn. In this article, we consider two well-studied extensions of Ramsey’s theorem. Improving a result of Rodl, we show that there is a constant c > 0 such that every 2-coloring of the edges of the complete graph on {2,3,…,n} contains a monochromatic clique S for which the sum of 1/logi over all vertices i ∈ S is at ...
Central Limit Theorem for Nonlinear Hawkes Processes
Zhu, Lingjiong
2012-01-01
Hawkes process is a self-exciting point process with clustering effect whose jump rate depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. Linear Hawkes process has an immigration-birth representation and can be computed more or less explicitly. It has been extensively studied in the past and the limit theorems are well understood. On the contrary, nonlinear Hawkes process lacks the immigration-birth representation and is much harder to analyze. In this paper, we obtain a functional central limit theorem for nonlinear Hawkes process.
Limit theorems for fragmentation processes with immigration
Knobloch, Robert
2012-01-01
In this paper we extend two limit theorems which were recently obtained for fragmentation processes to such processes with immigration. More precisely, in the setting with immigration we consider a limit theorem for the process counted with a random characteristic as well as the asymptotic behaviour of an empirical measure associated with the stopping line corresponding to the first blocks, in their respective line of descent, that are smaller than a given size. In addition, we determine the asymptotic decay rate of the size of the largest block in a homogeneous fragmentation process with immigration. The techniques used to proves these results are based on submartingale arguments.
Jarzynski's theorem for lattice gauge theory
Caselle, Michele; Costagliola, Gianluca; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-08-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a nonequilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schrödinger functional and for simulations at finite density using reweighting techniques.
Limit Theorems for Dispersing Billiards with Cusps
Bálint, P.; Chernov, N.; Dolgopyat, D.
2011-12-01
Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting "intermittent" behavior that alternates between regular and chaotic patterns. Their statistical properties are therefore weak and delicate. They are characterized by a slow (power-law) decay of correlations, and as a result the classical central limit theorem fails. We prove that a non-classical central limit theorem holds, with a scaling factor of {sqrt{nlog n}} replacing the standard {sqrt{n}} . We also derive the respective Weak Invariance Principle, and we identify the class of observables for which the classical CLT still holds.
The Goldstone boson equivalence theorem with fermions
Durand, Loyal; Riesselmann, Kurt
1995-01-01
The calculation of the leading electroweak corrections to physical transition matrix elements in powers of $M_H^2/v^2$ can be greatly simplified in the limit $M_H^2\\gg M_W^2,\\, M_Z^2$ through the use of the Goldstone boson equivalence theorem. This theorem allows the vector bosons $W^\\pm$ and $Z$ to be replaced by the associated scalar Goldstone bosons $w^\\pm$, $z$ which appear in the symmetry breaking sector of the Standard Model in the limit of vanishing gauge couplings. In the present pape...
Adiabatic Theorems and Reversible Isothermal Processes
Abou-Salem, W K
2005-01-01
Reversible isothermal processes of a finitely extended, driven quantum system in contact with an infinite heat bath are studied from the point of view of quantum statistical mechanics. Notions like heat flux, work and entropy are defined for trajectories of states close to, but distinct from states of joint thermal equilibrium. A theorem characterizing reversible isothermal processes as quasi-static processes ("isothermal theorem") is described. Corollaries concerning the changes of entropy and free energy in reversible isothermal processes and on the 0th law of thermodynamics are outlined.
Beyond the Brillouin limit with the Penning fusion experiment
International Nuclear Information System (INIS)
Several years ago, it was proposed that a dense nonneutral plasma could be produced in a Penning trap. Nonneutral plasmas have excellent confinement. Thus, such a dense plasma might produce simultaneously high density and good confinement (as needed for fusion). Recently, this theoretical conjecture has been demonstrated in a small (3 mm radius) electron experiment (PFX). Densities up to 35 times the Brillouin density (limiting number density in a static trap) have been inferred from the observed strong (100:1) spherical focussing. Electrons are injected at low energy from a single pole of the sphere. A surprising observation is the self-organization of the system into a spherical state, which occurs precisely when the trap parameters are adjusted to produce a spherical well. This organization is observed by a bootstrapping which produces a hysteresis. Additional observations which confirm the dense spherical focus are energy-scattered electrons and deflections of an electron probe beam by the space charge of the central focus
Acoustic confinement and Stimulated Brillouin Scattering in integrated optical waveguides
Poulton, Christopher G; Eggleton, Benjamin J
2013-01-01
We examine the effect of acoustic mode confinement on Stimulated Brillouin Scattering in optical waveguides that consist of a guiding core embedded in a solid substrate. We find that SBS can arise due to coupling to acoustic modes in three different regimes. First, the acoustic modes may be guided by total internal reflection; in this case the SBS gain depends directly on the degree of confinement of the acoustic mode in the core, which is in turn determined by the acoustic V-parameter. Second, the acoustic modes may be leaky, but may nevertheless have a sufficiently long lifetime to have a large effect on the SBS gain; the lifetime of acoustic modes in this regime depends not only on the contrast in acoustic properties between the core and the cladding, but is also highly dependent on the waveguide dimensions. Finally SBS may occur due to coupling to free modes, which exist even in the absence of acoustic confinement; we find that the cumulative effect of coupling to these non-confined modes results in signi...
Impact of nonlinear loss on Stimulated Brillouin Scattering
Wolff, Christian; Steel, Michael J; Eggleton, Benjamin J; Poulton, Christopher G
2015-01-01
We study the impact of two-photon absorption (2PA) and fifth-order nonlinear loss such as 2PA-induced free-carrier absorption in semiconductors on the performance of Stimulated Brillouin Scattering devices. We formulate the equations of motion including effective loss coefficients, whose explicit expressions are provided for numerical evaluation in any waveguide geometry. We find that 2PA results in a monotonic, algebraic relationship between amplification, waveguide length and pump power, whereas fifth-order losses lead to a non-monotonic relationship. We define a figure of merit for materials and waveguide designs in the presence of fifth-order losses. From this, we determine the optimal waveguide length for the case of 2PA alone and upper bounds for the total Stokes amplification for the case of 2PA as well as fifth-order losses. The analysis is performed analytically using a small-signal approximation and is compared to numerical solutions of the full nonlinear modal equations.
Modeling of stimulated Brillouin scattering in expanding plasmas
Hüller, S.; Masson-Laborde, P. E.; Pesme, D.; Labaune, C.; Bandulet, H.
2008-05-01
Numerical simulations of mm-size expanding plasmas have been performed in comparison with recent experiments at the LULI facility. The features of Stimulated Brillouin Scattering (SBS) are studied for an intense mono-speckle laser beam in continuation of previous work on optically smoothed laser beams. Very good agreement between the theoretical-numerical modeling and the experimental results is found, in particular concerning the SBS activity in the plasma and the backscatter level. The results underline the importance of nonlocal transport effects affecting the onset of self-focusing for temperatures below 1keV. The simulations with the monospeckle beam allow to identify the resonant filament instability [1] and the subsequent loss of coherence of the laser beam as the reason of the observed low-level backscatter levels measured in the experiments. To achieve reliable numerical modeling, a good characterisation of the plasma profiles and the timing with respect to the laser pulse shape, prior to simulations, proves to be extremely important.
Modeling of stimulated Brillouin scattering in expanding plasmas
Energy Technology Data Exchange (ETDEWEB)
Hueller, S; Masson-Laborde, P E; Pesme, D [Centre de Physique Theorique, CNRS UMR7644, ecole Polytechnique, Palaiseau (France); Labaune, C; Bandulet, H [LULI, CNRS UMR7605, ecole Polytechnique, Palaiseau (France)], E-mail: hueller@cpht.polytechnique.fr
2008-05-15
Numerical simulations of mm-size expanding plasmas have been performed in comparison with recent experiments at the LULI facility. The features of Stimulated Brillouin Scattering (SBS) are studied for an intense mono-speckle laser beam in continuation of previous work on optically smoothed laser beams. Very good agreement between the theoretical-numerical modeling and the experimental results is found, in particular concerning the SBS activity in the plasma and the backscatter level. The results underline the importance of nonlocal transport effects affecting the onset of self-focusing for temperatures below 1keV. The simulations with the monospeckle beam allow to identify the resonant filament instability and the subsequent loss of coherence of the laser beam as the reason of the observed low-level backscatter levels measured in the experiments. To achieve reliable numerical modeling, a good characterisation of the plasma profiles and the timing with respect to the laser pulse shape, prior to simulations, proves to be extremely important.
Microresonator Brillouin Laser Stabilization Using a Microfabricated Rubidium Cell
Loh, William; Leopardi, Holly F; Fortier, Tara M; Quinlan, Frank; Kitching, John; Papp, Scott B; Diddams, Scott A
2016-01-01
We frequency stabilize the output of a miniature stimulated Brillouin scattering (SBS) laser to rubidium atoms in a microfabricated cell to realize a laser system with frequency stability at the $10^{-11}$ level over seven decades in averaging time. In addition, our system has the advantages of robustness, low cost and the potential for integration that would lead to still further miniaturization. The SBS laser operating at 1560 nm exhibits a spectral linewidth of 820 Hz, but its frequency drifts over a few MHz on the 1 hour timescale. By locking the second harmonic of the SBS laser to the Rb reference, we reduce this drift by a factor of $10^3$ to the level of a few kHz over the course of an hour. For our combined SBS and Rb laser system, we measure a frequency noise of $4\\times10^4$ $Hz^2/Hz$ at 10 Hz offset frequency which rapidly rolls off to a level of 0.2 $Hz^2/Hz$ at 100 kHz offset. The corresponding Allan deviation is $\\leq2\\times10^{-11}$ for averaging times spanning $10^{-4}$ to $10^3$ s. By optical...
Brillouin resonance broadening due to structural variations in nanoscale waveguides
Wolff, C.; Van Laer, R.; Steel, M. J.; Eggleton, B. J.; Poulton, C. G.
2016-02-01
We study the impact of structural variations (that is slowly varying geometry aberrations and internal strain fields) on the width and shape of the stimulated Brillouin scattering (SBS) resonance in nanoscale waveguides. We find that they lead to an inhomogeneous resonance broadening through two distinct mechanisms: firstly, the acoustic frequency is directly influenced via mechanical nonlinearities; secondly, the optical wave numbers are influenced via the opto-mechanical nonlinearity leading to an additional acoustic frequency shift via the phase-matching condition. We find that this second mechanism is proportional to the opto-mechanical coupling and, hence, related to the SBS-gain itself. It is absent in intra-mode forward SBS, while it plays a significant role in backward scattering. In backward SBS increasing the opto-acoustic overlap beyond a threshold defined by the fabrication tolerances will therefore no longer yield the expected quadratic increase in overall Stokes amplification. Finally, we illustrate in a numerical example that in backward SBS and inter-mode forward SBS the existence of two broadening mechanisms with opposite sign also opens the possibility to compensate the effect of geometry-induced broadening. Our results can be transferred to other micro- and nano-structured waveguide geometries such as photonic crystal fibres.
