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.
Stimulated Brillouin Scattering Microscopic Imaging.
Ballmann, Charles W; Thompson, Jonathan V; Traverso, Andrew J; Meng, Zhaokai; Scully, Marlan O; Yakovlev, Vladislav V
2015-01-01
Two-dimensional stimulated Brillouin scattering microscopy is demonstrated for the first time using low power continuous-wave lasers tunable around 780 nm. Spontaneous Brillouin spectroscopy has much potential for probing viscoelastic properties remotely and non-invasively on a microscopic scale. Nonlinear Brillouin scattering spectroscopy and microscopy may provide a way to tremendously accelerate the data aquisition and improve spatial resolution. This general imaging setup can be easily adapted for specific applications in biology and material science. The low power and optical wavelengths in the water transparency window used in this setup provide a powerful bioimaging technique for probing the mechanical properties of hard and soft tissue.
Stimulated Brillouin Scattering Microscopic Imaging
Ballmann, Charles W.; Thompson, Jonathan V.; Traverso, Andrew J.; Meng, Zhaokai; Scully, Marlan O.; Yakovlev, Vladislav V.
2015-12-01
Two-dimensional stimulated Brillouin scattering microscopy is demonstrated for the first time using low power continuous-wave lasers tunable around 780 nm. Spontaneous Brillouin spectroscopy has much potential for probing viscoelastic properties remotely and non-invasively on a microscopic scale. Nonlinear Brillouin scattering spectroscopy and microscopy may provide a way to tremendously accelerate the data aquisition and improve spatial resolution. This general imaging setup can be easily adapted for specific applications in biology and material science. The low power and optical wavelengths in the water transparency window used in this setup provide a powerful bioimaging technique for probing the mechanical properties of hard and soft tissue.
Collective stimulated Brillouin scatter
Korotkevich, Alexander O; Rose, Harvey A
2011-01-01
We develop a statistical theory of stimulated Brillouin backscatter (BSBS) of a spatially and temporally partially incoherent laser beam for laser fusion relevant plasma. We find a new collective regime of BSBS which has a much larger threshold than the classical threshold of a coherent beam in long-scale-length laser fusion plasma. We identify two contributions to BSBS convective instability increment. The first is collective with intensity threshold independent of the laser correlation time and controlled by diffraction. The second is independent of diffraction, it grows with increase of the correlation time and does not have an intensity threshold. The instability threshold is inside the typical parameter region of National Ignition Facility (NIF). We also find that the bandwidth of KrF-laser-based fusion systems would be large enough to allow additional suppression of BSBS.
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
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.
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...
Bursting behaviours in cascaded stimulated Brillouin scattering
Institute of Scientific and Technical Information of China (English)
Liu Zhan-Jun; He Xian-Tu; Zheng Chun-Yang; Wang Yu-Gang
2012-01-01
Stimulated Brillouin scattering is studied by numerically solving the Vlasov-Maxwell system.A cascade of stimulated Brillouin scattering can occur when a linearly polarized laser pulse propagates in a plasma.It is found that a stimulated Brillouin scattering cascade can reduce the scattering and increase the transmission of light,as well as introduce a bursting behaviour in the evolution of the laser-plasma interaction.The bursting time in the reflectivity is found to be less than half the ion acoustic period.The ion temperature can affect the stimulated Brillouin scattering cascade,which can repeat several times at low ion temperatures and can be completely eliminated at high ion temperatures.For stimulated Brillouin scattering saturation,higher-harmonic generation and wave-wave interaction of the excited ion acoustic waves can restrict the amplitude of the latter.In addition,stimulated Brillouin scattering cascade can restrict the amplitude of the scattered light.
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.; Wolff, C.; Martijn de Sterke, C.; Lapine, M.; Kuhlmey, B. T.; Poulton, C. G.
2016-10-01
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.
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.
Vorticity, Stokes' Theorem and the Gauss's Theorem
Narayanan, M.
2004-12-01
Vorticity is a property of the flow of any fluid and moving fluids acquire properties that allow an engineer to describe that particular flow in greater detail. It is important to recognize that mere motion alone does not guarantee that the air or any fluid has vorticity. Vorticity is one of four important quantities that define the kinematic properties of any fluid flow. 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. However, the divergence theorem is a mathematical statement of the physical fact that, in the absence of the creation or destruction of matter, the density within a region of space can change only by having it flow into, or away from the region through its boundary. This is also known as Gauss's Theorem. It should also be noted that there are many useful extensions of Gauss's Theorem, including the extension to include surfaces of discontinuity in V. 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. Integral (Surface) [(DEL X V)] . dS = Integral (Contour) [V . dx] In this paper, the author outlines and stresses the importance of studying and teaching these mathematical techniques while developing a course in Hydrology and Fluid Mechanics. References Arfken, G. "Gauss's Theorem." 1.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985. Morse, P. M. and Feshbach, H. "Gauss's Theorem." In Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 37-38, 1953. Eric W. Weisstein. "Divergence Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DivergenceTheorem.html
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...
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...
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.
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.
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
Lagrange Theorem for polygroups
Directory of Open Access Journals (Sweden)
alireza sedighi
2014-12-01
Full Text Available So far?, ?isomorphism theorems in hyperstructure were proved for different structures of polygroups?, ?hyperrings and etc?. ?In this paper?, ?the polygroups properties is studied with the introduction of a suitable equivalence relation?. ?We show that the above relation is strongly regular?. ?Our main purpose in the paper is investigating Lagrang theorem and other expressing of isomorphism theorems for polygroups?.
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.
Genova, Alessandro; Pavanello, Michele
2015-12-01
In order to approximately satisfy the Bloch theorem, simulations of complex materials involving periodic systems are made {{n}\\text{k}} times more complex by the need to sample the first Brillouin zone at {{n}\\text{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).
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.
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.
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...
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 physics teaching.
On the Equivalence of Weyl Theorem and Generalized Weyl Theorem
Institute of Scientific and Technical Information of China (English)
M. BERKANI
2007-01-01
We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theo rem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a similar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.
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...
Plaisted, David A
2014-03-01
Automated theorem proving is the use of computers to prove or disprove mathematical or logical statements. Such statements can express properties of hardware or software systems, or facts about the world that are relevant for applications such as natural language processing and planning. A brief introduction to propositional and first-order logic is given, along with some of the main methods of automated theorem proving in these logics. These methods of theorem proving include resolution, Davis and Putnam-style approaches, and others. Methods for handling the equality axioms are also presented. Methods of theorem proving in propositional logic are presented first, and then methods for first-order logic. WIREs Cogn Sci 2014, 5:115-128. doi: 10.1002/wcs.1269 CONFLICT OF INTEREST: The authors has declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website. PMID:26304304
Trigonometry, Including Snell's Theorem.
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
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.
Brillouin Optomechanics in Coupled Silicon Microcavities
Espinel, Yovanny A V; Luiz, Gustavo O; Alegre, Thiago P M; Wiederhecker, Gustavo S
2016-01-01
The simultaneous control of optical and mechanical waves has enabled a range of fundamental and technological breakthroughs, from the demonstration of ultra-stable frequency reference devices to the exploration of the quantum-classical boundaries in laser-cooling experiments. More recently, such an opto-mechanical interaction has been observed in integrated nano-waveguides and microcavities in the Brillouin regime, where short-wavelength mechanical modes scatters light at several GHz. Here we engineer coupled optical microcavities spectra to enable a low threshold excitation of mechanical travelling-wave modes through backward stimulated Brillouin scattering. Exploring the backward scattering we propose microcavity designs supporting super high frequency modes ($\\sim25$ GHz) an large optomechanical coupling rates ($g_0/2\\pi \\sim 50$ kHz).
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).
Simulations of Brillouin Scattering in Optical Fibers
Mungan, Carl; Petersen, Eliot; Huang, Shuochen; White, Jeffrey
2013-03-01
Brillouin scattering arises when a laser beam generates density variations in a medium via electrostriction. The density variations modulate the refractive index, resulting in a grating that Bragg scatters pump light into a Stokes beam. The Stokes wave is downshifted in frequency by the Doppler effect because the grating is moving at the speed of acoustic phonons. To conserve both energy and momentum, the Brillouin photons are backscattered. This back-reflected radiation is a major factor limiting the transmission of laser power in optical fibers for practical applications. It is mathematically described by a set of coupled partial differential equations. I will describe some of the known analytic solutions of these equations, as well as how to find numeric solutions using MATLAB. JTO grant 11-SA-0405
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.
ON RANGE DECOMPOSITION THEOREMS
Institute of Scientific and Technical Information of China (English)
吴利生
1990-01-01
We prove the following theorems.Theorem 1.Suppose f:X→Y is a closed map.X is a ωγ and β space,then Y=Y0∪(∪n=1∞Yn),where f-1(y) is countably compact for each y ∈Y0 and Yn is closed discrete in Y for each n≥1,Theorem 2-3:Suppose f:X→Y is a closed map,X is stratifable space,then Y=Y0 ∪(∪n=1∞Yn),where f-1(y) is compact for each y∈Y0 and Yn is closed discrete in Y for each n≥1.
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.
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...
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....
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.
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.
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
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)
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
Directory of Open Access Journals (Sweden)
Mihai Turinici
2006-11-01
Full Text Available A drop theorem on ordered metric spaces is established from the (pre order version of Ekeland’s variational principle in Turinici [An St UAIC Ia (Math, 36 (1990, 329-352]. The logical equivalence between these results is also discussed.
Mihai Turinici
2006-01-01
A drop theorem on ordered metric spaces is established from the (pre) order version of Ekeland’s variational principle in Turinici [An St UAIC Ia (Math), 36 (1990), 329-352]. The logical equivalence between these results is also discussed.
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.
Multivariate irregular sampling theorem
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.
Quantification of plaque stiffness by Brillouin microscopy (Conference Presentation)
Antonacci, Giuseppe; Pedrigi, Ryan; Krams, Rob; Török, Peter
2016-03-01
Spontaneous Brillouin scattering is an inelastic scattering process arising from inherent thermal density fluctuations, or acoustic phonons, propagating in a medium. Over the last few years, Brillouin spectroscopy has shown great potential to become a reliable non-invasive diagnostic tool due to its unique capability of retrieving viscoelastic properties of materials such as strain and stiffness. The detection of the weak scattered light, in addition to the resolution of the Brillouin peaks (typically shifted by few GHz from the central peak) represent one of the greatest challenges in Brillouin. The recent development of high sensitivity CCD cameras has brought Brillouin spectroscopy from a point sampling technique to a new imaging modality. Furthermore, the application of Virtually Imaged Phased Array (VIPA) etalons has dramatically reduced insertion loss simultaneously allowing fast (myocardial infarction yet it is not currently possible to credibly assess its stiffness due to lack of suitable methods.
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...
Discovering the Theorem of Pythagoras
Lattanzio, Robert (Editor)
1988-01-01
In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.
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…
An Extension of Sobolev's Theorem
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Sobolev's Theorem is the most fundamental theorem in the theory of Invariant Cubature Formulas (ICFs). In this paper, a quantitative structure is established for the classical ICFs. Enlightened by this structure, the author generalizes the concept of ICFs and extends the Sobolev's Theorem to the case of generalized ICFs. Several illustrative examples are given.
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)
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.
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.
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 ...
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...
Sandwich classification theorem
Directory of Open Access Journals (Sweden)
Alexey Stepanov
2015-09-01
Full Text Available The present note arises from the author's talk at the conference ``Ischia Group Theory 2014''. For subgroups FleN of a group G denote by Lat(F,N the set of all subgroups of N , containing F . Let D be a subgroup of G . In this note we study the lattice LL=Lat(D,G and the lattice LL ′ of subgroups of G , normalized by D . We say that LL satisfies sandwich classification theorem if LL splits into a disjoint union of sandwiches Lat(F,N G (F over all subgroups F such that the normal closure of D in F coincides with F . Here N G (F denotes the normalizer of F in G . A similar notion of sandwich classification is introduced for the lattice LL ′ . If D is perfect, i.,e. coincides with its commutator subgroup, then it turns out that sandwich classification theorem for LL and LL ′ are equivalent. We also show how to find basic subroup F of sandwiches for LL ′ and review sandwich classification theorems in algebraic groups over rings.
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 ...
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)
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...
Ultralow-threshold cascaded Brillouin microlaser for tunable microwave generation.
Guo, Changlei; Che, Kaijun; Cai, Zhiping; Liu, Shuai; Gu, Guoqiang; Chu, Chengxu; Zhang, Pan; Fu, Hongyan; Luo, Zhengqian; Xu, Huiying
2015-11-01
We experimentally demonstrate an ultralow-threshold cascaded Brillouin microlaser for tunable microwave generation in a high-Q silica microsphere resonator. The threshold of the Brillouin microlaser is as low as 8 μW, which is close to the theoretical prediction. Moreover, the fifth-order Stokes line with a frequency shift up to 55 GHz is achieved with a coupled pump power of less than 0.6 mW. Benefiting from resonant wavelength shifts driven by thermal dynamics in the microsphere, we further realized tunable microwave signals with tuning ranges of 40 MHz at an 11 GHz band and 20 MHz at a 22 GHz band. To the best of our knowledge, it was the first attempt for tunable microwave source based on the whispering-gallery-mode Brillouin microlaser. Such a tunable microwave source from a cascaded Brillouin microlaser could find significant applications in aerospace, communication engineering, and metrology.
