Schroedinger operators with Rudin-Shapiro potentials are not palindromic
International Nuclear Information System (INIS)
Allouche, J.
1997-01-01
We prove a conjecture of A. Hof, O. Knill and B. Simon [Commun. Math. Phys. 174, 149 endash 159 (1995)] by showing that the Rudin-Shapiro sequence is not palindromic, i.e., does not contain arbitrarily long palindromes. We prove actually this property for all paperfolding sequences and all Rudin-Shapiro sequences deduced from paperfolding sequences. As a consequence and as guessed by the above authors, their method cannot be used for establishing that discrete Schroedinger operators with Rudin-Shapiro potentials have a purely singular continuous spectrum. copyright 1997 American Institute of Physics
The Symmetric Rudin-Shapiro Transform
DEFF Research Database (Denmark)
Harbo, Anders La-Cour
2003-01-01
A method for constructing spread spectrum sequences is presented. The method is based on a linear, orthogonal, symmetric transform, the Rudin-Shapiro transform (RST), which is in many respects quite similar to the Haar wavelet packet transform. The RST provides the means for generating large sets...... of spread spectrum signals. This presentation provides a simple definition of the symmetric RST that leads to a fast N log(N) and numerically stable implementation of the transform....
The Symmetric Rudin-Shapiro Transform
DEFF Research Database (Denmark)
Harbo, Anders La-Cour
2003-01-01
A method for constructing spread spectrum sequences is presented. The method is based on a linear, orthogonal, and symmetric transform given as the Rudin-Shapiro transform (RST), which is in many respects quite similar to the Haar wavelet packet transform. The RST provides the means for generatin...... large sets of spread spectrum signals. This presentation provides a simple definition of the symmetric RST that leads to a fast N log(N) and numerically stable implementation of the transform....
Gómez-Urrea, H. A.; Escorcia-García, J.; Duque, C. A.; Mora-Ramos, M. E.
2017-11-01
The transmittance spectrum of a one-dimensional hybrid photonic crystal built from the suitable arrangement of periodic and quasiregular Rudin-Shapiro heterolayers that include superconducting slabs is investigated. The four-layer Rudin-Shapiro structure is designed with three lossless dielectric layers and a low-temperature superconductor one. The dielectric function of the superconducting layer is modeled by the two-fluid Gorter-Casimir theory, and the transmittance is calculated with the use of the transfer matrix method. The obtained results reveal the presence of a cut-off frequency fc - a forbidden frequency band for propagation - that can be manipulated by changing the width of the superconducting layer, the temperature and the order of the Rudin-Shapiro sequence. In addition, the spatial distribution of the electric field amplitude for the propagating TM modes is also discussed. It is found that the maximum of localized electric field relative intensity - which reaches a value of several tens - corresponds to the frequency values above to the cut-off frequency, at which, the effective dielectric function of the hybrid unit cell becomes zero. The proposed structure could be another possible system for optical device design for temperature-dependent optical devices such as stop-band filters, or as bolometers.
Rudin-Osher-Fatemi Total Variation Denoising using Split Bregman
Directory of Open Access Journals (Sweden)
Pascal Getreuer
2012-05-01
Full Text Available Denoising is the problem of removing noise from an image. The most commonly studied case is with additive white Gaussian noise (AWGN, where the observed noisy image f is related to the underlying true image u by f=u+η and η is at each point in space independently and identically distributed as a zero-mean Gaussian random variable. Total variation (TV regularization is a technique that was originally developed for AWGN image denoising by Rudin, Osher, and Fatemi. The TV regularization technique has since been applied to a multitude of other imaging problems, see for example Chan and Shen's book. We focus here on the split Bregman algorithm of Goldstein and Osher for TV-regularized denoising.
Moller, Karla J.
2016-01-01
For the author's final Master Teacher article, she wishes to pay tribute to a scholar whose work in the field of children's literature has inspired her for years. Throughout her long and distinguished career, Rudine Sims Bishop, professor emerita from The Ohio State University, has shared extensive knowledge and numerous insights on issues related…
Gómez-Urrea, H. A.; Duque, C. A.; Mora-Ramos, M. E.
2015-11-01
The properties of the optical-phonon-associated polaritonic modes that appear under oblique light incidence in 1D superlattices made of photonic materials are studied. The investigated systems result from the periodic repetition of quasiregular Rudin-Shapiro (RS) multilayer units. It is assume that the structure consists of both passive non-dispersive layers of constant refraction index and active layers of uniaxial polar materials. In particular, we consider III-V wurtzite nitrides. The optical axis of these polaritonic materials is taken along the growth direction. Maxwell equations are solved using the transfer matrix technique for all admissible values of the incidence angle.
Virial theorem and hypervirial theorem in a spherical geometry
International Nuclear Information System (INIS)
Li Yan; Chen Jingling; Zhang Fulin
2011-01-01
The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)
The Non-Signalling theorem in generalizations of Bell's theorem
Walleczek, J.; Grössing, G.
2014-04-01
Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational
International Nuclear Information System (INIS)
Ma Zhongqi
2006-01-01
The Levinson theorem is a fundamental theorem in quantum scattering theory, which shows the relation between the number of bound states and the phase shift at zero momentum for the Schroedinger equation. The Levinson theorem was established and developed mainly with the Jost function, with the Green function and with the Sturm-Liouville theorem. In this review, we compare three methods of proof, study the conditions of the potential for the Levinson theorem and generalize it to the Dirac equation. The method with the Sturm-Liouville theorem is explained in some detail. References to development and application of the Levinson theorem are introduced. (topical review)
The Fluctuation Theorem and Dissipation Theorem for Poiseuille Flow
International Nuclear Information System (INIS)
Brookes, Sarah J; Reid, James C; Evans, Denis J; Searles, Debra J
2011-01-01
The fluctuation theorem and the dissipation theorem provide relationships to describe nonequilibrium systems arbitrarily far from, or close to equilibrium. They both rely on definition of a central property, the dissipation function. In this manuscript we apply these theorems to examine a boundary thermostatted system undergoing Poiseuille flow. The relationships are verified computationally and show that the dissipation theorem is potentially useful for study of boundary thermostatted systems consisting of complex molecules undergoing flow in the nonlinear regime.
Czech Academy of Sciences Publication Activity Database
Wang, Weizhou; Hobza, Pavel
2008-01-01
Roč. 73, 6/7 (2008), s. 862-872 ISSN 0010-0765 R&D Projects: GA MŠk LC512; GA AV ČR IAA400550510 Institutional research plan: CEZ:AV0Z40550506 Keywords : Berlin's theorem * H-bonding * Blue -shifting H-bonding Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 0.784, year: 2008
Flatto, Leopold
2009-01-01
Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. The theorem is of great depth in that it relates to a large and diverse body of mathematics. There are several proofs of the theorem, none of which is elementary. A particularly attractive feature of the theorem, which is easily understood but difficult to prove, is that it serves as a prism through which one can learn and appreciate a lot of beautiful mathematics. This book stresses the modern appro
The Non-Signalling theorem in generalizations of Bell's theorem
International Nuclear Information System (INIS)
Walleczek, J; Grössing, G
2014-01-01
Does 'epistemic non-signalling' ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the
Atmospheric Chemistry of (CF3)2CF-C≡N
DEFF Research Database (Denmark)
Andersen, Mads Peter Sulbæk; Kyte, Mildrid; Thirstrup Andersen, Simone
2017-01-01
FTIR/smog chamber experiments and ab initio quantum calculations were performed to investigate the atmospheric chemistry of (CF3)2CFCN, a proposed replacement compound for the industrially important sulfur hexafluoride, SF6. The present study determined k(Cl + (CF3)2CFCN) = (2.33 ± 0.87) × 10–17, k......(OH + (CF3)2CFCN) = (1.45 ± 0.25) × 10–15, and k(O3 + (CF3)2CFCN) ≤ 6 × 10–24 cm3 molecule–1 s–1, respectively, in 700 Torr of N2 or air diluent at 296 ± 2 K. The main atmospheric sink for (CF3)2CFCN was determined to be reaction with OH radicals. Quantum chemistry calculations, supported by experimental...
Fermat's Last Theorem A Theorem at Last!
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 1. Fermat's Last Theorem A Theorem at Last! C S Yogananda. General Article Volume 1 Issue 1 January 1996 pp 71-79. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/001/01/0071-0079 ...
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
Complex proofs of real theorems
Lax, Peter D
2011-01-01
Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, "The shortest and best way between two truths of the real domain often passes through the imaginary one." Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Müntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Żelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime ...
Energy Technology Data Exchange (ETDEWEB)
Escane, J.M. [Ecole Superieure d' Electricite, 91 - Gif-sur-Yvette (France)
2005-04-01
The first part of this article defines the different elements of an electrical network and the models to represent them. Each model involves the current and the voltage as a function of time. Models involving time functions are simple but their use is not always easy. The Laplace transformation leads to a more convenient form where the variable is no more directly the time. This transformation leads also to the notion of transfer function which is the object of the second part. The third part aims at defining the fundamental operation rules of linear networks, commonly named 'general theorems': linearity principle and superimposition theorem, duality principle, Thevenin theorem, Norton theorem, Millman theorem, triangle-star and star-triangle transformations. These theorems allow to study complex power networks and to simplify the calculations. They are based on hypotheses, the first one is that all networks considered in this article are linear. (J.S.)
Levinson, N
1940-01-01
A typical gap theorem of the type discussed in the book deals with a set of exponential functions { \\{e^{{{i\\lambda}_n} x}\\} } on an interval of the real line and explores the conditions under which this set generates the entire L_2 space on this interval. A typical gap theorem deals with functions f on the real line such that many Fourier coefficients of f vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various propertie
Díaz-de-Mera, Yolanda; Aranda, Alfonso; Bravo, Iván; Rodríguez, Diana; Rodríguez, Ana; Moreno, Elena
2008-10-01
The adverse environmental impacts of chlorinated hydrocarbons on the Earth's ozone layer have focused attention on the effort to replace these compounds by nonchlorinated substitutes with environmental acceptability. Hydrofluoroethers (HFEs) and fluorinated alcohols are currently being introduced in many applications for this purpose. Nevertheless, the presence of a great number of C-F bonds drives to atmospheric long-lived compounds with infrared absorption features. Thus, it is necessary to improve our knowledge about lifetimes and global warming potentials (GWP) for these compounds in order to get a complete evaluation of their environmental impact. Tropospheric degradation is expected to be initiated mainly by OH reactions in the gas phase. Nevertheless, Cl atoms reaction may also be important since rate constants are generally larger than those of OH. In the present work, we report the results obtained in the study of the reactions of Cl radicals with HFE-7000 (CF(3)CF(2)CF(2)OCH(3)) (1) and its isomer CF(3)CF(2)CF(2)CH(2)OH (2). Kinetic rate coefficients with Cl atoms have been measured using the discharge flow tube-mass spectrometric technique at 1 Torr of total pressure. The reactions of these chlorofluorocarbons (CFCs) substitutes have been studied under pseudo-first-order kinetic conditions in excess of the fluorinated compounds over Cl atoms. The temperature ranges were 266-333 and 298-353 K for reactions of HFE-7000 and CF(3)CF(2)CF(2)CH(2)OH, respectively. The measured room temperature rate constants were k(Cl+CF(3)CF(2)CF(2)OCH(3)) = (1.24 +/- 0.28) x 10(-13) cm(3) molecule(-1) s(-1)and k(Cl+CF(3)CF(2)CF(2)CH(2)OH) = (8.35 +/- 1.63) x 10(-13) cm(3) molecule(-1) s(-1) (errors are 2sigma + 10% to cover systematic errors). The Arrhenius expression for reaction 1 was k (1)(266-333 K) = (6.1 +/- 3.8) x 10(-13)exp[-(445 +/- 186)/T] cm(3) molecule(-1) s(-1) and k (2)(298-353 K) = (1.9 +/- 0.7) x 10(-12)exp[-(244 +/- 125)/T] cm(3) molecule(-1) s(-1) (errors
The quantitative Morse theorem
Loi, Ta Le; Phien, Phan
2013-01-01
In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \\cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse function theorem and the quantitative Morse lemma.
Two-quasineutron states in 98248Cf and 98250Cf and the neutron-neutron residual interactions
International Nuclear Information System (INIS)
Katori, K.; Ahmad, I.; Friedman, A. M.
2008-01-01
Two-quasineutron states in 248 Cf and 250 Cf were investigated by single-neutron transfer reactions, 249 Cf(d,t) 248 Cf and 249 Cf(d,p) 250 Cf. The majority of levels observed were assigned to 12 bands in 248 Cf and six bands in 250 Cf, constructed from the single-particle states in neighboring Cf nuclei. The effective two-body interactions between two odd neutrons coupled outside a deformed core were deduced from the differences in the energies of the bandheads formed by the parallel and antiparallel coupling of the intrinsic spins of the two single-particle states
Atmospheric chemistry of (CF3)2CHOCH3, (CF3)2CHOCHO, and CF3C(O)OCH3
DEFF Research Database (Denmark)
Østerstrøm, Freja From; Wallington, Timothy J.; Andersen, Mads Peter Sulbæk
2015-01-01
Smog chambers with in situ FTIR detection were used to measure rate coefficients in 700 Torr of air and 296 ± 2 K of: k(Cl+(CF3)2CHOCH3) = (5.41 ± 1.63) × 10(-12), k(Cl+(CF3)2CHOCHO) = (9.44 ± 1.81) × 10(-15), k(Cl+CF3C(O)OCH3) = (6.28 ± 0.98) × 10(-14), k(OH+(CF3)2CHOCH3) = (1.86 ± 0.41) × 10(-1...
Bertrand's theorem and virial theorem in fractional classical mechanics
Yu, Rui-Yan; Wang, Towe
2017-09-01
Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.
Smorynski, Craig
2017-01-01
This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mat...
... Accommodations for College Scholarships and Financial Aid 10 Things I Wish I Knew Before Coming to College CF and College: The Secret to Getting it All Done View All Managing My CF in College Resources ...
Generalized Dandelin’s Theorem
Kheyfets, A. L.
2017-11-01
The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.
Factor and Remainder Theorems: An Appreciation
Weiss, Michael
2016-01-01
The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…
Photoionisation study of Xe.CF{sub 4} and Kr.CF{sub 4} van-der-Waals molecules
Energy Technology Data Exchange (ETDEWEB)
Alekseev, V. A., E-mail: alekseev@va3474.spb.edu; Kevorkyants, R. [St. Petersburg State University, 7/9 Universitetskaya Nab., St. Petersburg 199034 (Russian Federation); Garcia, G. A.; Nahon, L. [Synchrotron Soleil, Orme des Merisiers, St. Aubin BP 48, 91192 Gif sur Yvette Cedex (France)
2016-05-14
We report on photoionization studies of Xe.CF{sub 4} and Kr.CF{sub 4} van-der-Waals complexes produced in a supersonic expansion and detected using synchrotron radiation and photoelectron-photoion coincidence techniques. The ionization potential of CF{sub 4} is larger than those of the Xe and Kr atoms and the ground state of the Rg.CF{sub 4}{sup +} ion correlates with Rg{sup +} ({sup 2}P{sub 3/2}) + CF{sub 4}. The onset of the Rg.CF{sub 4}{sup +} signals was found to be only ∼0.2 eV below the Rg ionization potential. In agreement with experiment, complementary ab initio calculations show that vertical transitions originating from the potential minimum of the ground state of Rg.CF{sub 4} terminate at a part of the potential energy surfaces of Rg.CF{sub 4}{sup +}, which are approximately 0.05 eV below the Rg{sup +} ({sup 2}P{sub 3/2}) + CF{sub 4} dissociation limit. In contrast to the neutral complexes, which are most stable in the face geometry, for the Rg.CF{sub 4}{sup +} ions, the calculations show that the minimum of the potential energy surface is in the vertex geometry. Experiments which have been performed only with Xe.CF{sub 4} revealed no Xe.CF{sub 4}{sup +} signal above the first ionization threshold of Xe, suggesting that the Rg.CF{sub 4}{sup +} ions are not stable above the first dissociation limit.
The Patchwork Divergence Theorem
Dray, Tevian; Hellaby, Charles
1994-01-01
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting "patchwork divergence theorem" which is independent of the metric signature in either region, and which is thus valid if the signature changes. (PA...
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.
On Krasnoselskii's Cone Fixed Point Theorem
Directory of Open Access Journals (Sweden)
Man Kam Kwong
2008-04-01
Full Text Available In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.
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.
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.
Guo, Qin; Zhang, Ni; Uchimaru, Tadafumi; Chen, Liang; Quan, Hengdao; Mizukado, Junji
2018-04-01
The rate constants for the gas-phase reactions of cyc-CF2CF2CF2CH=CH- with OH radicals were determined by a relative rate method between 253 and 328 K. The rate constant k1 at 298 K was measured to be (1.08 ± 0.04) × 10-13 cm3 molecule-1 s-1, and the Arrhenius expression was k1 = (3.72 ± 0.14) × 10-13 exp [(-370 ± 12)/T]. The atmospheric lifetime of cyc-CF2CF2CF2CH=CH- was calculated to be 107 d. The products and mechanism for the reaction of cyc-CF2CF2CF2CH=CH- with OH radicals were also investigated. CO, CO2, and COF2 were identified as the main carbon-containing products following the OH-initiated reaction. Moreover, the radiative efficiency (RE) was determined to be 0.143 W m-2 ppb-1, and the global warming potentials (GWPs) for 20, 100, and 500 yr were 54, 15, and 4, respectively. The photochemical ozone creation potential of the title compound was estimated to be 1.3.
Ortiz, Guillermo P.; Mochán, W. Luis
2018-02-01
Keller’s theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assumption that the response function relates an irrotational to a solenoidal field and that is valid for dispersive and dissipative anisotropic systems. We show that the usual statement of Keller’s theorem in terms of the conductivity is strictly valid only at zero frequency and we obtain a new generalization for finite frequencies. We develop applications of the theorem to the study of the optical properties of systems such as superlattices, 2D isotropic and anisotropic metamaterials and random media, to test the accuracy of theories and computational schemes, and to increase the accuracy of approximate calculations.
A Decomposition Theorem for Finite Automata.
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
The Classical Version of Stokes' Theorem Revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2005-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we prove that the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...
Avni, A; Avital, S; Gromet-Elhanan, Z
1991-04-25
Incubation of tobacco and lettuce thylakoids with 2 M LiCl in the presence of MgATP removes the beta subunit from their CF1-ATPase (CF1 beta) together with varying amounts of the CF1 alpha subunit (CF1 alpha). These 2 M LiCl extracts, as with the one obtained from spinach thylakoids (Avital, S., and Gromet-Elhanan, Z. (1991) J. Biol. Chem. 266, 7067-7072), could form active hybrid ATPases when reconstituted into inactive beta-less Rhodospirillum rubrum chromatophores. Pure CF1 beta fractions that have been isolated from these extracts could not form such active hybrids by themselves, but could do so when supplemented with trace amounts (less than 5%) of CF1 alpha. A mitochondrial F1-ATPase alpha subunit was recently reported to be a heat-shock protein, having two amino acid sequences that show a highly conserved identity with sequences found in molecular chaperones (Luis, A. M., Alconada, A., and Cuezva, J. M. (1990) J. Biol. Chem. 265, 7713-7716). These sequences are also conserved in CF1 alpha isolated from various plants, but not in F1 beta subunits. The above described reactivation of CF1 beta by trace amounts of CF1 alpha could thus be due to a chaperonin-like function of CF1 alpha, which involves the correct, active folding of isolated pure CF1 beta.
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.
Nonextensive Pythagoras' Theorem
Dukkipati, Ambedkar
2006-01-01
Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And hence, this property is referred to as Pythagoras' theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches of statistical estimation theory like information geometry. Equvalent of Pythagoras' theo...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose K is a compact set in the complex plane and 0 belongs to the boundary ∂K. Let A(K) denote the space of all functions f on K such that f is holo- morphic in a neighborhood of K and f(0) = 0. Also for any given positive integer ...
Enhancement of discharge performance of Li/CF x cell by thermal treatment of CF x cathode material
Zhang, Sheng S.; Foster, Donald; Read, Jeffrey
In this work we demonstrate that the thermal treatment of CF x cathode material just below the decomposition temperature can enhance discharge performance of Li/CF x cells. The performance enhancement becomes more effective when heating a mixture of CF x and citric acid (CA) since CA serves as an extra carbon source. Discharge experiments show that the thermal treatment not only reduces initial voltage delay, but also raises discharge voltage. Whereas the measurement of powder impedance indicates the thermal treatment does not increase electronic conductivity of CF x material. Based on these facts, we propose that the thermal treatment results in a limited decomposition of CF x, which yields a subfluorinated carbon (CF x- δ), instead of a highly conductive carbon. In the case of CF x/AC mixture, the AC provides extra carbon that reacts with F 2 and fluorocarbon radicals generated by the thermal decomposition of CF x to form subfluorinated carbon. The process of thermal treatment is studied by thermogravimetric analysis and X-ray diffraction, and the effect of treatment conditions such as heating temperature, heating time and CF x/CA ratio on the discharge performance of CF x cathode is discussed. As an example, a Li/CF x cell using CF x treated with CA at 500 °C under nitrogen for 2 h achieved theretical specific capacity when being discharged at C/5. Impedance analysis indicates that the enhanced performance is attributed to a significant reduction in the cell reaction resistance.