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
An existence theorem for Volterra integrodifferential equations with infinite delay
Directory of Open Access Journals (Sweden)
Ferenc Izsak
2003-01-01
Full Text Available Using Schauder's fixed point theorem, we prove an existence theorem for Volterra integrodifferential equations with infinite delay. As an appplication, we consider an $n$ species Lotka-Volterra competitive system.
Hindman's Theorem: An Ultrafilter Argument in Second Order Arithmetic
Towsner, Henry
2009-01-01
Hindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated into second order arithmetic.
A multivariate central limit theorem for continuous local martingales
Zanten, van, M.
1998-01-01
A theorem on the weak convergence of a properly normalized multivariate continuous local martingale is proved. The time-change theorem used for this purpose allows for short and transparent arguments.
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...
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.
A simpler derivation of the coding theorem
Lomnitz, Yuval
2012-01-01
A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information follow naturally in the proof. It may also be applicable to situations where typicality is not natural.
On the Non-Abelian Stokes Theorem
Diakonov, Dmitri; Petrov, Victor
2000-01-01
We present the non-Abelian Stokes theorem for the Wilson loop in various forms and discuss its meaning. Its validity has been recently questioned by Faber, Ivanov, Troitskaya and Zach. We demonstrate that all points of their criticism are based on mistakes in mathematics. Finally, we derive a variant of our formula for the Wilson loop in lattice regularization.
A coupling approach to Doob's theorem
Kulik, Alexei; Scheutzow, Michael
2014-01-01
We provide a coupling proof of Doob's theorem which says that the transition probabilities of a regular Markov process which has an invariant probability measure $\\mu$ converge to $\\mu$ in the total variation distance. In addition we show that non-singularity (rather than equivalence) of the transition probabilities suffices to ensure convergence of the transition probabilities for $\\mu$-almost all initial conditions.
Gap theorems for Ricci-harmonic solitons
Tadano, Homare
2015-01-01
In the present paper, by using estimates for the generalized Ricci curvature, we shall give some gap theorems for Ricci-harmonic solitons showing some necessary and sufficient conditions for the solitons to be harmonic-Einstein. Our results may be regarded as a generalization of recent works by H. Li, and M. Fernandez-Lopez and E. Garcia-Rio.
A strictly-positive mass theorem
International Nuclear Information System (INIS)
We show that the ADM 4-momentum of an isolated gravitational system (spatially asymptotically flat spacetime) satisfying the dominant energy condition cannot be null-like unless it is flat. Together with the positive mass theorem, this implies that the ADM 4-momentum of an isolated gravitational system must be strictly time-like. (orig.)
Multiplier theorems for special Hermite expansions on
Institute of Scientific and Technical Information of China (English)
张震球; 郑维行
2000-01-01
The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calderon-Zygmund decomposition. Then the multiplier theorem in Lp(1 < p < ω ) is obtained. The special Hermite expansions in twisted Hardy space are also considered. As an application, the multipli-ers for a certain kind of Laguerre expansions are given in Lp space.
Sandwich reactor lattices and Bloch's theorem
International Nuclear Information System (INIS)
The study of the neutron flux distribution in repetitive sandwiches of reactor material leads to results analogous to the 1-dimensional form of Bloch's theorem for the electronic structure in crystals. This principle makes it possible to perform analytically accurate homogenisations of sandwich lattices The method has been extended to cover multi group diffusion and transport theory. (author)
Non-Archimedean Big Picard Theorems
Cherry, William
2002-01-01
A non-Archimedean analog of the classical Big Picard Theorem, which says that a holomorphic map from the punctured disc to a Riemann surface of hyperbolic type extends accross the puncture, is proven using Berkovich's theory of non-Archimedean analytic spaces.
INTERPOLATION THEOREMS FOR SELF-ADJOINT OPERATORS
Institute of Scientific and Technical Information of China (English)
Shijun Zheng
2009-01-01
We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator L, without assuming the gra-dient estimate for its spectral kernel. The result applies to the cases where L is a uniformly elliptic operator or a Schr(o)dinger operator with electro-magnetic potential.
Donsker-Type Theorem for BSDEs
Briand, Philippe; Delyon, Bernard; Mémin, Jean
2001-01-01
This paper is devoted to the proof of Donsker's theorem for backward stochastic differential equations (BSDEs for short). The main objective is to give a simple method to discretize in time a BSDE. Our approach is based upon the notion of ``convergence of filtrations'' and covers the case of a $(y,z)$-dependent generator.
A Fixed Point Theorem for Discontinuous Functions
Herings, Jean-Jacques; Laan, Gerard van der; Talman, Dolf; Yang, Zaifu
2004-01-01
Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory.
Green's Theorem for Generalized Fractional Derivatives
Odzijewicz, Tatiana; Malinowska, Agnieszka B.; Delfim F. M. Torres
2012-01-01
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case when the generalized operators are reduced to the standard partial fractional derivatives and fractional integrals in the sense of Riemann-Liouville or Caputo.
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.
Generalizations of the Lax-Milgram Theorem
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Dimosthenis Drivaliaris
2007-05-01
Full Text Available We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular, we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all bounded linear functionals of the latter. We also give two applications to singular differential equations.
Generalizations of the Lax-Milgram Theorem
Directory of Open Access Journals (Sweden)
Yannakakis Nikos
2007-01-01
Full Text Available We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular, we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all bounded linear functionals of the latter. We also give two applications to singular differential equations.
Deduction Theorems in Weakly Implicative Logics
Czech Academy of Sciences Publication Activity Database
Cintula, Petr
Barcelona: Universitat de Barcelona, 2005. s. 19-20. [Algebraic and Topological Methods in Non-Classical Logics /2./. 15.06.2005-18.06.2005, Barcelona] Institutional research plan: CEZ:AV0Z10300504 Keywords : deduction theorem * substructural logic * BCI logic * weakly implicative logic Subject RIV: BA - General Mathematics
Random fixed point theorems on product spaces
Ismat Beg; Naseer Shahzad
1993-01-01
The existence of random fixed point of a locally contractive random operator in first variable on product spaces is proved. The concept continuous random height-selection is discussed. Some random fixed point theorems for nonexpansive self and nonself maps are also obtained in product spaces.
A non-archimedean Montel's theorem
Favre, Charles; Trucco, Eugenio
2011-01-01
We prove a version of Montel's theorem for analytic functions over a non-archimedean complete valued field. We propose a definition of normal family in this context, and give applications of our results to the dynamics of non-archimedean entire functions.
On Noethers theorem in quantum field theory
International Nuclear Information System (INIS)
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)
An extension theorem for conformal gauge singularities
Tod, Paul
2007-01-01
We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem.
Crum's Theorem for 'Discrete' Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2009-01-01
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem. describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in 'discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schrodinger equation is a difference equation.
Crum's Theorem for `Discrete' Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2009-01-01
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in `discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schr\\"odinger equation is a difference equation.
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].
JACKSON‘S THEOREM FOR COMPACT GROUPS
Institute of Scientific and Technical Information of China (English)
H.Vaezi; S.F.Rzaev
2002-01-01
In this article we consider the generalized shift operator defined by (Shuf)(g)=∫Gf(tut-1g)dt on compact group G and by help of this operator we define “Spherical” modulus of continuity.So we prove Stechkin and Jackson type theorems.
Extended Kelvin theorem in relativistic magnetohydrodynamics
Bekenstein, Jacob D.; Oron, Asaf
2000-01-01
We prove the existence of a generalization of Kelvin's circulation theorem in general relativity which is applicable to perfect isentropic magnetohydrodynamic flow. The argument is based on a new version of the Lagrangian for perfect magnetohydrodynamics. We illustrate the new conserved circulation with the example of a relativistic magnetohydrodynamic flow possessing three symmetries.
The virial theorem and planetary atmospheres
Toth, Viktor T.
2010-01-01
We derive a version of the virial theorem that is applicable to diatomic planetary atmospheres that are in approximate thermal equilibrium at moderate temperatures and pressures and are sufficiently thin such that the gravitational acceleration can be considered constant. We contrast a pedagogically inclined theoretical presentation with the actual measured properties of air.
The virial theorem for nonlinear problems
Amore, Paolo; Fernández, Francisco M.
2009-01-01
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation problem. In the former case we obtain the same main result derived earlier from the expansion in Chebyshev polynomials.
Tennis Rackets and the Parallel Axis Theorem
Christie, Derek
2014-01-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
A Bijective Proof For Forest Reciprocity Theorem
Huang, ShinnYih
2009-01-01
In this paper, we study the graph polynomial that counts spanning rooted forests f_g of a given graph. This polynomial has a remarkable reciprocity property. We give a new bijective proof for this theorem which has Prufer coding as a special case.
Limit theorems for Markov random fields
International Nuclear Information System (INIS)
Markov Random Fields (MRF's) have been extensively applied in Statistical Mechanics as well as in Bayesian Image Analysis. MRF's are a special class of dependent random variables located at the vertices of a graph whose joint distribution includes a parameter called the temperature. When the number of vertices of the graph tends to infinity, the normalized distribution of statistics based on these random variables converge in distribution. It can happen that for certain values of the temperature, that the rate of growth of these normalizing constants change drastically. This feature is generally used to explain the phenomenon of phase transition as understood by physicist. In this dissertation the author will show that this drastic change in normalizing constants occurs even in the relatively smooth case when all the random variables are Gaussian. Hence any image analytic MRF ought to be checked for such discontinuous behavior before any analysis is performed. Mixed limit theorems in Bayesian Image Analysis seek to replace intensive simulations of MRF's with limit theorems that approximate the distribution of the MRF's as the number of sites increases. The problem of deriving mixed limit theorems for MRF's on a one dimensional lattice graph with an acceptor function that has a second moment has been studied by Chow. A mixed limit theorem for the integer lattice graph is derived when the acceptor function does not have a second moment as for instance when the acceptor function is a symmetric stable density of index 0 < α < 2
Kelvin's Canonical Circulation Theorem in Hall Magnetohydrodynamics
Shivamoggi, B K
2016-01-01
The purpose of this paper is to show that, thanks to the restoration of the legitimate connection between the current density and the plasma flow velocity in Hall magnetohydrodynamics (MHD), Kelvin's Circulation Theorem becomes valid in Hall MHD. The ion-flow velocity in the usual circulation integral is now replaced by the canonical ion-flow velocity.
Scaling Identities for Solitons beyond Derrick's Theorem
Manton, Nicholas S.
2008-01-01
New integral identities satisfied by topological solitons in a range of classical field theories are presented. They are derived by considering independent length rescalings in orthogonal directions, or equivalently, from the conservation of the stress tensor. These identities are refinements of Derrick's theorem.