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.
A-Browder's Theorem and Generalized a-Weyl's Theorem
Institute of Scientific and Technical Information of China (English)
Xiao Hong CAO
2007-01-01
Two variants of the essential approximate point spectrum are discussed. We find for example that if one of them coincides with the left Drazin spectrum then the generalized a-Weyl's theorem holds, and conversely for a-isoloid operators. We also study the generalized a-Weyl's theorem for Class A operators.
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
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.…
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.
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.
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...
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.
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.
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.
Phase-locking in cascaded stimulated Brillouin scattering
Büttner, Thomas F S; Steel, M J; Hudson, Darren D; Eggleton, Benjamin J
2015-01-01
Cascaded stimulated Brillouin scattering (SBS) is a complex nonlinear optical process that results in the generation of several optical waves that are frequency shifted by an acoustic resonance frequency. Four-wave mixing (FWM) between these Brillouin shifted optical waves can create an equally spaced optical frequency comb with a stable spectral phase, i.e. a Brillouin frequency comb (BFC). Here, we investigate phase-locking of the spectral components of BFCs, considering FWM interactions arising from the Kerr-nonlinearity as well as from coupling by the acoustic field. Deriving for the first time the coupled-mode equations that include all relevant nonlinear interactions, we examine the contribution of the various nonlinear processes to phase-locking, and show that different regimes can be obtained that depend on the length scale on which the field amplitudes vary.
Phase-locking in cascaded stimulated Brillouin scattering
Büttner, Thomas F. S.; Poulton, Christopher G.; Steel, M. J.; Hudson, Darren D.; Eggleton, Benjamin J.
2016-02-01
Cascaded stimulated Brillouin scattering is a complex nonlinear optical process that results in the generation of several optical waves that are frequency shifted by an acoustic resonance frequency. Four-wave mixing (FWM) between these Brillouin shifted optical waves can create an equally spaced optical frequency comb with a stable spectral phase, i.e. a Brillouin frequency comb (BFC). Here, we investigate phase-locking of the spectral components of BFCs, considering FWM interactions arising from the Kerr-nonlinearity as well as from coupling by the acoustic field. Deriving for the first time the coupled-mode equations that include all relevant nonlinear interactions, we examine the contribution of the various nonlinear processes to phase-locking, and show that different regimes can be obtained that depend on the length scale on which the field amplitudes vary.
Temperature sensing based on a Brillouin fiber microwave generator
Yang, X. P.; Gan, J. L.; Xu, S. H.; Yang, Z. M.
2013-04-01
We propose and demonstrate a novel dual-frequency Brillouin fiber laser used for microwave generation. Based on this configuration, temperature sensing has been realized. The dual-frequency Brillouin lasing is generated independently from two pieces of fiber cascaded within one ring resonator. Microwave generation is acquired as the beat signal of the dual-frequency Brillouin fiber laser, with the beat frequency being linearly proportional to the temperature difference of the two fiber sections. In the experiment, the temperature coefficient of frequency shift is 1.015 ± 0.001 MHz °C-1. The temperature can be precisely measured by acquiring the frequency of the microwave generator, and this new configuration provides a promising application for temperature sensing.
Statistics, Causality and Bell's theorem
Gill, Richard D
2012-01-01
Bell's (1964) theorem is popularly supposed to establish the non-locality of quantum physics as a mathematical-physical theory. Building from this, observed violation of Bell's inequality in experiments such as that of Aspect and coworkers (1982) is popularly supposed to provide empirical proof of non-locality in the real world. This paper reviews recent work on Bell's theorem, linking it to issues in causality as understood by statisticians. The paper starts with a new proof of a strong (finite sample) version of Bell's theorem which relies only on elementary arithmetic and (counting) probability. This proof underscores the fact that Bell's theorem tells us that quantum theory is incompatible with the conjunction of three cherished and formerly uncontroversial physical principles, nicknamed here locality, realism, and freedom. The first, locality, is obviously connected to causality: causal influences need time to propagate spatially. Less obviously, the other two principles, realism and freedom, are also fo...
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.
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.
Brillouin spectroscopy of clotting dynamics in a model system
Bustamante-Lopez, Sandra C.; Traverso, Andrew J.; Yakovlev, Vladislav V.; Meissner, Kenith E.
2016-02-01
Keys to successful treatment of disease include early diagnosis and timely treatment. It is hypothesized that early clotting events may contribute to a pro-thrombotic state that exacerbates atherothrombotic vascular disease. Brillouin spectroscopy involves inelastic coupling of light with phonons and enables viscoelastic characterization of samples at the microscale. In this work, we apply Brillouin spectroscopy to a model fibrinogen-thrombin clotting system with the goal of measuring clotting dynamics at the microscale and providing characterization that is not possible with standard rheometric techniques. Here, the clotting dynamics of the model clotting system are measured at various fibrinogen and thrombin concentrations.
High-pressure Brillouin scattering in a simple molecular system
Shimizu, H
2002-01-01
Recent developments in high-pressure in situ Brillouin spectroscopy of a simple molecular system are reviewed by demonstrating experimental and analytical methods for the study of acoustic velocities in any direction, adiabatic elastic constants, and elastic anisotropy. Detailed applications to solid argon (Ar) are presented, at pressures up to 70 GPa in a diamond anvil cell, using recently developed approaches that combine the method of in situ Brillouin spectroscopy, for a single crystal of Ar up to 4 GPa, and the envelope method applied to both longitudinal acoustic and transverse acoustic modes, for recrystallized Ar between 4 and 70 GPa.
The Second Noether Theorem on Time Scales
Directory of Open Access Journals (Sweden)
Agnieszka B. Malinowska
2013-01-01
Full Text Available We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus.
The Kolmogorov-Riesz compactness theorem
Hanche-Olsen, Harald
2009-01-01
We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.
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...
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.
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
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.
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...
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
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
Institute of Scientific and Technical Information of China (English)
Muping Song; Bin Zhao; Xianmin Zhang
2005-01-01
In Brillouin distributed optical fiber sensor, using optical coherent detection to detect Brillouin scattering optical signal is a good method, but there exists the polarization correlated detection problem. A novel detecting scheme is presented and demonstrated experimentally, which adopts orthogonal polarization diversity reception to resolve the polarization correlated detection problem. A laser is used as pump and reference light sources, a microwave electric-optical modulator (EOM) is adopted to produce frequency shift reference light, a polarization controller is used to control the polarization of the reference light which is changed into two orthogonal polarization for two adjacent acquisition periods. The Brillouin scattering light is coherently detected with the reference light, and the Brillouin scattering optical signal is taken out based on Brillouin frequency shift. After electronic processing, better Brillouin distributed sensing signal is obtained. A 25-km Brillouin distributed optical fiber sensor is achieved.
Nambu-Goldstone theorem and spin-statistics theorem
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
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.
New Double Soft Emission Theorems
Cachazo, Freddy; Yuan, Ellis Ye
2015-01-01
We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, DBI, Einstein-Maxwell-Scalar, NLSM and Yang-Mills-Scalar. We use the recently found CHY representation of these theories in order to give a simple proof of the leading order part of all these theorems
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.
Improvement of Hartman's linearization theorem
Institute of Scientific and Technical Information of China (English)
SHI; Jinlin(史金麟)
2003-01-01
Hartman's linearization theorem tells us that if matrix A has no zero real part and f(x) isbounded and satisfies Lipchitz condition with small Lipchitzian constant, then there exists a homeomorphismof Rn sending the solutions of nonlinear system x' = Ax + f(x) onto the solutions of linear system x' = Ax.In this paper, some components of the nonlinear item f(x) are permitted to be unbounded and we provethe result of global topological linearization without any special limitation and adding any condition. Thus,Hartman's linearization theorem is improved essentially.
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
Pasicki, Lech
2011-01-01
Many versions of the Stokes theorem are known. More advanced of them require complicated mathematical machinery to be formulated which discourages the users. Our theorem is sufficiently simple to suit the handbooks and yet it is pretty general, as we assume the differential form to be continuous on a compact set F(A) and C1 "inside" while F(A) is built of "bricks" and its inner part is a C1 manifold. There is no problem of orientability and the integrals under consideration are convergent. The proof is based on integration by parts and inner approximation.
A normal form theorem around symplectic leaves
Crainic, M.N.; Marcut, I.T.
2012-01-01
We prove the Poisson geometric version of the Local Reeb Stability (from foliation theory) and of the Slice Theorem (from equivariant geometry), which is also a generalization of Conn’s linearization theorem.
Interpolation theorems on weighted Lorentz martingale spaces
Institute of Scientific and Technical Information of China (English)
Yong JIAO; Li-ping FAN; Pei-de LIU
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.
The Two Bell's Theorems of John Bell
Wiseman, Howard M
2014-01-01
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, "weak 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 ...
Von Laue's theorem and its applications
Wang, Changbiao
2012-01-01
Von Laue's theorem is strictly proved in detail to clarify confusions in textbook and literature. This theorem is used to analyze the classical electron and the static electric field confined in a finite region of space.
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.
Shell theorem for spontaneous emission
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Mortensen, Jakob Egeberg; Lodahl, Peter;
2013-01-01
and therefore is given exactly by the dipole approximation theory. This surprising result is a spontaneous emission counterpart to the shell theorems of classical mechanics and electrostatics and provides insights into the physics of mesoscopic emitters as well as great simplifications in practical calculations....
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.
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.)
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,…
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…
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)
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.
GENERALIZED RECIPROCAL THEOREMS AND THEIR APPLICATIONS
Institute of Scientific and Technical Information of China (English)
付宝连
2002-01-01
Generalized reciprocal theorems of non-coupled and coupled systems , which are valid for two deformed bodies with different constitutive relations are established by generalizing the idea of Betti ' s reciprocal theorem. When the constitutive relations of the two deformed bodies are all alike and linear elastic, the generalized reciprocal theorem of non-coupled systems just becomes Betti' s . Meanwhile, the generalized reciprocal theorems are applied to simulate calculations in elasticity.
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.
Synthetic Spectrum Approach for Brillouin Optical Time-Domain Reflectometry
Directory of Open Access Journals (Sweden)
Ken'ichi Nishiguchi
2014-03-01
Full Text Available We propose a novel method to improve the spatial resolution of Brillouin optical time-domain reflectometry (BOTDR, referred to as synthetic BOTDR (S-BOTDR, and experimentally verify the resolution improvements. Due to the uncertainty relation between position and frequency, the spatial resolution of a conventional BOTDR system has been limited to about one meter. In S-BOTDR, a synthetic spectrum is obtained by combining four Brillouin spectrums measured with different composite pump lights and different composite low-pass filters. We mathematically show that the resolution limit, in principle, for conventional BOTDR can be surpassed by S-BOTDR and experimentally prove that S-BOTDR attained a 10-cm spatial resolution. To the best of our knowledge, this has never been achieved or reported.
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
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).
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.
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...
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.
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...
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.)
A high-efficiency Brillouin fiber ring laser
Institute of Scientific and Technical Information of China (English)
Pingping Zhang; Shuling Hu; Shuying Chen; Yuanhong Yang; Chunxi Zhang
2009-01-01
A high-efficiency Brillouin fiber ring laser is demonstrated using the standard single-mode fiber.The laser exhibits a 3.6-mW threshold.The output power is 22 mW with 40-nlW pump power,and the maximum optical-to-optical efficiency is 55%. The output is single wavelength with a 3-dB linewidth of 5 MHz,and the interval of center frequency between the laser and the pump light is 11 GHz (0.088 nm).It is shown that the stimulated Brillouin scattering threshold of ring resonator is lower and the energy transfer efficiency is higher than those in fiber.
Stimulated Brillouin scattering revisited: Strong coupling regime and Rabi splitting
Huy, Kien Phan; Tchahame, Joel Cabrel; Sylvestre, Thibaut
2015-01-01
Stimulated Brillouin scattering in optical waveguides is a fundamental interaction between light and acoustic waves mediated by electrostriction and photoelasticity. In this paper, we revisit the usual theory of this inelastic scattering process to get a joint system in which the acoustic wave is strongly coupled to the interference pattern between the optical waves. We show in particular that, when the optoacoustic coupling rate is comparable to the phonon damping rate, the system enters in the strong coupling regime, giving rise to avoided crossing of the dispersion curve and Rabi-like splitting. We further find that optoacoustic Rabi splitting could in principle be observed using backward stimulated Brillouin scattering in sub-wavelength diameter tapered optical fibers with moderate peak pump power.
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.
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.
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
Ordering in mechanical geometry theorem proving
Institute of Scientific and Technical Information of China (English)
李洪波￥
1997-01-01
Ordering in mechanical geometry theorem proving is studied from geometric viewpoint and some new ideas are proposed. For Thebault’s theorem which is the most difficult theorem that has ever been proved by Wu’ s method, a very simple proof using Wu’s method under a linear order is discovered.
Stimulated Brillouin scattering in a two-level system
Postan, A.; Rai, Jagdish; Bowden, Charles M.