Pascal’s Theorem in Real Projective Plane
Coghetto Roland
2017-01-01
In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines.
Kinetics and mechanisms of reactions of CF, CHF, and CF2 radicals
International Nuclear Information System (INIS)
Hsu, D.S.Y.; Umstead, M.E.; Lin, M.C.
1978-01-01
This chapter reviews briefly methods for the production of CF, CHF and CF 2 , and inmore detail, the reactions of these interesting and important radicals. Although a considerable, but not extensive, amount of work has been done on the reactions of CF 2 , little of the chemistry of CF and CHF is known. This chapter also includes the preliminary results of some experiments carried out in this Laboratory on the dynamics of some of the reactions involving these radicals. These results were largely arrived at through investigations of the degree of vibrational excitation of the HF and CO reaction products, determined by HF and CO laser emission and CO laser resonance absorption measurements. The coverage of this review is restricted to the gas phase chemistry of these radicals, and does not include their addition reactions to olefins
Pascal’s Theorem in Real Projective Plane
Directory of Open Access Journals (Sweden)
Coghetto Roland
2017-07-01
Full Text Available In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem1. Pappus’ theorem is a special case of a degenerate conic of two lines.
From Einstein's theorem to Bell's theorem: a history of quantum non-locality
Wiseman, H. M.
2006-04-01
In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.
Topological interpretation of Luttinger theorem
Seki, Kazuhiro; Yunoki, Seiji
2017-01-01
Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because i) the Luttinger volume is represented as the winding number of the single-particle Green's function and thus ii) the deviation of the theorem, expressed with a ratio between the interacting and n...
A note on generalized Weyl's theorem
Zguitti, H.
2006-04-01
We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.
Directory of Open Access Journals (Sweden)
Coghetto Roland
2015-06-01
Full Text Available Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].
Riemannian and Lorentzian flow-cut theorems
Headrick, Matthew; Hubeny, Veronika E.
2018-05-01
We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.
An extended characterisation theorem for quantum logics
International Nuclear Information System (INIS)
Sharma, C.S.; Mukherjee, M.K.
1977-01-01
Two theorems are proved. In the first properties of an important mapping from an orthocomplemented lattice to itself are studied. In the second the characterisation theorem of Zierler (Pacific J. Math.; 11:1151 (1961)) is extended to obtain a very useful theorem characterising orthomodular lattices. Since quantum logics are merely sigma-complete orthomodular lattices, the principal result is, for application in quantum physics, a characterisation theorem for quantum logics. (author)
The Levy sections theorem revisited
International Nuclear Information System (INIS)
Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Silva, Sergio Da
2007-01-01
This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets
The Levy sections theorem revisited
Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Da Silva, Sergio
2007-06-01
This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.
DEFF Research Database (Denmark)
Törnquist, Asger Dag; Weiss, W.
2009-01-01
We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible.......We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible....
Green's theorem and Gorenstein sequences
Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su
2016-01-01
We study consequences, for a standard graded algebra, of extremal behavior in Green's Hyperplane Restriction Theorem. First, we extend his Theorem 4 from the case of a plane curve to the case of a hypersurface in a linear space. Second, assuming a certain Lefschetz condition, we give a connection to extremal behavior in Macaulay's theorem. We apply these results to show that $(1,19,17,19,1)$ is not a Gorenstein sequence, and as a result we classify the sequences of the form $(1,a,a-2,a,1)$ th...
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
DEFF Research Database (Denmark)
Andersen, Mads Peter Sulbæk; Hurley, MD; Ball, JC
2003-01-01
The synthesis, IR spectrum, and first-principles characterization of CF3CH(ONO)CF3 as well as its use as an OH radical source in kinetic and mechanistic studies are reported. CF3CH(ONO)CF3 exists in two conformers corresponding to rotation about the RCO-NO bond. The more prevalent trans conformer......C(O)CF3 and, by implication, OH radicals in 100% yield. CF3CH(ONO)CF3 photolysis is a convenient source of OH radicals in the studies of the yields of CO, CO2, HCHO, and HC(O)OH products which can be difficult to measure using more conventional OH radical sources (e.g., CH3ONO photolysis). CF3CH...
The de Finetti theorem for test spaces
International Nuclear Information System (INIS)
Barrett, Jonathan; Leifer, Matthew
2009-01-01
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
-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.
Commentaries on Hilbert's Basis Theorem | Apine | Science World ...
African Journals Online (AJOL)
The famous basis theorem of David Hilbert is an important theorem in commutative algebra. In particular the Hilbert's basis theorem is the most important source of Noetherian rings which are by far the most important class of rings in commutative algebra. In this paper we have used Hilbert's theorem to examine their unique ...
A density Corradi-Hajnal theorem
Czech Academy of Sciences Publication Activity Database
Allen, P.; Böttcher, J.; Hladký, Jan; Piguet, D.
2015-01-01
Roč. 67, č. 4 (2015), s. 721-758 ISSN 0008-414X Institutional support: RVO:67985840 Keywords : extremal graph theory * Mantel's theorem * Corradi-Hajnal theorem Subject RIV: BA - General Mathematics Impact factor: 0.618, year: 2015 http://cms.math.ca/10.4153/CJM-2014-030-6
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.
Coalgebraic Lindström Theorems
Kurz, A.; Venema, Y.
2010-01-01
We study modal Lindström theorems from a coalgebraic perspective. We provide three different Lindström theorems for coalgebraic logic, one of which is a direct generalisation of de Rijke's result for Kripke models. Both the other two results are based on the properties of bisimulation invariance,
Equivalent conserved currents and generalized Noether's theorem
International Nuclear Information System (INIS)
Gordon, T.J.
1984-01-01
A generalized Noether theorem is presented, relating symmetries and equivalence classes of local) conservation laws in classical field theories; this is contrasted with the standard theorem. The concept of a ''Noether'' field theory is introduced, being a theory for which the generalized theorem applies; not only does this include the cases of Lagrangian and Hamiltonian field theories, these structures are ''derived'' from the Noether property in a natural way. The generalized theorem applies to currents and symmetries that contain derivatives of the fields up to an arbitrarily high order
Strong versions of Bell's theorem
International Nuclear Information System (INIS)
Stapp, H.P.
1994-01-01
Technical aspects of a recently constructed strong version of Bell's theorem are discussed. The theorem assumes neither hidden variables nor factorization, and neither determinism nor counterfactual definiteness. It deals directly with logical connections. Hence its relationship with modal logic needs to be described. It is shown that the proof can be embedded in an orthodox modal logic, and hence its compatibility with modal logic assured, but that this embedding weakens the theorem by introducing as added assumptions the conventionalities of the particular modal logic that is adopted. This weakening is avoided in the recent proof by using directly the set-theoretic conditions entailed by the locality assumption
Absolute rate constants for the reaction of CF3O2 and CF3O radicals with NO at 295 K
DEFF Research Database (Denmark)
Sehested, J.; Nielsen, O.J.
1993-01-01
Using a pulse radiolysis UV absorption technique and subsequent simulations of experimental NO2 and FNO absorption transients, rate constants for reaction between CF3O and CF3O2 radicals with NO were determined, CF3O2+NO-->CF3O+NO2 (3), CF3O+NO-->CF2O+FNO (5). k3 was derived to be (1.68+/-0.26)x10...
Scandinavian Nurse Specialist Group/Cystic Fibrosis (SNSG/CF)
DEFF Research Database (Denmark)
Bregnballe, Vibeke; Erwander, Inger
2006-01-01
/CF comprises one CF nurse from each of the centers. The board meets twice a year to plan workshops and courses. SNSG/CF is part of the International Nurse Specialist Group/Cystic Fibrosis (INSG/CF). Results: Within the framework of SNSG/CF a 2-day workshop is held every second year for approximately 40...
DEFF Research Database (Denmark)
Hurley, MD; Ball, JC; Wallington, TJ
2004-01-01
Smog chamber/FTIR techniques were used to study the products and mechanism of the Cl atom initiated oxidation of 4:2 fluorotelomer alcohol (CF3(CF2)(3)CH2CH2OH) in 700 Torr of N-2/O-2 diluent at 296 K. CF3(CF2)(3)CH2CHO is the sole primary oxidation product. CF3(CF2)(3)CHO, CF3(CF2)(3)CH2COOH...... respectively. Using relative rate techniques, a value of k(Cl + CF3(CF2)(3)CH2CHO) = (1.84 +/- 0.30) x 10(-11) cm(3) molecule(-1) s(-1) was determined. The yield of the perfluorinated acid, CF3(CF2)(3)COOH, from the 4:2 fluorotelomer alcohol increased with the diluent gas oxygen concentration......, and CF3(CF2)(3)CH2C(O)OOH are secondary oxidation products. Further irradiation results in the formation of CF3(CF2)(3)COOH, COF2, and CF3OH. CF3(CF2)(3)CHO, CF3(CF2)(3)CH2COOH, and CF3(CF2)(3)CH2C(O)OOH are formed from CF3(CF2)(3)CH2CHO oxidation in yields of 46 27 and less than or equal to 27...
Geometry of the Adiabatic Theorem
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
A definability theorem for first order logic
Butz, C.; Moerdijk, I.
1997-01-01
In this paper we will present a definability theorem for first order logic This theorem is very easy to state and its proof only uses elementary tools To explain the theorem let us first observe that if M is a model of a theory T in a language L then clearly any definable subset S M ie a subset S
Borghi, Riccardo
2014-03-01
In the present letter, Newton’s theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton’s Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.
Does the central limit theorem always apply to phase noise? Some implications for radar problems
Gray, John E.; Addison, Stephen R.
2017-05-01
The phase noise problem or Rayleigh problem occurs in all aspects of radar. It is an effect that a radar engineer or physicist always has to take into account as part of a design or in attempt to characterize the physics of a problem such as reverberation. Normally, the mathematical difficulties of phase noise characterization are avoided by assuming the phase noise probability distribution function (PDF) is uniformly distributed, and the Central Limit Theorem (CLT) is invoked to argue that the superposition of relatively few random components obey the CLT and hence the superposition can be treated as a normal distribution. By formalizing the characterization of phase noise (see Gray and Alouani) for an individual random variable, the summation of identically distributed random variables is the product of multiple characteristic functions (CF). The product of the CFs for phase noise has a CF that can be analyzed to understand the limitations CLT when applied to phase noise. We mirror Kolmogorov's original proof as discussed in Papoulis to show the CLT can break down for receivers that gather limited amounts of data as well as the circumstances under which it can fail for certain phase noise distributions. We then discuss the consequences of this for matched filter design as well the implications for some physics problems.
Illustrating the Central Limit Theorem through Microsoft Excel Simulations
Moen, David H.; Powell, John E.
2005-01-01
Using Microsoft Excel, several interactive, computerized learning modules are developed to demonstrate the Central Limit Theorem. These modules are used in the classroom to enhance the comprehension of this theorem. The Central Limit Theorem is a very important theorem in statistics, and yet because it is not intuitively obvious, statistics…
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...
No-go theorems for the minimization of potentials
International Nuclear Information System (INIS)
Chang, D.; Kumar, A.
1985-01-01
Using a theorem in linear algebra, we prove some no-go theorems in the minimization of potentials related to the problem of symmetry breaking. Some applications in the grand unified model building are mentioned. Another application of the algebraic theorem is also included to demonstrate its usefulness
Energy Technology Data Exchange (ETDEWEB)
Stepanov, Sergey
2010-04-26
Tunable Diode Laser Absorption Spectroscopy in the mid InfraRed spectral range (IR-TDLAS) has been applied to investigate the behaviour of CF, CF{sub 2} and C{sub 2}F{sub 4} species produced in pulsed CF{sub 4}/H{sub 2} capacitively coupled radio frequency plasmas (13.56 MHz CCP). This experimental technique was shown to be suitable for temporally resolved measurements of the absolute number density of the target molecules in the studied fluorocarbon discharges. The temporal resolution of about 20..40 ms typically achieved in the standard data acquisition mode (''stream mode'') was sufficient for the real-time measurements of CF{sub 2} and C{sub 2}F{sub 4}, but not of CF whose kinetics was observed to be much faster. Therefore, a more sophisticated approach (''burst mode'') providing a temporal resolution of 0.94 ms was established and successfully applied to CF density measurements. In order to enable the TDLAS measurements of the target species, preliminary investigations on their spectroscopic data had been carried out. In particular, pure C{sub 2}F{sub 4} has been produced in laboratory by means of vacuum thermal decomposition (pyrolysis) of polytetrafluoroethylene and used as a reference gas. Therefore, an absorption structure consisting of several overlapping C{sub 2}F{sub 4} lines around 1337.11 cm{sup -1} was selected and carefully calibrated, which provided the first absolute measurements of the species by means of the applied experimental technique. The absolute number density traces measured for CF, CF{sub 2} and C{sub 2}F{sub 4} in the studied pulsed plasmas were then analysed, in which two differential balance equations were proposed for each of the species to describe their behaviour during both ''plasma on'' and ''plasma off'' phases. Analytical solutions of the balance equations were used to fit the experimental data and hence to deduce important information on the
Energy Technology Data Exchange (ETDEWEB)
Stepanov, Sergey
2010-04-26
Tunable Diode Laser Absorption Spectroscopy in the mid InfraRed spectral range (IR-TDLAS) has been applied to investigate the behaviour of CF, CF{sub 2} and C{sub 2}F{sub 4} species produced in pulsed CF{sub 4}/H{sub 2} capacitively coupled radio frequency plasmas (13.56 MHz CCP). This experimental technique was shown to be suitable for temporally resolved measurements of the absolute number density of the target molecules in the studied fluorocarbon discharges. The temporal resolution of about 20..40 ms typically achieved in the standard data acquisition mode (''stream mode'') was sufficient for the real-time measurements of CF{sub 2} and C{sub 2}F{sub 4}, but not of CF whose kinetics was observed to be much faster. Therefore, a more sophisticated approach (''burst mode'') providing a temporal resolution of 0.94 ms was established and successfully applied to CF density measurements. In order to enable the TDLAS measurements of the target species, preliminary investigations on their spectroscopic data had been carried out. In particular, pure C{sub 2}F{sub 4} has been produced in laboratory by means of vacuum thermal decomposition (pyrolysis) of polytetrafluoroethylene and used as a reference gas. Therefore, an absorption structure consisting of several overlapping C{sub 2}F{sub 4} lines around 1337.11 cm{sup -1} was selected and carefully calibrated, which provided the first absolute measurements of the species by means of the applied experimental technique. The absolute number density traces measured for CF, CF{sub 2} and C{sub 2}F{sub 4} in the studied pulsed plasmas were then analysed, in which two differential balance equations were proposed for each of the species to describe their behaviour during both ''plasma on'' and ''plasma off'' phases. Analytical solutions of the balance equations were used to fit the experimental data and hence to deduce important information on the kinetics of the studied molecules. In particular, during the ''plasma off'' phase
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.
The matrix Euler-Fermat theorem
International Nuclear Information System (INIS)
Arnol'd, Vladimir I
2004-01-01
We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem
Directory of Open Access Journals (Sweden)
D. Hassell
2017-12-01
Full Text Available The CF (Climate and Forecast metadata conventions are designed to promote the creation, processing, and sharing of climate and forecasting data using Network Common Data Form (netCDF files and libraries. The CF conventions provide a description of the physical meaning of data and of their spatial and temporal properties, but they depend on the netCDF file encoding which can currently only be fully understood and interpreted by someone familiar with the rules and relationships specified in the conventions documentation. To aid in development of CF-compliant software and to capture with a minimal set of elements all of the information contained in the CF conventions, we propose a formal data model for CF which is independent of netCDF and describes all possible CF-compliant data. Because such data will often be analysed and visualised using software based on other data models, we compare our CF data model with the ISO 19123 coverage model, the Open Geospatial Consortium CF netCDF standard, and the Unidata Common Data Model. To demonstrate that this CF data model can in fact be implemented, we present cf-python, a Python software library that conforms to the model and can manipulate any CF-compliant dataset.
A Converse to the Cayley-Hamilton Theorem
Indian Academy of Sciences (India)
follows that qj = api, where a is a unit. Thus, we must have that the expansion of I into irreducibles is unique. Hence, K[x] is a UFD. A famous theorem of Gauss implies that K[XI' X2,. ,xn] is also an UFD. Gauss's Theorem: R[x] is a UFD, if and only if R is a UFD. For a proof of Gauss's theorem and a detailed proof of the fact that ...
Converse Barrier Certificate Theorem
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer
2013-01-01
This paper presents a converse barrier certificate theorem for a generic dynamical system.We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold. Other authors have developed a related result, by assuming that the dynamical system has no singular...... points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work...
Stacked spheres and lower bound theorem
Indian Academy of Sciences (India)
BASUDEB DATTA
2011-11-20
Nov 20, 2011 ... Preliminaries. Lower bound theorem. On going work. Definitions. An n-simplex is a convex hull of n + 1 affinely independent points. (called vertices) in some Euclidean space R. N . Stacked spheres and lower bound theorem. Basudeb Datta. Indian Institute of Science. 2 / 27 ...
Dimensional analysis beyond the Pi theorem
Zohuri, Bahman
2017-01-01
Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First ...
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...
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...
Theorems of Tarski's Undefinability and Godel's Second Incompleteness - Computationally
Salehi, Saeed
2015-01-01
We present a version of Godel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions (first discussed by M. Detlefsen 2001). We also argue that Tarski's theorem on the Undefinability of Truth is Godel's First Incompleteness Theorem relativized to definable oracles; here a unification of these two theorems is given.
Engelbrecht, Siegfried; Lill, H; Junge, Wolfgang
1986-01-01
Chloroplast ATPase (CF1) was isolated from spinach, pea and maize thylakoids by EDTA extraction followed by anion-exchange chromatography. CF1 was purified and resolved by HPLC into integral CF1, and CF1 lacking the delta & epsilon subunits: CF1(-delta) and CF1(-epsilon). Washing Mono-Q-bound CF1
Generalized Optical Theorem Detection in Random and Complex Media
Tu, Jing
The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar
Other trigonometric proofs of Pythagoras theorem
Luzia, Nuno
2015-01-01
Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \\cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing, geometrically, the half-angle formula $\\cos\\theta=1-2\\sin^2 \\frac{\\theta}{2}$.
The Pomeranchuk theorem and its modifications
International Nuclear Information System (INIS)
Fischer, J.; Saly, R.
1980-01-01
A review of the various modifications and improvements of the Pomeranchuk theorem and also of related statements is given. The present status of the Pomeranchuk relation based on dispersion relation is discussed. Numerous problems related to the Pomeranchuk theorem and some answers to these problems are collected in a clear table
Adiabatic theorem and spectral concentration
International Nuclear Information System (INIS)
Nenciu, G.
1981-01-01
The spectral concentration of arbitrary order, for the Stark effect is proved to exist for a large class of Hamiltonians appearing in nonrelativistic and relativistic quantum mechanics. The results are consequences of an abstract theorem about the spectral concentration for self-ad oint operators. A general form of the adiabatic theorem of quantum mechanics, generalizing an earlier result of the author as well as some results of Lenard, is also proved [ru
Nonperturbative Adler-Bardeen theorem
International Nuclear Information System (INIS)
Mastropietro, Vieri
2007-01-01
The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions
A general comparison theorem for backward stochastic differential equations
Cohen, Samuel N.; Elliott, Robert J.; Pearce, Charles E. M.
2010-01-01
A useful result when dealing with backward stochastic differential equations is the comparison theorem of Peng (1992). When the equations are not based on Brownian motion, the comparison theorem no longer holds in general. In this paper we present a condition for a comparison theorem to hold for backward stochastic differential equations based on arbitrary martingales. This theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectat...
Debattista, Josephine
2000-01-01
Pythagoras 580 BC was a Greek mathematician who became famous for formulating Pythagoras Theorem but its principles were known earlier. The ancient Egyptians wanted to layout square (90°) corners to their fields. To solve this problem about 2000 BC they discovered the 'magic' of the 3-4-5 triangle.
On Comparison Theorems for Conformable Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Mehmet Zeki Sarikaya
2016-10-01
Full Text Available In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm's separation and Sturm's comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented to verify the proposed theorem.
The classical version of Stokes' Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we show how the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together with a 'fattening' technique for surfaces and the inverse function theorem....
Howell, Russell W.; Schrohe, Elmar
2017-01-01
Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…
Search strategy for theorem proving in artificial systems. I
Energy Technology Data Exchange (ETDEWEB)
Lovitskii, V A; Barenboim, M S
1981-01-01
A strategy is contrived, employing the language of finite-order predicate calculus, for finding proofs of theorems. A theorem is formulated, based on 2 known theorems on purity and absorption, and used to determine 5 properties of a set of propositions. 3 references.