Pauli and The Spin-Statistics Theorem
International Nuclear Information System (INIS)
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
Fundamental theorems of extensional untyped $\\lambda$-calculus revisited
Directory of Open Access Journals (Sweden)
Alexandre Lyaletsky
2015-10-01
Full Text Available This paper presents new proofs of three following fundamental theorems of the untyped extensional $\\lambda$-calculus: the $\\eta$-Postpo-nement theorem, the $\\beta\\eta$-Normal form theorem, and the Norma-lization theorem for $\\beta\\eta$-reduction. These proofs do not involve any special extensions of the standard language of $\\lambda$-terms but nevertheless are shorter and much more comprehensive than their known analogues.
Ehrenfest theorem, Galilean invariance and nonlinear Schr"odinger equations
Kälbermann, G
2003-01-01
Galilean invariant Schr"odinger equations possessing nonlinear terms coupling the amplitude and the phase of the wave function can violate the Ehrenfest theorem. An example of this kind is provided. The example leads to the proof of the theorem: A Galilean invariant Schr"odinger equation derived from a lagrangian density obeys the Ehrenfest theorem. The theorem holds for any linear or nonlinear lagrangian.
Theorems of Tarski's Undefinability and Godel's Second Incompleteness - Computationally
Salehi, Saeed
2015-01-01
We show that the existence of a finitely axiomatized theory which can prove all the true $\\Sigma_1$ sentences may imply Godel's Second Incompleteness Theorem, by incorporating some bi-theoretic version of the derivability conditions (first discussed by 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 shown.
Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime
Energy Technology Data Exchange (ETDEWEB)
Lehmann, G.; Spatschek, K. H. [Institut für Theoretische Physik, Heinrich-Heine-Universität Düsseldorf, D–40225 Düsseldorf (Germany)
2013-07-15
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.
Cohen, Raphael; London, Yosef; Antman, Yair; Zadok, Avi
2014-05-19
A new technique for Brillouin scattering-based, distributed fiber-optic measurements of temperature and strain is proposed, analyzed, simulated, and demonstrated. Broadband Brillouin pump and signal waves are drawn from the filtered amplified spontaneous emission of an erbium-doped fiber amplifier, providing high spatial resolution. The reconstruction of the position-dependent Brillouin gain spectra along 5 cm of a silica single-mode fiber under test, with a spatial resolution of 4 mm, is experimentally demonstrated using a 25 GHz-wide amplified spontaneous emission source. A 4 mm-long localized hot spot is identified by the measurements. The uncertainty in the reconstruction of the local Brillouin frequency shift is ± 1.5 MHz. The single correlation peak between the pump and signal is scanned along a fiber under test using a mechanical variable delay line. The analysis of the expected spatial resolution and the measurement signal-to-noise ratio is provided. The measurement principle is supported by numerical simulations of the stimulated acoustic field as a function of position and time. Unlike most other Brillouin optical correlation domain analysis configurations, the proposed scheme is not restricted by the bandwidth of available electro-optic modulators, microwave synthesizers, or pattern generators. Resolution is scalable to less than one millimeter in highly nonlinear media. PMID:24921326
Non-local effect in Brillouin optical time-domain analyzer based on Raman amplification
International Nuclear Information System (INIS)
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)
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.
A Full Characterization on Fixed-Point Theorem, Minimax Inequality, Saddle Point, and KKM Theorem
Tian, Guoqiang
2012-01-01
This paper provides necessary and sufficient conditions for fixed-point theorems, minimax inequalities and some related theorems defined on arbitrary topological spaces that may be discrete, continuum, non-compact or non-convex. We establish a single condition, γ-recursive transfer lower semicontinuity, which fully characterizes the existence of equilibrium of minimax inequality without imposing any kind of convexity nor any restriction on topological space. The result then is employed to ful...
ON GÖDEL'S INCOMPLETENESS THEOREM(S), ARTIFICIAL INTELLIGENCE/LIFE, AND HUMAN MIND
CHRISTIANTO, V.; FLORENTIN SMARANDACHE
2015-01-01
In the present paper we have discussed concerning Gödel’s incompleteness theorem(s) and plausible implications to artificial intelligence/life and human mind. Perhaps we should agree with Sullins III, that the value of this finding is not to discourage certain types of research in AL, but rather to help move us in a direction where we can more clearly define the results of that research.
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...
Goedel incompleteness theorems and the limits of their applicability. I
International Nuclear Information System (INIS)
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.
Limit theorems for extremes with random sample size
Silvestrov, Dmitrii S.; Teugels, Jozef L.
1998-01-01
This paper is devoted to the investigation of limit theorems for extremes with random sample size under general dependence-independence conditions for samples and random sample size indexes. Limit theorems of weak convergence type are obtained as well as functional limit theorems for extremal processes with random sample size indexes.
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
Brillouin limit for electron plasmas confined on magnetic surfaces
International Nuclear Information System (INIS)
As is well known, the density of pure electron plasmas that are confined by a magnetic field is limited by the Brillouin density, nB ε0B2/2me. However, the electron density can be limited to a much lower value when the electrons are confined on magnetic surfaces, such as the surfaces produced by a stellarator. If the electron temperature is a spatial constant, the electron force-balance equation, me/e ν-→ ∇-→ν + ∇-→p / en = ∇-→Φ-ν-→xB-→, can be rewritten as ∇-→Φ* = ν-→xB-→*. The effective electric potential and the effective magnetic field are Φ* Φ - me/2eν2 - Tln(n) and B-→* B-→ - me/e ∇ x ν-→. The electron density for magnetic confinement in a cylinder with B-→ = Bz-circumflex is bounded by the Brillouin limit. If one assumes the electrons are pressureless and have a spatially constant density n0, then Φ = (en0/4ε0)r2. Both B-→* and Φ* vanish when n0 = nB, and the equation ∇-→Φ* = ν-→ x B-→* has no solutions for n0 > nB. The confinement of electrons on magnetic surfaces is lost when the field lines of the effective magnetic field B-→* leave the confinement region and strike the chamber walls. If the magnetic surfaces of the true field B-→ are described by the toroidal flux, ψt that they enclose, so B-→ ∇-→ψt = 0, then confinement is easily lost when ∇-→ψt ∇-→ x ν-→ has Fourier terms that resonate with the rotational transform of B-→, for then the B-→* surfaces are split by islands. The resonant Fourier terms are given by (B-→ x ∇-→ψt) ∇-→(ν||/B). In other words, resonant Fourier terms in the parallel flow of the electrons can cause a break up of the surfaces of the B-→* field. The parallel flow is determined by the condition that ∇-→ (nν-→) = 0, which implies B-→ ∇-→(v||/B) = -∇-→ (nν-→perpendicular).When n0B, the divergence of the perpendicular flow is given by ∇-→ (nν-→perpendicular) = (B-→ x ∇-→Φ) ∇-→(n/B2) . Variations
Regions for Brillouin seed pulse growth in relativistic laser-plasma interaction
Energy Technology Data Exchange (ETDEWEB)
Lehmann, G.; Schluck, F.; Spatschek, K. H. [Institut fuer Theoretische Physik, Heinrich-Heine-Universitaet Duesseldorf, D-40225 Duesseldorf (Germany)
2012-09-15
Parametric plasma processes received renewed interest in the context of generating ultraintense and ultrashort laser pulses up to the exawatt-zetawatt regime. For Brillouin scattering and seed pulse amplification at high intensities, the strong coupling regime is of special interest. The intensity-driven low-frequency modes depend on the amplitudes of the laser fields. It is investigated here how these modes develop in the relativistic regime. Then, a unified treatment of Raman and Brillouin processes becomes necessary. Assuming circular polarization, it is shown that with increasing intensity an overlap of the originally different Raman, Brillouin, and modulational instability branches occurs. Numerical simulations with a linearized Maxwell-fluid code confirm the analytically predicted behavior.
Mizuno, Yosuke; Nakamura, Kentaro
2014-01-01
We observe an interference pattern using a simple fiber-optic interferometer consisting of an electrical spectrum analyzer and a narrowband light source, which is commonly employed for observing the Brillouin gain spectrum. This interference pattern expands well beyond the frequency range corresponding to the Brillouin frequency shift in silica fibers (approximately 11 GHz at 1550 nm). Using both silica single-mode and polymer optical sensing fibers, we then experimentally prove that the distinctive noise in a self-heterodyne-based Brillouin measurement with an unoptimized polarization state originates from the interference between the reference light and the Fresnel-reflected light. This noise can be almost completely suppressed by employing a delay line that is longer than the coherence length of the light source and by artificially applying a high loss near the open end of the sensing fiber.
Exploiting the self-similar nature of Raman and Brillouin amplification
Trines, R.; Alves, E. P.; Fonseca, R. A.; Silva, L. O.; Webb, E.; Fiuza, F.; Cairns, R. A.; Bingham, R.; Norreys, P.
2015-11-01
Raman and Brillouin amplification are two schemes for amplifying and compressing short laser pulses in plasma. Depending on the laser and plasma configurations, these schemes could potentially deliver the high-energy high-power pulses needed for inertial confinement fusion, especially fast-ignition fusion. Analytical self-similar models for both Raman and Brillouin amplification have already been derived, but the consequences of this self-similar behavior are little known and hardly ever put to good use. In this talk, we will give an overview of the self-similar laws that govern the evolution of the probe pulse in Raman and Brillouin amplification, and show how these laws can be exploited, in particular regarding the parameters of the initial probe pulse, to control the properties of the final amplified probe and improve the efficiency of the process.
Betin, A. A.; Vasilev, A. F.; Kulagin, O. V.; Manishin, V. G.; Iashin, V. E.
1985-09-01
Consideration is given to the conditions for the existence and observation of wave front reversal in focused light beams due to nonstationary stimulated Mandel'shtam-Brillouin scattering. Experimental observations were carried out for light beams having small scale spatial inhomogeneities at a wavelength of 1.05 microns. The precision of the wave front reversal is determined, and the reflection coefficients of the Mandel'shtam-Brillouin scattering mirrors are measured with respect to quasi-homogeneous light beams under saturation conditions. The relative duration of the light pulses was t sub i/T2 = 0.15-1 (where T2 is the hypersound relaxation time). It is shown that the maximum duration of the pulses, which were reflected by a stimulated Mandel'shtam-Brillouin mirror, was limited by competing nonlinear breakdown and self-focusing processes. The accuracy of a correction for wave front reversal is also determined.
Accuracy limitations on Brillouin lidar measurements of temperature and sound speed in the ocean.
Fry, E S; Emery, Y; Quan, X; Katz, J W
1997-09-20
There are five mutually dependent variables relevant to Brillouin lidar measurements of temperature and sound speed in the ocean; they are (1) the Brillouin shift, (2) the sound speed, (3) the index of refraction, (4) the temperature, and (5) the salinity. We use three well-known relations to analyze rigorously the interdependence of these five variables. Clearly, a Brillouin shift measurement does not provide a stand-alone determination of temperature or sound speed; one more variable or one more relation must be known. The use of mean values of salinity that have been obtained by an analysis of a large set of historical in situ data is considered for this additional relation. PMID:18259560
Regions for Brillouin seed pulse growth in relativistic laser-plasma interaction
Lehmann, G.; Schluck, F.; Spatschek, K. H.