1992-03-01
Resonances in the interaction of a saturable two-level system with stimulated Brillouin scattering are discussed. These resonances appear due to the coupling between the two-level system and the resonant acoustic waves that are excited in the host substance by a coherent electromagnetic field of two mutually detuned, counterpropagating laser beams. Results for sodium vapor mixed with nitrogen buffer gas are presented.
Transformation optics simulation method for stimulated Brillouin scattering
Zecca, Roberto; Smith, David R; Larouche, Stéphane
2016-01-01
We develop a novel approach to enable the full-wave simulation of stimulated Brillouin scattering and related phenomena in a frequency-domain, finite-element environment. The method uses transformation optics techniques to implement a time-harmonic coordinate transform that reconciles the different frames of reference used by electromagnetic and mechanical finite-element solvers. We show how this strategy can be successfully applied to bulk and guided systems, comparing the results with the predictions of established theory.
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)
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
Self-pulsation threshold of Raman amplified Brillouin fiber cavities
DEFF Research Database (Denmark)
Ott, Johan Raunkjær; Pedersen, Martin Erland Vestergaard; Rottwitt, Karsten
2009-01-01
An implicit equation for the oscillation threshold of stimulated Brillouin scattering from Raman amplified signals in fibers with external feedback is derived under the assumption of no depletion. This is compared to numerical investigations of Raman amplification schemes showing good agreement...... for high reflectivities. For low reflectivities and high attenuation or long fibers, the assumption of no depletion is shown not to be valid. In these cases the effects of the depletion on the self-pulsation is examined....
Probing axial orientation of collagen fibers with Brillouin microspectroscopy
Meng, Zhaokai; Yakovlev, Vladislav V.
2015-03-01
Collagen is an important structural component in many biological tissues including bone, teeth, skin, and vascular endothelial layer. Its fibrillar arrangement can produce tissues with distinct anisotropies and is responsible for its unique elastic properties. However, current methods of retrieving orientation of those fibers show low sensitivity to the out-of-plane orientations. In this report, we employed Brillouin microspectroscopy to probe the local sound velocity, which, in its turn, is found to have a strong correlation to the local fibrillar arrangements.
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 ...
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.
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.
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.
In situ radiation influence on strain measurement performed by Brillouin sensors
PHERON, X; Ouerdane, Y.; Girard, S; MARCANDELLA, C; DELEPINE LESOILLE, S; Bertrand, J; Taillade, Frédéric; MERLIOT, Erick; SIKALI MAMDEM, Y; Boukenter, A.
2011-01-01
A new approach is proposed to monitor in situ gamma radiation influence on Brillouin optical fiber extensometers. Experimental results are illustrated with two fiber samples under gamma radiation up to total dose of about 600Gy. The Brillouin frequency shift has poor sensitivity at such radiations level, neither the spectral Brillouin signature nor its dependence with strain. Meanwhile, propagation losses increase under radiations, with an amplitude linked to fiber dopants. The target applica...
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.
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...
In situ radiation influence on strain measurement performance of Brillouin sensors
Pheron, X.; Ouerdane, Y.; Girard, S.; Marcandella, C.; Delepine-Lesoille, S.; Bertrand, J.; Taillade, F.; Merliot, E.; Sikali Mamdem, Y.; Boukenter, A.
2011-05-01
A new approach is proposed to monitor in situ the influence of gamma radiations on Brillouin properties of optical fiber extensometers. Experimental results are illustrated with the characterization of two fibers samples up to total dose of about 600Gy. The Brillouin frequency shift remains unaffected at such radiations level, as well as the spectral Brillouin signature or its dependence with strain. Meanwhile, propagation losses increase under radiations with an amplitude related to fiber dopants. The target application is nuclear wastes repository monitoring where higher doses are expected. UV radiation preliminary tests show that compaction phenomenon may occur at such high doses, inducing Brillouin frequency shift up to 20 MHz.
Meng, Zhaokai; Hanson, Jessica A.; Yakovlev, Vladislav V.
2016-03-01
Mechanical properties of tissues play an important role in biological development. However, the current elasticity-specific imaging techniques are either destructive / invasive, or have a limited spatial and/or temporal resolution. Recently, we introduced Brillouin microscopy imaging as a local non-invasive probe of microscopic viscoelasticity in cells and tissues. In this study, by taking advantage of Brillouin spectroscopy, we imaged the viscoelasticity properties of different compartments of living zebrafish embryos, including yolk-sac, skin, spine and heart. Brillouin and Raman spectra were collected simultaneously at each location using a recently developed Brillouin/Raman microscope.
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.
The Classical Version of Stokes' Theorem Revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2005-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we prove that the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... 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 correspondence alluded...
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...... of the vector field in a tubular shell around the given surface. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the 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 correspondence alluded to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used...
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)
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
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
Pythagoras Theorem and Relativistic Kinematics
Mulaj, Zenun; Dhoqina, Polikron
2010-01-01
In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.
A Miniaturisation of Ramsey's Theorem
de Smet, Michiel; Weiermann, Andreas
We approximate the strength of the infinite Ramsey Theorem by iterating a finitary version. This density principle, in the style of Paris, together with PA will give rise to a first-order theory which achieves a lot of the strength of ACA0 and the original infinitary version. To prove our result, we use a generalisation of the results by Bigorajska and Kotlarski about partitioning α-large sets.
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.
Compactness theorems of fuzzy semantics
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically. The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.
An improvement of Papadakis' theorem
Institute of Scientific and Technical Information of China (English)
ZHANG Zhihua; MU Lehua; ZHANG Peixuan
2004-01-01
There exist many orthonormal wavelets which cannot be derived by multiresolution analysis (MRA) with a single scaling function.In 2000,Papadakis announced that any orthonormal wavelet is derived by a generalized MRA with countable scaling functions at most.We improve Papadakis' theorem and find that for any othonormal wavelet,the least number of the corresponding scaling functions is just the essential supremum of the dimension function of the orthonormal wavelet.Moreover,we construct directly the fewest scaling functions.
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 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.
Simplified configuration of Brillouin optical correlation-domain reflectometry
Hayashi, Neisei; Nakamura, Kentaro
2014-01-01
We develop a simple and cost-efficient configuration of Brillouin optical correlation-domain reflectometry (BOCDR), the setup of which does not include an additional reference path used in standard BOCDR systems. The Fresnel-reflected light from an open end of a sensing fiber is used as reference light. The limitations of spatial resolution, measurement range, and their ratio are theoretically clarified, and then a distributed strain measurement with a < 100-mm spatial resolution and a 4.1-m measurement range is demonstrated with a high signal-to-noise ratio.
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.
Rayleigh-Brillouin Scattering in Binary Gas Mixtures
Gu, Ziyu; van de Water, Willem; Marques, Wilson
2015-01-01
Precise measurements are performed on spectral lineshapes of spontaneous Rayleigh-Brillouin scattering in mixtures of the noble gases Ar and Kr, with He. Admixture of a light He atomic fraction results in marked changes of the spectra, although in all experiments He is merely a spectator atom: it affects the relaxation of density fluctuations of the heavy constituent, but its contribution to the scattered light intensity is negligibly small. The results are compared to a theory for the spectral lineshape without adjustable parameters, yielding excellent agreement for the case of binary mono-atomic gases, signifying a step towards modeling and understanding of light scattering in more complex molecular media.
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.
The Helmholtz theorem and retarded fields
Heras, Ricardo
2016-01-01
Textbooks frequently use the Helmholtz theorem to derive expressions for the electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for the time-dependent electric and magnetic fields, even when there is no formal objection to doing so because the proof of the theorem does not involve time derivatives but only spatial derivatives. Here we address the question as to whether the Helmholtz theorem is useful to derive expressions for the fields of Maxwell's equations. We show that when this theorem is applied to Maxwell's equations we obtain instantaneous expressions of the electric and magnetic fields, which are formally correct but of little practical usefulness. We then discuss two generalizations of the theorem which are shown to be useful to derive the retarded fields.
The Helmholtz theorem and retarded fields
Heras, Ricardo
2016-11-01
Textbooks frequently use the Helmholtz theorem to derive expressions for electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for time-dependent electric and magnetic fields, even when there is no formal objection to doing so because the proof of the theorem does not involve time derivatives but only spatial derivatives. Here we address the question as to whether the Helmholtz theorem is useful in deriving expressions for the fields of Maxwell’s equations. We show that when this theorem is applied to Maxwell’s equations we obtain instantaneous expressions of the electric and magnetic fields, which are formally correct but of little practical usefulness. We then discuss two generalizations of the theorem which are shown to be useful in deriving the retarded fields.
Brillouin Lasing with a CaF_2 Whispering Gallery Mode Resonator
Grudinin, Ivan S; Maleki, Lute
2008-01-01
Stimulated Brillouin scattering with both pump and Stokes beams in resonance with whispering gallery modes of an ultra high Q CaF_2 resonator is demonstrated for the first time. The resonator is pumped with 1064 nm light and has a Brillouin lasing threshold of 3.5 microwatt. Potential applications include optical generation of microwaves and sensitive gyros.
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.
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.
Counterexamples To Bertini Theorems for Test Ideals
Bydlon, Andrew
2016-01-01
In algebraic geometry, Bertini theorems are an extremely important tool. A generalization of the classical theorem to multiplier ideals show that multiplier ideals restrict to a general hyperplane section. In characteristic $p > 0$, the test ideal can be seen to be the characteristic $p > 0$ analog of the multiplier ideal. However, in this paper it is shown that the same type of Bertini type theorem does not hold for test ideals.
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...
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 ...
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.
Bayesian Posteriors Without Bayes' Theorem
Hill, Theodore P
2012-01-01
The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the classical Bayesian posterior is the unique posterior that minimizes the loss of Shannon information in combining the prior and the likelihood distributions. These results, direct corollaries of recent results about conflations of probability distributions, reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics.
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.
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.
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...
Reshak, A. H.; Hambali, N. A. M. Ahmad; Shahimin, M. M.; Wahid, M. H. A.; Anwar, Nur Elina; Alahmed, Zeyad A.; Chyský, J.
2016-10-01
This paper is focusing on simulation and analyzing of S-band multi-wavelength Brillouin-Raman fiber laser performance utilizing fiber Bragg grating and Raman amplifier in ring cavity. Raman amplifier-average power model is employed for signal amplification. This laser system is operates in S-band wavelength region due to vast demanding on transmitting the information. Multi-wavelength fiber lasers based on hybrid Brillouin-Raman gain configuration supported by Raman scattering effect have attracted significant research interest due to its ability to produced multi-wavelength signals from a single light source. In multi-wavelength Brillouin-Raman fiber, single mode fiber is utilized as the nonlinear gain medium. From output results, 90% output coupling ratio has ability to provide the maximum average output power of 43 dBm at Brillouin pump power of 20 dBm and Raman pump power of 14 dBm. Furthermore, multi-wavelength Brillouin-Raman fiber laser utilizing fiber Bragg grating and Raman amplifier is capable of generated 7 Brillouin Stokes signals at 1480 nm, 1510 nm and 1530 nm.
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.
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.
Vallès, Jean
2012-01-01
Our aim is to prove a Poncelet type theorem for a line configuration on the complex projective. More precisely, we say that a polygon with 2n sides joining 2n vertices A1, A2,..., A2n is well inscribed in a configuration Ln of n lines if each line of the configuration contains exactly two points among A1, A2, ..., A2n. Then we prove : "Let Ln be a configuration of n lines and D a smooth conic in the complex projective plane. If it exists one polygon with 2n sides well inscribed in Ln and circumscribed around D then there are infinitely many such polygons. In particular a general point in Ln is a vertex of such a polygon." We propose an elementary proof based on Fr\\'egier's involution. We begin by recalling some facts about these involutions. Then we explore the following question : When does the product of involutions correspond to an involution? It leads to Pascal theorem, to its dual version proved by Brianchon, and to its generalization proved by M\\"obius.
Freiman's theorem for solvable groups
Tao, Terence
2009-01-01
Freiman's theorem asserts, roughly speaking, if that a finite set in a torsion-free abelian group has small doubling, then it can be efficiently contained in (or controlled by) a generalised arithmetic progression. This was generalised by Green and Ruzsa to arbitrary abelian groups, where the controlling object is now a coset progression. We extend these results further to solvable groups of bounded derived length, in which the coset progressions are replaced by the more complicated notion of a ``coset nilprogression''. As one consequence of this result, any subset of such a solvable group of small doubling is is controlled by a set whose iterated products grow polynomially, and which are contained inside a virtually nilpotent group. As another application we establish a strengthening of the Milnor-Wolf theorem that all solvable groups of polynomial growth are virtually nilpotent, in which only one large ball needs to be of polynomial size. This result complements recent work of Breulliard-Green, Fisher-Katz-...
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…
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.
Euler and the Fundamental Theorem of Algebra.
Duham, William
1991-01-01
The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)
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.
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 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…
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.
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.
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.
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.
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.
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…
Aspects of the Flavour Expansion Theorem
Paraskevas, M
2015-01-01
The Flavour Expansion Theorem, which has been recently proposed as a more general and elegant algebraic method, for the derivation of the commonly used Mass Insertion Approximation, is revisited. The theorem is reviewed, with respect to its straightforward applications in Flavour physics, and compared against the standard diagrammatic flavour basis techniques, in cases where the latter become inadequate.