Decomposition of Potent Greenhouse Gases SF6, CF4 and SF5CF3 by Dielectric Barrier Discharge
International Nuclear Information System (INIS)
Zhang Renxi; Wang Jingting; Cao Xu; Hou Huiqi
2016-01-01
For their distinguished global warming potential (GWP100) and long atmosphere lifespan, CF 4 , SF 6 and SF 5 CF 3 were significant in the field of greenhouse gas research. The details of discharging character and the optimal parameter were discussed by using a Dielectric Barrier Discharge (DBD) reactor to decompose these potent greenhouse gases in this work. The results showed that SF 6 could be decomposed by 92% under the conditions of 5 min resident time and 3000 V applied voltage with the partial pressure of 2.0 kPa, 28.2 kPa, and 1.8 kPa for SF 6 , air and water vapor, respectively. 0.4 kPa CF 4 could be decomposed by 98.2% for 4 min resident time with 30 kPa Ar added. The decomposition of SF 5 CF 3 was much more effective than that of SF 6 and CF 4 and moreover, 1.3 kPa SF 5 CF 3 , discharged with 30 kPa O 2 , Ar and air, could not be detected when the resident time was 80 s, 40 s, and 120 s, respectively. All the results indicated that DBD was a feasible technique for the abatement of potent greenhouse gases. (paper)
Tight closure and vanishing theorems
International Nuclear Information System (INIS)
Smith, K.E.
2001-01-01
Tight closure has become a thriving branch of commutative algebra since it was first introduced by Mel Hochster and Craig Huneke in 1986. Over the past few years, it has become increasingly clear that tight closure has deep connections with complex algebraic geometry as well, especially with those areas of algebraic geometry where vanishing theorems play a starring role. The purpose of these lectures is to introduce tight closure and to explain some of these connections with algebraic geometry. Tight closure is basically a technique for harnessing the power of the Frobenius map. The use of the Frobenius map to prove theorems about complex algebraic varieties is a familiar technique in algebraic geometry, so it should perhaps come as no surprise that tight closure is applicable to algebraic geometry. On the other hand, it seems that so far we are only seeing the tip of a large and very beautiful iceberg in terms of tight closure's interpretation and applications to algebraic geometry. Interestingly, although tight closure is a 'characteristic p' tool, many of the problems where tight closure has proved useful have also yielded to analytic (L2) techniques. Despite some striking parallels, there had been no specific result directly linking tight closure and L∼ techniques. Recently, however, the equivalence of an ideal central to the theory of tight closure was shown to be equivalent to a certain 'multiplier ideal' first defined using L2 methods. Presumably, deeper connections will continue to emerge. There are two main types of problems for which tight closure has been helpful: in identifying nice structure and in establishing uniform behavior. The original algebraic applications of tight closure include, for example, a quick proof of the Hochster-Roberts theorem on the Cohen-Macaulayness of rings of invariants, and also a refined version of the Brianqon-Skoda theorem on the uniform behaviour of integral closures of powers of ideals. More recent, geometric
The Osgood-Schoenflies theorem revisited
International Nuclear Information System (INIS)
Siebenmann, L C
2005-01-01
The very first unknotting theorem of a purely topological character established that every compact subset of the Euclidean plane homeomorphic to a circle can be moved onto a round circle by a globally defined self-homeomorphism of the plane. This difficult hundred-year-old theorem is here celebrated with a partly new elementary proof, and a first but tentative account of its history. Some quite fundamental corollaries of the proof are sketched, and some generalizations are mentioned
Preservation theorems on finite structures
International Nuclear Information System (INIS)
Hebert, M.
1994-09-01
This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ''homomorphism into'' case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
2014-01-01
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
Some fixed point theorems in fuzzy reflexive Banach spaces
International Nuclear Information System (INIS)
Sadeqi, I.; Solaty kia, F.
2009-01-01
In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.
International Nuclear Information System (INIS)
Kim, Jung-Hyung; Shin, Yong-Hyeon; Chung, Kwang-Hwa; Yoo, Yong-Shim
2004-01-01
The behavior of the CF 2 radical was studied in a CF 4 inductively coupled plasma. The CF 2 radical was measured using a laser-induced fluorescence method. Absolute electron density was measured using a cutoff probe and the electron temperature was measured using a double probe to study the relationship between these electron properties and the CF 2 radical. To examine the relationship between them, the CF 2 radical and electron density were measured as a function of the rf power, which is a major external parameter influencing the electron density. As the rf power was increased, the CF 2 radical density increased in the range of low electron density, and then decreased beyond a critical electron density. The dependence of the CF 2 radical density on the electron density was theoretically analyzed with rate equations. The theoretical result was in good agreement with experiment
The Goldstone equivalence theorem and AdS/CFT
Energy Technology Data Exchange (ETDEWEB)
Anand, Nikhil; Cantrell, Sean [Department of Physics & Astronomy, Johns Hopkins University,Baltimore, MD 21218 (United States)
2015-08-03
The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the non-conserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields. We then go on to generalize the theorem using conformal blocks in two and four-dimensional CFTs. We show that when the scaling dimensions of the exchanged operators are large compared to both their spins and the dimension of the current, the conformal blocks satisfy an equivalence theorem.
Atmospheric chemistry of (CF3)2CFOCH3
DEFF Research Database (Denmark)
Andersen, Lene Løffler; Østerstrøm, Freja From; Nielsen, Ole John
2014-01-01
FTIR smog chamber techniques were used to measure k(Cl + (CF 3)2CFOCH3) = (1.80 ± 0.42) × 10-13, k(Cl + (CF3)2CFOCHO) = (1.47 ± 0.56) × 10-14, and k(OH + (CF3) 2CFOCH3) = (1.55 ± 0.24) × 10-14 cm3 molecule-1 s-1. The chlorine-atom initiated oxidation of (CF3)2CFOCH3 in air in the absence of NOX r...
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered...... we apply the key instrumental concepts and verify the various steps towards this alternative proof of the divergence theorem....
International Nuclear Information System (INIS)
Halliwell, J.J.
2014-01-01
Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH inequalities are well-known to be necessary conditions, but Fine's theorem is the striking result that they are also sufficient conditions. Here two transparent and self-contained proofs of Fine's theorem are presented. The first is a physically motivated proof using an explicit local hidden variables model. The second is an algebraic proof which uses a representation of the probabilities in terms of correlation functions. - Highlights: • A discussion of the various approaches to proving Fine's theorem. • A new physically-motivated proof using a local hidden variables model. • A new algebraic proof. • A new form of the CHSH inequalities
Hoorn, Van der R.A.L.; Roth, R.; Wit, De P.J.G.M.
2001-01-01
The tomato resistance genes Cf-4 and Cf-9 confer specific, hypersensitive response-associated recognition of Cladosporium carrying the avirulence genes Avr4 and Avr9, respectively. Cf-4 and Cf-9 encode type I transmembrane proteins with extracellular leucine-rich repeats (LRRs). Compared with Cf-9,
Radon-Nikodym type theorem for α-completely positive maps
International Nuclear Information System (INIS)
Heo, Jaeseong; Ji, Un Cig
2010-01-01
We introduce a new notion of α-completely positive map on a C*-algebra as a generalization of the notion of completely positive map. Then we study a theorem of the Radon-Nikodym type that there is a one-to-one correspondence between α-completely positive maps and positive operators and, as an application of the Radon-Nikodym type theorem, we give a characterization of pure α-completely positive maps. Finally, we study a covariant version of the Stinespring's theorem for a covariant α-completely positive map (see Theorem 4.3).
On Pythagoras Theorem for Products of Spectral Triples
D'Andrea, Francesco; Martinetti, Pierre
2013-01-01
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some un...
Pauli and The Spin-Statistics Theorem
International Nuclear Information System (INIS)
Duck, Ian; Sudarshan, E.C.G.
1998-03-01
This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties.Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that 'everyone knows the spin-statistics theorem, but no one understands it'. This book simplifies and clarifies the formal statements of the theorem, and also corrects the invariably flawed intuitive explanations which are frequently put forward. The book will be of interest to many practising physicists in all fields who have long been frustrated by the impenetrable discussions on the subject which have been available until now.It will also be accessible to students at an advanced undergraduate level as an introduction to modern physics based directly on the classical writings of the founders, including Pauli, Dirac, Heisenberg, Einstein and many others
Modeling of silicon etching in CF sub 4 /O sub 2 and CF sub 4 /H sub 2 plasmas
Energy Technology Data Exchange (ETDEWEB)
Trachtenberg, I.; Edgar, T.F. (Dept. of Chemical Engineering, Univ. of Texas at Austin, Austin, TX (US)); Venkatesan, S.P. (Morgantown Energy Technology Center, Morgantown, WV (US))
1990-07-01
A one-dimensional radial flow reactor model that includes fairly detailed free radical gas-phase chemistry has been developed for the etching of silicon in CF{sub 4}/O{sub 2} and CF{sub 4}/H{sub 2} plasmas. Attention has been restricted to transport and reaction of neutral species. The model equations were solved by orthogonal collocation. The sensitivities of the model predictions to flow rate, inlet gas composition, electron density, silicon loading, and other factors have been examined. The major loss path for fluorine atoms is different in CF{sub 4}/O{sub 2} and CF{sub 4}/H{sub 2} systems, and this results in significant qualitative differences in the parametric sensitivities of the two systems.
Saikia, Manjil P.
2013-01-01
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \\cite{thales}, \\cite{wiki} and \\cite{wiki2} for the historical comments and sources.
Indian Academy of Sciences (India)
eralizing the method of proof of the well known. Cantor's ... Godel's first incompleteness theorem is proved. ... that the number of elements in any finite set is a natural number. ..... proof also has a Godel number; of course, you have to fix.
Double soft theorem for perturbative gravity
Saha, Arnab
2016-01-01
Following up on the recent work of Cachazo, He and Yuan \\cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.
A Converse of Fermat's Little Theorem
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
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...
International Nuclear Information System (INIS)
Cahill, K.
1975-11-01
Local field theory is used to derive formulas that express certain boundary values of the N-point function as sums of products of scattering amplitudes. These formulas constitute a generalization of the optical theorem and facilitate the analysis of multiparticle scattering functions [fr
Houston, Louis M.
2012-01-01
Sign data are the signs of signal added to noise. It is well known that a constant signal can be recovered from sign data. In this paper, we show that an integral over variant signal can be recovered from an integral over sign data based on the variant signal. We refer to this as a generalized sign data average. We use this result to derive a Green's theorem for sign data. Green's theorem is important to various seismic processing methods, including seismic migration. Results in this paper ge...
A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
程立新; 腾岩梅
2003-01-01
This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.
Liouville's theorem and phase-space cooling
International Nuclear Information System (INIS)
Mills, R.L.; Sessler, A.M.
1993-01-01
A discussion is presented of Liouville's theorem and its consequences for conservative dynamical systems. A formal proof of Liouville's theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur
A primer on Higgs boson low-energy theorems
International Nuclear Information System (INIS)
Dawson, S.; Haber, H.E.; California Univ., Santa Cruz, CA
1989-05-01
We give a pedagogical review of Higgs boson low-energy theorems and their applications in the study of light Higgs boson interactions with mesons and baryons. In particular, it is shown how to combine the chiral Lagrangian method with the Higgs low-energy theorems to obtain predictions for the interaction of Higgs bosons and pseudoscalar mesons. Finally, we discuss the relation between the low-energy theorems and a technique which makes use of the trace of the QCD energy-momentum tensor. 35 refs
DISCRETE FIXED POINT THEOREMS AND THEIR APPLICATION TO NASH EQUILIBRIUM
Sato, Junichi; Kawasaki, Hidefumi
2007-01-01
Fixed point theorems are powerful tools in not only mathematics but also economic. In some economic problems, we need not real-valued but integer-valued equilibriums. However, classical fixed point theorems guarantee only real-valued equilibria. So we need discrete fixed point theorems in order to get discrete equilibria. In this paper, we first provide discrete fixed point theorems, next apply them to a non-cooperative game and prove the existence of a Nash equilibrium of pure strategies.
International Nuclear Information System (INIS)
Park, Mu-In
2008-01-01
Hawking's area theorem can be understood from a quasi-stationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual BTZ black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon 'can decrease', rather than increase, with the quasi-stationary process. However, I find that the area for the outer horizon 'never decreases' such that the usual area theorem still works in our examples, though this is quite non-trivial in general. There exists an instability problem of the inner horizons but it seems that the instability is not important in my analysis. I also find a generalized area theorem by combining those of the outer and inner horizons
Optimal no-go theorem on hidden-variable predictions of effect expectations
Blass, Andreas; Gurevich, Yuri
2018-03-01
No-go theorems prove that, under reasonable assumptions, classical hidden-variable theories cannot reproduce the predictions of quantum mechanics. Traditional no-go theorems proved that hidden-variable theories cannot predict correctly the values of observables. Recent expectation no-go theorems prove that hidden-variable theories cannot predict the expectations of observables. We prove the strongest expectation-focused no-go theorem to date. It is optimal in the sense that the natural weakenings of the assumptions and the natural strengthenings of the conclusion make the theorem fail. The literature on expectation no-go theorems strongly suggests that the expectation-focused approach is more general than the value-focused one. We establish that the expectation approach is not more general.
The Classical Version of Stokes' Theorem Revisited
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
The divergence theorem for unbounded vector fields
De Pauw, Thierry; Pfeffer, Washek F.
2007-01-01
In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector. elds that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is. nite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions.
... exocrine.html. UPCMD (1998 – 2002). Cystic Fibrosis. University Pathology Consortium, LLC [On-line information]. Available online at http://www.upcmd.com/dot/examples/00218/description.html. Sainato, D., (2002, March). Genetic Testing for CF Going Mainstream? Clinical Laboratory ...
Gleason-Busch theorem for sequential measurements
Flatt, Kieran; Barnett, Stephen M.; Croke, Sarah
2017-12-01
Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957), 10.1512/iumj.1957.6.56050]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003), 10.1103/PhysRevLett.91.120403], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.
The relativistic virial theorem
International Nuclear Information System (INIS)
Lucha, W.; Schoeberl, F.F.
1989-11-01
The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)
The large deviations theorem and ergodicity
International Nuclear Information System (INIS)
Gu Rongbao
2007-01-01
In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions
Dalen, D. van
The following pages make form a new chapter for the book Logic and Structure. This chapter deals with the incompleteness theorem, and contains enough basic material for the treatment of the required notions of computability, representability and the like. This chapter will appear in the next
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…
International Nuclear Information System (INIS)
Veltman, H.
1990-01-01
The equivalence theorem states that, at an energy E much larger than the vector-boson mass M, the leading order of the amplitude with longitudinally polarized vector bosons on mass shell is given by the amplitude in which these vector bosons are replaced by the corresponding Higgs ghosts. We prove the equivalence theorem and show its validity in every order in perturbation theory. We first derive the renormalized Ward identities by using the diagrammatic method. Only the Feynman-- 't Hooft gauge is discussed. The last step of the proof includes the power-counting method evaluated in the large-Higgs-boson-mass limit, needed to estimate the leading energy behavior of the amplitudes involved. We derive expressions for the amplitudes involving longitudinally polarized vector bosons for all orders in perturbation theory. The fermion mass has not been neglected and everything is evaluated in the region m f ∼M much-lt E much-lt m Higgs
Out-of-time-order fluctuation-dissipation theorem
Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito
2018-01-01
We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.
Scale symmetry and virial theorem
International Nuclear Information System (INIS)
Westenholz, C. von
1978-01-01
Scale symmetry (or dilatation invariance) is discussed in terms of Noether's Theorem expressed in terms of a symmetry group action on phase space endowed with a symplectic structure. The conventional conceptual approach expressing invariance of some Hamiltonian under scale transformations is re-expressed in alternate form by infinitesimal automorphisms of the given symplectic structure. That is, the vector field representing scale transformations leaves the symplectic structure invariant. In this model, the conserved quantity or constant of motion related to scale symmetry is the virial. It is shown that the conventional virial theorem can be derived within this framework
On Pythagoras Theorem for Products of Spectral Triples
D'Andrea, Francesco; Martinetti, Pierre
2013-05-01
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.
Convergence theorems for certain classes of nonlinear mappings
International Nuclear Information System (INIS)
Chidume, C.E.
1992-01-01
Recently, Xinlong Weng announced a convergence theorem for the iterative approximation of fixed points of local strictly pseudo-contractive mappings in uniformly smooth Banach spaces, (Proc. Amer. Math. Soc. Vol.113, No.3 (1991) 727-731). An example is presented which shows that this theorem of Weng is false. Then, a convergence theorem is proved, in certain real Banach spaces, for approximation a solution of the inclusion f is an element of x + Tx, where T is a set-valued monotone operator. An explicit error estimate is also presented. (author). 26 refs
Markov's theorem and algorithmically non-recognizable combinatorial manifolds
International Nuclear Information System (INIS)
Shtan'ko, M A
2004-01-01
We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem
A note on the weighted Khintchine-Groshev Theorem
DEFF Research Database (Denmark)
Hussain, Mumtaz; Yusupova, Tatiana
Let W(m,n;ψ−−) denote the set of ψ1,…,ψn-approximable points in Rmn. The classical Khintchine-Groshev theorem assumes a monotonicity condition on the approximating functions ψ−−. Removing monotonicity from the Khintchine-Groshev theorem is attributed to different authors for different cases of m...... and n. It can not be removed for m=n=1 as Duffin-Shcaeffer provided the counter example. We deal with the only remaining case m=2 and thereby remove all unnecessary conditions from the Khintchine-Groshev theorem....
Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle
Evans, Denis J.; Searles, Debra J.; Mittag, Emil
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
A Hohenberg-Kohn theorem for non-local potentials
International Nuclear Information System (INIS)
Meron, E.; Katriel, J.
1977-01-01
It is shown that within any class of commuting one-body potentials a Hohenberg-Kohn type theorem is satisfied with respect to an appropriately defined density. The Hohenberg-Kohn theorem for local potentials follows as a special case. (Auth.)
Non-renormalisation theorems in string theory
International Nuclear Information System (INIS)
Vanhove, P.
2007-10-01
In this thesis we describe various non renormalisation theorems for the string effective action. These results are derived in the context of the M theory conjecture allowing to connect the four gravitons string theory S matrix elements with that of eleven dimensional supergravity. These theorems imply that N = 8 supergravity theory has the same UV behaviour as the N = 4 supersymmetric Yang Mills theory at least up to three loops, and could be UV finite in four dimensions. (author)
Singularity theorems from weakened energy conditions
International Nuclear Information System (INIS)
Fewster, Christopher J; Galloway, Gregory J
2011-01-01
We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.
COMPARISON THEOREMS AND APPLICATIONS OF OSCILLATION OF NEUTRAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
燕居让
1991-01-01
We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equation is reduced to that of nonneutral delay differential equa-tion, from which we give a series of oscillation theorems for neutral delay differentialequation.
Integrable equations, addition theorems, and the Riemann-Schottky problem
International Nuclear Information System (INIS)
Buchstaber, Viktor M; Krichever, I M
2006-01-01
The classical Weierstrass theorem claims that, among the analytic functions, the only functions admitting an algebraic addition theorem are the elliptic functions and their degenerations. This survey is devoted to far-reaching generalizations of this result that are motivated by the theory of integrable systems. The authors discovered a strong form of the addition theorem for theta functions of Jacobian varieties, and this form led to new approaches to known problems in the geometry of Abelian varieties. It is shown that strong forms of addition theorems arise naturally in the theory of the so-called trilinear functional equations. Diverse aspects of the approaches suggested here are discussed, and some important open problems are formulated.
The Weinberg-Witten theorem on massless particles: an essay
International Nuclear Information System (INIS)
Loebbert, F.
2008-01-01
In this essay we deal with the Weinberg-Witten theorem which imposes limitations on massless particles. First we motivate a classification of massless particles given by the Poincare group as the symmetry group of Minkowski spacetime. We then use the fundamental structure of the background in the form of Poincare covariance to derive restrictions on charged massless particles known as the Weinberg-Witten theorem. We address possible misunderstandings in the proof of this theorem motivated by several papers on this topic. In the last section the consequences of the theorem are discussed. We treat it in the context of known particles and as a constraint for emergent theories. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
International Nuclear Information System (INIS)
Young, J.P.; Haire, R.G.; Peterson, J.R.; Ensor, D.D.; Fellows, R.L.
1980-01-01
Spectrophotometric and x-ray powder diffraction methods have been applied to a study of the ingrowth of californium-249 by β - decay of berkelium-249 in crystalline 249 BkBr 3 . It was found that the Cf daughter grows in with the same oxidation state and crystal structure as the parent. Thus, six-coordinate BkBr 3 (AlCl 3 -type monoclinic structure) generates six-coordinate CfBr 3 , and eight-coordinate BkBr 3 (PuBr 3 -type orthorhombic structure) generates eight-coordinate CfBr 3 , a previously unknown form of CfBr 3 . It was also found that the daughter Cf(III) in the BkBr 3 parent compound can be reduced to Cf(II) by treatment with H 2 , as it can in pure CfBr 3 . 5 figures
International Nuclear Information System (INIS)
Prochaska, F.T.; Andrews, L.