2012-09-01
Parametric plasma processes received renewed interest in the context of generating ultraintense and ultrashort laser pulses up to the exawatt-zetawatt regime. For Brillouin scattering and seed pulse amplification at high intensities, the strong coupling regime is of special interest. The intensity-driven low-frequency modes depend on the amplitudes of the laser fields. It is investigated here how these modes develop in the relativistic regime. Then, a unified treatment of Raman and Brillouin processes becomes necessary. Assuming circular polarization, it is shown that with increasing intensity an overlap of the originally different Raman, Brillouin, and modulational instability branches occurs. Numerical simulations with a linearized Maxwell-fluid code confirm the analytically predicted behavior.
Regions for Brillouin seed pulse growth in relativistic laser-plasma interaction
International Nuclear Information System (INIS)
Parametric plasma processes received renewed interest in the context of generating ultraintense and ultrashort laser pulses up to the exawatt-zetawatt regime. For Brillouin scattering and seed pulse amplification at high intensities, the strong coupling regime is of special interest. The intensity-driven low-frequency modes depend on the amplitudes of the laser fields. It is investigated here how these modes develop in the relativistic regime. Then, a unified treatment of Raman and Brillouin processes becomes necessary. Assuming circular polarization, it is shown that with increasing intensity an overlap of the originally different Raman, Brillouin, and modulational instability branches occurs. Numerical simulations with a linearized Maxwell-fluid code confirm the analytically predicted behavior.
Guided acoustic and optical waves in silicon-on-insulator for Brillouin scattering and optomechanics
Sarabalis, Christopher J; Safavi-Naeini, Amir H
2016-01-01
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 1/(Wm) for backward and forward Brillouin scattering, respectively.
Improvement of comb lines quality employing double-pass architecture in Brillouin-Raman laser
International Nuclear Information System (INIS)
We demonstrate a generation of multiple wavelength lasers incorporating a Brillouin-Raman fiber laser using a double-pass structure. The Raman and Brillouin amplification medium is provided by the combination of 11 km long dispersion-compensating-fiber and 25 km long large-effective-area-fiber. The laser structure is primarily pumped by single Raman pump wavelength at 1455 nm. The loop mirror is utilized as the reflector, which allows Stokes lines and pump light to propagate back into the cavity. A flat output of multiwavelength lasers with uniform optical signal-to-noise ratio across the flat bandwidth is realized from the proposed laser structure
Brillouin study of phonons, magnons and magnetoelastic coupling in the antiferromagnet KNiF3
Ganot, F.; Dugautier, S.; Moch, P.; Nouet, J.
1981-03-01
Brillouin scattering by magnons and acoustic phonons in KNiF3 has been studied as function of the temperature. At low temperature, we observe unusually large splittings of the phonon Brillouin lines, related to the multidomains structure of the samples. Using our determination of the anisotropy constant, K = 1.1×104 erg/cm3, we calculate from the splitting of the longitudinal [1, 1, 0] phonon a magnetoelastic coefficient ‖b2‖ = 3.3×107 erg/cm3. We also study the domains reorientation under an applied magnetic field.
Fiber break location technique utilizing stimulated Brillouin scattering effects in optical fiber
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
A simple model is developed to study the mechanism of stimulated Brillouin scattering (SBS) suppression with frequency-modulated laser in optical fiber. By taking into account the laser frequency distribution along the fiber induced by frequency modulation, the average effective Brillouin gain is calculated to determine the SBS threshold. Experimental results show agreement with the numerical analysis. The application for SBS suppression in interferometric fiber sensing system is also discussed in this paper. The results show that the maximum input power can be increased effectively by frequency modulation method. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Casas-Bedoya, Alvaro; Morrison, Blair; Pagani, Mattia; Marpaung, David; Eggleton, Benjamin J
2015-09-01
We demonstrate the first, to the best of our knowledge, functional signal processing device based on stimulated Brillouin scattering in a silicon nanowire. We use only 1 dB of on-chip stimulated Brillouin scattering gain to create an RF photonic notch filter with 48 dB of suppression, 98 MHz linewidth, and 6 GHz frequency tuning. This device has potential applications in on-chip microwave signal processing and establishes the foundation for the first CMOS-compatible high-performance RF photonic filter. PMID:26368735
Diagnostic techniques for photonic materials based on Raman and Brillouin spectroscopies
Institute of Scientific and Technical Information of China (English)
M. Mattarelli; M. Ferrari; Y. Jestin; G. Nunzi Conti; S. Pelli; G.C. Righini; S.Caponi; A. Chiappini; M. Montagna; E. Moser; F. Rossi; C.Tosello; C. Armellini; A. Chiasera
2007-01-01
The elastic and vibrational properties of a material, bulk or planar waveguide, are studied by Brillouin and Raman spectroscopy to follow the process of nanocrystals growth in glass-ceramics. The nanoparticles cause the appearance, in the low frequency Raman spectrum, of characteristic peaks, whose position depends on the size of the crystals. At the same time, sharp crystal peaks, due to optical phonons, appear in the Raman spectra, allowing the determination of the nucleated phase, and a frequency shift of the Brillouin peaks is observed.
Causarum Investigatio and the Two Bell's Theorems of John Bell
Wiseman, Howard M
2015-01-01
"Bell's theorem" can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the joint assumptions of Locality and Predetermination. His 1976 theorem is their incompatibility with the single property of Local Causality. This is contrary to Bell's own later assertions, that his 1964 theorem began with the assumption of Local Causality, even if not by that name. Although the two Bell's theorems are logically equivalent, their assumptions are not. Hence, the earlier and later theorems suggest quite different conclusions, embraced by operationalists and realists, respectively. The key issue is whether Locality or Local Causality is the appropriate notion emanating from Relativistic Causality, and this rests on one's basic notion of causation. For operationalists the appropriate notion is what is here called the Principle of Agent-Causation, while for realists it is Reichenbach's Principle of common cause. By...
On c-theorems in arbitrary dimensions
Bhattacharyya, Arpan; Sen, Kallol; Sinha, Aninda
2012-01-01
The dilaton action in 3+1 dimensions plays a crucial role in the proof of the a-theorem. This action arises using Wess-Zumino consistency conditions and crucially relies on the existence of the trace anomaly. Since there are no anomalies in odd dimensions, it is interesting to ask how such an action could arise otherwise. Motivated by this we use the AdS/CFT correspondence to examine both even and odd dimensional CFTs. We find that in even dimensions, by promoting the cut-off to a field, one can get an action for this field which coincides with the WZ action in flat space. In three dimensions, we observe that by finding an exact Hamilton-Jacobi counterterm, one can find a non-polynomial action which is invariant under global Weyl rescalings. We comment on how this finding is tied up with the F-theorem conjectures.
Weinberg Soft Theorems from Weinberg Adiabatic Modes
Mirbabayi, Mehrdad
2016-01-01
Soft theorems for the scattering of low energy photons and gravitons and cosmological consistency conditions on the squeezed-limit correlation functions are both understood to be consequences of invariance under large gauge transformations. We apply the same method used in cosmology -- based on the identification of an infinite set of "adiabatic modes" and the corresponding conserved currents -- to derive flat space soft theorems for electrodynamics and gravity. We discuss how the recent derivations based on the asymptotic symmetry groups (BMS) can be continued to a finite size sphere surrounding the scattering event, when the soft photon or graviton has a finite momentum. We give a finite distance derivation of the antipodal matching condition previously imposed between future and past null infinities, and explain why all but one radiative degrees of freedom decouple in the soft limit. In contrast to earlier works on BMS, we work with adiabatic modes which correspond to large gauge transformations that are $...
Locomotion in complex fluids: Integral theorems
Lauga, Eric
2014-01-01
The biological fluids encountered by self-propelled cells display complex microstructures and rheology. We consider here the general problem of low-Reynolds number locomotion in a complex fluid. {Building on classical work on the transport of particles in viscoelastic fluids,} we demonstrate how to mathematically derive three integral theorems relating the arbitrary motion of an isolated organism to its swimming kinematics {in a non-Newtonian fluid}. These theorems correspond to three situations of interest, namely (1) squirming motion in a linear viscoelastic fluid, (2) arbitrary surface deformation in a weakly non-Newtonian fluid, and (3) small-amplitude deformation in an arbitrarily non-Newtonian fluid. Our final results, valid for a wide-class of {swimmer geometry,} surface kinematics and constitutive models, at most require mathematical knowledge of a series of Newtonian flow problems, and will be useful to quantity the locomotion of biological and synthetic swimmers in complex environments.
Parameterized quantum field theory without Haag's theorem
Seidewitz, Ed
2015-01-01
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that quantum field theory can be formulated, using an invariant, fifth path parameter in addition to the usual four position parameters, in such a way that Haag's theorem no longer applies, but such that the Dyson perturbation expansion for the sc...
Kinesin and the Crooks and Carnot theorems
Calzetta, E
2008-01-01
The literature on the thermodynamic analysis of the kinesin cycle regarded as a molecular motor is quite bewildering to the uninitiated. For example, the published predictions for thermal efficiency at stalling range from 0 (A. W. C. Lau, D. Lacoste and K. Mallick, Phys. Rev. Lett. 99, 158102 (2007); D. Lacoste, A. W. C. Lau and K. Mallick, Phys. Rev. E78, 011915 (2008)) to 100% (G. Oster and H. Wang, in Molecular Motors, edited by M. Schliwa (Wiley-VCH Verlag GmbH, Weinheim (2003), p. 207). This latter statement is worrysome since it seems to make Carnot's theorem irrelevant. In this note we show there is a sensible ideal kinesin cycle to which the real cycle may be compared. The ideal cycle has a thermal efficiency of less than one, and the real one is less efficient than the ideal one always, in compliance with Carnot's theorem.
Aging and nonergodicity beyond the Khinchin theorem.
Burov, S; Metzler, R; Barkai, E
2010-07-27
The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin's theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics. PMID:20624984
Optimizing the Graph Minors Weak Structure Theorem
Giannopoulou, Archontia C
2011-01-01
One of the major results of [N. Robertson and P. D. Seymour. Graph minors. XIII. The disjoint paths problem. J. Combin. Theory Ser. B, 63(1):65--110, 1995], also known as the weak structure theorem, revealed the local structure of graphs excluding some graph as a minor: each such graph $G$ either has small treewidth or contains the subdivision of a wall that can be arranged "bidimensionally" inside $G$, given that some small set of vertices are removed. We prove an optimized version of that theorem where (i) the relation between the treewidth of the graph and the height of the wall is linear (thus best possible) and (ii) the number of vertices to be removed is minimized.
``Bloch wave'' modification of stimulated Raman by stimulated Brillouin scattering
Dodd, E. S.; Vu, H. X.; DuBois, D. F.; Bezzerides, B.