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...
Double soft theorem for perturbative gravity
Saha, Arnab Priya
2016-09-01
Following up on the recent work of Cachazo, He and Yuan [1], we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.
A 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.
The Euler Line and Nine-Point-Circle Theorems.
Eccles, Frank M.
1999-01-01
Introduces the Euler line theorem and the nine-point-circle theorem which emphasize transformations and the power of functions in a geometric concept. Presents definitions and proofs of theorems. (ASK)
Generalized fluctuation theorems for classical systems
Agarwal, G S
2015-01-01
Fluctuation theorems have a very special place in the study of non equilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen Fluctuation Theorem which is in terms of the distribution of the work $p(W)/p(-W)=\\exp(\\alpha W)$. We derive the general form of the fluctuation theorems for an arbitrary Gaussian Markov process and find conditions when the parameter $\\alpha$ becomes a universal parameter $1/kT$. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is non-trivial. The generalized theorems are equally valid for non-equilibrium steady states.
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...
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
Brillouin optical correlation domain reflectometry with lock-in detection scheme
Yao, Yuguo; Kishi, Masato; Hotate, Kazuo
2016-07-01
We propose a Brillouin optical correlation domain reflectometry (BOCDR) technique with a lock-in detection scheme in this paper. By designing a new system using the lock-in detection scheme and amplifying a small spontaneous Brillouin signal with a lock-in amplifier, a Brillouin scattering spectrum with a stable shape is obtained. By further introducing a periodical on/off phase modulation for chopping for lock-in detection, the undesired optical background spectrum is effectively reduced, and a 20 cm section with 7,000 µε strain is clearly measured.
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 ℃.
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
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.
Multimode Brillouin spectrum in a long tapered birefringent photonic crystal fiber.
Tchahame, Joël Cabrel; Beugnot, Jean-Charles; Kudlinski, Alexandre; Sylvestre, Thibaut
2015-09-15
We investigate the stimulated Brillouin scattering (SBS) in a long tapered birefringent solid-core photonic crystal fiber (PCF) and compare our results with a similar but untapered PCF. It is shown that the taper generates a broadband and multipeaked Brillouin spectrum, while significantly increasing the threshold power. Furthermore, we observe that the strong fiber birefringence gives rise to a frequency shift of the Brillouin spectrum which increases along the fiber. Numerical simulations are also presented to account for the taper effect and the birefringence. Our findings open a new means to control or inhibit the SBS by tapering photonic crystal fibers. PMID:26371916
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 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
Dynamical Chern-Simons Theory in the Brillouin Zone
Lian, Biao; Vafa, Farzan; Zhang, Shou-Cheng
2016-01-01
Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here we show that for three-dimensional (3d) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a dynamical fluctuating field of a Chern-Simons gauge theory. The gapless nodal lines in the momentum space play the role of Wilson loop observables, while their linking and knot invariants modify the gravitational theta angle. This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow. We also show how topological strings may be realized in the 6 dimensional phase space, where the physical space defects play the role of topological D-branes.
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.
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.
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.
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...
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.
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.
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.
Linear Sequences and Weighted Ergodic Theorems
Directory of Open Access Journals (Sweden)
Tanja Eisner
2013-01-01
Full Text Available We present a simple way to produce good weights for several types of ergodic theorem including the Wiener-Wintner type multiple return time theorem and the multiple polynomial ergodic theorem. These weights are deterministic and come from orbits of certain bounded linear operators on Banach spaces. This extends the known results for nilsequences and return time sequences of the form for a measure preserving system and , avoiding in the latter case the problem of finding the full measure set of appropriate points .
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
Interval logic. Proof theory and theorem proving
DEFF Research Database (Denmark)
Rasmussen, Thomas Marthedal
2002-01-01
. 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 formalisms...... of a direction of an interval, and present a sound and complete Hilbert proof system for it. Because of its generality, SIL can conveniently act as a general formalism in which other interval logics can be encoded. We develop proof theory for SIL including both a sequent calculus system and a labelled natural...
Haag's theorem in renormalised quantum field theories
Klaczynski, Lutz
2016-01-01
We review a package of no-go results in axiomatic quantum field theory with Haag's theorem at its centre. Since the concept of operator-valued distributions in this framework comes very close to what we believe canonical quantum fields are about, these results are of consequence to quantum field theory: they suggest the seeming absurdity that this highly victorious theory is incapable of describing interactions. We single out unitarity of the interaction picture's intertwiner as the most salient provision of Haag's theorem and critique canonical perturbation theory to argue that renormalisation bypasses Haag's theorem by violating this very assumption.
Dual Raman-Brillouin Microscope for Chemical and Mechanical Characterization and Imaging.
Traverso, Andrew J; Thompson, Jonathan V; Steelman, Zachary A; Meng, Zhaokai; Scully, Marlan O; Yakovlev, Vladislav V
2015-08-01
We present a unique confocal microscope capable of measuring the Raman and Brillouin spectra simultaneously from a single spatial location. Raman and Brillouin scattering offer complementary information about a material's chemical and mechanical structure, respectively, and concurrent monitoring of both of these spectra would set a new standard for material characterization. We achieve this by applying recent innovations in Brillouin spectroscopy that reduce the necessary acquisition times to durations comparable to conventional Raman spectroscopy while attaining a high level of spectral accuracy. To demonstrate the potential of the system, we map the Raman and Brillouin spectra of a molded poly(ethylene glycol) diacrylate (PEGDA) hydrogel sample in cyclohexane to create two-dimensional images with high contrast at microscale resolutions. This powerful tool has the potential for very diverse analytical applications in basic science, industry, and medicine.
Steelman, Zachary; Meng, Zhaokai; Traverso, Andrew J; Yakovlev, Vladislav V
2015-05-01
Bacterial meningitis is a disease of pronounced clinical significance, especially in the developing world. Immediate treatment with antibiotics is essential, and no single test can provide a conclusive diagnosis. It is well established that elevated total protein in cerebrospinal fluid (CSF) is associated with bacterial meningitis. Brillouin spectroscopy is a widely used optical technique for noninvasive determination of the elastic moduli of materials. We found that elevated protein levels in CSF alter the fluid elasticity sufficiently to be measurable by Brillouin spectroscopy, with model healthy and diseased fluids distinguishable to marked significance (P = 0.014), which increases with sample concentration by dialysis. Typical raw output of a 2-stage VIPA Brillouin spectrometer: inelastically scattered Brillouin peaks (arrows) and elastically scattered incident radiation (center cross).
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.
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.
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.
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.
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....
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...
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.
First numerical experiences with overlap fermions based on the Brillouin kernel
Durr, Stephan
2016-01-01
Numerical experiences are reported with overlap fermions which employ the Brillouin action as a kernel. After discussing the dispersion relations of both the kernel and the resulting chiral action, some of the physics features are addressed on quenched backgrounds. We find that the overlap with Brillouin kernel is much better localized than the overlap with Wilson kernel. Also a preliminary account is given of the cost of the formulation, in terms of CPU time and memory.
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...
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.
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.
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}
Affine and Projective Tree Metric Theorems
Harel, Matan; Pachter, Lior
2011-01-01
The tree metric theorem provides a combinatorial four point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A similar (but weaker) four point condition characterizes dissimilarity maps derived from circular split systems (Kalmanson metrics). The tree metric theorem was first discovered in the context of phylogenetics and forms the basis of many tree reconstruction algorithms, whereas Kalmanson metrics were first considered by computer scientists, and are notable in that they are a non-trivial class of metrics for which the traveling salesman problem is tractable. We present a unifying framework for these theorems based on combinatorial structures that are used for graph planarity testing. These are (projective) PC-trees, and their affine analogs, PQ-trees. In the projective case, we generalize a number of concepts from clustering theory, including hierarchies, pyramids, ultrametrics and Robinsonian matrices, and the theorems that relate them. As with tree metric...
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.
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.
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.
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.
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.
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.
The virial theorem for nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: paolo.amore@gmail.com, E-mail: fernande@quimica.unlp.edu.ar
2009-09-15
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular, we consider conservative nonlinear oscillators and obtain the same main result derived earlier from the expansion in Chebyshev polynomials. (letters and comments)
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...
A New GLKKM Theorem and Its Application to Abstract Economies
Institute of Scientific and Technical Information of China (English)
WEN Kai-ting
2012-01-01
In this paper,a new GLKKM theorem in L-convex spaces is established.As applications,a new fixed point theorem and a maximal element theorem are obtained in Lconvex spaces.Finally,equilibrium existence theorems for abstract economies and qualitative games in L-convex spaces are yielded.
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.
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…
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.
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.
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)
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.
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.
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...
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.
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.
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.
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...
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...
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.
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.
Performance of the distributed Brillouin sensor: Benefits and penalties due to pump depletion
Ravet, Fabien
Disaster prevention in civil infrastructures requires the use of techniques that allow temperature and strain measurements in real time over lengths of a few meters to tens of kilometres. The distributed Brillouin sensor (DBS) technique has the advantage to combine all these characteristics. The sensing mechanism of the DBS involves the interaction of two counter-propagating lightwaves, the Stokes and the pump, in an optical fibre. Spatial information is obtained through time domain analysis. The sensing data are recorded from the measurement of the pump depletion. We explore the benefits and the drawbacks of this approach and show that there is a power range for which the sensing performances are optima. To achieve that goal, Brillouin fibre generator (BFG) and amplifier (BFA) were studied leading to the derivation of a threshold definition for the BFA, which is the configuration of the DBS. Within that context, numerical and analytical models describing the stimulated Brillouin scattering (SBS) interaction are introduced and validated experimentally. Even if pump depletion is carefully controlled, the Brillouin spectrum shape, and hence the sensor performance, still depend on the sensing parameters such as power, pulse and fibre characteristics. We use a signal processing method grounded in the physics of Brillouin scattering. An analytical approximation, valid for the optimum sensing region, reconstructs the Brillouin spectrum distribution from input sensing parameters and measured data. These data are obtained with a spectrum analysis methodology, based on three original tools: the Rayleigh equivalent criterion, the lengthstress diagram, and the spectrum form factors. This methodology has been successfully used on experimental spectra. The DBS and the signal processing approach were then used to monitor the structural changes in steel pipes and in a composite column, all subjected to heavy loads. The DBS measured the strain distribution of those structures
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...
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
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.
The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory
Directory of Open Access Journals (Sweden)
Claude Semay
2015-01-01
Full Text Available The envelope theory is a convenient method to compute approximate solutions for bound state equations in quantum mechanics. It is shown that these approximate solutions obey a kind of Hellmann–Feynman theorem, and that the comparison theorem can be applied to these approximate solutions for two ordered Hamiltonians.
Institute of Scientific and Technical Information of China (English)
马吉溥
2000-01-01
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally fine property for Frechet derivatives f’ (x) and generalized rank theorem for f ’( x), a local conjugacy theorem, i. e. a characteristic condition for f being conjugate to f (x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: be C1 nonlinear map, where U (x0) is an open set containing point x0∈E. With the locally fine property for Frechet derivatives f′(x) and generalized rank theorem for f′(x), a local conjugacy theorem, i.e. a characteristic condition for f being conjugate to f′(x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
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
WEYL'S TYPE THEOREMS AND HYPERCYCLIC OPERATORS
Institute of Scientific and Technical Information of China (English)
M.H. M. Rashid
2012-01-01
For a bounded operator T acting on an infinite dimensional separable Hilbert space H,we prove the following assertions: (i) If T or T* ∈ SC,then generalized aBrowder's theorem holds for f(T) for every f ∈ Hol(σ(T)).(ii) If T or T* ∈ HC has topological uniform descent at all λ ∈ iso(σ(T)),then generalized Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)).(iii) If T ∈ HC has topological uniform descent at all λ ∈ E(T),then T satisfies generalized Weyl's theorem.(iv) Let T ∈ HC.If T satisfies the growth condition Gd(d ≥ 1),then generalized Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)).(v) If T ∈ SC,then,f(σSBF-+ (T)) =σSBF-+ (f(T)) for all f ∈ Hol(σ(T)).(vi) Let T be a-isoloid such that T* ∈ HC.If T - λI has finite ascent at every λ ∈ Ea(T)and if F is of finite rank on H such that TF =FT,then T + F obeys generalized a-Weyl's theorem.
Generalized fluctuation theorems for classical systems
Agarwal, G. S.; Dattagupta, Sushanta
2015-11-01
The fluctuation theorem has a very special place in the study of nonequilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen fluctuation theorem which is in terms of the distribution of the work p (W )/p (-W )=exp(α W ) . We derive the general form of the fluctuation theorems for an arbitrary multidimensional Gaussian Markov process. Interestingly, the parameter α is by no means universal, hitherto taken for granted in the case of linear Gaussian processes. As a matter of fact, conditions under which α does become a universal parameter 1 /K T are found to be rather restrictive. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is nontrivial. The generalized theorems are equally valid for nonequilibrium steady states and could be especially important in the presence of anisotropic diffusion.
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.