1978-01-01
The molecules CFBr 3 , CF 2 Br 2 , CF 3 Br, and C-13 enriched CF 3 Br have been subjected to matrix radiolysis and argon resonance photoionization during condensation with excess argon at 15 K. Infrared spectra showed stable and free radical products and new absorptions due to charged species. The molecular ion bands exhibited different behavior on filtered high-pressure mercury arc photolysis. Absorptions reduced by 220 to 1000-nm light are assigned to CFBr 2 + , CF 2 Br + , and CF 3 + ; other bands destroyed by photolysis are assigned to the parent cations. Li and Na atom reactions with the fluorobromomethane molecules confirmed the identification of the CFBr 2 and CF 2 Br free radicals. Other product bands destroyed by mercury arc light, some of which were generated upon photolysis of the sodium-fluorobromomethane samples, are assigned to molecular anions. 5 figures, 6 tables
Theorems of low energy in Compton scattering
International Nuclear Information System (INIS)
Chahine, J.
1984-01-01
We have obtained the low energy theorems in Compton scattering to third and fouth order in the frequency of the incident photon. Next we calculated the polarized cross section to third order and the unpolarized to fourth order in terms of partial amplitudes not covered by the low energy theorems, what will permit the experimental determination of these partial amplitudes. (Author) [pt
Zamolodchikov's c-theorem and string effective actions
International Nuclear Information System (INIS)
Mavromatos, N.E.; Miramontes, J.L.
1988-01-01
Zamolodchikov's c-theorem for 2D renormalisable field theories is presented in a way which allows for a straightforward application to the case of bosonic σ-models. As a consistency check in the latter case, the Curci-Paffuti relation is rederived. It is also shown that the 'metric' in coupling constant space in this case is a c-number function of the backgrounds. Attempts to derive off-shell functional relations between the Weyl anomaly coefficients and field variations of string effective actions, compatible with the c-theorem, are discussed by emphasising the necessity of performing explicit perturbative calculations in order to arrive at definite conclusions. Comments concerning the extension of the c-theorem to the case of supersymmetric and heterotic σ-models are also made. (orig.)
There is No Quantum Regression Theorem
International Nuclear Information System (INIS)
Ford, G.W.; OConnell, R.F.
1996-01-01
The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem. copyright 1996 The American Physical Society
Californium oxygen system for 1.50 < O/Cf < 1.72
International Nuclear Information System (INIS)
Turcotte, R.P.; Haire, R.G.
1975-01-01
The californium-oxygen system was studied as a function of temperature, oxygen pressure, and stoichiometry by manometric and x-ray diffraction methods. The results establish rhombohedral Cf 7 O 12 as the stable compound obtained by heating Cf 2 O 3 in air. The isobaric oxidation-reduction cycles Cf 2 O 3 → Cf 7 O 12 → Cf 2 O 3 , observed in constant rate of heating (cooling) experiments, occur with large hysteresis. A close parallel to other fluorite related lanthanide and actinide oxide systems is established. (auth)
Adiabatic Theorem for Quantum Spin Systems
Bachmann, S.; De Roeck, W.; Fraas, M.
2017-08-01
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
Theorem Proving In Higher Order Logics
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
Soft theorems from conformal field theory
International Nuclear Information System (INIS)
Lipstein, Arthur E.
2015-01-01
Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambtwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.
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...
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.
Generalizations of the Nash Equilibrium Theorem in the KKM Theory
Directory of Open Access Journals (Sweden)
Sehie Park
2010-01-01
Full Text Available The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minimax theorem, the von Neumann-Fan intersection theorem, the Fan-type analytic alternative, and the Nash equilibrium theorem for abstract convex spaces satisfying the partial KKM principle. These results are compared with previously known cases for G-convex spaces. Consequently, our results unify and generalize most of previously known particular cases of the same nature. Finally, we add some detailed historical remarks on related topics.
Testing the No-Hair Theorem with Sgr A*
Directory of Open Access Journals (Sweden)
Tim Johannsen
2012-01-01
Full Text Available The no-hair theorem characterizes the fundamental nature of black holes in general relativity. This theorem can be tested observationally by measuring the mass and spin of a black hole as well as its quadrupole moment, which may deviate from the expected Kerr value. Sgr A*, the supermassive black hole at the center of the Milky Way, is a prime candidate for such tests thanks to its large angular size, high brightness, and rich population of nearby stars. In this paper, I discuss a new theoretical framework for a test of the no-hair theorem that is ideal for imaging observations of Sgr A* with very long baseline interferometry (VLBI. The approach is formulated in terms of a Kerr-like spacetime that depends on a free parameter and is regular everywhere outside of the event horizon. Together with the results from astrometric and timing observations, VLBI imaging of Sgr A* may lead to a secure test of the no-hair theorem.
Quantization of Chirikov Map and Quantum KAM Theorem.
Shi, Kang-Jie
KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions
Cosmological constant, inflation and no-cloning theorem
Energy Technology Data Exchange (ETDEWEB)
Huang Qingguo, E-mail: huangqg@itp.ac.cn [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Science, Beijing 100190 (China); Lin Fengli, E-mail: linfengli@phy.ntnu.edu.tw [Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Department of Physics, National Taiwan Normal University, Taipei, 116, Taiwan (China)
2012-05-30
From the viewpoint of no-cloning theorem we postulate a relation between the current accelerated expansion of our universe and the inflationary expansion in the very early universe. It implies that the fate of our universe should be in a state with accelerated expansion. Quantitatively we find that the no-cloning theorem leads to a lower bound on the cosmological constant which is compatible with observations.
Cluster structure in Cf nuclei
International Nuclear Information System (INIS)
Singh, Shailesh K.; Biswal, S.K.; Bhuyan, M.; Patra, S.K.; Gupta, R.K.
2014-01-01
Due to the availability of advance experimental facilities, it is possible to probe the nuclei upto their nucleon level very precisely and analyzed the internal structure which will help us to resolve some mysterious problem of the decay of nuclei. Recently, the relativistic nuclear collision, confirmed the α cluster type structure in the 12 C which is the mile stone for the cluster structure in nuclei. The clustering phenomena in light and intermediate elements in nuclear chart is very interesting. There is a lot of work done by our group in the clustering behaviour of the nuclei. In this paper, the various prospectus of clustering in the isotopes of Cf nucleus including fission state is discussed. Here, 242 Cf isotope for the analysis, which is experimentally known is taken. The relativistic mean field model with well established NL3 parameter set is taken. For getting the exact ground state configuration of the isotopes, the calculation for minimizing the potential energy surface is performed by constraint method. The clustering structure of other Cf isotopes is discussed
Elastic hadron scattering and optical theorem
Lokajicek, Milos V.; Prochazka, Jiri
2014-01-01
In principle all contemporary phenomenological models of elastic hadronic scattering have been based on the assumption of optical theorem validity that has been overtaken from optics. It will be shown that the given theorem which has not been actually proved cannot be applied to short-ranged strong interactions in any case. The actual progress in description of collision processes might then exist only if the initial states are specified on the basis of impact parameter values of colliding particles and probability dependence on this parameter is established.
Two fixed point theorems on quasi-metric spaces via mw- distances
Energy Technology Data Exchange (ETDEWEB)
Alegre, C.
2017-07-01
In this paper we prove a Banach-type fixed point theorem and a Kannan-type theorem in the setting of quasi-metric spaces using the notion of mw-distance. These theorems generalize some results that have recently appeared in the literature. (Author)
On the Riesz representation theorem and integral operators ...
African Journals Online (AJOL)
We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions. Keywords: Vector integral, integral operators, operator ...
A generalization of the virial theorem for strongly singular potentials
International Nuclear Information System (INIS)
Gesztesy, F.; Pittner, L.
1978-09-01
Using scale transformations the authors prove a generalization of the virial theorem for the eigenfunctions of non-relativistic Schroedinger Hamiltonians which are defined as the Friedrichs extension of strongly singular differential operators. The theorem also applies to situations where the ground state has divergent kinetic and potential energy and thus the usual version of the virial theorem becomes meaningless. (Auth.)
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...
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
Quantum voting and violation of Arrow's impossibility theorem
Bao, Ning; Yunger Halpern, Nicole
2017-06-01
We propose a quantum voting system in the spirit of quantum games such as the quantum prisoner's dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's impossibility theorem. Arrow's theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's theorem. A quantum version of majority rule, we show, violates this quantum Arrow conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.
Generalized Perron--Frobenius Theorem for Nonsquare Matrices
Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David
2013-01-01
The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the...
Goedel incompleteness theorems and the limits of their applicability. I
International Nuclear Information System (INIS)
Beklemishev, Lev D
2011-01-01
This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.
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.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
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…
Four theorems on the psychometric function.
May, Keith A; Solomon, Joshua A
2013-01-01
In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus
Four theorems on the psychometric function.
Directory of Open Access Journals (Sweden)
Keith A May
Full Text Available In a 2-alternative forced-choice (2AFC discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise x β(Transducer, where β(Noise is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer depends on the transducer. We derive general expressions for β(Noise and β(Transducer, from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx(b, β ≈ β(Noise x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is
On the Leray-Hirsch Theorem for the Lichnerowicz cohomology
International Nuclear Information System (INIS)
Ait Haddoul, Hassan
2004-03-01
The purpose of this paper is to prove the Leray-Hirsch theorem for the Lichnerowicz; cohomology with respect to basic and vertical closed 1-forms. This is a generalization of the Kfirmeth theorem to fiber bundles. (author)
A Note on a Broken-Cycle Theorem for Hypergraphs
Directory of Open Access Journals (Sweden)
Trinks Martin
2014-08-01
Full Text Available Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there
Kochen-Specker theorem studied with neutron interferometer.
Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut
2011-04-01
The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
Kochen-Specker theorem studied with neutron interferometer
Energy Technology Data Exchange (ETDEWEB)
Hasegawa, Yuji, E-mail: Hasegawa@ati.ac.a [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria); Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria)
2011-04-01
The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291{+-}0.008 not {<=} 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
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.
Converse Barrier Certificate Theorems
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer
2016-01-01
This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither...
Direct and converse theorems the elements of symbolic logic
Gradshtein, I S; Stark, M; Ulam, S
1963-01-01
Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chap
Bacteriophage Lysin CF-301, a Potent Antistaphylococcal Biofilm Agent.
Schuch, Raymond; Khan, Babar K; Raz, Assaf; Rotolo, Jimmy A; Wittekind, Michael
2017-07-01
Biofilms pose a unique therapeutic challenge because of the antibiotic tolerance of constituent bacteria. Treatments for biofilm-based infections represent a major unmet medical need, requiring novel agents to eradicate mature biofilms. Our objective was to evaluate bacteriophage lysin CF-301 as a new agent to target Staphylococcus aureus biofilms. We used minimum biofilm-eradicating concentration (MBEC) assays on 95 S. aureus strains to obtain a 90% MBEC (MBEC 90 ) value of ≤0.25 μg/ml for CF-301. Mature biofilms of coagulase-negative staphylococci, Streptococcus pyogenes , and Streptococcus agalactiae were also sensitive to disruption, with MBEC 90 values ranging from 0.25 to 8 μg/ml. The potency of CF-301 was demonstrated against S. aureus biofilms formed on polystyrene, glass, surgical mesh, and catheters. In catheters, CF-301 removed all biofilm within 1 h and killed all released bacteria by 6 h. Mixed-species biofilms, formed by S. aureus and Staphylococcus epidermidis on several surfaces, were removed by CF-301, as were S. aureus biofilms either enriched for small-colony variants (SCVs) or grown in human synovial fluid. The antibacterial activity of CF-301 was further demonstrated against S. aureus persister cells in exponential-phase and stationary-phase populations. Finally, the antibiofilm activity of CF-301 was greatly improved in combinations with the cell wall hydrolase lysostaphin when tested against a range of S. aureus strains. In all, the data show that CF-301 is highly effective at disrupting biofilms and killing biofilm bacteria, and, as such, it may be an efficient new agent for treating staphylococcal infections with a biofilm component. Copyright © 2017 American Society for Microbiology.
Bacteriophage Lysin CF-301, a Potent Antistaphylococcal Biofilm Agent
Schuch, Raymond; Khan, Babar Khalid; Raz, Assaf; Rotolo, Jimmy A.; Wittekind, Michael
2017-01-01
Biofilms pose a unique therapeutic challenge because of the antibiotic tolerance of constituent bacteria. Treatments for biofilm-based infections represent a major unmet medical need, requiring novel agents to eradicate mature biofilms. Our objective was to evaluate bacteriophage lysin CF-301 as a new agent to target Staphylococcus aureus biofilms. We used minimum biofilm-eradicating concentration (MBEC) assays on 95 S. aureus strains to obtain a 90% MBEC (MBEC90) value of <= 0.25 mu g/ml for CF-301. Mature biofilms of coagulase-negative staphylococci, Streptococcus pyogenes, and Streptococcus agalactiae were also sensitive to disruption, with MBEC90 values ranging from 0.25 to 8 mu g/ml. The potency of CF-301 was demonstrated against S. aureus biofilms formed on polystyrene, glass, surgical mesh, and catheters. In catheters, CF-301 removed all biofilm within 1 h and killed all released bacteria by 6 h. Mixed-species biofilms, formed by S. aureus and Staphylococcus epidermidis on several surfaces, were removed by CF-301, as were S. aureus biofilms either enriched for small-colony variants (SCVs) or grown in human synovial fluid. The antibacterial activity of CF-301 was further demonstrated against S. aureus persister cells in exponential-phase and stationary-phase populations. Finally, the antibiofilm activity of CF-301 was greatly improved in combinations with the cell wall hydrolase lysostaphin when tested against a range of S. aureus strains. In all, the data show that CF-301 is highly effective at disrupting biofilms and killing biofilm bacteria, and, as such, it may be an efficient new agent for treating staphylococcal infections with a biofilm component.
Bacteriophage Lysin CF-301, a Potent Antistaphylococcal Biofilm Agent
Schuch, Raymond
2017-05-02
Biofilms pose a unique therapeutic challenge because of the antibiotic tolerance of constituent bacteria. Treatments for biofilm-based infections represent a major unmet medical need, requiring novel agents to eradicate mature biofilms. Our objective was to evaluate bacteriophage lysin CF-301 as a new agent to target Staphylococcus aureus biofilms. We used minimum biofilm-eradicating concentration (MBEC) assays on 95 S. aureus strains to obtain a 90% MBEC (MBEC90) value of <= 0.25 mu g/ml for CF-301. Mature biofilms of coagulase-negative staphylococci, Streptococcus pyogenes, and Streptococcus agalactiae were also sensitive to disruption, with MBEC90 values ranging from 0.25 to 8 mu g/ml. The potency of CF-301 was demonstrated against S. aureus biofilms formed on polystyrene, glass, surgical mesh, and catheters. In catheters, CF-301 removed all biofilm within 1 h and killed all released bacteria by 6 h. Mixed-species biofilms, formed by S. aureus and Staphylococcus epidermidis on several surfaces, were removed by CF-301, as were S. aureus biofilms either enriched for small-colony variants (SCVs) or grown in human synovial fluid. The antibacterial activity of CF-301 was further demonstrated against S. aureus persister cells in exponential-phase and stationary-phase populations. Finally, the antibiofilm activity of CF-301 was greatly improved in combinations with the cell wall hydrolase lysostaphin when tested against a range of S. aureus strains. In all, the data show that CF-301 is highly effective at disrupting biofilms and killing biofilm bacteria, and, as such, it may be an efficient new agent for treating staphylococcal infections with a biofilm component.
Level comparison theorems and supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Baumgartner, B.; Grosse, H.
1986-01-01
The sign of the Laplacian of the spherical symmetric potential determines the order of energy levels with the same principal Coulomb quantum number. This recently derived theorem has been generalized, extended and applied to various situations in particle, nuclear and atomic physics. Besides a comparison theorem the essential step was the use of supersymmetric quantum mechanics. Recently worked out applications of supersymmetric quantum mechanics to index problems of Dirac operators are mentioned. (Author)
Generalized Panofsky-Wenzel theorem and hybrid coupling
Smirnov, A V
2001-01-01
The Panofsky-Wenzel theorem is reformulated for the case in which phase slippage between the wave and beam is not negligible. The extended theorem can be applied in analysis of detuned waveguides, RF injectors, bunchers, some tapered waveguides or high-power sources and multi-cell cavities for dipole and higher order modes. As an example, the relative contribution of the Lorentz' component of the deflecting force is calculated for a conventional circular disk-loaded waveguide.
Joint probability distributions and fluctuation theorems
International Nuclear Information System (INIS)
García-García, Reinaldo; Kolton, Alejandro B; Domínguez, Daniel; Lecomte, Vivien
2012-01-01
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation–dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators
Fully Quantum Fluctuation Theorems
Åberg, Johan
2018-02-01
Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.
Deviations from Wick's theorem in the canonical ensemble
Schönhammer, K.
2017-07-01
Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.
Groups of galaxies. III. the CfA survey
International Nuclear Information System (INIS)
Geller, M.J.; Huchra, J.P.
1983-01-01
We present a statistically homogeneous group catalog (CfA) based on the CfA redshift survey (Huchra et al.). Groups in the catalog are all density enhancements in redshift space of a factor greater than 20. Group members are identified according to the procedure described in our previous study (Huchra and Geller) of a shallower whole-sky sample. All groups contain at least three members. Of the 176 groups in the CfA catalog, 102 have been identified in one or more previous studies. Because our algorithm searches for volume rather than surface density enhancements, the groups in a given region generally change only through the addition of fainter members when the magnitude limit of the galaxy catalog increases. In the region of overlap, agreement between our shallow catalog and the CfA catalog is excellent
Action-angle variables and a KAM theorem for b-Poisson manifolds
Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey
2015-01-01
In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [14] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved.
A new proof of the positive energy theorem
International Nuclear Information System (INIS)
Witten, E.
1981-01-01
A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by Schoen and Yau). The relevance of these results to the stability of Minkowski space is discussed. (orig.)
Yang, Chuan-Fu
Inverse spectral problems are considered for differential pencils with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions. We give formulations of the associated inverse problems such as Titchmarsh-Weyl theorem, Hochstadt-Lieberman theorem and Mochizuki-Trooshin theorem, and prove corresponding uniqueness theorems. The obtained results are generalizations of the similar results for the classical Sturm-Liouville operator on a finite interval.
Virtual continuity of the measurable functions of several variables, and Sobolev embedding theorems
Vershik, Anatoly; Zatitskiy, Pavel; Petrov, Fedor
2013-01-01
Classical Luzin's theorem states that the measurable function of one variable is "almost" continuous. This is not so anymore for functions of several variables. The search of right analogue of the Luzin theorem leads to a notion of virtually continuous functions of several variables. This probably new notion appears implicitly in the statements like embeddings theorems and traces theorems for Sobolev spaces. In fact, it reveals their nature as theorems about virtual continuity. This notion is...
The low-energy theorem of pion photoproduction using the Skyrme model
International Nuclear Information System (INIS)
Ikehashi, T.; Ohta, K.
1995-01-01
We reassess the validity of the current-algebra based low-energy theorem of pion photoproduction on the nucleon using the Skyrme model. We find that one of the off-shell electromagnetic form factors of the nucleon exhibits infrared divergence in the chiral limit. This contribution introduces an additional term to the threshold amplitude predicted by the low-energy theorem. The emergence of the additional term indicates an unavoidable necessity of off-shell form factors in deriving the low-energy theorem. In the case of neutral pion production, the new contribution to the threshold amplitude is found to be comparable in magnitude to the low-energy theorem's prediction and has the opposite sign. In the charged pion production channels, the correction to the theorem is shown to be relatively small. (orig.)
Rosenthal, Mark; Narang, Indra; Edwards, Liz; Bush, Andrew
2009-03-01
Peripheral muscle dysfunction is increasingly recognized as complicating respiratory disease, but this is difficult to measure non-invasively. Can skeletal muscle function and efficiency be measured during exercise non-invasively using respiratory mass spectrometry (RMS); and is the known exercise dysfunction in cystic fibrosis (CF) children related in part to a disease specific defect of skeletal muscle, or a non-specific manifestation of chronic airway infection and inflammation. Calculations of effective pulmonary blood flow and stroke volume, blood oxygen content and oxygen dispatch from the lungs, skeletal muscle oxygen extraction and consumption, anerobic threshold and capacity, and gross, net and work efficiency in 106 controls and 36 children (18 CF) with bronchiectasis, all aged from 8 to 17 years. Normal values for control subjects are tabulated. CF and non-CF bronchiectatic subjects had similar physiology, and skeletal muscle abnormalities could not be detected. Reduced oxygen dispatch from the lungs, due to an inability to raise stroke volume, without an increase in functional residual capacity was the major factor in reduced exercise ability. Non-invasive RMS can be used to determine skeletal muscle function in children. The changes observed in CF subjects were very similar to non-CF bronchiectatic subjects and thus a CF specific defect was not demonstrated.