2013-03-01
Using the reduced-description particle-in-cell (RPIC) method, we study the coupling of backward stimulated Raman scattering (BSRS) and backward stimulated Brillouin scattering (BSBS) in regimes where the reflectivity involves the nonlinear behavior of particles trapped in the daughter plasma waves. The temporal envelope of a Langmuir wave (LW) obeys a Schrödinger equation where the potential is the periodic electron density fluctuation resulting from an ion-acoustic wave (IAW). The BSRS-driven LWs in this case have a Bloch wave structure and a modified dispersion due to the BSBS-driven spatially periodic IAW, which includes frequency band gaps at kLW˜kIAW/2˜k0 (kLW, kIAW, and k0 are the wave number of the LW, IAW, and incident pump electromagnetic wave, respectively). This band structure and the associated Bloch wave harmonic components are distinctly observed in RPIC calculations of the electron density fluctuation spectra and this structure may be observable in Thomson scatter. Bloch wave components grow up in the LW spectrum, and are not the result of isolated BSRS. Self-Thomson scattered light from these Bloch wave components can have forward scattering components. The distortion of the LW dispersion curve implies that the usual relationship connecting the frequency shift of the BSRS-scattered light and the density of origin of this light may become inaccurate. The modified LW frequency results in a time-dependent frequency shift that increases as the IAW grows, detunes the BSRS frequency matching condition, and reduces BSRS growth. A dependence of the BSRS reflectivity on the IAW Landau damping results because this damping determines the levels of IAWs. The time-dependent reflectivity in our simulations is characterized by bursts of sub-picosecond pulses of BSRS alternating with multi-ps pulses of BSBS, and BSRS is observed to decline precipitously as soon as SBS begins to grow from low levels. In strong BSBS regimes, the Bloch wave effects in BSRS are
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.
A Dirichlet unit theorem for Drinfeld modules
Taelman, Lenny
2009-01-01
We show that the module of integral points on a Drinfeld module satisfies a an analogue of Dirichlet's unit theorem, despite its failure to be finitely generated. As a consequence, we obtain a construction of a canonical finitely generated sub-module of the module of integral points. We use the results to give a precise formulation of a conjectural analogue of the class number formula.
Arrow’s theorem in judgment aggregation
Dietrich, Franz; List, Christian
2005-01-01
In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using “systematicity” and “independence” conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s ...
Stability theorems for symplectic and contact pairs
Bande, G.; Ghiggini, P.; Kotschick, D.
2004-01-01
We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the condition that its kernel hyperplane distribution have constant class in the sense of E. Cartan.
A new comparison theorem of multidimensional BSDEs
Wu, Panyu
2010-01-01
In this paper, we define a new total order on R^N and use this order together with backward stochastic viability property(for short BSVP) to study the property of the generator of backward stochastic differential equation(for short BSDE) when the price of contingent claim can be represented by a BSDE in the no-arbitrage financial market. The main result is the necessary and sufficient condition for comparison theorem of multidimensional BSDEs under this order.
Thermal Tachyons and the "g"-Theorem
Chaudhuri, Shyamoli
2002-01-01
We give a pedagogical introduction to Affleck and Ludwig's g-theorem, distinguishing its applications in field theory vs string theory. We clarify the recent proposal that the vacuum degeneracy $g$ of a noncompact worldsheet sigma model with a continuous spectrum of scaling dimensions is lowered under renormalization group flow while preserving the central charge. As an illustration we argue that the IR stable endpoint of the relevant flow of the worldsheet RG induced by a thermal tachyon in ...
A Central Limit Theorem for Punctuated Equilibrium
Bartoszek, Krzysztof
2016-01-01
Current evolutionary biology models usually assume that a phenotype undergoes gradual change. This is in stark contrast to biological intuition, which indicates that change can also be punctuated - the phenotype can jump. Such a jump can especially occur at speciation, i.e. dramatic change occurs that drives the species apart. Here we derive a central limit theorem for punctuated equilibrium. We show that, if adaptation is fast, for weak convergence to hold, dramatic change has to be a rare e...
Virial Theorem in Nonlocal Newtonian Gravity
Bahram Mashhoon
2016-01-01
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...
Limit theorems for sequences of random trees
Balding, David; Ferrari, Pablo A.; Fraiman, Ricardo; Sued, Mariela
2004-01-01
We consider a random tree and introduce a metric in the space of trees to define the ``mean tree'' as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.
The Lebesgue decomposition theorem for arbitrary contents
König, Heinz
2005-01-01
The decomposition theorem named after Lebesgue asserts that certain set functions have canonical representations as sums of particular set functions called the absolutely continuous and the singular ones with respect to some fixed set function. The traditional versions are for the bounded measures with respect to some fixed measure on a \\sigma algebra, in final form due to Hahn 1921, and for the bounded contents with respect to some fixed content on an algebra, due to Bochner-Phillips 194...
From the Goldbach Conjecture to the Theorem
Pereyra, P H
2007-01-01
In the present work we demonstrate that the so called Goldbach conjecture from 1742, All positive even numbers greater than two can be expressed as a sum of two primes, due to Leonhard Euler, is a true statement. This result is partially based on the Wilson theorem, and complementary on our reasoning to cast the problem into a diophantine equation. The latter is the master equation for the conjectures proof.
A New Extension Theorem for Concave Operators
Jian-wen Peng; Wei-dong Rong; Jen-Chih Yao
2009-01-01
We present a new and interesting extension theorem for concave operators as follows. Let be a real linear space, and let be a real order complete PL space. Let the set be convex. Let be a real linear proper subspace of , with , where for some . Let be a concave operator such that whenever and . Then there exists a concave operator such that (i) is an extension of , that is, for all , and (ii) whenever .
A simple proof of Sarkozy's theorem
Lyall, Neil
2011-01-01
It is a striking and elegant fact (proved independently by Furstenberg and Sarkozy) that in any subset of the natural numbers of positive upper density there necessarily exist two distinct elements whose difference is given by a perfect square. In this article we present a new and simple proof of this result by adapting an argument originally developed by Croot and Sisask to give a new proof of Roth's theorem.
Limit theorems for self-similar tilings
Bufetov, Alexander I
2012-01-01
We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic formula is given for ergodic integrals in terms of these finitely-additive measures, and, as a corollary, limit theorems are obtained for dynamical systems given by self-similar tilings.
On the Danilov-Gizatullin Isomorphism Theorem
Flenner, Hubert; Kaliman, Shulim; ZAIDENBERG, MIKHAIL
2008-01-01
A Danilov-Gizatullin surface is a normal affine surface V, which is a complement to an ample section S in a Hirzebruch surface of index d. By a surprising result due to Danilov and Gizatullin, V depends only on the self-intersection number of S and neither on d nor on S. In this note we provide a new and simple proof of this Isomorphism Theorem.
Uniform Zariski's Theorem On Fundamental Groups
Kaliman, Shulim
1997-01-01
The Zariski theorem says that for every hypersurface in a complex projective (resp. affine) space of dimension at least 3 and for every generic plane in the projective (resp. affine) space the natural embedding generates an isomorphism of the fundamental groups of the complements to the hypersurface in the plane and in the space. If a family of hypersurfaces depends algebraically on parameters then it is not true in general that there exists a plane such that the natural embedding generates i...
Stochastic Reynolds theorem and generalized subgrid tensor
Resseguier, Valentin; Mémin, Etienne; Chapron, Bertrand
2015-01-01
International audience We propose a representation that allows decomposing the flow velocity in terms of a smooth component and a highly oscillating random component. This decomposion leads through a stochastic representation of the Reynolds transport theorem to a large-scale expression of the Navier-Stokes equations. In this work we show the benefit of such a representation to construct low order dynamical systems that include naturally a dissipative term related to the action of the smal...
Fixed point theorems and their applications
Farmakis, Ioannis
2013-01-01
This is the only book that deals comprehensively with fixed point theorems overall of mathematics. Their importance is due, as the book demonstrates, to their wide applicability. Beyond the first chapter, each of the other seven can be read independently of the others so the reader has much flexibility to follow his/her own interests. The book is written for graduate students and professional mathematicians and could be of interest to physicists, economists and engineers.
Asymptotic representation theorems for poverty indices
Lo, Gane Samb; Sall, Serigne Touba
2010-01-01
We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotics of the bulk of poverty indices and issues in poverty analysis. Our representation results uniformly hold on a large collection of poverty indices. They enable the continuous measure of poverty with longitudinal data.
User interaction widgets for interactive theorem proving
Zacchiroli, Stefano
2007-01-01
Matita (that means pencil in Italian) is a new interactive theorem prover under development at the University of Bologna. When compared with state-of-the-art proof assistants, Matita presents both traditional and innovative aspects. The underlying calculus of the system, namely the Calculus of (Co)Inductive Constructions (CIC for short), is well-known and is used as the basis of another mainstream proof assistant—Coq—with which Matita is to some extent compatible. In the sam...
The untyped stack calculus and Bohm's theorem
Alberto Carraro
2013-01-01
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.
Two beautiful proofs of Pick's theorem
Raman Sundström, Manya; Öhman, Lars-Daniel
2011-01-01
We present two different proofs of Pick’s theorem and analyse in what ways might be perceived as beautiful by working mathematicians. In particular, we discuss two concepts, generality and specificity, that appear to contribute to beauty in different ways. We also discuss possible implications on insight into the nature of beauty in mathematics, and how the teaching of mathematics could be impacted, especially in countries in which discussions of beauty and aesthetics are notably absent from...
An isomorphism theorem for random interlacements
Sznitman, Alain-Sol
2011-01-01
We consider continuous-time random interlacements on a transient weighted graph. We prove an identity in law relating the field of occupation times of random interlacements at level u to the Gaussian free field on the weighted graph. This identity is closely linked to the generalized second Ray-Knight theorem, and uniquely determines the law of occupation times of random interlacements at level u.
Voting, Lobbying, and the Decentralization Theorem
Lockwood, Benjamin
2007-01-01
This paper revisits the fiscal "decentralization theorem", by relaxing the role of the assumption that governments are benevolent, while retaining the assumption of policy uniformity. If instead, decisions are made by direct majority voting, (i) centralization can welfare-dominate decentralization even if there are no externalities and regions are heterogenous; (ii) decentralization can welfare-dominate centralization even if there are positive externalities and regions are hom...
Central limit theorem and deformed exponentials
International Nuclear Information System (INIS)
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)
Virial Theorem in Nonlocal Newtonian Gravity
Bahram Mashhoon
2015-01-01
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 theorem for confined universal Fermi gases
Thomas, J E
2008-01-01
Optically-trapped two-component Fermi gases near a broad Feshbach resonance exhibit universal thermodynamics, where the properties of the gas are independent of the details of the two-body scattering interactions. We present a global proof that such a universal gas obeys the virial theorem for {\\it any} trapping potential $U$ and any spin mixture, without assuming either the local density approximation or harmonic confinement. The total energy of the gas is given in scale invariant form by $E...
Degeneracy, the virial theorem, and stellar collapse
Cardall, Christian Y.