Ravet, Fabien; Bao, Xiaoyi; Snoddy, Jeff; Li, Yun; Chen, Liang
2009-06-01
The Brillouin fiber amplifier (BFA) has been used in Brillouin optical time and frequency domain analyzer based sensors. For BFA based distributed sensor the optimized working condition is to have the highest Brillouin gain, i.e., highest SNR, which avoids high pump depletion induced gain saturation. We have found that the optimum working condition for distributed sensor system is associated with the stimulated Brillouin scattering (SBS) threshold for BFA, which can be experimentally determined with Stokes power inflexion and/or Stokes spectrum linewidth minimum methods. This threshold depends on both pump and probe power instead of just the pump power as in Brillouin fiber generator (BFG), as well as on sensing length as confirmed by our experimental results and theoretical simulation. This was achieved by introducing the concept of absorption coefficient of the sensing medium defined as the ratio of the total output power to the total input power. We find that the medium absorption is minimized when input Stokes power is an order of magnitude lower than BFA threshold. This minimum is a signature of the balance between maximum Stokes gain and pump depletion which is also the reason why Stokes spectrum linewidth goes through a minimum.
Brillouin scattering, piezobirefringence, and dispersion of photoelastic coefficients of CdS and ZnO
DEFF Research Database (Denmark)
Berkowicz, R.; Skettrup, Torben
1975-01-01
We have measured the dispersion of the Brillouin scattering from acoustoelectrical domains in CdS and ZnO. These spectra are compared with the birefringence spectra obtained by applying uniaxial stress. The resonant cancellation of the Brillouin scattering occurs at the spectral position of the i......We have measured the dispersion of the Brillouin scattering from acoustoelectrical domains in CdS and ZnO. These spectra are compared with the birefringence spectra obtained by applying uniaxial stress. The resonant cancellation of the Brillouin scattering occurs at the spectral position...... of the isotropic point of the stress-induced birefringence. From these spectra it is concluded that the Brillouin scattering in CdS and ZnO is determined by elasto-optic effects alone. The spectra of some of the photoelastic coefficients have been determined. A model dielectric constant is derived where both....... It is found that the exchange interaction between the excitons may change the values of the photoelastic coefficients in ZnO about 10%....
Some Limit Theorems in Geometric Processes
Institute of Scientific and Technical Information of China (English)
Yeh Lam; Yao-hui Zheng; Yuan-lin Zhang
2003-01-01
Geometric process (GP) was introduced by Lam[4,5], it is defined as a stochastic process {Xn, n =1, 2,...} for which there exists a real number a > 0, such that {an-1Xn, n = 1, 2,...} forms a renewal process (RP). In this paper, we study some limit theorems in GP. We first derive the Wald equation for GP and then obtain the limit theorems of the age, residual life and the total life at t for a GP. A general limit theorem for Sn with a > 1 is also studied. Furthermore, we make a comparison between GP and RP, including the comparison of their limit distributions of the age, residual life and the total life at t.
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...
Causality, Bell's theorem, and Ontic Definiteness
Henson, Joe
2011-01-01
Bell's theorem shows that the reasonable relativistic causal principle known as "local causality" is not compatible with the predictions of quantum mechanics. It is not possible maintain a satisfying causal principle of this type while dropping any of the better-known assumptions of Bell's theorem. However, another assumption of Bell's theorem is the use of classical logic. One part of this assumption is the principle of "ontic definiteness", that is, that it must in principle be possible to assign definite truth values to all propositions treated in the theory. Once the logical setting is clarified somewhat, it can be seen that rejecting this principle does not in any way undermine the type of causal principle used by Bell. Without ontic definiteness, the deterministic causal condition known as Einstein Locality succeeds in banning superluminal influence (including signalling) whilst allowing correlations that violate Bell's inequalities. Objections to altering logic, and the consequences for operational and...
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.
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.
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.
The aftermath of the intermediate value theorem
Directory of Open Access Journals (Sweden)
Morales Claudio H
2004-01-01
Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (17811848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.
The aftermath of the intermediate value theorem
Directory of Open Access Journals (Sweden)
Claudio H. Morales
2004-08-01
Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000Ã‚Â–300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (1781Ã‚Â–1848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.
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.
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.
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.
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
Bao, Xiaoyi; Liang, Hao; Dong, Yongkang; Li, Wenhai; Li, Yun; Chen, Liang
2010-04-01
Long distance sensing based on Brillouin scattering with centimeter spatial resolution, and yet high strain or temperature resolution requires the optimization of the optical and electronic system. In optical domain the limiting factors include gain saturation of the Stokes signal and pump depletion induced the Brillouin spectrum distortion, and thus a low gain is desired that requires low pump power, which sets a limit in the signal to noise ratio (SNR). The detection system must have high gain and narrow bandwidth to reduce electronic noise. The coded pulse offers the best solution as a low power solution of long distance sensing based on BOTDA to improve the signal to noise ratio (SNR), comparing two most common used formats: non-return-to-zero (NRZ) and return-to-zero (RZ), RZ coded pulses offer minimum distortion in the spatial resolution and the Brillouin spectrum, because the signal in RZ format returns to zero in very bit, while in NRZ coded pulse the signal returns to zero after continuous "1"s, which brings the higher gain and lower bandwidth comparing that in RZ coded pulse for BOTDA system. Hence NRZ coded pulse BOTDA would introduce spatial broadening and lower the spatial resolution. With minimum distortion of RZ signal we can use differential Brillouin gain to realize DPP-BOTDA technique for sub-meter spatial resolution. The minimum coded pulse width must be larger than the acoustic wave relaxation time to avoid the distorted Brillouin gain spectrum. Using LEAF fiber we achieved 50km sensing length and 50cm spatial resolution with the strain resolution of 8μɛ which is equivalent to 0.7MHz Brillouin frequency shift, this is the 1st sub-meter spatial resolution for 50km sensing length combined with high strain resolution.
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.
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.
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.
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)
Characterization of red blood cells (RBCs) using dual Brillouin/Raman micro-spectroscopy
Meng, Zhaokai; Bustamante-Lopez, Sandra C.; Yakovlev, Vladislav V.; Meissner, Kenith E.
2016-04-01
Erythrocytes, or red blood cells, transport oxygen to and carbon dioxide from the body's tissues and organs. Red blood cell mechanical properties are altered in a number of diseases such as sickle cell anaemia and malaria. Additionally, mechanically modified red blood cell ghosts are being considered as a long-term, biocompatible carrier for drug delivery and for blood analyte sensing. Brillouin spectroscopy enables viscoelastic characterization of samples at the microscale. In this report, Brillouin spectroscopy is applied to characterize the mechanical properties of red blood cells and red blood cell ghosts.
Guided acoustic and optical waves in silicon-on-insulator for Brillouin scattering and optomechanics
Sarabalis, Christopher J.; Hill, Jeff T.; Safavi-Naeini, Amir H.
2016-10-01
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 W-1m-1 for backward and forward Brillouin scattering, respectively.
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
Institute of Scientific and Technical Information of China (English)
Ji-Sheng Zhang; Yong-Qian Li; Shuo Zhang; Li-Juan Zhao
2008-01-01
Microwave heterodyne detection can be used to measure the temperature and strain distribution along a fiber with high accuracy in a Brillouin optical time domain reflectometry (BOTDR) system. This method involves simultaneous measurement of Brillouin scattering and Rayleigh scattering in fiber, and scanning of Briliouin spectrum to obtain the desired information. This paper presents a simultaneous measurement system of temperature and strain based on microwave detection and analyzed the system performances such as measurement accuracy, dynamic range, and spatial resolution theoretically. The analysis shows that the system can achieve a temperature resolution of 1℃ and a strain resolution of 100 με.
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.
Stokes' theorem, volume growth and parabolicity
Valtorta, Daniele
2010-01-01
We present some new Stokes'type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications to comparison and uniqueness results involving the p-Laplacian are deduced.
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.
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.
SOME REFINEMENTS OF ENESTROM-KAKEYA THEOREM
Institute of Scientific and Technical Information of China (English)
A.Aziz; B.A.Zargar
2007-01-01
In this paper we present certain interesting refinements of a well-known Enestrom-Kakeya theorem in the theory of distribution of zeros of polynomials which among other things also improve upon some results of Aziz and Mohammad, Govil and Rehman and others.
Generalization of the Hellmann-Feynman theorem
Energy Technology Data Exchange (ETDEWEB)
Esteve, J.G., E-mail: esteve@unizar.e [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y Fisica de Sistemas complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza (Spain); Falceto, Fernando [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y Fisica de Sistemas complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza (Spain); Garcia Canal, C. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata and IFLP-CONICET (Argentina)
2010-01-25
The well-known Hellmann-Feynman theorem of quantum mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition of the Hamiltonian of the system also depends on that parameter.
Answering Junior Ant's "Why" for Pythagoras' Theorem
Pask, Colin
2002-01-01
A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…
On 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)
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].
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 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.
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.
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.
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...
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.
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.
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.
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)
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.
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.
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.
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.
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.
Average sampling theorems for shift invariant subspaces
Institute of Scientific and Technical Information of China (English)
孙文昌; 周性伟
2000-01-01
The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.
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
Two Theorems on Calculating the Relative Entropy of Entanglement
Institute of Scientific and Technical Information of China (English)
WU Sheng-Jun; ZHANG Yong-De; WU Qiang
2001-01-01
We present two theorems on calculating the relative entropy of entanglement. Theorem 1 is an extension of Vedral and Plenio's theorem (Phys. Rev. A 57 (1998) 1619) for pure states, which is useful for calculating the relative entropy of entanglement for all pure states as well as for a class of mixed states. Theorem 2 gives the relative entropy of entanglement for any bipartite state whose tripartite purification has two separable reduced bipartite states.
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.
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.
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.
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.
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
2014-01-01
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
ON 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.
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.
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
Brillouin scattering study of the ferroelectric phase transition in tris-sarcosine calcium chloride
Hikita, Tomoyuki; Schnackenberg, Paul; Schmidt, V. Hugo
1985-01-01
Brillouin spectra from longitudinal phonons in ferroelectric tris-sarcosine calcium chloride propagating along [100], [010], and [001] have been measured as functions of temperature. Large anomalies were found in the Brillouin shift and linewidth in the [100] and [001] phonons. These anomalies are interpreted as arising from the linear coupling of the polarization and the phonons. From the temperature where the linewidth is maximum, the relaxation time of the polarization fluctuations is estimated to be τ=3.1×10-12/(Tc-T) sec, where Tc is the ferroelectric transition temperature. We also observed anomalies in Brillouin shift and linewidth of the [010] phonons which propagate along the ferroelectric b axis. These anomalies are interpreted as coming from electro- strictive coupling. The energy-relaxation time was estimated to be τE=2.5×10-10/(T-Tc) sec in the paraelectric phase and τE=1.0×10-9/(Tc-T) sec in the ferroelectric phase, by comparing our Brillouin results with those of the ultrasonic measurements.
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.
All solid-state diode pumped Nd:YAG MOPA with stimulated Brillouin phase conjugate mirror
Offerhaus, H.L.; Godfried, H.P.; Witteman, W.J.
1996-01-01
At the Nederlands Centrum voor Laser Research (NCLR) a 1 kHz diode-pumped Nd:YAG Master Oscillator Power Amplifier (MOPA) chain with a Stimulated Brillouin Scattering (SBS) Phase Conjugate mirror is designed and operated. A small Brewster angle Nd:YAG slab (2 by 2 by 20 mm) is side pumped with 200 μ
Institute of Scientific and Technical Information of China (English)
胡业民; 胡希伟
2001-01-01
Numerical analyses for the nonlinear evolutions of stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) processes are given. Various effects of the second- and third-order nonlinear susceptibilities on the SRS and SBS processes are studied. The nonlinear evolutions of SRS and SBS processes are atfected more efficiently than their linear growth rates by the nonlinear susceptibility.
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.
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.
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
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...
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.
Multideviations: The hidden structure of Bell's theorems
Fogel, Brandon
2015-01-01
Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open problem. Here I provide a new set of tools, which I refer to as "multideviations", for finding and analyzing these inequalities for the fully general case. In Part I, I introduce the multideviation framework and then use it to prove an important theorem: the Bell distributions can be generated from the set of joint distributions over all observables by deeming specific degrees of freedom unobservable. In Part II, I show how the theorem provides a new method for finding tight Bell inequalities. I then specify a set of new tight Bell inequalities for arbitrary event spaces -- the "even/odd" inequalities -- which have a straightforward interpretation when expressed in terms of multideviations. The even/odd inequalities concern degrees of freedom that are independent of those invol...
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...
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.
2016-09-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-01-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571
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.
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.
Generalized Sampling Theorem for Bandpass Signals
Directory of Open Access Journals (Sweden)
Prokes Ales
2006-01-01
Full Text Available The reconstruction of an unknown continuously defined function from the samples of the responses of linear time-invariant (LTI systems sampled by the th Nyquist rate is the aim of the generalized sampling. Papoulis (1977 provided an elegant solution for the case where is a band-limited function with finite energy and the sampling rate is equal to times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.