Dynamic Newton-Puiseux Theorem
DEFF Research Database (Denmark)
Mannaa, Bassel; Coquand, Thierry
2013-01-01
A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization...
A Maximal Element Theorem in FWC-Spaces and Its Applications
Hu, Qingwen; Miao, Yulin
2014-01-01
A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672
Atmospheric chemistry of CF3CH2CH2OH
DEFF Research Database (Denmark)
Hurley, Michael D.; Misner, Jessica A.; Ball, James C.
2005-01-01
Relative rate techniques were used to study the kinetics of the reactions of Cl atoms and OH radicals with CF3CH2C(O)H and CF3CH2CH2OH in 700 Torr of N-2 or air diluent at 296 2 K. The rate constants determined were k(Cl+CF3CH2C(O)H) = (1.81 +/- 0.27) x 10(-11), k(OH+CF3CH2C(O)H) = (2.57 +/- 0.44...
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
Quantum nonlocality and reality 50 years of Bell's theorem
Gao, Shan
2016-01-01
Description Contents Resources Courses About the Authors Combining twenty-six original essays written by an impressive line-up of distinguished physicists and philosophers of physics, this anthology reflects some of the latest thoughts by leading experts on the influence of Bell's theorem on quantum physics. Essays progress from John Bell's character and background, through studies of his main work, and on to more speculative ideas, addressing the controversies surrounding the theorem, and investigating the theorem's meaning and its deep implications for the nature of physical reality. Combined, they present a powerful comment on the undeniable significance of Bell's theorem for the development of ideas in quantum physics over the past 50 years. Questions surrounding the assumptions and significance of Bell's work still inspire discussion in the field of quantum physics. Adding to this with a theoretical and philosophical perspective, this balanced anthology is an indispensable volume for students and researc...
On the c-theorem in higher genus
International Nuclear Information System (INIS)
Espriu, D.; Mavromatos, N.E.
1990-01-01
We study the extension of the c-therorem to arbitrary genus Riemann surfaces. We analyze the breakdown of conformal invariance caused by the need of cutting off regions of moduli space to regulate divergences and argue how these can be absorbed in the bare couplings on the sphere. An extension of the c-theorem then follows. We also discuss the relationship between the c-theorem and the effective action when corrections from higher genera are accounted for. (orig.)
The Hellman-Feynman theorem at finite temperature
International Nuclear Information System (INIS)
Cabrera, A.; Calles, A.
1990-01-01
The possibility of a kind of Hellman-Feynman theorem at finite temperature is discussed. Using the cannonical ensembles, the derivative of the internal energy is obtained when it depends explicitly on a parameter. It is found that under the low temperature regime the derivative of the energy can be obtained as the statistical average of the derivative of the hamiltonian operator. The result allows to speak of the existence of the Hellman-Feynman theorem at finite temperatures (Author)
Kochen-Specker theorem studied with neutron interferometer
International Nuclear Information System (INIS)
Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut
2011-01-01
The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008 not ≤ 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
CFTR mutation analysis and haplotype associations in CF patients☆
Cordovado, S.K.; Hendrix, M.; Greene, C.N.; Mochal, S.; Earley, M.C.; Farrell, P.M.; Kharrazi, M.; Hannon, W.H.; Mueller, P.W.
2011-01-01
Most newborn screening (NBS) laboratories use second-tier molecular tests for cystic fibrosis (CF) using dried blood spots (DBS). The Centers for Disease Control and Prevention’s NBS Quality Assurance Program offers proficiency testing (PT) in DBS for CF transmembrane conductance regulator (CFTR) gene mutation detection. Extensive molecular characterization on 76 CF patients, family members or screen positive newborns was performed for quality assurance. The coding, regulatory regions and por...
Strong converse theorems using Rényi entropies
Energy Technology Data Exchange (ETDEWEB)
Leditzky, Felix; Datta, Nilanjana [Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WB (United Kingdom); Wilde, Mark M. [Department of Physics and Astronomy, Center for Computation and Technology, Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)
2016-08-15
We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint http://arxiv.org/abs/1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.
Guided Discovery of the Nine-Point Circle Theorem and Its Proof
Buchbinder, Orly
2018-01-01
The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…
Neutron total cross section measurements on 249Cf
International Nuclear Information System (INIS)
Carlton, R.F.; Harvey, J.A.; Hill, N.W.; Pandey, M.S.; Benjamin, R.W.
1979-01-01
Neutron total cross section measurements were performed on a sample of 249 Cf (5.65 mg total weight) with the ORELA as a source of pulsed neutrons. The sample, the inverse thickness of which was 1542 barns/atom, consisted of 85.3% 249 Cf and 14.4% 249 Bk, and was cooled to liquid nitrogen temperature. Analyses were also made of data from a thin sample (l/n = 17430) of 65% 249 Cf in the region of the large fission resonance at 0.7 eV. Fifty-five resonances in 249 Cf were observed and analyzed over the energy range 0.1 eV to 90 eV by use of an R-matrix multilevel formalism. The resonance parameters obtained were used to determine the level spacing and the s-wave neutron and fission strength functions. Thermal total cross section measurements were also performed. 5 figures, 3 tables
An extension of Brosowski-Meinardus theorem on invariant approximation
International Nuclear Information System (INIS)
Liaqat Ali Khan; Abdul Rahim Khan.
1991-07-01
We obtain a generalization of a fixed point theorem of Dotson for non-expansive mappings on star-shaped sets and then use it to prove a unified Brosowski-Meinardus theorem on invariant approximation in the setting of p-normed linear spaces. (author). 13 refs
K S Krishnan's 1948 Perception of the Sampling Theorem
Indian Academy of Sciences (India)
K S Krishnan's 1948 Perception of the. Sampling Theorem. Raiiah Simon is a. Professor at the Institute of Mathematical. Sciences, Chennai. His primary interests are in classical and quantum optics, geometric phases, group theoretical techniques and quantum information science. Keywords. Sompling theorem, K S ...
An improved version of the Mar otto Theorem
International Nuclear Information System (INIS)
Li Changpin; Chen Guanrong
2003-01-01
In 1975, Li and Yorke introduced the first precise definition of discrete chaos and established a very simple criterion for chaos in one-dimensional difference equations, 'period three implies chaos' for brevity. After three years. Marotto generalized this result to n-dimensional difference equations, showing that the existence of a snap-back repeller implies chaos in the sense of Li-Yorke. This theorem is up to now the best one in predicting and analyzing discrete chaos in multidimensional difference equations. Yet, it is well known that there exists an error in the condition of the original Marotto Theorem, and several authors had tried to correct it in different ways. In this paper, we further clarify the issue, with an improved version of the Marotto Theorem derived
A remark on the energy conditions for Hawking's area theorem
Lesourd, Martin
2018-06-01
Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
Markvorsen, Steen
2006-01-01
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered only much later in more advanced math courses - is comprehensible with only a little extension of the first year curriculum. Moreover, it is more intuitive than the static proof. We support this intuit...
Papadimitriou, Vassileios C; Lazarou, Yannis G; Talukdar, Ranajit K; Burkholder, James B
2011-01-20
Rate coefficients, k, for the gas-phase reactions of Cl atoms and NO(3) radicals with 2,3,3,3-tetrafluoropropene, CF(3)CF═CH(2) (HFO-1234yf), and 1,2,3,3,3-pentafluoropropene, (Z)-CF(3)CF═CHF (HFO-1225ye), are reported. Cl-atom rate coefficients were measured in the fall-off region as a function of temperature (220-380 K) and pressure (50-630 Torr; N(2), O(2), and synthetic air) using a relative rate method. The measured rate coefficients are well represented by the fall-off parameters k(0)(T) = 6.5 × 10(-28) (T/300)(-6.9) cm(6) molecule(-2) s(-1) and k(∞)(T) = 7.7 × 10(-11) (T/300)(-0.65) cm(3) molecule(-1) s(-1) for CF(3)CF═CH(2) and k(0)(T) = 3 × 10(-27) (T/300)(-6.5) cm(6) molecule(-2) s(-1) and k(∞)(T) = 4.15 × 10(-11) (T/300)(-0.5) cm(3) molecule(-1) s(-1) for (Z)-CF(3)C═CHF with F(c) = 0.6. Reaction product yields were measured in the presence of O(2) to be (98 ± 7)% for CF(3)C(O)F and (61 ± 4)% for HC(O)Cl in the CF(3)CF═CH(2) reaction and (108 ± 8)% for CF(3)C(O)F and (112 ± 8)% for HC(O)F in the (Z)-CF(3)CF═CHF reaction, where the quoted uncertainties are 2σ (95% confidence level) and include estimated systematic errors. NO(3) reaction rate coefficients were determined using absolute and relative rate methods. Absolute measurements yielded upper limits for both reactions between 233 and 353 K, while the relative rate measurements yielded k(3)(295 K) = (2.6 ± 0.25) × 10(-17) cm(3) molecule(-1) s(-1) and k(4)(295 K) = (4.2 ± 0.5) × 10(-18) cm(3) molecule(-1) s(-1) for CF(3)CF═CH(2) and (Z)-CF(3)CF═CHF, respectively. The Cl-atom reaction with CF(3)CF═CH(2) and (Z)-CF(3)CF═CHF leads to decreases in their atmospheric lifetimes and global warming potentials and formation of a chlorine-containing product, HC(O)Cl, for CF(3)CF═CH(2). The NO(3) reaction has been shown to have a negligible impact on the atmospheric lifetimes of CF(3)CF═CH(2) and (Z)-CF(3)CF═CHF. The energetics for the reaction of Cl, NO(3), and OH with CF
A perceptron network theorem prover for the propositional calculus
Drossaers, M.F.J.
In this paper a short introduction to neural networks and a design for a perceptron network theorem prover for the propositional calculus are presented. The theorem prover is a representation of a variant of the semantic tableau method, called the parallel tableau method, by a network of
Matching factorization theorems with an inverse-error weighting
Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; Pisano, Cristian; Signori, Andrea
2018-06-01
We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.
An arithmetic transference proof of a relative Szemer\\'edi theorem
Zhao, Yufei
2013-01-01
Recently Conlon, Fox, and the author gave a new proof of a relative Szemer\\'edi theorem, which was the main novel ingredient in the proof of the celebrated Green-Tao theorem that the primes contain arbitrarily long arithmetic progressions. Roughly speaking, a relative Szemer\\'edi theorem says that if S is a set of integers satisfying certain conditions, and A is a subset of S with positive relative density, then A contains long arithmetic progressions, and our recent results show that S only ...
A non-renormalization theorem for conformal anomalies
International Nuclear Information System (INIS)
Petkou, Anastasios; Skenderis, Kostas
1999-01-01
We provide a non-renormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal anomaly of 2-point functions both by a computation in the conformal field theory and via the AdS/CFT correspondence. Our results imply that 2- and 3-point functions of chiral primary operators in N=4 SU(N) SYM will not renormalize provided that a 'generalized Adler-Bardeen theorem' holds. We further show that recent arguments connecting the non-renormalizability of the above-mentioned correlation functions to a bonus U(1) Y symmetry are incomplete due to possible U(1) Y violating contact terms. The tree level contribution to the contact terms may be set to zero by considering appropriately normalized operators. Non-renormalizability of the above-mentioned correlation functions, however, will follow only if these contact terms saturate by free fields
The Boundary Crossing Theorem and the Maximal Stability Interval
Directory of Open Access Journals (Sweden)
Jorge-Antonio López-Renteria
2011-01-01
useful tools in the study of the stability of family of polynomials. Although both of these theorem seem intuitively obvious, they can be used for proving important results. In this paper, we give generalizations of these two theorems and we apply such generalizations for finding the maximal stability interval.
The nekhoroshev theorem and long-term stabilities in the solar system
Directory of Open Access Journals (Sweden)
Guzzo M.
2015-01-01
Full Text Available The Nekhoroshev theorem has been often indicated in the last decades as the reference theorem for explaining the dynamics of several systems which are stable in the long-term. The Solar System dynamics provides a wide range of possible and useful applications. In fact, despite the complicated models which are used to numerically integrate realistic Solar System dynamics as accurately as possible, when the integrated solutions are chaotic the reliability of the numerical integrations is limited, and a theoretical long-term stability analysis is required. After the first formulation of Nekhoroshev’s theorem in 1977, many theoretical improvements have been achieved. On the one hand, alternative proofs of the theorem itself led to consistent improvements of the stability estimates; on the other hand, the extensions which were necessary to apply the theorem to the systems of interest for Solar System Dynamics, in particular concerning the removal of degeneracies and the implementation of computer assisted proofs, have been developed. In this review paper we discuss some of the motivations and the results which have made Nekhoroshev’s theorem a reference stability result for many applications in the Solar System dynamics.
A Randomized Central Limit Theorem
International Nuclear Information System (INIS)
Eliazar, Iddo; Klafter, Joseph
2010-01-01
The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√(n)), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √(n). This Letter considers scaling schemes which are stochastic and non-uniform, and presents a 'Randomized Central Limit Theorem' (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Levy laws.
Bai, Feng-Yang; Jia, Zi-Man; Pan, Xiu-Mei
2018-06-01
In this work, a systematic investigation of the atmospheric oxidation mechanism of (CF3)2CXOCH3 and their oxidative products (CF3)2CXOCHO (X = H, F) initiated by OH radical or Cl atom is performed by density functional theory. This study reveals that the introduction of NO and O2 promotes the formation of organic nitrates, which are hygroscopic and are inclined to form secondary organic aerosols (SOA) and can affect the air quality. The rate constants of the individual reactions are found to be in agreement with the experimental results. One of the intriguing findings of this work is that the peroxynitrite of (CF3)2CHOCH2OONO formed from the subsequent reactions of (CF3)2CHOCH3 is more favorable to isomerize to organic nitrate (CF3)2CHOCH2ONO2 than to dissociate into alkoxy radical (CF3)2CHOCH2O and NO2 because of the lower energy barrier of isomerization. The second significant observation is that the organic nitrate can be degraded more favorably with the presence of NH3, CH3NH2, and CH3NHCH3 than its naked decomposition reaction (CF3)2CHOCH2ONO2→(CF3)2CHOCHO + HONO. The ammonium salt, a vital part of haze, is harmful to human health and can be formed in the existence of the NH3, CH3NH2, and CH3NHCH3. In addition, the toxic substance of peroxyalkyl nitrate (CF3)2CHOC(O)ONO2 which can reduce the visibility of the atmosphere is produced as the primary subsequent oxidation product of (CF3)2CHOCHO in a NO-rich environment. The main species detected experimentally are confirmed by this study. The computational results are crucial to risk assessment and pollution prevention of the volatile organic compounds (VOCs).
A no-hair theorem for black holes in f(R) gravity
Cañate, Pedro
2018-01-01
In this work we present a no-hair theorem which discards the existence of four-dimensional asymptotically flat, static and spherically symmetric or stationary axisymmetric, non-trivial black holes in the frame of f(R) gravity under metric formalism. Here we show that our no-hair theorem also can discard asymptotic de Sitter stationary and axisymmetric non-trivial black holes. The novelty is that this no-hair theorem is built without resorting to known mapping between f(R) gravity and scalar–tensor theory. Thus, an advantage will be that our no-hair theorem applies as well to metric f(R) models that cannot be mapped to scalar–tensor theory.
Baxam, Carl C.; Margalit, N.
1991-01-01
Swelling of (CF(x))(sub n) electrodes in commercial Li/(CF(x))(sub n) cells presents a limiting factor in cell design optimization. Examination of cathodes from such cells, after discharge, reveals a relation between cell operating temperatures and cathode swelling. Attempts to explain the swelling using the prevailing model for the cathode reaction have failed. A more suitable reaction mechanism is proposed based on the observed behavior of (CF(x))(sub n) electrodes on discharge and a comparison of the reaction products of (CF(x))(sub n) and polytetra fluoroethylene (PTFE) with lithium amalgams. The proposed mechanism is in agreement with the experimental data found in the literature.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
International Nuclear Information System (INIS)
Stenlund, Mikko
2016-01-01
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
Energy Technology Data Exchange (ETDEWEB)
Stenlund, Mikko, E-mail: mikko.stenlund@helsinki.fi [University of Helsinki, Department of Mathematics and Statistics (Finland)
2016-09-15
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
Burke, D G; Harrison, M J; Fleming, C; McCarthy, M; Shortt, C; Sulaiman, I; Murphy, D M; Eustace, J A; Shanahan, F; Hill, C; Stanton, C; Rea, M C; Ross, R P; Plant, B J
2017-03-01
Clostridium difficile is an anaerobic Gram-positive, spore-forming, toxin-producing bacillus transmitted among humans through the faecal-oral route. Despite increasing carriage rates and the presence of C. difficile toxin in stool, patients with CF rarely appear to develop typical manifestations of C. difficile infection (CDI). In this study, we examined the carriage, toxin production, ribotype distribution and antibiotic susceptibility of C. difficile in a cohort of 60 adult patients with CF who were pre-lung transplant. C. difficile was detected in 50% (30/60) of patients with CF by culturing for the bacteria. C. difficile toxin was detected in 63% (19/30) of C. difficile-positive stool samples. All toxin-positive stool samples contained toxigenic C. difficile strains harbouring toxin genes, tcdA and tcdB. Despite the presence of C. difficile and its toxin in patient stool, no acute gastrointestinal symptoms were reported. Ribotyping of C. difficile strains revealed 16 distinct ribotypes (RT), 11 of which are known to be disease-causing including the hyper-virulent RT078. Additionally, strains RT002, RT014, and RT015, which are common in non-CF nosocomial infection were described. All strains were susceptible to vancomycin, metronidazole, fusidic acid and rifampicin. No correlation was observed between carriage of C. difficile or any characteristics of isolated strains and any recorded clinical parameters or treatment received. We demonstrate a high prevalence of hypervirulent, toxigenic strains of C. difficile in asymptomatic patients with CF. This highlights the potential role of asymptomatic patients with CF in nosocomial transmission of C. difficile. Copyright © 2016 European Cystic Fibrosis Society. Published by Elsevier B.V. All rights reserved.
Some functional limit theorems for compound Cox processes
Energy Technology Data Exchange (ETDEWEB)
Korolev, Victor Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Institute of Informatics Problems FRC CSC RAS (Russian Federation); Chertok, A. V. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Euphoria Group LLC (Russian Federation); Korchagin, A. Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Kossova, E. V. [Higher School of Economics National Research University, Moscow (Russian Federation); Zeifman, Alexander I. [Vologda State University, S.Orlova, 6, Vologda (Russian Federation); Institute of Informatics Problems FRC CSC RAS, ISEDT RAS (Russian Federation)
2016-06-08
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
Some functional limit theorems for compound Cox processes
International Nuclear Information System (INIS)
Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.
2016-01-01
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
A short list color proof of Grotzsch's theorem
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable.......We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable....
[Early aseptic loosening of the CF 30 femoral stem].
Kovanda, M; Havlícek, V; Hudec, J
2007-02-01
The CF 30 stem in combination with a cementless acetabulum was used at the First Department of Orthopedic Surgery in Brno in the years 1994 to 1995. From the second year following implantation, aseptic stem loosening was recorded. In order to find explanation of this early loosening, the authors, in cooperation with the Institute of Solid Mechanics, Mechatronics and Biomechanics, carried out the stress-strain analysis in a model system. Eighty patients (31 men and 49 women) received a cemented CF30 femoral component in 1994. Of them, 16 patients underwent revision arthroplasty, three died of causes unrelated to the surgery, and four were lost to follow-up. The final clinical and radiographic check-up was carried out in 2001. The results of a comprehensive examination were available in 57 patients with a CF30 stem. The patients were evaluated on the basis of the Harris hip score and anteroposterior radiographs of the hip. X-ray films obtained immediately after surgery and those taken at regular intervals during follow-up were compared. The following characteristics were noted: translucent lines in individual zones along the stem at the cement-bone interface; osteolysis, i. e., non-linear translucent areas, at least 5 mm long, at the cement-bone interface; and subsidence of the femoral component, i. e., migration of the stem distal to the tip of the greater trochanter. The CF 30 stem survival curve showed that aseptic stem loosening occurred from post-implantation year 2, and increased during the following years. At 6 years and 6 months, a total of 16 patients underwent revision surgery, involving reimplantation in 14 and implant removal in 2 patients. Potential causes of aseptic loosening: Polyethylene wear.However, no acetabular loosening was found in this group, although acetabular components are reported to become loose more often than femoral components. By comparison of the stem survival curves for Poldi and CF 30 stems it appeared that, at 6 years and 6 months
Graphite moderated 252Cf source
International Nuclear Information System (INIS)
Sajo B, L.; Barros, H.; Greaves, E. D.; Vega C, H. R.