2008-01-01
Formulae for the energies of degenerate non-relativistic and ultra-relativistic Fermi gases play multiple roles in simple arguments related to the collapse of a stellar core to a neutron star. These formulae, deployed in conjunction with the virial theorem and a few other basic physical principles, provide surprisingly good estimates of the temperature, mass, and radius (and therefore also density and entropy) of the core at the onset of collapse; the final radius and composition of the cold ...
Higgs Physics and the Equivalence Theorem
Riesselmann, Kurt
1995-01-01
The equivalence theorem is an extremely useful tool to calculate heavy Higgs {\\it and} top-quark effects for processes that have center-of-mass-energies (much) larger than the $W$ boson mass. After an explanation of the renormalization procedures involved, the results for one- and two-loop radiative corrections to the fermionic Higgs decay, $H\\rightarrow f\\bar f$, are given and discussed. Finally, the renormalization scheme dependence is examined, and the reliability of the perturbative serie...
Theorems for Asymptotic Safety of Gauge Theories
Bond, Andrew D
2016-01-01
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 emphasized. 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.
Generalizations of the primitive element theorem
Directory of Open Access Journals (Sweden)
Panagiotis Nikolopoulos
1991-09-01
Full Text Available In this paper we generalize the primitive element theorem to the generation of separable algebras over fields and rings. We prove that any finitely generated separable algebra over an infinite field is generated by two elements and if the algebra is commutative it can be generated by one element. We then derive similar results for finitely generated separable algebras over semilocal rings.
Fluctuation Theorem in an Atmospheric Circulation Model
Schalge, Bernd; Wouters, Jeroen; Fraedrich, Klaus; Lunkeit, Frank
2012-01-01
Evidence for the validity of the Fluctuation Theorem (FT) in an atmospheric Global Circulation Model is found. The model is hydrostatic with variable numbers of vertical levels and different horizontal resolutions. For finite time intervals the largest local Lyapunov exponent (LLLE) is found to be negative consistent with predictions of the FT. The effect is present for resolutions up to wave numbers l=42 (~ 250km) and 10 levels.
Soft Theorems from Conformal Field Theory
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 ambitwistor 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.
Soft Theorems from Effective Field Theory
Larkoski, Andrew J; Stewart, Iain W
2014-01-01
The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate t...
Coherent cyclotron motion beyond Kohn's theorem
Maag, T.; Bayer, A.; Baierl, S.; Hohenleutner, M.; Korn, T.; Schüller, C.; Schuh, D.; Bougeard, D.; Lange, C.; Huber, R.; Mootz, M.; Sipe, J. E.; Koch, S. W.; Kira, M.
2016-02-01
In solids, the high density of charged particles makes many-body interactions a pervasive principle governing optics and electronics. However, Walter Kohn found in 1961 that the cyclotron resonance of Landau-quantized electrons is independent of the seemingly inescapable Coulomb interaction between electrons. Although this surprising theorem has been exploited in sophisticated quantum phenomena, such as ultrastrong light-matter coupling, superradiance and coherent control, the complete absence of nonlinearities excludes many intriguing possibilities, such as quantum-logic protocols. Here, we use intense terahertz pulses to drive the cyclotron response of a two-dimensional electron gas beyond the protective limits of Kohn's theorem. Anharmonic Landau ladder climbing and distinct terahertz four- and six-wave mixing signatures occur, which our theory links to dynamic Coulomb effects between electrons and the positively charged ion background. This new context for Kohn's theorem unveils previously inaccessible internal degrees of freedom of Landau electrons, opening up new realms of ultrafast quantum control for electrons.
Two Forbidden Induced Minor Theorems for Antimatroids
Altomare, Christian Joseph
2012-01-01
Antimatroids were discovered by Dilworth in the context of lattices [4] and introduced by Edelman and Jamison as convex geometries in[5]. The author of the current paper independently discovered (possibly infinite) antimatroids in the context of proof systems in mathematical logic [1]. Carlson, a logician, makes implicit use of this view of proof systems as possibly infinite antimatroids in [2]. Though antimatroids are in a sense dual to matroids, far fewer antimatroid forbidden minor theorems are known. Some results of this form are proved in [6], [7], [8], and [9]. This paper proves two forbidden induced minor theorems for these objects, which we think of as proof systems. Our first main theorem gives a new proof of the forbidden induced minor characterization of partial orders as proof systems, proved in [8] in the finite case and stated in [10] for what we call strong aut descendable proof systems. It essentially states that, pathologies aside, there is a certain unique simplest nonposet. Our second main ...
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)
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 ηC 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
Lipstein, Arthur E.
2015-06-01
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.
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
QUASI-LOCAL CONJUGACY THEOREMS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
ZHANG WEIRONG; MA JIPU
2005-01-01
Let f: U(xo)() E → F be a C1 map and f'(x0) be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties: f'(x0) is double splitting and R(f'(x)) ∩ N(T0+) = {0} near x0. However,in infinite dimensional Banach spaces, f'(x0) is not always double splitting (i.e., the generalized inverse of f'(x0) does not always exist), but its bounded outer inverse of f'(x0) always exists.Only using the C1 map f and the outer inverse T0# of f'(x0), the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if x0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.
No ghost theorem and cohomology theorem for strings in arbitrary static backgrounds
International Nuclear Information System (INIS)
This paper considers a string moving in an arbitrary time-independent background given by an arbitrary conformal field theory of appropriate central charge (e.g., c = 25 for bosonic string) and one flat time-like dimension. The authors show that the physical subspace of the Hilbert space is positive semi-definite (no ghost theorem) and that the cohomology of the BRST operator is trivial except for the ghost number one (for open bosonic string) sector (cohomology theorem). Both the proofs are reductio ad absurdum proofs based on the corresponding theorems for the strings moving in flat background. In cases where there is an extra flat space-like dimension (besides the flat time-like one), the transverse subspace with positive-definite norm can be constructed
Nizzoli, F.; A Franchini; Santoro, G.
1984-01-01
We present calculations of surface waves and Brillouin scattering intensity for polycarbonate films supported by a pyrex substrate in the thickness range 0-0.6 µm. Comparison between calculated and experimental spectra shows that it is possible to obtain accurate information concerning the thickness of the film and the value and sign of the photoelastic constants.
Wei, Heming; Zhao, Xuefeng; Kong, Xianglong; Zhang, Pinglei; Cui, Yanjun; Sun, Changsen
2013-01-01
The Brillouin optical time-domain analysis (BOTDA)-based optical fiber method has been proposed to measure strain variations caused by corrosion expansion. Spatial resolutions of 1 m can be achieved with this kind of Brillouin sensor for detecting the distributed strain. However, when the sensing fiber is wound around the steel rebar in a number of circles in a range of several meters, this spatial resolution still has limitations for corrosion monitoring. Here, we employed a low-coherent fiber-optic strain sensor (LCFS) to survey the performance of Brillouin sensors based on the fact that the deformation measured by the LCFS equals the integral of the strains obtained from Brillouin sensors. An electrochemical accelerated corrosion experiment was carried out and the corrosion expansion was monitored by both BOTDA and the LCFS. Results demonstrated that the BOTDA can only measure the expansion strain of about 1,000 με, which was generated by the 18 mm steel rebar corrosion, but, the LCFS had high sensitivity from the beginning of corrosion to the destruction of the structure, and no obvious difference in expansion speed was observed during the acceleration stage of the corrosion developed in the reinforced concrete (RC) specimens. These results proved that the BOTDA method could only be employed to monitor the corrosion inside the structure in the early stage. PMID:24379048
High-coherence light extraction through a compact Brillouin/erbium fiber laser
Chen, Mo; Wang, Jianfei; Chen, Wei; Sun, Shilin; Meng, Zhou
2016-05-01
High-coherence light is stringently demanded in high-accuracy interferometric optical fiber sensors, where the phase noise of the light source greatly affects the sensitivity of the whole system. Distributed-feedback laser diodes with a phase noise of -80 ~ -90 dB/Hz1/2 at 1 kHz (with 1 m optical path difference) is now easily obtained, but the interferometric fiber sensors requires the laser source with the phase noise lower than -100 dB/Hz1/2. Lasers with ultra-low-noise usually require complicated and sophisticated techniques. We propose a novel structure to realize high-coherence light extraction through a compact Brillouin/erbium fiber laser (BEFL) which uses a length of 4 m erbium-doped fiber as both the Brillouin and linear gain media. The phase noise of the Brillouin pump light is greatly smoothed and suppressed after being transferred to the Brillouin Stokes light. High-coherence light with the phase noise of about -104 dB/Hz1/2 at 1 kHz is extracted through the compact BEFL from a commercialized laser diode with the phase noise of about -89 dB/Hz1/2. The capability of phase noise suppression in the compact BEFL presents much importance especially in large-array interferometric fiber sensor systems.
Monitoring of large structures for safety issues using Brillouin distributed sensing
Thévenaz, Luc; Chang, Ki-Tae; Niklès, Marc
2003-01-01
Brillouin time-domain analysis in optical fibres is a novel technique making possible a distributed measurement of temperature and strain over long distance and will deeply modify our view about monitoring large structures, such as dams, bridges, tunnels and pipelines.
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. PMID:19714043
Alahbabi, M.; CHO, Y. T.; Newson, T.P.
2003-01-01
We report the longest distributed temperature sensor based on microwave heterodyne detection of the frequency of the anti-Stokes Brillouin signal. At a sensing range of 100km, the temperature accuracy was 8degC, with a spatial resolution of 50m.
Elooz, David; Antman, Yair; Levanon, Nadav; Zadok, Avi
2014-03-24
A new scheme for distributed Brillouin sensing of strain and temperature in optical fibers is proposed, analyzed and demonstrated experimentally. The technique combines between time-domain and correlation-domain analysis. Both Brillouin pump and signal waves are repeatedly co-modulated by a relatively short, high-rate phase sequence, which introduces Brillouin interactions in a large number of discrete correlation peaks. In addition, the pump wave is also modulated by a single amplitude pulse, which leads to a temporal separation between the generation of different peaks. The Brillouin amplification of the signal wave at individual peak locations is resolved in the time domain. The technique provides the high spatial resolution and long range of unambiguous measurement offered by correlation-domain Brillouin analysis, together with reduced acquisition time through the simultaneous interrogation of a large number of resolution points. In addition, perfect Golomb codes are used in the phase modulation of the two waves instead of random sequences, in order to reduce noise due to residual, off-peak Brillouin interactions. The principle of the method is supported by extensive numerical simulations. Using the proposed scheme, the Brillouin gain spectrum is mapped experimentally along a 400 m-long fiber under test with a spatial resolution of 2 cm, or 20,000 resolution points, with only 127 scans per choice of frequency offset between pump and signal. Compared with corresponding phase-coded, Brillouin correlation domain analysis schemes with equal range and resolution, the acquisition time is reduced by a factor of over 150. A 5 cm-long hot spot, located towards the output end of the pump wave, is properly identified in the measurements. The method represents a significant advance towards practical high-resolution and long range Brillouin sensing systems. PMID:24663994
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...