Wigner-Eckart theorem for induced symmetries
Energy Technology Data Exchange (ETDEWEB)
Klein, D.J. (Texas A and M University, Galveston (USA). Department of Marine Sciences); Seligman, T.H. (Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Fisica)
1982-01-01
A unified treatment is given for all group-theoretic problems arising from the evaluation of matrix elements involving operators and states of induced symmetries. To achieve this general treatment two group-theoretic theorems are proven, the first characterizing recoupling coefficients between different symmetry adaptation schemes, and the second making a double coset factorization of a group algebraic matrix basis element. A number of problems previously discussed in the literature, including the conventional Wigner-Eckart theorem and more recent double coset expansions of matrix elements, are realized as special cases in the present treatment. These results entail two new types of recoupling coefficients, namely DC coefficients and 3-symmetry symbols, so that some of their properties are indicated.
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.
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 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...
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.
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 .
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.
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.
Hildebrandt's theorem for the essential spectrum
Directory of Open Access Journals (Sweden)
Janko Bračič
2015-01-01
Full Text Available We prove a variant of Hildebrandt's theorem which asserts that the convex hull of the essential spectrum of an operator \\(A\\ on a complex Hilbert space is equal to the intersection of the essential numerical ranges of operators which are similar to \\(A\\. As a consequence, it is given a necessary and sufficient condition for zero not being in the convex hull of the essential spectrum of \\(A\\.
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...
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.
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.
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...
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 ...
Reciprocity Theorems for Ab Initio Force Calculations
Wei, C; Mele, E J; Rappe, A M; Lewis, Steven P.; Rappe, Andrew M.
1996-01-01
We present a method for calculating ab initio interatomic forces which scales quadratically with the size of the system and provides a physically transparent representation of the force in terms of the spatial variation of the electronic charge density. The method is based on a reciprocity theorem for evaluating an effective potential acting on a charged ion in the core of each atom. We illustrate the method with calculations for diatomic molecules.
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...
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 ...
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...
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 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.
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...
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.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Manghnani, M.H.
1992-06-05
This report describes a research project that was conducted from August 15, 1985 to February 28, 1992. The project was based on the ultrasonic studies of natural and synthetic silicate melts, and the study of Brillouin scattering of synthetic silicates and oxides. Measurements of the compressional wave velocity and attenuation can be established using the ultrasonic methods. Temperature dependences of silicates can be established by the Brillouin scattering. (MB)
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
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.
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...
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...
Average Kinetic Energy of Heavy Quark and Virial Theorem
Hwang, Dae Sung; Kim, C. S.; 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 $et$ $al.$
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...
Inconsistency of Carnot's theorem's proof by R. Clausius
Ihnatovych, V
2013-01-01
R. Clausius proved Carnot's theorem basing on postulate "Heat cannot, of itself, pass from a colder to a hotter body". Alexander Gukhman demonstrated that Carnot's theorem can be proved based on the postulate "Heat cannot, of itself, pass from a hotter to a colder body". He concluded that Carnot's theorem does not follow from Clausius' postulate. The following paper gives a detailed justification of Gukhman's derivation.
Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators
Institute of Scientific and Technical Information of China (English)
王雪红; 郭军义; 李艳
2012-01-01
In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ?/?λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.
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.
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...
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...
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.
Convolution Theorems for Quaternion Fourier Transform: Properties and Applications
Mawardi Bahri
2013-01-01
General convolution theorems for two-dimensional quaternion Fourier transforms(QFTs) are presented. It is shown that these theorems are not only valid for real-valued functions, but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare 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 algebra fr...
Convolution Theorems for Quaternion Fourier Transform: Properties and Applications
Directory of Open Access Journals (Sweden)
Mawardi Bahri
2013-01-01
Full Text Available 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 algebra framework.
Convolution Theorems for Quaternion Fourier Transform: Properties and Applications
Mawardi Bahri; Ryuichi Ashino; 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 algebra framework.
Institute of Scientific and Technical Information of China (English)
R. Parvizi; S. W. Harun; N. M. Ali; N. S. Shahabuddin; H. Ahmad
2011-01-01
@@ A simple technique for achieving a stable, room temperature and multi-wavelength lasing with narrow linewidth is demonstrated using Brillouin fiber laser (BFL) with a 100-m-long photonic crystal fiber (PCF) in conjunction with a dual-pass configuration. A broadband fiber Bragg grating (FBG) operating in the C-band region is incorporated at the end side of the setup to allow a dual-pass operation. The proposed BFL can operate at any wavelength depending on the Brillouin pump wavelength and the FBG's reflection region used. With a Brillouin pump (BP) of 15.7 dBm, approximately 7 Stokes and 4 anti-Stokes lines are obtained with a line spacing of 0.08 nm.%A simple technique for achieving a stable, room temperature and multi-wavelength lasing with narrow linewidth is demonstrated using Brillouin fiber laser (BFL) with a 100-m-long photonic crystal fiber (PCF) in conjunction with a dual-pass configuration. A broadband fiber Bragg grating (FBG) operating in the C-band region is incorporated at the end side of the setup to allow a dual-pass operation. The proposed BFL can operate at any wavelength depending on the Brillouin pump wavelength and the FBG's reflection region used. With a Brillouin pump (BP) of 15.7 dBm, approximately 7 Stokes and 4 anti-Stokes lines are obtained with a line spacing of 0.08 nm.
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.
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.
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.
A Cauchy-Davenport theorem for semigroups
Tringali, Salvatore
2012-01-01
We generalize the Davenport transform and use it to prove that, for a (possibly non-commutative) cancellative semigroup $\\mathbb A = (A, +)$ and non-empty subsets $X,Y$ of $A$ such that the subsemigroup generated by $Y$ is commutative, we have $|X + Y| \\ge \\min(\\omega(Y), |X| + |Y| - 1)$, where $\\omega(Y) := \\sup_{y_0 \\in Y \\cap \\mathbb A^{\\times}} \\inf_{y \\in Y \\setminus \\{y_0\\}} ||$. This carries over the Cauchy-Davenport theorem to the broader setting of semigroups, and it implies, in part...
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.
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.
APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION
Institute of Scientific and Technical Information of China (English)
杨守志; 程正兴; 唐远炎
2003-01-01
An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution. The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation, a piece-wise linear function, and posseses an explicit computation formula. Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function.
Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem
Directory of Open Access Journals (Sweden)
Juliana Bueno-Soler
2016-09-01
Full Text Available This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs. We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes’ theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.
Low-noise Brillouin random fiber laser with a random grating-based resonator.
Xu, Yanping; Gao, Song; Lu, Ping; Mihailov, Stephen; Chen, Liang; Bao, Xiaoyi
2016-07-15
A novel Brillouin random fiber laser (BRFL) with the random grating-based Fabry-Perot (FP) resonator is proposed and demonstrated. Significantly enhanced random feedback from the femtosecond laser-fabricated random grating overwhelms the Rayleigh backscattering, which leads to efficient Brillouin gain for the lasing modes and reduced lasing threshold. Compared to the intensity and frequency noises of the Rayleigh feedback resonator, those of the proposed random laser are effectively suppressed due to the reduced resonating modes and mode competition resulting from the random grating-formed filters. Using the heterodyne technique, the linewidth of the coherent random lasing spike is measured to be ∼45.8 Hz. PMID:27420494
Directory of Open Access Journals (Sweden)
Xiaoyi Bao
2013-01-01
Full Text Available A distributed optical fiber sensor with the capability of simultaneously measuring temperature and strain is proposed using a large effective area non-zero dispersion shifted fiber (LEAF with sub-meter spatial resolution. The Brillouin frequency shift is measured using Brillouin optical time-domain analysis (BOTDA with differential pulse-width pair technique, while the spectrum shift of the Rayleigh backscatter is measured using optical frequency-domain reflectometry (OFDR. These shifts are the functions of both temperature and strain, and can be used as two independent parameters for the discrimination of temperature and strain. A 92 m measurable range with the spatial resolution of 50 cm is demonstrated experimentally, and accuracies of ±1.2 °C in temperature and ±15 με in strain could be achieved.
Yi, Lilin; Zhang, Tao; Hu, Weisheng
2011-11-01
A novel all-optical encryption/decryption method based on stimulated Brillouin scattering (SBS) effect in optical fiber is proposed for the first time. The operation principle is explained in detail and the encryption and decryption performance is experimentally evaluated. The encryption keys could be the SBS gain amplitude, bandwidth, central wavelength and spectral shape, which are configurable and flexibly controlled by the users. We experimentally demonstrate the SBS encryption/decryption process of a 10.86-Gb/s non-return-to-zero (NRZ) data by using both phase-modulated and current-dithered Brillouin pumps for proof-of-concept. Unlike the traditional optical encryption methods of chaotic communications and optical code-division-multiplexing access (OCDMA), the SBS based encryption/decryption technique can directly upgrade the current optical communication system to a secure communication system without changing the terminal transceivers, which is completely compatible with the current optical communication systems.
Photonic crystal fibre Brillouin laser based on Bragg grating Fabry-Perot cavity
Institute of Scientific and Technical Information of China (English)
Geng Dan; Yang Dong-Xiao; Shen Guo-Feng; Zhang Xian-Min
2008-01-01
A photonic crystal fibre Brillouin laser based on fibre Bragg grating Fabry-Perot cavity is presented. A highly nonlinear photonic crystal fibre 25 m in length is used as Brillouin gain medium and fibre Bragg grating Fabry-Perot cavity is chosen in order to enhance the laser conversion efficiency and suppress the higher-order Stokes waves. The laser reaches the threshold at input power of 35 mW, and the experimental laser conversion efficiency achieves 18% of the input power of 140 mW and does not show higher-order Stokes waves. A photonic crystal fibre BriUouin laser withshorter fibre length and lower threshold is experimentally realized.
Unified approach to cascaded stimulated Brillouin scattering and frequency-comb generation
Dong, Mark; Winful, Herbert G.
2016-04-01
We present a unified approach to cascaded stimulated Brillouin scattering and frequency-comb generation in which the multitude of interacting pump, Stokes, and anti-Stokes optical fields is 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 is 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 this approach on some published experiments and find excellent agreement with the results.
Phase-locking in Multi-Frequency Brillouin Oscillator via Four Wave Mixing
Buettner, Thomas F S; Hudson, Darren D; Pant, Ravi; Poulton, Christopher G; Judge, Alexander C; Eggleton, Benjamin J
2014-01-01
Stimulated Brillouin scattering (SBS) and Kerr-nonlinear four wave-mixing (FWM) are among the most important and widely studied nonlinear effects in optical fibres. At high powers SBS can be cascaded producing multiple Stokes waves spaced by the Brillouin frequency shift. Here, we investigate the complex nonlinear interaction of the cascade of Stokes waves, generated in a Fabry-Perot chalcogenide fibre resonator through the combined action of SBS and FWM. We demonstrate the existence of parameter regimes, in which pump and Stokes waves attain a phase-locked steady state. Real-time measurements of 40ps pulses with 8GHz repetition rate are presented, confirming short-and long-term stability. Numerical simulations qualitatively agree with experiments and show the significance of FWM in phase-locking of pump and Stokes waves. Our findings can be applied for the design of novel picosecond pulse sources with GHz repetition rate for optical communication systems.
Hu, Shuling; Xiao, Zeyu; Wang, Huanhuan
2015-07-01
A tunable and reconfigurable single passband microwave photonic filter based on stimulated Brillouin scattering (SBS) and intensity modulation is presented and theoretically analyzed. Three Brillouin pumps with equal intensity are generated by selecting appropriate bias voltages and modulation indices. Then a reconfigurable passband can be achieved by superposition of the three pumps. Simulation results demonstrate that the proposed filter has a 22-GHz continuous tuning range with a high out-of-band rejection ratio above 40 dB. The -3-dB bandwidth can be tuned from 12 to 95 MHz, and the flatness is less than 1.5 dB. This technique uses a low-frequency (0 to 35 MHz) modulation signal to realize passband reshaping, and has potential applications in communication and radar systems.
Wu, Hao; Wang, Ruoxu; Liu, Deming; Fu, Songnian; Zhao, Can; Wei, Huifeng; Tong, Weijun; Shum, Perry Ping; Tang, Ming
2016-04-01
We proposed and demonstrated a few-mode fiber (FMF) based optical-fiber sensor for distributed curvature measurement through quasi-single-mode Brillouin frequency shift (BFS). By central-alignment splicing FMF and single-mode fiber (SMF) with a fusion taper, a SMF-components-compatible distributed curvature sensor based on FMF is realized using the conventional Brillouin optical time-domain analysis system. The distributed BFS change induced by bending in FMF has been theoretically and experimentally investigated. The precise BFS response to the curvature along the fiber link has been calibrated. A proof-of-concept experiment is implemented to validate its effectiveness in distributed curvature measurement. PMID:27192275
Lee, Byoung Wan; Ryeom, Junho; Ko, Jae-Hyeon; Kim, Dong Wook; Park, Chan Hum; Park, Jaehoon; Ko, Young Ho; Kim, Kwang Joo
2016-07-01
The elastic properties of a biocompatible silk film were investigated under temperature and pressure variations by using Brillouin spectroscopy. The Brillouin frequency shift decreased monotonically upon heating and showed a sudden change at the glass transition temperature. The existence of water molecules in the film increased the longitudinal modulus by approximately 10% and induced a relaxation peak in the hypersonic damping at ~60 ◦ C. The pressure dependences of the sound velocities of the longitudinal and the transverse acoustic modes and the refractive index were determined for the first time at pressures up to ~15.5 GPa. All these properties increased upon compression; these changes indicated that the free volume in the silk film collapsed at a pressure of about 3 GPa.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
Woolgar, Eric; Wylie, William
2016-02-01
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Berger, R.L.; Kaiser, T.B.; Lasinski, B.F. [and others
1996-06-01
Using the three-dimensional code (F3D), the authors compute the filamentation and backscattering of laser light. The results show that filamentation can be controlled and stimulated Brillouin backscattering (SBBS) can be reduced by using random phase plates (RPP) and small f-numbers or smoothing by spectral dispersion (SSD) with large bandwidth. An interesting result is that, for uniform plasmas, the SBBS amplification takes place over several laser axial coherence lengths (coherence length = speckle length).