2014-08-01
The thorium molten salt reactor is an attractive and affordable nuclear power option for developing countries with insufficient infrastructure and limited technological capability. In the aim of personnel training and experience gathering at the Universidad Simon Bolivar there is in progress a project of developing a subcritical thorium liquid fuel reactor. The neutron source to run this subcritical reactor is a 252 Cf source and the reactor will use high-purity graphite as moderator. Using the MCNP5 code the neutron spectra of the 252 Cf in the center of the graphite moderator has been estimated along the channel where the liquid thorium salt will be inserted; also the ambient dose equivalent due to the source has been determined around the moderator. (Author)
On the information-theoretic approach to G\\"odel's incompleteness theorem
D'Abramo, Germano
2002-01-01
In this paper we briefly review and analyze three published proofs of Chaitin's theorem, the celebrated information-theoretic version of G\\"odel's incompleteness theorem. Then, we discuss our main perplexity concerning a key step common to all these demonstrations.
On Frobenius, Mazur, and Gelfand-Mazur theorems on division ...
African Journals Online (AJOL)
... R of real numbers, the field C of complex numbers, or the non-commutative algebra Q of quaternions. Gelfand [15] proved that every normed division algebra over the field C is isomorphic to C. He named this theorem, which is fundamental for the development of the theory of Banach Algebras, the Gelfand-Mazur theorem.
Ternary-fragmentation-driving potential energies of 252Cf
Karthikraj, C.; Ren, Zhongzhou
2017-12-01
Within the framework of a simple macroscopic model, the ternary-fragmentation-driving potential energies of 252Cf are studied. In this work, all possible ternary-fragment combinations of 252Cf are generated by the use of atomic mass evaluation-2016 (AME2016) data and these combinations are minimized by using a two-dimensional minimization approach. This minimization process can be done in two ways: (i) with respect to proton numbers (Z1, Z2, Z3) and (ii) with respect to neutron numbers (N1, N2, N3) of the ternary fragments. In this paper, the driving potential energies for the ternary breakup of 252Cf are presented for both the spherical and deformed as well as the proton-minimized and neutron-minimized ternary fragments. From the proton-minimized spherical ternary fragments, we have obtained different possible ternary configurations with a minimum driving potential, in particular, the experimental expectation of Sn + Ni + Ca ternary fragmentation. However, the neutron-minimized ternary fragments exhibit a driving potential minimum in the true-ternary-fission (TTF) region as well. Further, the Q -value energy systematics of the neutron-minimized ternary fragments show larger values for the TTF fragments. From this, we have concluded that the TTF region fragments with the least driving potential and high Q values have a strong possibility in the ternary fragmentation of 252Cf. Further, the role of ground-state deformations (β2, β3, β4, and β6) in the ternary breakup of 252Cf is also studied. The deformed ternary fragmentation, which involves Z3=12 -19 fragments, possesses the driving potential minimum due to the larger oblate deformations. We also found that the ground-state deformations, particularly β2, strongly influence the driving potential energies and play a major role in determining the most probable fragment combinations in the ternary breakup of 252Cf.
Quantum de Finetti theorem in phase-space representation
International Nuclear Information System (INIS)
Leverrier, Anthony; Cerf, Nicolas J.
2009-01-01
The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
Some commutativity theorems for a certain class of rings
International Nuclear Information System (INIS)
Khan, M.A.
1994-08-01
In the present paper we first establish the commutativity theorem for semiprime ring satisfying the polynomial identity [x n ,y]x r = ±y s [x,y m ]y t for all x,y in R, where m,n,r,s and t are fixed nonnegative integers, and further, we investigate commutativity of rings with unity under some additional hypothesis. Moreover, it is also shown that the above result is true for s-unital. Also, we provide some counter examples which show that the hypothesis of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital. (author). 21 refs
Hadronic interactions of the J/ψ and Adler's theorem
International Nuclear Information System (INIS)
Bourque, A.; Gale, C.; Haglin, K.L.
2004-01-01
Effective Lagrangian models of charmonium have recently been used to estimate dissociation cross sections with light hadrons. Detailed study of the symmetry properties reveals possible shortcomings relative to chiral symmetry. We therefore propose a new Lagrangian and point out distinguishing features amongst the different approaches. Moreover, we test the models against Adler's theorem, which requires, in the appropriate limit, the decoupling of pions from the theory for the normal parity sector. Using the newly proposed Lagrangian, which exhibits SU L (N f )xSU R (N f ) symmetry and complies with Adler's theorem, we find dissociation cross sections with pions that are reduced in an energy-dependent way, with respect to cases where the theorem is not fulfilled
Towards a Novel no-hair Theorem for Black Holes
Hertog, T
2006-01-01
We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.
Standardization and Confluence in Pure Lambda-Calculus Formalized for the Matita Theorem Prover
Directory of Open Access Journals (Sweden)
Ferruccio Guidi
2012-01-01
Full Text Available We present a formalization of pure lambda-calculus for the Matita interactive theorem prover, including the proofs of two relevant results in reduction theory: the confluence theorem and the standardization theorem. The proof of the latter is based on a new approach recently introduced by Xi and refined by Kashima that, avoiding the notion of development and having a neat inductive structure, is particularly suited for formalization in theorem provers.
Unified quantum no-go theorems and transforming of quantum pure states in a restricted set
Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun
2017-12-01
The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.
On the interpretation and relevance of the Fundamental Theorem of Natural Selection.
Ewens, Warren J; Lessard, Sabin
2015-09-01
The attempt to understand the statement, and then to find the interpretation, of Fisher's "Fundamental Theorem of Natural Selection" caused problems for generations of population geneticists. Price's (1972) paper was the first to lead to an understanding of the statement of the theorem. The theorem shows (in the discrete-time case) that the so-called "partial change" in mean fitness of a population between a parental generation and an offspring generation is the parental generation additive genetic variance in fitness divided by the parental generation mean fitness. In the continuous-time case the partial rate of change in mean fitness is equal to the parental generation additive genetic variance in fitness with no division by the mean fitness. This "partial change" has been interpreted by some as the change in mean fitness due to changes in gene frequency, and by others as the change in mean fitness due to natural selection. (Fisher variously used both interpretations.) In this paper we discuss these interpretations of the theorem. We indicate why we are unhappy with both. We also discuss the long-term relevance of the Fundamental Theorem of Natural Selection, again reaching a negative assessment. We introduce and discuss the concept of genic evolutionary potential. We finally review an optimizing theorem that involves changes in gene frequency, the additive genetic variance in fitness and the mean fitness itself, all of which are involved in the Fundamental Theorem of Natural Selection, and which is free of the difficulties in interpretation of the Fundamental Theorem of Natural Selection. Copyright © 2015 Elsevier Inc. All rights reserved.
The universality of the Carnot theorem
International Nuclear Information System (INIS)
Gonzalez-Ayala, Julian; Angulo-Brown, F
2013-01-01
It is common in many thermodynamics textbooks to illustrate the Carnot theorem through the use of diverse state equations for gases, paramagnets, and other simple thermodynamic systems. As is well known, the universality of the Carnot efficiency is easily demonstrated in a temperature–entropy diagram, which means that η C is independent of the working substance. In this paper we remark that the universality of the Carnot theorem goes beyond conventional state equations, and is fulfilled by gas state equations that do not correspond to an ideal gas in the dilution limit, namely V → ∞. Some of these unconventional state equations have certain thermodynamic ‘anomalies’ that nonetheless do not forbid them from obeying the Carnot theorem. We discuss how this very general behaviour arises from Maxwell relations, which are connected with a geometrical property expressed through preserving area transformations. A rule is proposed to calculate the Maxwell relations associated with a thermodynamic system by using the preserving area relationships. In this way it is possible to calculate the number of possible preserving area mappings by giving the number of possible Jacobian identities between all pairs of thermodynamic variables included in the corresponding Gibbs equation. This paper is intended for undergraduates and specialists in thermodynamics and related areas. (paper)
Opechowski's theorem and commutator groups
International Nuclear Information System (INIS)
Caride, A.O.; Zanette, S.I.
1985-01-01
It is shown that the conditions of application of Opechowski's theorem for double groups of subgroups of O(3) are directly associated to the structure of their commutator groups. Some characteristics of the structure of classes are also discussed. (Author) [pt
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).
Kolmogorov-Arnold-Moser Theorem
Indian Academy of Sciences (India)
system (not necessarily the 2-body system). Kolmogorov was the first to provide a solution to the above general problem in a theorem formulated in 1954 (see Suggested. Reading). However, he provided only an outline of the proof. The actual proof (with all the details) turned to be quite difficult and was provided by Arnold ...
International Nuclear Information System (INIS)
Gourgiotis, A.; Isnard, H.; Nonell, A.; Aubert, M.; Stadelmann, G.; Dupont, E.; AlMahamid, I.; Tiang, G.; Rao, L.; Lukens, W.; Cassette, P.; Panebianco, S.; Letourneau, A.; Chartier, F.
2013-01-01
The French Atomic Energy Commission has carried out several experiments for the study of minor-actinide transmutation processes in high intensity thermal neutron flux. In this context a Cm sample enriched in 248 Cm (97%) was irradiated in a thermal neutron flux at the High Flux Reactor (HFR) of the Laue-Langevin Institute (ILL). The precise and accurate determination of Cf isotope ratios and of 249 Bk/ 248 Cm and 249 Cf/ 248 Cm elemental ratios in the 248 Cm irradiated sample is crucial for the calculation of actinide neutron capture cross-sections.This work describes an analytical procedure for the separation and the isotope ratio measurement of Bk and Cf in the irradiated sample.The Bk and Cf separation is based on a lanthanides separation protocol previously developed by the laboratory. Well-defined retention times for Bk and Cf were obtained by coupling the Ionic Chromatography (IC) with an ICP-QMS. All conditions of element separation by IC and the different steps of the analytical protocol in order to obtain the isotopic and elemental ratios are presented. Relative uncertainties of Cf isotopic ratios range from 0.3% to 0.5% and the uncertainty of the 249 Bk/ 248 Cm and 249 Cf/ 248 Cm elemental ratios are respectively 6.1% and 3.2%.This level of uncertainty for both isotopic and elemental ratios is in perfect agreement with the requirement for transmutation studies. (authors)
Limit theorems for stationary increments Lévy driven moving averages
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas; Lachièze-Rey, Raphaël; Podolskij, Mark
of the kernel function g at 0. First order asymptotic theory essentially comprise three cases: stable convergence towards a certain infinitely divisible distribution, an ergodic type limit theorem and convergence in probability towards an integrated random process. We also prove the second order limit theorem...
Formalization of the Integral Calculus in the PVS Theorem Prover
Butler, Ricky W.
2004-01-01
The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
Probability densities and the radon variable transformation theorem
International Nuclear Information System (INIS)
Ramshaw, J.D.
1985-01-01
D. T. Gillespie recently derived a random variable transformation theorem relating to the joint probability densities of functionally dependent sets of random variables. The present author points out that the theorem can be derived as an immediate corollary of a simpler and more fundamental relation. In this relation the probability density is represented as a delta function averaged over an unspecified distribution of unspecified internal random variables. The random variable transformation is derived from this relation
Quantum work fluctuation theorem: Nonergodic Brownian motion case
International Nuclear Information System (INIS)
Bai, Zhan-Wu
2014-01-01
The work fluctuations of a quantum Brownian particle driven by an external force in a general nonergodic heat bath are studied under a general initial state. The exact analytical expression of the work probability distribution function is derived. Results show the existence of a quantum asymptotic fluctuation theorem, which is in general not a direct generalization of its classical counterpart. The form of this theorem is dependent on the structure of the heat bath and the specified initial condition.
Noncommutative gauge field theories: A no-go theorem
International Nuclear Information System (INIS)
Chaichian, M.; Tureanu, A.; Presnajder, P.; Sheikh-Jabbari, M.M.
2001-06-01
Studying the mathematical structure of the noncommutative groups in more detail, we prove a no-go theorem for the noncommutative gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local noncommutative u(n) algebra only admits the irreducible nxn matrix-representation. Hence the gauge fields, as elements of the algebra, are in nxn matrix form, while the matter fields can only be either in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple group factors, the matter fields can transform nontrivially under at most two noncommutative group factors. In other words, the matter fields cannot carry more than two simple noncommutative gauge group charges. This no-go theorem imposes strong restrictions on the construction of the noncommutative version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED. (author)
Fluctuation theorems and atypical trajectories
International Nuclear Information System (INIS)
Sahoo, M; Lahiri, S; Jayannavar, A M
2011-01-01
In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work (W c ), thermodynamic work (W), total entropy (Δs tot ) and dissipated heat (Q), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at the macroscale. The distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit a peak in the regime of typical behaviour only.
A uniform Tauberian theorem in dynamic games
Khlopin, D. V.
2018-01-01
Antagonistic dynamic games including games represented in normal form are considered. The asymptotic behaviour of value in these games is investigated as the game horizon tends to infinity (Cesàro mean) and as the discounting parameter tends to zero (Abel mean). The corresponding Abelian-Tauberian theorem is established: it is demonstrated that in both families the game value uniformly converges to the same limit, provided that at least one of the limits exists. Analogues of one-sided Tauberian theorems are obtained. An example shows that the requirements are essential even for control problems. Bibliography: 31 titles.
The aftermath of the intermediate value theorem
Directory of Open Access Journals (Sweden)
Morales Claudio H
2004-01-01
Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (17811848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.
Laboratory-scale shielded cell for 252Cf
International Nuclear Information System (INIS)
Anderl, R.A.; Cargo, C.H.
1979-01-01
A shielded-cell facility for storing and handling remotely up to 2 milligram quantities of unencapsulated 252 Cf has been built in a radiochemistry laboratory at the Test Reactor Area of the Idaho National Engineering Laboratory. Unique features of this facility are its compact bulk radiation shield of borated gypsum and transfer lines which permit the transport of fission product activity from 252 Cf fission sources within the cell to a mass separator and to a fast radiochemistry system in nearby rooms
A general conservative extension theorem in process algebras with inequalities
d' Argenio, P.R.; Verhoef, Chris
1997-01-01
We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to
Capacity theory with local rationality the strong Fekete-Szegö theorem on curves
Rumely, Robert
2013-01-01
This book is devoted to the proof of a deep theorem in arithmetic geometry, the Fekete-Szegö theorem with local rationality conditions. The prototype for the theorem is Raphael Robinson's theorem on totally real algebraic integers in an interval, which says that if [a,b] is a real interval of length greater than 4, then it contains infinitely many Galois orbits of algebraic integers, while if its length is less than 4, it contains only finitely many. The theorem shows this phenomenon holds on algebraic curves of arbitrary genus over global fields of any characteristic, and is valid for a broad class of sets. The book is a sequel to the author's work Capacity Theory on Algebraic Curves and contains applications to algebraic integers and units, the Mandelbrot set, elliptic curves, Fermat curves, and modular curves. A long chapter is devoted to examples, including methods for computing capacities. Another chapter contains extensions of the theorem, including variants on Berkovich curves. The proof uses both alg...
DEFF Research Database (Denmark)
Andersen, Mads Peter Sulbæk; Hurley, MD; Wallington, TJ
2004-01-01
Smog chambers equipped with FTIR spectrometers were used to study the Cl atom and OH radical initiated oxidation of CH3O(CF2CF2O)(n)CH3 (n = 1-3) in 720 +/- 20 Torr of air at 296 +/- 3 K. Relative rate techniques were used to measure k(Cl + CH3O(CF2CF2O)(n)CH3) (3.7 +/- 10.7) x 10(-13) and k......(OH + CH3O(CF2CF2O)(n)CH3) = (2.9 +/- 0.5) x 10(-11) cm(3) molecule(-1) s(-1) leading to an estimated atmospheric lifetime of 2 years for CH3O(CF2CF2O),CH3. The Cl initiated oxidation of CH3O(CF2CF2O),CH3 in air diluent gives CH3O(CF2CF2O)(n)C(O)H in a yield which is indistinguishable from 100 Further...... oxidation leads to the diformate, H(O)CO(CF2CF2O)(n)C(O)H. A rate constant of k(Cl + CH3O(CF2CF2O)(n)CHO) = (1.81 +/- 0.36) x 10(-13) cm(3) molecule(-1) s-1 was determined. Quantitative infrared spectra for CH3O(CF2CF2O)(n)CH3 (n = 1-3) were recorded and used to estimate halocarbon global warming potentials...
A Geometrical Approach to Bell's Theorem
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
A Meinardus Theorem with Multiple Singularities
Granovsky, Boris L.; Stark, Dudley
2012-09-01
Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.
System control for the modulated 252Cf source ''Shuffler''
International Nuclear Information System (INIS)
Stephens, M.M.
1975-06-01
The design and theory of operation of the control chassis for a 252 Cf nondestructive assay system are described. This system repetitively transfers a 252 Cf source from the irradiation region to a shielded position before measuring the delayed neutrons. The design criteria for the system were: rapid movement and precise positioning of the 252 Cf source, precise positioning of the sample, and very accurate timing of the irradiate and count cycles. To achieve these results crystal oscillators were used for timing, and stepping motors were used to position the sample and the source. (U.S.)
A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued Functions
Directory of Open Access Journals (Sweden)
Tomás Pérez Becerra
2018-01-01
Full Text Available Using a bounded bilinear operator, we define the Henstock-Stieltjes integral for vector-valued functions; we prove some integration by parts theorems for Henstock integral and a Riesz-type theorem which provides an alternative proof of the representation theorem for real functions proved by Alexiewicz.
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....
General H-theorem and Entropies that Violate the Second Law
Directory of Open Access Journals (Sweden)
Alexander N. Gorban
2014-04-01
Full Text Available H-theorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the entropy production is positive for random transformation of signals (the information processing lemma. Originally, the H-theorem and the information processing lemma were proved for the classical Boltzmann-Gibbs-Shannon entropy and for the correspondent divergence (the relative entropy. Many new entropies and divergences have been proposed during last decades and for all of them the H-theorem is needed. This note proposes a simple and general criterion to check whether the H-theorem is valid for a convex divergence H and demonstrates that some of the popular divergences obey no H-theorem. We consider systems with n states Ai that obey first order kinetics (master equation. A convex function H is a Lyapunov function for all master equations with given equilibrium if and only if its conditional minima properly describe the equilibria of pair transitions Ai ⇌ Aj . This theorem does not depend on the principle of detailed balance and is valid for general Markov kinetics. Elementary analysis of pair equilibria demonstrate that the popular Bregman divergences like Euclidian distance or Itakura-Saito distance in the space of distribution cannot be the universal Lyapunov functions for the first-order kinetics and can increase in Markov processes. Therefore, they violate the second law and the information processing lemma. In particular, for these measures of information (divergences random manipulation with data may add information to data. The main results are extended to nonlinear generalized mass action law kinetic equations.
Metrical theorems on systems of small inhomogeneous linear forms
DEFF Research Database (Denmark)
Hussain, Mumtaz; Kristensen, Simon
In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed.......In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed....
A generalization of Abel's Theorem and the Abel-Jacobi map
DEFF Research Database (Denmark)
Dupont, Johan Louis; Kamber, Franz W.
We generalize Abel’s classical theorem on linear equivalence of divisors on a Riemann surface. For every closed submanifold Md ⊂ Xn in a compact oriented Riemannian n–manifold, or more generally for any d–cycle Z relative to a triangulation of X, we define a (simplicial) (n − d − 1)–gerbe Z......, the Abel gerbe determined by Z, whose vanishing as a Deligne cohomology class generalizes the notion of ‘linear equivalence to zero’. In this setting, Abel’s theorem remains valid. Moreover, we generalize the classical Inversion Theorem for the Abel–Jacobi map, thereby proving that the moduli space of Abel...
Atmospheric chemistry of CF3O radicals: Reaction with H2O
DEFF Research Database (Denmark)
Wallington, T.J.; Hurley, M.D.; Schneider, W.F.
1993-01-01
Evidence is presented that CF3O radicals react with H2O in the gas phase at 296 K to give CF3OH and OH radicals. This reaction is calculated to be exothermic by 1.7 kcal mol-I implying a surprisingly strong CF3O-H bond energy of 120 +/- 3 kcal mol-1. Results from a relative rate experimental study...... suggest that the rate constant for the reaction of CF3O radicals with H2O lies in the range (0.2-4.0) X 10(-17) cm3 molecule-1 s-1. Implications for the atmospheric chemistry of CF3O radicals are discussed....
Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem
Li, Lei; Liu, Jian-Guo; Lu, Jianfeng
2017-10-01
We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.