Fluctuation theorem for out-of-time-ordered correlator
Halpern, Nicole Yunger
2016-01-01
The out-of-time-ordered correlator (OTOC) diagnoses quantum chaos and the scrambling of quantum information via the spread of entanglement. The OTOC encodes forward and reverse evolutions and has deep connections with the flow of time. So do fluctuation theorems such as Jarzynski's Equality, derived in nonequilibrium statistical mechanics. I unite these two powerful, seemingly disparate tools by deriving a fluctuation theorem for the OTOC. The fluctuation theorem is analogous to Jarzynski's Equality. The theorem's left-hand side equals the OTOC. The right-hand side implies a platform-nonspecific protocol for experimentally measuring the OTOC in an indirect manner fundamentally different from existing proposals. Time evolution need not be reversed in any trial. The theorem opens holography, condensed matter, and quantum information to new insights from fluctuation theorems and vice versa.
Convolution Theorems for Quaternion Fourier Transform: Properties and Applications
Ryuichi Ashino; Mawardi Bahri; Rémi Vaillancourt
2013-01-01
General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion al...
Extending Bell's Theorem: Ruling out Paramater Independent Hidden Variable Theories
Leegwater, G. J.
2016-03-01
Bell's Theorem may well be the best known result in the foundations of quantum mechanics. Here, it is presented as stating that for any hidden variable theory the combination of the conditions Parameter Independence, Outcome Independence, Source Independence and Compatibility with Quantum Theory leads to a contradiction. Based on work by Roger Colbeck and Renato Renner, an extension of Bell's Theorem is considered. In this extension the theorem is strengthened by replacing Outcome Independence by a strictly weaker condition.
Reflexivity and the diagonal argument in proofs of limitative theorems
Młynarski, Kajetan
2011-01-01
This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\\"odel's theorem). The fact, that a formal system contains a sentence, which introduces reflexitivity, does not imply, that the same system does not contain a sentence or a proof procedure which solves this problem. Second basic method of proof - diagonal argument (i.e. showing non-eqiunumerosity o...
Automated Theorem Proving for Cryptographic Protocols with Automatic Attack Generation
Jan Juerjens; Thomas A. Kuhn
2016-01-01
Automated theorem proving is both automatic and can be quite efficient. When using theorem proving approaches for security protocol analysis, however, the problem is often that absence of a proof of security of a protocol may give little hint as to where the security weakness lies, to enable the protocol designer to improve the protocol. For our approach to verify cryptographic protocols using automated theorem provers for first-order logic (such as e-SETHEO or SPASS), we demonstrate a method...
A reconstruction theorem for almost-commutative spectral triples
Ćaćić, Branimir
2012-01-01
We propose an expansion of the definition of almost-commutative spectral triple that accommodates non-trivial fibrations and is stable under inner fluctuation of the metric, and then prove a reconstruction theorem for almost-commutative spectral triples under this definition as a simple consequence of Connes's reconstruction theorem for commutative spectral triples. Along the way, we weaken the orientability hypothesis in the reconstruction theorem for commutative spectral triples, and follow...
Non-equilibrium thermodynamic potential and flux fluctuation theorem
Energy Technology Data Exchange (ETDEWEB)
Criado-Sancho, M. [Departamento de Ciencias y Tecnicas Fisicoquimicas, Facultad de Ciencias, UNED, 28040 Madrid (Spain); Casas-Vazquez, J. [Departament de Fisica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Catalonia (Spain); Jou, D., E-mail: David.Jou@uab.e [Departament de Fisica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Catalonia (Spain)] [Institut d' Estudis Catalans, Carme 47, 08001 Barcelona, Catalonia (Spain)
2009-09-07
A flux fluctuation theorem proposed recently [Seitaridou, et al., J. Phys. Chem. B 111 (2007) 2288] on the relative probability of direct and reverse diffusion fluxes in a non-equilibrium steady state is related here to a non-equilibrium thermodynamic potential used in extended irreversible thermodynamics. This connection allows one to provide a new derivation of the theorem, which complements the previous one, to generalize it to other fluxes, and illustrates the thermodynamic relevance of this theorem.
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
Proceedings Workshop on Partiality and Recursion in Interactive Theorem Provers
Bove, Ana; Niqui, Milad; 10.4204/EPTCS.43
2010-01-01
This volume contains the proceedings of the Workshop on Partiality and Recursion in Interactive Theorem Provers (PAR 2010) which took place on July 15 in Edinburgh, UK. This workshop was held as a satellite workshop of the International Conference on Interactive Theorem Proving (ITP 2010), itself part of the Federated Logic Conference 2010 (FLoC 2010). This workshop is a venue for researchers working on new approaches to cope with partial functions and terminating general (co)recursion in theorem provers.
A Fundamental Theorem on the Structure of Symplectic Integrators
Chin, Siu A.
2005-01-01
I show that the basic structure of symplectic integrators is governed by a theorem which states {\\it precisely}, how symplectic integrators with positive coefficients cannot be corrected beyond second order. All previous known results can now be derived quantitatively from this theorem. The theorem provided sharp bounds on second-order error coefficients explicitly in terms of factorization coefficients. By saturating these bounds, one can derive fourth-order algorithms analytically with arbi...
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.
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 that a theory fails to prove its own consistency, but that a theory actively holds its own inconsistency for possible. We first give a careful presentation of the result. Then, we provide two versi...
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...
Average Kinetic Energy of Heavy Quark and Virial Theorem
Hwang, Dae Sung; Kim, C.S.(Department of Physics, IPAP, Yonsei University, Seoul, 120-749, Republic of Korea); Namgung, Wuk
1996-01-01
We derive the virial theorem of the relativistic two-body system for the study of the B-meson physics. It is also shown that the solution of the variational equation always satisfies the virial theorem. From the virial theorem we also obtained $\\mu_\\pi^2 \\equiv -\\lambda_1 \\equiv = 0.40\\sim 0.58$ GeV$^2$, which is consistent with the result of the QCD sum rule calculations of Ball $et$ $al.$
Fluctuation theorems for excess and housekeeping heats for underdamped systems
Lahiri, Sourabh; Jayannavar, A. M.
2013-01-01
We present a simple derivation of the integral fluctuation theorems for excess housekeeping heat for an underdamped Langevin system, without using the concept of dual dynamics. In conformity with the earlier results, we find that the fluctuation theorem for housekeeping heat holds when the steady state distributions are symmetric in velocity, whereas there is no such requirement for the excess heat. We first prove the integral fluctuation theorem for the excess heat, and then show that it nat...
Lampart, Jonas; Lewin, Mathieu
2015-12-01
We prove a generalized version of the RAGE theorem for N-body quantum systems. The result states that only bound states of systems with {0 ≤slant n ≤slant N} particles persist in the long time average. The limit is formulated by means of an appropriate weak topology for many-body systems, which was introduced by the second author in a previous work, and is based on reduced density matrices. This topology is connected to the weak-* topology of states on the algebras of canonical commutation or anti-commutation relations, and we give a formulation of our main result in this setting.
Jackson's Theorem on Bounded Symmetric Domains
Institute of Scientific and Technical Information of China (English)
Ming Zhi WANG; Guang Bin REN
2007-01-01
Polynomial approximation is studied on bounded symmetric domain Ω in C n for holo-morphic function spaces X ,such as Bloch-type spaces,Bergman-type spaces,Hardy spaces,Ω algebra and Lipschitz space.We extend the classical Jackson ’s theorem to several complex variables:E k f,X ) ω (1 /k,f,X ),where E k f,X )is the deviation of the best approximation of f ∈X by polynomials of degree at mostk with respect to the X -metric and ω (1/k,f,X )is the corresponding modulus of continuity.
A pattern theorem for lattice clusters
Madras, Neal
1999-01-01
We consider general classes of lattice clusters, including various kinds of animals and trees on different lattices. We prove that if a given local configuration ("pattern") of sites and bonds can occur in large clusters, then it occurs at least cN times in most clusters of size n, for some constant c>0. An analogous theorem for self-avoiding walks was proven in 1963 by Kesten. The results also apply to weighted sums, and in particular we can take a$sub n$ to be the probability that the perco...
Penrose's singularity theorem in a Finsler spacetime
Babak Aazami, Amir; Javaloyes, Miguel Angel
2016-01-01
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting. This activity is supported by the programme 'Young leaders in research' 18942/JLI/13 by Fundación Séneca, Regional Agency for Science and Technology from the Region of Murcia, and by the World Premier International Research Center Initiative (WPI), MEXT, Japan.
Region-Based Borsuk-Ulam Theorem
Peters, J. F.; Tozzi, A.
2016-01-01
This paper introduces a region-based extension of the Borsuk-Ulam Theorem (denoted by reBUT). A region is a subset of a surface on a finite-dimensional $n$-sphere. In topology, an $n$-sphere is a generalization of the circle. For a continuous function on an $n$-sphere into $n$-dimensional Euclidean space, there exists a pair of antipodal n-sphere regions with matching descriptions that map into Euclidean space $\\mathbb{R}^n$. Applications of reBUT are given in the evaluation of brain activity...
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
J M M Senovilla
2007-07-01
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating Universes, expanding everywhere with a non-vanishing spatial average of the matter variables, show severe geodesic incompletness in the past. Another way of stating the result is that, under the same conditions, any singularity-free model must have a vanishing spatial average of the energy density (and other physical variables). This is very satisfactory and provides a clear decisive difference between singular and non-singular cosmologies.
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.
An extension of Harrington's noncupping theorem
Institute of Scientific and Technical Information of China (English)
喻良; 丁德成
2003-01-01
(i) Call a c.e. degree b anti-cupping relative to x, if there is a c.e. a ＜ b such that foranyc.e. w w ximpliesaUw bUx.(ii) Call a c.e. degree b everywhere anti-cupping (e.a.c.), if it is anti-cupping relative to x foreach c.e. degree x.By a tree method, we prove that every high c.e. degree has e.a.c. property by extendingHarrington's anti-cupping theorem.
No-cloning theorem on quantum logics
Miyadera, Takayuki; Imai, Hideki
2009-10-01
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.
Godel's Incompleteness Theorems and Platonic Metaphysics
Mikovic, Aleksandar
2015-01-01
We argue by using Godel's incompletness theorems in logic that platonism is the best metaphysics for science. This is based on the fact that a natural law in a platonic metaphysics represents a timeless order in the motion of matter, while a natural law in a materialistic metaphysics can be only defined as a temporary order which appears at random in the chaotic motion of matter. Although a logical possibility, one can argue that this type of metaphysics is highly implausible. Given that mathematics fits naturally within platonism, we conclude that a platonic metaphysics is more preferable than a materialistic metaphysics.
On Clifford's theorem for singular curves
Franciosi, Marco
2011-01-01
Let C be a 2-connected Gorenstein curve either reduced or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim scheme such that the space H^0(C, I_S K_C) contains a generically invertible section). Under some general assumptions on S or C we show that h^0(C, I_S K_C) <= p_a(C) - deg (S)/2 and if equality holds then either S is trivial, or C is honestly hyperelliptic or 3-disconnected. As a corollary we give a generalization of Clifford's theorem for reduced curves.