Directory of Open Access Journals (Sweden)
Xingjun Lv
2011-11-01
Full Text Available In this paper, a novel kind of method to monitor corrosion expansion of steel rebars in steel reinforced concrete structures named fiber optic coil winding method is proposed, discussed and tested. It is based on the fiber optical Brillouin sensing technique. Firstly, a strain calibration experiment is designed and conducted to obtain the strain coefficient of single mode fiber optics. Results have shown that there is a good linear relationship between Brillouin frequency and applied strain. Then, three kinds of novel fiber optical Brillouin corrosion expansion sensors with different fiber optic coil winding packaging schemes are designed. Sensors were embedded into concrete specimens to monitor expansion strain caused by steel rebar corrosion, and their performance was studied in a designed electrochemical corrosion acceleration experiment. Experimental results have shown that expansion strain along the fiber optic coil winding area can be detected and measured by the three kinds of sensors with different measurement range during development the corrosion. With the assumption of uniform corrosion, diameters of corrosion steel rebars were obtained using calculated average strains. A maximum expansion strain of 6,738 με was monitored. Furthermore, the uniform corrosion analysis model was established and the evaluation formula to evaluate mass loss rate of steel rebar under a given corrosion rust expansion rate was derived. The research has shown that three kinds of Brillouin sensors can be used to monitor the steel rebar corrosion expansion of reinforced concrete structures with good sensitivity, accuracy and monitoring range, and can be applied to monitor different levels of corrosion. By means of this kind of monitoring technique, quantitative corrosion expansion monitoring can be carried out, with the virtues of long durability, real-time monitoring and quasi-distribution monitoring.
International Nuclear Information System (INIS)
In this paper, the stimulated Brillouin scattering (SBS) and the backward stimulated Raman scattering (BSRS) excited by a focused Gaussian laser in liquid water with different attenuation coefficients are investigated experimentally. Experimental results indicate that the relationships between SBS and BSRS are not merely competitive; the former has an obvious amplifying effect on the latter. Also, two different physical mechanisms were discussed in order to explain these phenomena
Stimulated Brillouin scattering during electron gyro-harmonic heating at EISCAT
Fu, H. Y.; Scales, W. A.; Bernhardt, P. A.; S. J. Briczinski; Kosch, M. J.; Senior, A.; Rietveld, M. T.; Yeoman, T. K.; J. M. Ruohoniemi
2015-01-01
Published version. Source at http://doi.org/10.5194/angeo-33-983-2015. Observations of secondary radiation, stimulated electromagnetic emission (SEE), produced during ionospheric modification experiments using ground-based, high-power, high-frequency (HF) radio waves are considered. The High Frequency Active Auroral Research Program (HAARP) facility is capable of generating narrowband SEE in the form of stimulated Brillouin scatter (SBS) and stimulated ion Bernstein scatter (SIBS) in the S...
Local analysis of stimulated Brillouin interaction in installed fiber optics cables
Nikles, M.; Thévenaz, Luc; Salina, P.; Robert, P. A.
1996-01-01
Brillouin gain spectrum measurement along an optical fiber has recently gained a lot of interests owing to its potentiality for strain monitoring in installed telecom cables. The purpose of the paper is to show that this potentiality is now effective, since field measurements of installed fiber optics cables currently in operation are demonstrated. A portable instrument has been developed, based on an original experimental configuration developed in our Institute which is briefly described
Xiao, Yongchuan; Guo, Jing; Wu, Kui; Qu, Pengfei; Qi, Huajuan; Liu, Caixia; Ruan, Shengping; Chen, Weiyou; Dong, Wei
2013-02-11
A single passband microwave photonic filter with ultrawide tunable range based on stimulated Brillouin scattering is theoretically analyzed. Combining the gain and loss spectrums, tuning range with 44GHz is obtained without crosstalk by introducing two pumps. Adding more pumps, Tuning range multiplying with the multiplication factor equaling to the total quantity of pump can be achieved, which has potential application in microwave and millimeter wave wireless communication systems.
Casas-Bedoya, Alvaro; Morrison, Blair; Pagani, Mattia; Marpaung, David; Eggleton, Benjamin J.
2015-09-01
We demonstrate the first functional signal processing device based on stimulated Brillouin scattering in a silicon nanowire. We use only 1 dB of on-chip SBS 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.
Xiao, Yongchuan; Guo, Jing; Wu, Kui; Qu, Pengfei; Qi, Huajuan; Liu, Caixia; Ruan, Shengping; Chen, Weiyou; Dong, Wei
2013-02-11
A single passband microwave photonic filter with ultrawide tunable range based on stimulated Brillouin scattering is theoretically analyzed. Combining the gain and loss spectrums, tuning range with 44GHz is obtained without crosstalk by introducing two pumps. Adding more pumps, Tuning range multiplying with the multiplication factor equaling to the total quantity of pump can be achieved, which has potential application in microwave and millimeter wave wireless communication systems. PMID:23481728
Wide-range wavevector selectivity of magnon gases in Brillouin light scattering spectroscopy
Sandweg, C. W.; Jungfleisch, M. B.; Vasyuchka, V I; Serga, A. A.; Clausen, P.; Schultheiss, H.; Hillebrands, B.; Kreisel, A.(University of Colorado, 80309, Boulder, Colorado, USA); Kopietz, P.
2010-01-01
Brillouin light scattering spectroscopy is a powerful technique for the study of fast magnetization dynamics with both frequency- and wavevector resolution. Here, we report on a distinct improvement of this spectroscopic technique towards two-dimensional wide-range wavevector selectivity in a backward scattering geometry. Spin-wave wavevectors oriented perpendicular to the bias magnetic field are investigated by tilting the sample within the magnet gap. Wavevectors which are oriented parallel...
Breakdown of the Brillouin limit and classical fluxes in rotating collisional plasmas
Energy Technology Data Exchange (ETDEWEB)
Rax, J. M., E-mail: jean-marcel.rax@polytechnique.edu [Université de Paris XI and LOA, ENSTA–Ecole Polytechnique, 91128 Palaiseau (France); Fruchtman, A. [HIT, Holon Institute of Technology, 52 Golomb St., Holon 58102 (Israel); Gueroult, R.; Fisch, N. J. [PPPL, Princeton University, Princeton, New Jersey 08540 (United States)
2015-09-15
The classical collisionless analysis displaying the occurrence of slow and fast rigid body rotation modes in magnetized plasmas is extended to collisional discharges. Collisions speed up the fast mode, slow down the slow one, and break down the classical Brillouin limit. Rigid body rotation has a strong impact on transport, and a collisional radial transport regime, different from the classical Braginskii collisional flux, is identified and analyzed.
Casas-Bedoya, Alvaro; Pagani, Mattia; Marpaung, David; Eggleton, Benjamin J
2015-01-01
We demonstrate the first functional signal processing device based on stimulated Brillouin scattering in a silicon nanowire. We use only 1 dB of on-chip SBS 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.
Shi, Jinwei; Chen, Xudong; Ouyang, Min; Liu, Juan; Liu, Dahe
2009-06-10
A polarization-controlling device was developed based on the fact that there can be a time delay between the seeder and the pumping beams during the amplification of a stimulated Brillouin scattering signal. The device causes two coaxially transmitted pulsed beams with orthogonal polarizations to have the same polarization in order to implement amplification by the pumping effect. An experiment showed that good pumping amplification can be achieved by using this technique. PMID:19516374
Institute of Scientific and Technical Information of China (English)
范洪义
2002-01-01
We study the Wentzel-Kramers-Brillouin (WKB) approximation for dynamic systems with kinetic couplings inentangled state representations. The result shows that the kinetic coupling will affect the position of classicalturning points where the condition of using the WKB approximation breaks down. The modified WKB approx-imation formula is derived in the entangled state representation, for example, the common eigenvector of therelative coordinate and the total momentum of two particles. The corresponding Bohr-Sommerfeld quantizationrule is also derived.
Besner, Sebastien; Shao, Peng; Scarcelli, Giuliano; Pineda, Roberto; Yun, Seok-Hyun (Andy)
2016-03-01
Keratoconus is a degenerative disorder of the eye characterized by human cornea thinning and morphological change to a more conical shape. Current diagnosis of this disease relies on topographic imaging of the cornea. Early and differential diagnosis is difficult. In keratoconus, mechanical properties are found to be compromised. A clinically available invasive technique capable of measuring the mechanical properties of the cornea is of significant importance for understanding the mechanism of keratoconus development and improve detection and intervention in keratoconus. The capability of Brillouin imaging to detect local longitudinal modulus in human cornea has been demonstrated previously. We report our non-contact, non-invasive, clinically viable Brillouin imaging system engineered to evaluate mechanical properties human cornea in vivo. The system takes advantage of a highly dispersive 2-stage virtually imaged phased array (VIPA) to detect weak Brillouin scattering signal from biological samples. With a 1.5-mW light beam from a 780-nm single-wavelength laser source, the system is able to detect Brillouin frequency shift of a single point in human cornea less than 0.3 second, at a 5μm/30μm lateral/axial resolution. Sensitivity of the system was quantified to be ~ 10 MHz. A-scans at different sample locations on a human cornea with a motorized human interface. We imaged both normal and keratoconic human corneas with this system. Whereas no significantly difference were observed outside keratocnic cones compared with normal cornea, a highly statistically significantly decrease was found in the cone regions.
Single-crystal Brillouin spectroscopy with CO{sub 2} laser heating and variable q
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jin S.; Bass, Jay D. [Department of Geology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States); Zhu, Gaohua [Materials Research Department, Toyota Research Institute of North America, Ann Arbor, Michigan 48105 (United States)
2015-06-15
We describe a Brillouin spectroscopy system integrated with CO{sub 2} laser-heating and Raman spectroscopic capabilities. Temperature is determined by measurements of the grey-body thermal radiation emitted by the hot sample, with the system response calibrated relative to a standard tungsten ribbon lamp. High-pressure laser-heating Brillouin scattering measurements of acoustic velocities on liquid water and ice compressed in a diamond-anvil cell were performed at temperatures up to 2500 ± 150 K at high pressure. Single-crystal laser-heating Brillouin measurements were made on the (111) plane of San Carlos olivine at ∼13 GPa, 1300 ± 200 K. The pressure as measured by ruby fluorescence is shown to be within ±0.5 GPa of the pressure on the olivine sample during laser heating when KCl and KBr are used as pressure-transmitting media. In addition, the system is designed for continuously variable scattering angles from forward scattering (near 0° scattering angle) up to near back scattering (∼141°). This novel setup allows us to probe a wide range of wave vectors q for investigation of phonon dispersion on, for example, crystals with large unit cells (on the scale of hundreds of nm)
Influence of laser linewidth on performance of Brillouin optical time domain reflectometry
Institute of Scientific and Technical Information of China (English)
Hao Yun-Qi; Ye Qing; Pan Zheng-Qing; Cai Hai-Wen; Qu Rong-Hui
2013-01-01
The effects of optical sources with different laser linewidths on Brillouin optical time domain reflectometry (BOTDR) are investigated numerically and experimentally.Simulation results show that the spectral linewidth of spontaneous Brillouin scattering remains almost constant when the laser linewidth is less than 1 MHz at the same pulse width; otherwise,it increases sharply.A comparison between a fiber laser (FL) with 4-kHz linewidth at 3 dB and a distributed feedback (DFB) laser with 3-MHz linewidth is made experimentally.When a constant laser power is launched into the sensing fiber,the fitting linewidths of the beat signals (backscattered Brillouin light and local oscillator (LO)) is about 5 MHz wider for the DFB laser than for the FL and the intensity of the beat signal is about a half.Furthermore,the frequency fluctuation in the long sensing fiber is lower for the FL source,yielding about 2 MHz less than that of the DFB laser,indicating higher temperature/strain resolution.The experimental results are in good agreement with the numerical simulations.
Equidistance difference optimum method to enhance measuring space of Brillouin optical fiber sensor
He, Jianping; Zhou, Zhi; Ou, Jinping
2013-09-01
Brillouin optic time-domain analysis/reflectometry (BOTDA/R) is a fully distributed optical sensing technique that can provide strain or temperature information along the whole length of a single-mode fiber and has attracted worldwide attentions in recent years. However, both spatial and distance resolution of BOTDA/R are too low to satisfy the measurement of local damage, and enhancing the performance of spatial or distance resolution is considered to be a problem. A novel equidistance difference optimum method is proposed to compensate for the weak spatial and distance resolution of BOTDA/R. The principle of the proposed method is introduced, and two demonstration tests are carried out to validate the local damage detection ability. The experimental results show that the Brillouin optical fiber sensor measuring space can cover any part of the sensor without changing the default values of the Brillouin system, which can greatly enrich the information of measured elements and detect the local damages well.