Fourier diffraction theorem for diffusion-based thermal tomography
International Nuclear Information System (INIS)
Baddour, Natalie
2006-01-01
There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging
Is the Quantum State Real? An Extended Review of ψ-ontology Theorems
Directory of Open Access Journals (Sweden)
Matthew Saul Leifer
2014-11-01
Full Text Available Towards the end of 2011, Pusey, Barrett and Rudolph derived a theorem that aimed to show that the quantum state must be ontic (a state of reality in a broad class of realist approaches to quantum theory. This result attracted a lot of attention and controversy. The aim of this review article is to review the background to the Pusey–Barrett–Rudolph Theorem, to provide a clear presentation of the theorem itself, and to review related work that has appeared since the publication of the Pusey–Barrett–Rudolph paper. In particular, this review: Explains what it means for the quantum state to be ontic or epistemic (a state of knowledge; Reviews arguments for and against an ontic interpretation of the quantum state as they existed prior to the Pusey–Barrett–Rudolph Theorem; Explains why proving the reality of the quantum state is a very strong constraint on realist theories in that it would imply many of the known no-go theorems, such as Bell's Theorem and the need for an exponentially large ontic state space; Provides a comprehensive presentation of the Pusey–Barrett–Rudolph Theorem itself, along with subsequent improvements and criticisms of its assumptions; Reviews two other arguments for the reality of the quantum state: the first due to Hardy and the second due to Colbeck and Renner, and explains why their assumptions are less compelling than those of the Pusey–Barrett–Rudolph Theorem; Reviews subsequent work aimed at ruling out stronger notions of what it means for the quantum state to be epistemic and points out open questions in this area. The overall aim is not only to provide the background needed for the novice in this area to understand the current status, but also to discuss often overlooked subtleties that should be of interest to the experts. Quanta 2014; 3: 67–155.
Anomaly manifestation of Lieb-Schultz-Mattis theorem and topological phases
Cho, Gil Young; Hsieh, Chang-Tse; Ryu, Shinsei
2017-11-01
The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that they can both be described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it were an internal symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, we find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly that is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gaplessness local in the parameter space.
Formalization of the Integral Calculus in the PVS Theorem Prover
Directory of Open Access Journals (Sweden)
Ricky Wayne Butler
2009-04-01
Full Text Available The PVS Theorem prover is a widely used formal verification tool used for the analysis of safetycritical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht’s classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
Bell's theorem, accountability and nonlocality
International Nuclear Information System (INIS)
Vona, Nicola; Liang, Yeong-Cherng
2014-01-01
Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner (2011 Nature Commun. 2 411), we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)
DEFF Research Database (Denmark)
Wallington, TJ; Hurley, MD; Nielsen, OJ
2004-01-01
Fourier transform infrared (FTIR) smog chamber techniques were used to measure k(Cl + CF3CFHCF2OCF3) = (4.09 +/- 0.42) x 10(-17), k(OH + CF3CFHCF2OCF3) = (1.43 +/- 0.28) x 10(-15), k(Cl + CF3CFHCF2OCF2H) = (6.89 +/- 1.29) x 10(-17), and k(OH + CF3CFHCF2OCF2H) = (1.79 +/- 0.34) x 10(-15) cm(3) mol...... respectively. The 100-year time horizon global warming potentials of CF3CFHCF2OCF3 and CF3CFHCF2OCF2H relative to CO2 are 4530 and 4340. Results are discussed with respect to the atmospheric chemistry of hydrofluoroethers....
Waller, Niels
2018-01-01
Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.
Bayes' theorem and its application to nuclear power plant safety
International Nuclear Information System (INIS)
Matsuoka, Takeshi
2013-01-01
Bayes' theorem has been paid in much attention for its application to Probabilistic Safety Assessment (PSA). In this lecture, the basis for understanding Bayes' theorem is first explained and how to interpret the Bayes' equation with respect to the pair of conjugate distributions between prior distribution and likelihood. Then for the application to PSA, component failure data are evaluated by Bayes' theorem by using the examples of demand probability of the start of diesel generator and failure of pressure sensor. Frequencies of nuclear power plant accidents are also evaluated by Bayes' theorem for the example case of frequency of 'fires in reactor compartment' and 'core melt' frequency with the experience of Fukushima dai-ichi accidents. Lastly, several contrasting arguments are introduced briefly between favorable and critical peoples regarding the Bayes' methods. (author)
Non-renormalization theorems andN=2 supersymmetric backgrounds
International Nuclear Information System (INIS)
Butter, Daniel; Wit, Bernard de; Lodato, Ivano
2014-01-01
The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed
Twelve years before the quantum no-cloning theorem
Ortigoso, Juan
2018-03-01
The celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Found. Phys. 1, 23-33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park's demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning.
Strong limit theorems in noncommutative L2-spaces
Jajte, Ryszard
1991-01-01
The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.
A power counting theorem for Feynman integrals on the lattice
International Nuclear Information System (INIS)
Reisz, T.
1988-01-01
A convergence theorem is proved, which states sufficient conditions for the existence of the continuum limit for a wide class of Feynman integrals on a space-time lattice. A new kind of a UV-divergence degree is introduced, which allows the formulation of the theorem in terms of power counting conditions. (orig.)
International Nuclear Information System (INIS)
Cooperstock, F.I.; Lim, P.H.
1986-01-01
Theorems expressing the time derivatives of retarded volume and surface integrals are presented as well as the Gauss divergence theorem for retarded functions with discontinuities. These theorems greatly facilitate the analysis of gravitational radiation from the motion of disjoint matter distributions in general relativity and could find useful application in other branches of physics
2011-05-11
... methods: Federal eRulemaking Portal: Go to http://www.regulations.gov . Follow the instructions for... Investigation of a General Electric Company (GE) CF34-10E turbofan engine experiencing high fan frame vibrations... likely to exist or develop in other products of the same type design. Proposed AD Requirements This...
CF 2000 ECUMÊNICA: EPISÓDIO OU NOVA FASE DA CF?
Directory of Open Access Journals (Sweden)
Gabriele Cipriani
2001-01-01
Full Text Available No ano 2000, sete igrejas cristãs, membros do Conselho Nacional de Igrejas Cristãs do Brasil (CONIC, surpreenderam a opinião pública brasileira colocando-se na contramão da competição cotidiana que caracteriza o anúncio do Evangelho no Brasil. Promoveram em conjunto uma Campanha da Fraternidade (CF criada e realizada há 36 anos pela CNBB. Isso tinha algo de incrível.
Multivariable Chinese Remainder Theorem
Indian Academy of Sciences (India)
IAS Admin
to sleep. The 3rd thief wakes up and finds the rest of the coins make 7 equal piles excepting a coin which he pockets. If the total number of coins they stole is not more than 200, what is the exact number? With a bit of hit and miss, one can find that 157 is a possible number. The Chinese remainder theorem gives a systematic ...
Angle Defect and Descartes' Theorem
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
Optical theorem and its history
International Nuclear Information System (INIS)
Newton, R.G.
1978-01-01
A translation is presented of a paper submitted to the symposium ''Concepts and methods in microscopic physics'' held at Washington University in 1974. A detailed description is given of the history of the optical theorem, its various formulations and derivations and its use in the scattering theory. (Z.J.)
International Nuclear Information System (INIS)
Lloyd, Mark Anthony
1999-01-01
We in the nuclear power industry consider ourselves to be at the forefront of civilised progress. Yet, all too often, even we ourselves don't believe our public relations statements about nuclear power. Why is this? Let us approach the question by considering Godel's Theorem. Godel's Theorem is extremely complicated mathematically, but for our purposes can be simplified to the maxim that one cannot validate a system from within that system. Scientists, especially those in the fields of astronomy and nuclear physics, have long realised the implications of Godel's Theorem. The people to whom we must communicate look to us, who officially know everything about our industry, to comfort and reassure them. And we forget that we can only comfort them by addressing their emotional needs, not by demonstrating our chilling o bjectivity . Let us try something completely new in communication. Instead of looking for incremental rules which will help us marginally differentiate the way we communicate about minor or major incidents, let us leapfrog across 'objectivity' to meaning and relevance. If we truly believe that nuclear energy is a good thing, this leap should not be difficult. Finally, if we as communicators are not prepared to be meaningful and relevant - not prepared to leapfrog beyond weasel terms like 'minor incident' - what does that say about the kinds of people we believe the nuclear community to be? Are nuclear people a group apart, divisible from the rest of the human race by their evil? In fact the nuclear community is a living, laughing, normal part of a whole society; and is moreover a good contributor to the technological progress that society demands. When we ourselves recognise this, we will start to communicate nuclear issues in the same language as the rest of society. We will start to speak plainly and convincingly, and our conviction will leapfrog our audience into being able to believe us
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.
Investigation of the characteristics of 252Cf-detectors
International Nuclear Information System (INIS)
Karlsson, Erik
2004-12-01
In the first chapter the characteristic behaviors of two Cf detectors have been investigated by performing pilot measurements. The detector with the stronger source gives an unstable signal with a low signal/noise ratio. Therefore this detector has not been further investigated. The ionization chamber reacts on both fission products and alpha decay. An energy experiment showed that there were large difficulties to separate those decays. A plastic scintillator, which reacts on both photons and neutrons, was used for neutron detection. Energy spectrums were performed and the result showed that it is difficult to set an energy threshold to separate the neutrons and the photons. The discrimination will rather be achieved by time of flight methods which is discussed under the second chapter in this thesis; Experimental results. An other experiment was done in order to investigate whether it is possible to detect any delayed components from the spontaneous fission of Cf. The result showed that delayed components existed. Either they are delayed neutrons from exited fission products, or it is some delay related to the charge collection in the Cf detector. Correlation measurements showed that few events are coincident. Only 50% of the signals from the plastic scintillator are correlated with the Cf source
Radon transformation on reductive symmetric spaces:Support theorems
DEFF Research Database (Denmark)
Kuit, Job Jacob
2013-01-01
We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and derive support theorems for these transforms. A reductive symmetric space is a homogeneous space G/H for a reductive Lie group G of the Harish-Chandra class, where H is an open sub...... is based on the relation between the Radon transform and the Fourier transform on G/H, and a Paley–Wiener-shift type argument. Our results generalize the support theorem of Helgason for the Radon transform on a Riemannian symmetric space....
Convergence theorems for Banach space valued integrable multifunctions
Directory of Open Access Journals (Sweden)
Nikolaos S. Papageorgiou
1987-01-01
Full Text Available In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω (1≤p≤∞. Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.
Poisson's theorem and integrals of KdV equation
International Nuclear Information System (INIS)
Tasso, H.
1978-01-01
Using Poisson's theorem it is proved that if F = integral sub(-infinity)sup(+infinity) T(u,usub(x),...usub(n,t))dx is an invariant functional of KdV equation, then integral sub(-infinity)sup(+infinity) delta F/delta u dx integral sub(-infinity)sup(+infinity) delta T/delta u dx is also an invariant functional. In the case of a polynomial T, one finds in a simple way the known recursion ΔTr/Δu = Tsub(r-1). This note gives an example of the usefulness of Poisson's theorem. (author)
Extension and reconstruction theorems for the Urysohn universal metric space
Czech Academy of Sciences Publication Activity Database
Kubiś, Wieslaw; Rubin, M.
2010-01-01
Roč. 60, č. 1 (2010), s. 1-29 ISSN 0011-4642 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Urysohn space * bilipschitz homeomorphism * modulus of continuity * reconstruction theorem * extension theorem Subject RIV: BA - General Mathematics Impact factor: 0.265, year: 2010 http://dml.cz/handle/10338.dmlcz/140544
On the Fourier integral theorem
Koekoek, J.
1987-01-01
Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the
Electron and photon impact studies of CF3I
International Nuclear Information System (INIS)
Mason, N.J.; Eden, S.; Limao Vieire, P.; Kendall, P.; Pathak, S.; Dawes, A.; Tegeder, P.; Kitajima, M.; Okamoto, M.; Tanaka, H.; Samukawa, S.; Cho, H.; Hoffmann, S.
2002-01-01
The manufacture of ultra-large-scale-integrated circuits, requires a well collimated, specially uniform, high density plasma source operating under low pressure conditions. The main feed gases used are perfluorocarbons, however these are also strong greenhouse gases, therefore must be replaced by alternative compounds with low global warming potentials. CF 3 I is one possible replacement, due to its high photolysis rate, is expected to have a very short lifetime in the atmosphere. It is also predicted to be able to produced high yields of CF 3 radicals in any etching plasma, since its weak C - I bond should be possible to break by direct electron impact. Prior adapting existing industrial plasma reactors to use CF 3 I, it is necessary to run simulations of the reactant plasma, requiring a detailed database of the electron interactions with the feed gases, however such CF 3 I data does not exist. Thus an exhaustive series of experiments to measure elastic and inelastic scattering from CF 3 I including a study of its electronic state spectroscopy using photon absorption and electron scattering techniques were performed. Electron energy loss spectroscopy (EELS) and photo-absorption spectroscopy were employed. A comprehensive set of differential cross sections for the elastic scattering CF 3 I over the impact energy region from 1.5 to 60 eV for scattering angles between 20 and 130 were compiled. The photo-absorption spectrum is characterized by three regions, the first is a very weak continuum around centered about 4.7 eV; the second consists of four prominent band structures observed around 7.4, 8.1, 9.0 and 9.8 eV, respectively, containing vibrational structure from 7 to 10 eV; the third (above the ionization potentials) could only be studied by using EELS and additional broad peaks were observed. (nevyjel)
A New Simple Approach for Entropy and Carnot Theorem
International Nuclear Information System (INIS)
Veliev, E. V.
2004-01-01
Entropy and Carnot theorem occupy central place in the typical Thermodynamics courses at the university level. In this work, we suggest a new simple approach for introducing the concept of entropy. Using simple procedure in TV plane, we proved that for reversible processes ∫dQ/T=0 and it is sufficient to define entropy. And also, using reversible processes in TS plane, we give an alternative simple proof for Carnot theorem
H-theorems from macroscopic autonomous equations
Czech Academy of Sciences Publication Activity Database
De Roeck, W.; Maes, C.; Netočný, Karel
2006-01-01
Roč. 123, č. 3 (2006), s. 571-583 ISSN 0022-4715 Institutional research plan: CEZ:AV0Z10100520 Keywords : H-theorem, entropy * irreversible equations Subject RIV: BE - Theoretical Physics Impact factor: 1.437, year: 2006
Differentiability in density-functional theory: Further study of the locality theorem
International Nuclear Information System (INIS)
Lindgren, Ingvar; Salomonson, Sten
2004-01-01
The locality theorem in density-functional theory (DFT) states that the functional derivative of the Hohenberg-Kohn universal functional can be expressed as a local multiplicative potential function, and this is the basis of DFT and of the successful Kohn-Sham model. Nesbet has in several papers [Phys. Rev. A 58, R12 (1998); ibid.65, 010502 (2001); Adv. Quant. Chem, 43, 1 (2003)] claimed that this theorem is in conflict with fundamental quantum physics, and as a consequence that the Hohenberg-Kohn theory cannot be generally valid. We have commented upon these works [Comment, Phys. Rev. A 67, 056501 (2003)] and recently extended the arguments [Adv. Quantum Chem. 43, 95 (2003)]. We have shown that there is no such conflict and that the locality theorem is inherently exact. In the present work we have furthermore verified this numerically by constructing a local Kohn-Sham potential for the 1s2s 3 S state of helium that generates the many-body electron density and shown that the corresponding 2s Kohn-Sham orbital eigenvalue agrees with the ionization energy to nine digits. Similar result is obtained with the Hartree-Fock density. Therefore, in addition to verifying the locality theorem, this result also confirms the so-called ionization-potential theorem
Lin, Ju; Li, Jie; Li, Xiaolei; Wang, Ning
2016-10-01
An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.
Zhao, Hang; Lu, Yinxiang
2016-01-01
Nickel films were grown on citric acid (CA), malic acid (MA) and oxalic acid (OA) modified cuprammonium fabric (CF) substrates via electroless nickel deposition. The nickel films were examined using scanning electron microscopy (SEM) and X-ray diffraction (XRD). Their individual deposition rate and electromagnetic interference (EMI) shielding effectiveness (SE) were also investigated to compare the properties of electroless nickel films. SEM images illustrated that the nickel film on MA modified CF substrate was smooth and uniform, and the density of nickel nuclei was much higher. Compared with that of CA modified CF, the coverage of nickel nuclei on OA and MA modified CF substrate was very limited and the nickel particles size was too big. XRD analysis showed that the nickel films deposited on the different modified CF substrates had a structure with Ni (1 1 1) preferred orientation. All the nickel coatings via different acid modification were firmly adhered to the CF substrates, as demonstrated by an ultrasonic washing test. The result of tensile test indicated that the electroless nickel plating on CF has ability to strengthen the CF substrate while causes limited effect on tensile elongation. Moreover, the nickel film deposited on MA modified CF substrate showed more predominant in EMI SE than that deposited on CA or OA modified CF.
Graphite moderated {sup 252}Cf source
Energy Technology Data Exchange (ETDEWEB)
Sajo B, L.; Barros, H.; Greaves, E. D. [Universidad Simon Bolivar, Nuclear Physics Laboratory, Apdo. 89000, 1080A Caracas (Venezuela, Bolivarian Republic of); Vega C, H. R., E-mail: fermineutron@yahoo.com [Universidad Autonoma de Zacatecas, Unidad Academica de Estudios Nucleares, Cipres No. 10, Fracc. La Penuela, 98068 Zacatecas (Mexico)
2014-08-15
The thorium molten salt reactor is an attractive and affordable nuclear power option for developing countries with insufficient infrastructure and limited technological capability. In the aim of personnel training and experience gathering at the Universidad Simon Bolivar there is in progress a project of developing a subcritical thorium liquid fuel reactor. The neutron source to run this subcritical reactor is a {sup 252}Cf source and the reactor will use high-purity graphite as moderator. Using the MCNP5 code the neutron spectra of the {sup 252}Cf in the center of the graphite moderator has been estimated along the channel where the liquid thorium salt will be inserted; also the ambient dose equivalent due to the source has been determined around the moderator. (Author)
Asymptotic twistor theory and the Kerr theorem
International Nuclear Information System (INIS)
Newman, Ezra T
2006-01-01
We first review asymptotic twistor theory with its real subspace of null asymptotic twistors: a five-dimensional CR manifold. This is followed by a description of the Kerr theorem (the identification of shear-free null congruences, in Minkowski space, with the zeros of holomorphic functions of three variables) and an asymptotic version of the Kerr theorem that produces regular asymptotically shear-free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes. A surprising aspect of this work is the role played by analytic curves in H-space, each curve generating an asymptotically flat null geodesic congruence. Also there is a discussion of the physical space realizations of the two associated five- and three-dimensional CR manifolds
Proofs and generalizations of the pythagorean theorem
Directory of Open Access Journals (Sweden)
Lialda B. Cavalcanti
2011-01-01
Full Text Available This article explores a topic developed by a group of researchers of the Science and Technology Teaching School of Instituto Federal de Pernambuco, Brazil (IFPE, in assistance to the development of the Mathematics Practical and Teaching Laboratory of the distance learning Teaching Licensure, financed by the Universidad Abierta de Brasil. In this article, we describe the peculiarities present in the proofs of the Pythagorean theorem with the purpose of illustrating some of these methods. The selection of these peculiarities was founded and based on the comparison of areas by means of the superimposition of geometrical shapes and used several different class resources. Some generalizations of this important theorem in mathematical problem-solving are also shown.
KLN theorem and infinite statistics
International Nuclear Information System (INIS)
Grandou, T.
1992-01-01
The possible extension of the Kinoshita-Lee-Nauenberg (KLN) theorem to the case of infinite statistics is examined. It is shown that it appears as a stable structure in a quantum field theory context. The extension is provided by working out the Fock space realization of a 'quantum algebra'. (author) 2 refs
Fermion fractionization and index theorem
International Nuclear Information System (INIS)
Hirayama, Minoru; Torii, Tatsuo
1982-01-01
The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)
The Geometric Mean Value Theorem
de Camargo, André Pierro
2018-01-01
In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…
Enterococcus faecalis Sex Pheromone cCF10 Enhances Conjugative Plasmid Transfer In Vivo.
Hirt, Helmut; Greenwood-Quaintance, Kerryl E; Karau, Melissa J; Till, Lisa M; Kashyap, Purna C; Patel, Robin; Dunny, Gary M
2018-02-13
Cell-cell communication mediated by peptide pheromones (cCF10 [CF]) is essential for high-frequency plasmid transfer in vitro in Enterococcus faecalis To examine the role of pheromone signaling in vivo , we established either a CF-producing (CF+) recipient or a recipient producing a biologically inactive variant of CF (CF- recipient) in a germfree mouse model 3 days before donor inoculation and determined transfer frequencies of the pheromone-inducible plasmid pCF10. Plasmid transfer was detected in the upper and middle sections of the intestinal tract 5 h after donor inoculation and was highly efficient in the absence of antibiotic selection. The transconjugant/donor ratio reached a maximum level approaching 1 on day 4 in the upper intestinal tract. Plasmid transfer was significantly lower with the CF- recipient. While rescue of the CF- mating defect by coculture with CF+ recipients is easily accomplished in vitro , no extracellular complementation occurred in vivo This suggests that most pheromone signaling in the gut occurs between recipient and donor cells in very close proximity. Plasmid-bearing cells (donors plus transconjugants) steadily increased in the population from 0.1% after donor inoculation to about 10% at the conclusion of the experiments. This suggests a selective advantage of pCF10 carriage distinct from antibiotic resistance or bacteriocin production. Our results demonstrate that pheromone signaling is required for efficient pCF10 transfer in vivo In the absence of CF+ recipients, a low level of transfer to CF- recipients occurred in the gut. This may result from low-level host-mediated induction of the donors in the gastrointestinal (GI) tract, similar to that previously observed in serum. IMPORTANCE Horizontal gene transfer is a major factor in the biology of Enterococcus faecalis , an important nosocomial pathogen. Previous studies showing efficient conjugative plasmid transfer in the gastrointestinal (GI) tracts of experimental animals did
Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator
Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi
2018-03-01
Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.