On Grothendieck's Riemann-Roch Theorem
Navarro, Alberto
2016-01-01
We prove that, for smooth quasi-projective varieties over a field, the $K$-theory $K(X)$ of vector bundles is the universal cohomology theory where $c_1(L\\otimes \\bar L)=c_1(L)+c_1(\\bar L)-c_1(L)c_1(\\bar L)$. Then, we show that Grothendieck's Riemann-Roch theorem is a direct consequence of this universal property, as well as the universal property of the graded $K$-theory $GK^\\bullet (X)\\otimes \\mathbb{Q}$.
Bernstein's Lethargy Theorem in Frechet Spaces
Aksoy, Asuman Guven; Lewicki, Grzegorz
2015-01-01
In this paper we consider Bernstein's Lethargy Theorem (BLT) in the context of Fr\\'{e}chet spaces. Let $X$ be an infinite-dimensional Fr\\'echet space and let $\\mathcal{V}=\\{V_n\\}$ be a nested sequence of subspaces of $ X$ such that $ \\bar{V_n} \\subseteq V_{n+1}$ for any $ n \\in \\mathbb{N}$ and $ X=\\bar{\\bigcup_{n=1}^{\\infty}V_n}.$ Let $ e_n$ be a decreasing sequence of positive numbers tending to 0. Under an additional natural condition on $\\sup\\{\\{dist}(x, V_n)\\}$, we prove that there exists...
New proofs of the trace theorem of Sobolev spaces
Miyazaki, Yoichi
2008-01-01
We present three new proofs of the trace theorem of $L_{p}$ Sobolev spaces, which do not rely on the theory of interpolation spaces. The first method originates in Morrey’s proof for the Sobolev embedding theorem concerning the Hölder-Zygmund space. The second method is based on Muramatu’s integral formula and the third method is based on an integral operator with Gauss kernel. These methods give unified viewpoints for the proofs of the trace theorem and the Sobolev embedding theorem.
Raychaudhuri equation and singularity theorems in Finsler spacetimes
Minguzzi, E.
2015-09-01
The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain. Indeed, so do the theorems by Hawking, Penrose, Hawking and Penrose, Geroch, Gannon, Tipler and Kriele, and also the Topological Censorship theorem and so on. It is argued that the notable results in causality theory connected to achronal sets, future sets, domains of dependence, limit curve theorems, length functional, Lorentzian distance and geodesic connectedness, extend to the Finslerian domain. Results concerning the spacetime asymptotic structure, horizons differentiability and conformal transformations are also included.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
Energy Technology Data Exchange (ETDEWEB)
Woolgar, Eric, E-mail: ewoolgar@ualberta.ca [Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1 (Canada); Wylie, William, E-mail: wwylie@syr.edu [215 Carnegie Building, Department of Mathematics, Syracuse University, Syracuse, New York 13244 (United States)
2016-02-15
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
De Finetti theorem on the CAR algebra
Crismale, Vito
2012-01-01
The symmetric states on a quasi local C*-algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki-Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self--containing interest.
Leary, Ian J
2010-01-01
For every simplicial complex X, we construct a locally CAT(0) cubical complex T_X, a cellular isometric involution i on T_X and a map t_X from T_X to X with the following properties: t_Xi = t_X; t_X is a homology isomorphism; the induced map from the quotient of T_X by the involution i to X is a homotopy equivalence; the induced map from the fixed point subspace for i in T_X to X is a homology isomorphism. The construction is functorial in X. One corollary is an equivariant Kan-Thurston theorem: every connected proper G-CW-complex has the same equivariant homology as the classifying space for proper actions of some other group. From this we obtain an extension of Quillen's theorem on the spectrum of an equivariant cohomology ring and an extension of a result of Block concerning assembly conjectures. Another corollary of our main result is that there can be no algorithm to decide whether a CAT(0) cubical group is generated by torsion. In appendices we prove some foundational results concerning cubical complexe...
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...
A vector bundle proof of Poncelet theorem
Vallès, Jean
2012-01-01
In the town of Saratov where he was prisonner, Poncelet, continuing the work of Euler and Steiner on polygons simultaneously inscribed in a circle and circumscribed around an other circle, proved the following generalization : "Let C and D be two smooth conics in the projective complex plane. If D passes through the n(n-1)/2 vertices of a complete polygon with n sides tangent to C then D passes through the vertices of infinitely many such polygons." According to Marcel Berger this theorem is the nicest result about the geometry of conics. Even if it is, there are few proofs of it. To my knowledge there are only three. The first proof, published in 1822 and based on infinitesimal deformations, is due to Poncelet. Later, Jacobi proposed a new proof based on finite order points on elliptic curves; his proof, certainly the most famous, is explained in a modern way and in detail by Griffiths and Harris. In 1870 Weyr proved a Poncelet theorem in space (more precisely for two quadrics) that implies the one above whe...
Ground-state-energy theorem and the virial theorem of a many-particle system in d dimensions
Iwamoto, N.
1984-01-01
The equivalence of Pauli's ground-state-energy theorem and the virial theorem is demonstrated for a many-particle system interacting with an interparticle potential in d dimensions at zero and finite temperatures. Pauli's theorem has an integral form in which the variable is the coupling constant e-squared, while the virial theorem has a differential form in which the variable has the number density n. The essence of the equivalence proof consists in changing the variable from n to e-squared by noting the dependence of the excess free energy on dimensionless quantities for zero-temperature and classical cases.
Zou, Lufan; Bao, Xiaoyi; Wan, Yidun; Ravet, Fabien; Chen, Liang
2005-05-01
We present a sensing principle of the distributed fiber Brillouin strain and temperature sensor by coherent probe-pump technique that offers a new method to achieve centimeter spatial resolution with high frequency resolution. A combination of continuous wave (cw) and pulse source as the probe (Stokes) beam and cw laser as the pump beam have resulted in stronger Brillouin interaction of Stokes and pump inside the pulse-length in the form of cw-pump and pulse-pump interactions. We find that the coherent portion inside the pulse-length of these two interactions due to the same phase has a very high Brillouin amplification. The Brillouin profile originating from the coherent interaction of pulse-pump with cw-pump results in high temperature and strain accuracy with centimeter resolution, which has been verified by successfully detecting 1.5 cm out-layer crack on an optical ground wire (OPGW) cable.
Dragic, P. D.; Pamato, M. G.; Iordache, V.; Bass, J. D.; Kucera, C. J.; Jones, M.; Hawkins, T. W.; Ballato, J.
2016-01-01
An all-glass optical fiber derived from single-crystal LuAG is investigated for its potential use in athermal Brillouin distributed strain sensors. Such sensor systems are comprised of fiber whose Brillouin frequency shift is independent of temperature, but not independent of strain. Bulk Brillouin spectroscopy measurements on the precursor LuAG crystal are performed to gain insight into the crystal-to-glass transition. Results suggest that both the mass density and acoustic velocity are reduced relative to the crystal phase, in common with the other rare earth aluminosilicates. Advantages of the LuAG derived fiber over other rare earth garnet-derived fibers for the sensing application are a stronger strain response and larger Brilloun gain with narrower Brillouin spectral width.
Xu, Ronghui; Zhang, Xuping; Hu, Junhui; Xia, Lan
2015-03-01
In this paper, a single-passband microwave photonic filter based on a self-seeded multiwavelength Brillouin-erbium fiber laser is demonstrated experimentally. In the filter, the multiwavelength Brillouin comb generated from the laser is used as the filter taps. The Brillouin comb is with the feature of quasi-Gaussian continuous distribution, which can ensure the filter realizes single-passband characteristic. The baseband response is suppressed effectively with the help of phase modulation. The single-passband filter has an out-of-band rejection of 25 dB. By adjusting the Brillouin multiwavelengh, the 3-dB bandwidth and the center frequency of the filter can be changed.
Fixed Point Theorems in Quaternion-Valued Metric Spaces
2014-01-01
The aim of this paper is twofold. First, we introduce the concept of quaternion metric spaces which generalizes both real and complex metric spaces. Further, we establish some fixed point theorems in quaternion setting. Secondly, we prove a fixed point theorem in normal cone metric spaces for four self-maps satisfying a general contraction condition.
The Kochen-Specker Theorem Revisited in Quantum Measure Theory
Dowker, Fay; Ghazi-Tabatabai, Yousef
2007-01-01
The Kochen-Specker Theorem is widely interpreted to imply that non-contextual hidden variable theories that agree with the predictions of Copenhagen quantum mechanics are impossible. The import of the theorem for a novel observer independent interpretation of quantum mechanics, due to Sorkin, is investigated.
Some dual theorems for convex inclusion and applications
International Nuclear Information System (INIS)
This paper consists of a study of duality and optimality for a general optimization problem. From a general proposition on inconsistent systems of convex inclusions we give some dual theorems for general extreme problem. As consequence we have some dual theorems for mathematical programming problems and optimal control problems described by discrete inclusions with delay. (author). 6 refs
An Algebraic Proof of Quillen's Resolution Theorem for K_1
Whale, Ben
2009-01-01
In his 1973 paper Quillen proved a resolution theorem for the K-Theory of an exact category; his proof was homotopic in nature. By using the main result of a paper by Nenashev, we are able to give an algebraic proof of Quillen's Resolution Theorem for K_1 of an exact category.
Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Du Wei-Shih
2010-01-01
Full Text Available We establish some new coupled fixed point theorems for various types of nonlinear contractive maps in the setting of quasiordered cone metric spaces which not only obtain several coupled fixed point theorems announced by many authors but also generalize them under weaker assumptions.
Computer Algebra Systems and Theorems on Real Roots of Polynomials
Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.
2010-01-01
A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)
Rainwater-Simons-type convergence theorems for generalized convergence methods
Hardtke, Jan-David
2010-01-01
We extend the well-known Rainwater-Simons convergence theorem to various generalized convergence methods such as strong matrix summability, statistical convergence and almost convergence. In fact we prove these theorems not only for boundaries but for the more general notion of (I)-generating sets introduced by Fonf and Lindenstrauss.
Yan Theorem in L∞ with Applications to Asset Pricing
Institute of Scientific and Technical Information of China (English)
2007-01-01
We prove an L∞ version of the Yan theorem and deduce from it a necessary condition for the absence of free lunches in a model of financial markets, in which asset prices are a continuous Rd valued process and only simple investment strategies are admissible. Our proof is based on a new separation theorem for convex sets of finitely additive measures.
A unified optical theorem for scalar and vectorial wave fields
Wapenaar, C.P.A.; Douma, H.
2012-01-01
The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived t
Tensor product theorem for Hitchin pairs -An algebraic approach
Balaji, V
2010-01-01
We give an algebraic approach to the study of Hitchin pairs and prove the tensor product theorem for Higgs semistable Hitchin pairs over smooth projective curves defined over algebraically closed fields $k$ of characteristic $0$ and characteristic $p$, with $p$ satisfying some natural bounds. We also prove the corresponding theorem for polystable bundles.
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.