Single-crystal Brillouin spectroscopy with CO2 laser heating and variable q
Zhang, Jin S.; Bass, Jay D.; Zhu, Gaohua
2015-06-01
We describe a Brillouin spectroscopy system integrated with CO2 laser-heating and Raman spectroscopic capabilities. Temperature is determined by measurements of the grey-body thermal radiation emitted by the hot sample, with the system response calibrated relative to a standard tungsten ribbon lamp. High-pressure laser-heating Brillouin scattering measurements of acoustic velocities on liquid water and ice compressed in a diamond-anvil cell were performed at temperatures up to 2500 ± 150 K at high pressure. Single-crystal laser-heating Brillouin measurements were made on the (111) plane of San Carlos olivine at ˜13 GPa, 1300 ± 200 K. The pressure as measured by ruby fluorescence is shown to be within ±0.5 GPa of the pressure on the olivine sample during laser heating when KCl and KBr are used as pressure-transmitting media. In addition, the system is designed for continuously variable scattering angles from forward scattering (near 0° scattering angle) up to near back scattering (˜141°). This novel setup allows us to probe a wide range of wave vectors q for investigation of phonon dispersion on, for example, crystals with large unit cells (on the scale of hundreds of nm).
Brillouin optical time-domain analysis sensor with pump pulse amplification.
Mompó, Juan José; Urricelqui, Javier; Loayssa, Alayn
2016-06-13
We demonstrate a simple technique to provide conventional Brillouin optical time-domain analysis sensors with mitigation for pump pulse attenuation. The technique is based on operating the sensor in loss configuration so that energy is transferred from the probe wave to the pump pulse that becomes amplified as it counter-propagates with the probe wave. Furthermore, the optical frequency of the probe wave is modulated along the fiber so that the pump pulse experiences a flat total gain spectrum that equally amplifies all the spectral components of the pulse, hence, preventing distortion. This frequency modulation of the probe brings additional advantages because it provides increased tolerance to non-local effects and to spontaneous Brillouin scattering noise, so that a probe power above the Brillouin threshold of the fiber can be safely deployed, hence, increasing the signal-to-noise ratio of the measurement. The method is experimentally demonstrated in a 100-km fiber link, obtaining a measurement uncertainty of 1 MHz at the worst-contrast position. PMID:27410288
Stevens, Lewis L.; Orler, E. Bruce; Dattelbaum, Dana M.; Ahart, Muhtar; Hemley, Russell J.
2007-09-01
The acoustic properties of three polymer elastomers, a cross-linked poly(dimethylsiloxane) (Sylgard® 184), a cross-linked terpolymer poly(ethylene-vinyl acetate-vinyl alcohol), and a segmented thermoplastic poly(ester urethane) copolymer (Estane® 5703), have been measured from ambient pressure to approximately 12GPa by using Brillouin scattering in high-pressure diamond anvil cells. The Brillouin-scattering technique is a powerful tool for aiding in the determination of equations of state for a variety of materials, but to date has not been applied to polymers at pressures exceeding a few kilobars. For the three elastomers, both transverse and longitudinal acoustic modes were observed, though the transverse modes were observed only at elevated pressures (>0.7GPa) in all cases. From the Brillouin frequency shifts, longitudinal and transverse sound speeds were calculated, as were the C11 and C12 elastic constants, bulk, shear, and Young's moduli, and Poisson's ratios, and their respective pressure dependencies. P-V isotherms were then constructed, and fit to several empirical/semiempirical equations of state to extract the isothermal bulk modulus and its pressure derivative for each material. Finally, the lack of shear waves observed for any polymer at ambient pressure, and the pressure dependency of their appearance is discussed with regard to instrumental and material considerations.
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.
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...
On the inversion of Fueter's theorem
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2016-10-01
The well known Fueter theorem allows to construct quaternionic regular functions or monogenic functions with values in a Clifford algebra defined on open sets of Euclidean space R n + 1, starting from a holomorphic function in one complex variable or, more in general, from a slice hyperholomorphic function. Recently, the inversion of this theorem has been obtained for odd values of the dimension n. The present work extends the result to all dimensions n by using the Fourier multiplier method. More precisely, we show that for any axially monogenic function f defined in a suitable open set in R n + 1, where n is a positive integer, we can find a slice hyperholomorphic function f → such that f =Δ (n - 1) / 2 f →. Both the even and the odd dimensions are treated with the same, viz., the Fourier multiplier, method. For the odd dimensional cases the result obtained by the Fourier multiplier method coincides with the existing result obtained through the pointwise differential method.
Randomized central limit theorems: A unified theory
Eliazar, Iddo; Klafter, Joseph
2010-08-01
The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles’ aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles’ extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic—scaling all ensemble components by a common deterministic scale. However, there are “random environment” settings in which the underlying scaling schemes are stochastic—scaling the ensemble components by different random scales. Examples of such settings include Holtsmark’s law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)—in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes—and present “randomized counterparts” to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.
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.
Generalized theorems for nonlinear state space reconstruction.
Directory of Open Access Journals (Sweden)
Ethan R Deyle
Full Text Available Takens' theorem (1981 shows how lagged variables of a single time series can be used as proxy variables to reconstruct an attractor for an underlying dynamic process. State space reconstruction (SSR from single time series has been a powerful approach for the analysis of the complex, non-linear systems that appear ubiquitous in the natural and human world. The main shortcoming of these methods is the phenomenological nature of attractor reconstructions. Moreover, applied studies show that these single time series reconstructions can often be improved ad hoc by including multiple dynamically coupled time series in the reconstructions, to provide a more mechanistic model. Here we provide three analytical proofs that add to the growing literature to generalize Takens' work and that demonstrate how multiple time series can be used in attractor reconstructions. These expanded results (Takens' theorem is a special case apply to a wide variety of natural systems having parallel time series observations for variables believed to be related to the same dynamic manifold. The potential information leverage provided by multiple embeddings created from different combinations of variables (and their lags can pave the way for new applied techniques to exploit the time-limited, but parallel observations of natural systems, such as coupled ecological systems, geophysical systems, and financial systems. This paper aims to justify and help open this potential growth area for SSR applications in the natural sciences.
Generalizations of Karp's theorem to elastic scattering theory
Tuong, Ha-Duong
Karp's theorem states that if the far field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle in R2 is invariant under the group of rotations, then the scatterer is a circle. The theorem is generalized to the elastic scattering problems and the axisymmetric scatterers in R3.
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.
Linear Strategy for Boolean Ring Based Theorem Proving
Institute of Scientific and Technical Information of China (English)
WU Jinzhao; LIU Zhuojun
2000-01-01
Two inference rules are discussed in boolean ring based theorem proving, and linear strategy is developed. It is shown that both of them are complete for linear strategy. Moreover, by introducing a partial ordering on atoms, pseudo O-linear and O-linear strategies are presented. The former is complete, the latter, however, is complete for clausal theorem proving.
The Non-countable Summation Type Hahn-Schur Theorems
Institute of Scientific and Technical Information of China (English)
LUETong-fu; HUJian-hua; CHOMin-hyung
2005-01-01
The classical countable summation type Hahn-Schur theorem is a famous result in summation theory and measure theory. An interesting problem is whether the theorem can be generalized to non-countable summation case? In this paper, we show that the answer is true.
The Structure Theorem for Complete Intersections of Grade 4
Institute of Scientific and Technical Information of China (English)
Oh-Jin Kang; Hyoung J. Ko
2005-01-01
Serre showed that a Gorenstein ideal of grade 2 is a complete intersection, and Buchsbaum and Eisenbud proved a structure theorem for Gorenstein ideals of grade 3. It is found that a certain complete matrix defines a perfect ideal K3(f).As an application,we present a structure theorem for complete intersections of grade 4.
Fixed Point Theorems in Quaternion-Valued Metric Spaces
Directory of Open Access Journals (Sweden)
Ahmed El-Sayed Ahmed
2014-01-01
Full Text Available 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.
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.
Leaning on Socrates to Derive the Pythagorean Theorem
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the formula b2 +…
A note on the weighted Khintchine-Groshev Theorem
DEFF Research Database (Denmark)
Hussain, Mumtaz; Yusupova, Tatiana
Let W(m,n;ψ−−) denote the set of ψ1,…,ψn-approximable points in Rmn. The classical Khintchine-Groshev theorem assumes a monotonicity condition on the approximating functions ψ−−. Removing monotonicity from the Khintchine-Groshev theorem is attributed to different authors for different cases of m...
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.)
On Euler's Theorem for Homogeneous Functions and Proofs Thereof.
Tykodi, R. J.
1982-01-01
Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)
N(o)ther-type theorem of piecewise algebraic curves
Institute of Scientific and Technical Information of China (English)
WANG Renhong; ZHU Chungang
2004-01-01
The piecewise algebraic curve is a generalization of the classical algebraic curve.This paper describes the improvement of the Nother-type theorem of piecewise algebraic curves on the star region.Moreover,the Nother-type theorem of piecewise algebraic curves on the cross-cut partition is discussed.
Virial theorem in quasi-coordinates and Lie algebroid formalism
Cariñena, José F.; Irina GHEORGHIU; Martínez, Eduardo; Santos, Patrícia
2014-01-01
In this paper, the geometric approach to the virial theorem developed in \\cite{CFR12} is written in terms of quasi-velocities (see \\cite{CNCS07}). A generalization of the virial theorem for mechanical systems on Lie algebroids is also given, using the geometric tools of Lagrangian and Hamiltonian mechanics on the prolongation of the Lie algebroid.
Mann Iteration of Weak Convergence Theorems in Banach Space
Institute of Scientific and Technical Information of China (English)
Liang-gen Hu; Jin-ping Wang
2009-01-01
In this paper, by using Mann's iteration process we will establish several weak convergence theorems for approximating a fixed point of κ-strictly pseudocontractive mappings with respect to p in p-uniformly convex Banach spaces. Our results answer partially the open question proposed by Marino and Xu, and extend Reich's theorem from nonexpausive mappings to κ-strict pseudocontractive mappings.
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 note on the homomorphism theorem for hemirings
Directory of Open Access Journals (Sweden)
D. M. Olson
1978-01-01
Full Text Available The fundamental homomorphism theorem for rings is not generally applicable in hemiring theory. In this paper, we show that for the class of N-homomorphism of hemirings the fundamental theorem is valid. In addition, the concept of N-homomorphism is used to prove that every hereditarily semisubtractive hemiring is of type (K.
A central limit theorem for a new statistic on permutations
Chatterjee, Sourav; Diaconis, Persi
2016-01-01
This paper does three things: It proves a central limit theorem for a novel permutation statistic, the number of descents plus the number of descents in the inverse. It provides a clear illustration of a new approach to proving central limit theorems more generally. It gives us an opportunity to acknowledge the work of our teacher and friend B. V. Rao.
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
Some fixed point theorems for Hardy-Rogers type mappings
Directory of Open Access Journals (Sweden)
B. E. Rhoades
1984-01-01
Full Text Available The first result establishes a fixed point theorem for three maps of a complete metric space. The contractive definition is a generalization of that of Hardy and Rogers, and the commuting condition of Jungck is replaced by the concept of weakly commuting. The other results are extensions of some theorems of Kannan.
An ideal topology type convergent theorem on scale effect algebras
Institute of Scientific and Technical Information of China (English)
WU JunDe; ZHOU XuanChang; Minhyung CHO
2007-01-01
The famous Antosik-Mikusinski convergent theorem on the Abel topological groups has very extensive applications in measure theory, summation theory and other analysis fields. In this paper, we establish the theorem on a class of effect algebras equipped with the ideal topology. This paper shows also that the ideal topology of effect algebras is a useful topology in studying the quantum logic theory.
THE KILLING FORMS AND DECOMPOSITION THEOREMS OF LIE SUPERTRIPLE SYSTEMS
Institute of Scientific and Technical Information of China (English)
Zhang Zhixue; Jia Peipei
2009-01-01
In this article, the Killing form of a Lie supertriple system (LSTS) and that of its imbedding Lie superalgebra (LSA) are investigated, and a unique decomposition theorem for a quasiclassical LSTS with trivial center is established by means of the parallel decomposition theorem for a quasiclassical LSA.
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.
Generalization of Bombieri’s theorem and its applications
Institute of Scientific and Technical Information of China (English)
林家发; 展涛
1995-01-01
By using the so-called Hooley-Huxley Contour and zero density estimates for Dirichlet L-function, Bombieri’s theorem is established for a class of arithmetic functions whose generating functions satisfy certain analytic conditions. As applications of our theorem, the mean value estimates of L-functions and the distribution of integers representable as sums of two squares are discussed.
The virial theorem for the Polarizable Continuum Model.
Cammi, R
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential. PMID:24588153
The virial theorem for the polarizable continuum model
Energy Technology Data Exchange (ETDEWEB)
Cammi, R., E-mail: roberto.cammi@unipr.it [Dipartimento di Chimica, Università di Parma, Parco Area delle Scienze 17/A, I-43100 Parma (Italy)
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.
The virial theorem for the Polarizable Continuum Model.
Cammi, R
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.