Vapour–to–liquid nucleation: Nucleation theorems for nonisothermal–nonideal case
Energy Technology Data Exchange (ETDEWEB)
Malila, J.; McGraw, R.; Napari, I.; Laaksonen, A.
2010-08-29
Homogeneous vapour-to-liquid nucleation, a basic process of aerosol formation, is often considered as a type example of nucleation phenomena, while most treatment of the subject introduce several simplifying assumptions (ideal gas phase, incompressible nucleus, isothermal kinetics, size-independent surface free energy...). During last decades, nucleation theorems have provided new insights into properties of critical nuclei facilitating direct comparison between laboratory experiments and molecular simulations. These theorems are, despite of their generality, often applied in forms where the aforementioned assumptions are made. Here we present forms of nucleation theorems that explicitly take into account these effects and allow direct estimation of their importance. Only assumptions are Arrhenius-type kinetics of nucleation process and exclusion carrier gas molecules from the critical nucleus.
A general product measurability theorem with applications to variational inequalities
Directory of Open Access Journals (Sweden)
Kenneth L. Kuttler
2016-03-01
Full Text Available This work establishes the existence of measurable weak solutions to evolution problems with randomness by proving and applying a novel theorem on product measurability of limits of sequences of functions. The measurability theorem is used to show that many important existence theorems within the abstract theory of evolution inclusions or equations have straightforward generalizations to settings that include random processes or coefficients. Moreover, the convex set where the solutions are sought is not fixed but may depend on the random variables. The importance of adding randomness lies in the fact that real world processes invariably involve randomness and variability. Thus, this work expands substantially the range of applications of models with variational inequalities and differential set-inclusions.
Fixed-point theorems for families of weakly non-expansive maps
Mai, Jie-Hua; Liu, Xin-He
2007-10-01
In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.
Splitting spacetime and cloning qubits: linking no-go theorems across the ER=EPR duality
Energy Technology Data Exchange (ETDEWEB)
Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States); Pollack, Jason; Remmen, Grant N. [Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States)
2015-11-15
We analyze the no-cloning theorem in quantum mechanics through the lens of the proposed ER=EPR (Einstein-Rosen = Einstein-Podolsky-Rosen) duality between entanglement and wormholes. In particular, we find that the no-cloning theorem is dual on the gravity side to the no-go theorem for topology change, violating the axioms of which allows for wormhole stabilization and causality violation. Such a duality between important no-go theorems elucidates the proposed connection between spacetime geometry and quantum entanglement. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Enterococcus faecalis Sex Pheromone cCF10 Enhances Conjugative Plasmid Transfer In Vivo
Directory of Open Access Journals (Sweden)
Helmut Hirt
2018-02-01
Full Text Available Cell-cell communication mediated by peptide pheromones (cCF10 [CF] is essential for high-frequency plasmid transfer in vitro in Enterococcus faecalis. To examine the role of pheromone signaling in vivo, we established either a CF-producing (CF+ recipient or a recipient producing a biologically inactive variant of CF (CF− recipient in a germfree mouse model 3 days before donor inoculation and determined transfer frequencies of the pheromone-inducible plasmid pCF10. Plasmid transfer was detected in the upper and middle sections of the intestinal tract 5 h after donor inoculation and was highly efficient in the absence of antibiotic selection. The transconjugant/donor ratio reached a maximum level approaching 1 on day 4 in the upper intestinal tract. Plasmid transfer was significantly lower with the CF− recipient. While rescue of the CF− mating defect by coculture with CF+ recipients is easily accomplished in vitro, no extracellular complementation occurred in vivo. This suggests that most pheromone signaling in the gut occurs between recipient and donor cells in very close proximity. Plasmid-bearing cells (donors plus transconjugants steadily increased in the population from 0.1% after donor inoculation to about 10% at the conclusion of the experiments. This suggests a selective advantage of pCF10 carriage distinct from antibiotic resistance or bacteriocin production. Our results demonstrate that pheromone signaling is required for efficient pCF10 transfer in vivo. In the absence of CF+ recipients, a low level of transfer to CF− recipients occurred in the gut. This may result from low-level host-mediated induction of the donors in the gastrointestinal (GI tract, similar to that previously observed in serum.
A Short Proof of Klee's Theorem
Zanazzi, John J.
2013-01-01
In 1959, Klee proved that a convex body $K$ is a polyhedron if and only if all of its projections are polygons. In this paper, a new proof of this theorem is given for convex bodies in $\\mathbb{R}^3$.
Czech Academy of Sciences Publication Activity Database
Narins, L.; Tran, Tuan
2017-01-01
Roč. 85, č. 2 (2017), s. 496-524 ISSN 0364-9024 Institutional support: RVO:67985807 Keywords : Turán’s theorem * stability method * multipartite version Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.601, year: 2016
The Completeness Theorem of Godel
Indian Academy of Sciences (India)
GENERAL I ARTICLE. The Completeness Theorem of Godel. 2. Henkin's Proof for First Order Logic. S M Srivastava is with the. Indian Statistical,. Institute, Calcutta. He received his PhD from the Indian Statistical. Institute in 1980. His research interests are in descriptive set theory. I Part 1. An Introduction to Math- ematical ...
On the Stone-Weierstrass theorem for scalar and vector valued functions
International Nuclear Information System (INIS)
Khan, L.A.
1991-09-01
In this paper we discuss the formulation of the Stone-Weierstrass approximation theorem for vector-valued functions and then determine whether the classical Stone-Weierstrass theorem for scalar-valued functions can be deduced from the above one. We also state some open problems in this area. (author). 15 refs
There's Something About Gödel The Complete Guide to the Incompleteness Theorem
Berto, Francesco
2009-01-01
Berto's highly readable and lucid guide introduces students and the interested reader to Gödel's celebrated Incompleteness Theorem, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments.Offers a clear understanding of this difficult subject by presenting each of the key steps of the Theorem in separate chaptersDiscusses interpretations of the Theorem made by celebrated contemporary thinkersSheds light on the wider extra-mathematical and philosophical implications of Gödel's theoriesWritten in an accessible, non-technical style
The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum
Energy Technology Data Exchange (ETDEWEB)
Alpay, Daniel, E-mail: dany@math.bgu.ac.il; Kimsey, David P., E-mail: dpkimsey@gmail.com [Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Colombo, Fabrizio, E-mail: fabrizio.colombo@polimi.it [Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133 Milano (Italy)
2016-02-15
In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of S-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With this paper we complete the foundation of spectral analysis of quaternionic operators. The S-spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. The lack of a suitable notion of spectrum was a major obstruction to fully understand the spectral theorem for quaternionic normal operators. A prime motivation for studying the spectral theorem for quaternionic unbounded normal operators is given by the subclass of unbounded anti-self adjoint quaternionic operators which play a crucial role in the quaternionic quantum mechanics.
A variational proof of Thomson's theorem
Energy Technology Data Exchange (ETDEWEB)
Fiolhais, Miguel C.N., E-mail: miguel.fiolhais@cern.ch [Department of Physics, City College of the City University of New York, 160 Convent Avenue, New York, NY 10031 (United States); Department of Physics, New York City College of Technology, 300 Jay Street, Brooklyn, NY 11201 (United States); LIP, Department of Physics, University of Coimbra, 3004-516 Coimbra (Portugal); Essén, Hanno [Department of Mechanics, Royal Institute of Technology (KTH), Stockholm SE-10044 (Sweden); Gouveia, Tomé M. [Cavendish Laboratory, 19 JJ Thomson Avenue, Cambridge CB3 0HE (United Kingdom)
2016-08-12
Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.
Vanishing theorems and effective results in algebraic geometry
International Nuclear Information System (INIS)
Demailly, J.P.; Goettsche, L.; Lazarsfeld, R.
2001-01-01
The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks
Refinement of Representation Theorems for Context-Free Languages
Fujioka, Kaoru
In this paper, we obtain some refinement of representation theorems for context-free languages by using Dyck languages, insertion systems, strictly locally testable languages, and morphisms. For instance, we improved the Chomsky-Schützenberger representation theorem and show that each context-free language L can be represented in the form L = h (D ∩ R), where D is a Dyck language, R is a strictly 3-testable language, and h is a morphism. A similar representation for context-free languages can be obtained, using insertion systems of weight (3, 0) and strictly 4-testable languages.
Vanishing theorems and effective results in algebraic geometry
Energy Technology Data Exchange (ETDEWEB)
Demailly, J P [Universite de Grenoble (France); Goettsche, L [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Lazarsfeld, R [University of Michigan (United States)
2001-12-15
The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks.
Theorem on axially symmetric gravitational vacuum configurations
Energy Technology Data Exchange (ETDEWEB)
Papadopoulos, A; Le Denmat, G [Paris-6 Univ., 75 (France). Inst. Henri Poincare
1977-01-24
A theorem is proved which asserts the non-existence of axially symmetric gravitational vacuum configurations with non-stationary rotation only. The eventual consequences in black-hole physics are suggested.
Nash-Williams’ cycle-decomposition theorem
DEFF Research Database (Denmark)
Thomassen, Carsten
2016-01-01
We give an elementary proof of the theorem of Nash-Williams that a graph has an edge-decomposition into cycles if and only if it does not contain an odd cut. We also prove that every bridgeless graph has a collection of cycles covering each edge at least once and at most 7 times. The two results...
Directory of Open Access Journals (Sweden)
SEVER ANGEL POPESCU
2015-03-01
Full Text Available In this note we make some remarks on the classical Laguerre’s theorem and extend it and some other old results of Walsh and Gauss-Lucas to the so called trace series associated with transcendental elements of the completion of the algebraic closure of Q in C, with respect to the spectral norm:
Lagrange’s Four-Square Theorem
Directory of Open Access Journals (Sweden)
Watase Yasushige
2015-02-01
Full Text Available This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23].
A THEOREM ON CENTRAL VELOCITY DISPERSIONS
International Nuclear Information System (INIS)
An, Jin H.; Evans, N. Wyn
2009-01-01
It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere (SIS), the logarithmic cusp slope γ of the tracers must be given exactly by γ = 2β, where β is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster than that of the SIS, the velocity dispersion of the tracers must diverge at the center too. In particular, if the logarithmic halo cusp slope is larger than two, the diverging velocity dispersion also traces the behavior of the potential. The implication of our theorem on projected quantities is also discussed. We argue that our theorem should be understood as a warning against interpreting results based on simplifying assumptions such as isotropy and spherical symmetry.
Cystic Fibrosis (CF): Chloride Sweat Test
... on this topic for: Parents Kids Teens Cystic Fibrosis Cystic Fibrosis and Nutrition Cystic Fibrosis (CF) Respiratory Screen: Sputum Cystic Fibrosis: Diet and Nutrition Cystic Fibrosis Cystic Fibrosis: Diet and Nutrition View more Partner Message ...
The g-theorem and quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo [Centro Atómico Bariloche and CONICET,S.C. de Bariloche, Río Negro, R8402AGP (Argentina)
2016-10-25
We study boundary renormalization group flows between boundary conformal field theories in 1+1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the g-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.
Quantum no-singularity theorem from geometric flows
Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag
2018-04-01
In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.
The Pi-Theorem Applications to Fluid Mechanics and Heat and Mass Transfer
Yarin, L P
2012-01-01
This volume presents applications of the Pi-Theorem to fluid mechanics and heat and mass transfer. The Pi-theorem yields a physical motivation behind many flow processes and therefore it constitutes a valuable tool for the intelligent planning of experiments in fluids. After a short introduction to the underlying differential equations and their treatments, the author presents many novel approaches how to use the Pi-theorem to understand fluid mechanical issues. The book is a great value to the fluid mechanics community, as it cuts across many subdisciplines of experimental fluid mechanics.
International Nuclear Information System (INIS)
Palmer, R.
1994-06-01
Electromagnetic fields can be separated into near and far components. Near fields are extensions of static fields. They do not radiate, and they fall off more rapidly from a source than far fields. Near fields can accelerate particles, but the ratio of acceleration to source fields at a distance R, is always less than R/λ or 1, whichever is smaller. Far fields can be represented as sums of plane parallel, transversely polarized waves that travel at the velocity of light. A single such wave in a vacuum cannot give continuous acceleration, and it is shown that no sums of such waves can give net first order acceleration. This theorem is proven in three different ways; each method showing a different aspect of the situation
Limit theorems for multi-indexed sums of random variables
Klesov, Oleg
2014-01-01
Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who ...
More on Weinberg's no-go theorem in quantum gravity
Nagahama, Munehiro; Oda, Ichiro
2018-05-01
We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.
Testing Moderating Detection Systems with 252Cf-Based Reference Neutron Fields
International Nuclear Information System (INIS)
Hertel, Nolan E.; Sweezy, Jeremy; Sauber, Jeremiah S.; Vaughn, David; Cook, Andrew; Tays, Jeff; Ro, Tae-Ik
2001-01-01
Calibration measurements were carried out on a probe designed to measure ambient dose equivalent in accordance with ICRP Pub 60 recommendations. It consists of a cylindrical 3 He proportional counter surrounded by a 25-cm-diameter spherical polyethylene moderator. Its neutron response is optimized for dose rate measurements of neutrons between thermal energies and 20 MeV. The instrument was used to measure the dose rate in four separate neutron fields: unmoderated 252 Cf, D 2 O-moderated 252 Cf, polyethylene-moderated 252 Cf, and WEP neutron howitzer with 252 Cf at its center. Dose equivalent measurements were performed at source-detector centerline distances from 50 to 200 cm. The ratio of air-scatter- and room-return-corrected ambient dose equivalent rates to ambient dose equivalent rates calculated with the code MCNP are tabulated
Locally Hamiltonian systems with symmetry and a generalized Noether's theorem
International Nuclear Information System (INIS)
Carinena, J.F.; Ibort, L.A.
1985-01-01
An analysis of global aspects of the theory of symmetry groups G of locally Hamiltonian dynamical systems is carried out for particular cases either of the symmetry group, or the differentiable manifold M supporting the symplectic structure, or the action of G on M. In every case it is obtained a generalization of Noether's theorem. It has been looked at the classical Noether's theorem for Lagrangian systems from a modern perspective
A short list color proof of Grötzsch's theorem
DEFF Research Database (Denmark)
Thomassen, Carsten
2003-01-01
We give a short proof of the result that every planar graph of girth 5 is 3-choosable and hence also of Grotzsch's theorem saying that every planar triangle-free graph is 3-colorable.......We give a short proof of the result that every planar graph of girth 5 is 3-choosable and hence also of Grotzsch's theorem saying that every planar triangle-free graph is 3-colorable....
Rate constants for the reaction of CF3O radicals with hydrocarbons at 298 K
DEFF Research Database (Denmark)
Kelly, C.; Treacy, J.; Sidebottom, H.W.
1993-01-01
Rate constant ratios of the reactions of CF3O radicals with a number of hydrocarbons have been determined at 298 +/- 2 K and atmospheric pressure using a relative rate method. Using a previously determined value k(CF30 + C2H6) = 1.2 x 10(-12) cm3 molecule-1 s-1 these rate constant ratios provide...... estimates of the rate constants: k(CF3O + CH4) = (1.2 +/- 0.1) x 10(-14), k(CF3O + c-C3H6) = (3.6 +/- 0.2) x 10(-13), k(CF3O + C3H8) = (4.7 +/- 0.7) x 10(-12), k(CF3O + (CH3)3CH) = (7.2 +/- 0.5) x 10(-12), k(CF3O + C2H4) = (3.0 +/- 0.1) x 10(-11) and k(CF3O + C6H6) = (3.6 +/- 0.1) x 10(-11) cm3 molecule-1 s......-1. The importance of the reactions of CF3O radicals with hydrocarbons under atmospheric conditions is discussed....
Reproductive Toxicity Screen of Trifluoroiodomethane (CF31) in Sprague-Dawley Rats
National Research Council Canada - National Science Library
Dodd, Darol
1998-01-01
.... The purpose of this study was to determine and evaluate the potential for CF3I to produce reproductive toxicity and to provide additional information on the effect of CF3I exposure on the thyroid...
Relaxed Bell inequalities and Kochen-Specker theorems
Energy Technology Data Exchange (ETDEWEB)
Hall, Michael J. W. [Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200 (Australia)
2011-08-15
The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must be individually or jointly relaxed in any model of such correlations. The necessary degrees of relaxation are quantified here via natural distance and information-theoretic measures. This allows quantitative comparisons between different models in terms of the resources, such as the number of bits of randomness, communication, and/or correlation, that they require. For example, measurement dependence is a relatively strong resource for modeling singlet-state correlations, with only 1/15 of one bit of correlation required between measurement settings and the underlying variable. It is shown how various ''relaxed'' Bell inequalities may be obtained, which precisely specify the complementary degrees of relaxation required to model any given violation of a standard Bell inequality. The robustness of a class of Kochen-Specker theorems, to relaxation of measurement independence, is also investigated. It is shown that a theorem of Mermin remains valid unless measurement independence is relaxed by 1/3. The Conway-Kochen ''free will'' theorem and a result of Hardy are less robust, failing if measurement independence is relaxed by only 6.5% and 4.5%, respectively. An appendix shows that existence of an outcome-independent model is equivalent to existence of a deterministic model.
Two theorems on flat space-time gravitational theories
International Nuclear Information System (INIS)
Castagnino, M.; Chimento, L.
1980-01-01
The first theorem states that all flat space-time gravitational theories must have a Lagrangian with a first term that is an homogeneous (degree-1) function of the 4-velocity usup(i), plus a functional of nsub(ij)usup(i)usup(j). The second theorem states that all gravitational theories that satisfy the strong equivalence principle have a Lagrangian with a first term gsub(ij)(x)usup(i)usup(j) plus an irrelevant term. In both cases the theories must issue from a unique variational principle. Therefore, under this condition it is impossible to find a flat space-time theory that satisfies the strong equivalence principle. (author)
Restriction Theorem for Principal bundles in Arbitrary Characteristic
DEFF Research Database (Denmark)
Gurjar, Sudarshan
2015-01-01
The aim of this paper is to prove two basic restriction theorem for principal bundles on smooth projective varieties in arbitrary characteristic generalizing the analogues theorems of Mehta-Ramanathan for vector bundles. More precisely, let G be a reductive algebraic group over an algebraically...... closed field k and let X be a smooth, projective variety over k together with a very ample line bundle O(1). The main result of the paper is that if E is a semistable (resp. stable) principal G-bundle on X w.r.t O(1), then the restriction of E to a general, high multi-degree, complete-intersection curve...
Assessment of CF lung disease using motion corrected PROPELLER MRI: a comparison with CT
Energy Technology Data Exchange (ETDEWEB)
Ciet, Pierluigi [General Hospital Ca' Foncello, Radiology Department, Treviso (Italy); Sophia Children' s Hospital, Pediatric Pulmonology Erasmus MC, Rotterdam (Netherlands); Erasmus MC, Radiology, Rotterdam (Netherlands); Serra, Goffredo; Catalano, Carlo [University of Rome ' ' Sapienza' ' , Radiology, Rome (Italy); Bertolo, Silvia; Morana, Giovanni [General Hospital Ca' Foncello, Radiology Department, Treviso (Italy); Spronk, Sandra [Erasmus MC, Radiology, Rotterdam (Netherlands); Erasmus MC, Epidemiology, Rotterdam (Netherlands); Ros, Mirco [Ca' Foncello Hospital, Pediatrics, Treviso (Italy); Fraioli, Francesco [University College London (UCL), Institute of Nuclear Medicine, London (United Kingdom); Quattrucci, Serena [University of Rome Sapienza, Pediatrics, Rome (Italy); Assael, M.B. [Azienda Ospedaliera di Verona, Verona CF Center, Verona (Italy); Pomerri, Fabio [University of Padova, Department of Medicine-DIMED, Padova (Italy); Tiddens, Harm A.W.M. [Sophia Children' s Hospital, Pediatric Pulmonology Erasmus MC, Rotterdam (Netherlands); Erasmus MC, Radiology, Rotterdam (Netherlands)
2016-03-15
To date, PROPELLER MRI, a breathing-motion-insensitive technique, has not been assessed for cystic fibrosis (CF) lung disease. We compared this technique to CT for assessing CF lung disease in children and adults. Thirty-eight stable CF patients (median 21 years, range 6-51 years, 22 female) underwent MRI and CT on the same day. Study protocol included respiratory-triggered PROPELLER MRI and volumetric CT end-inspiratory and -expiratory acquisitions. Two observers scored the images using the CF-MRI and CF-CT systems. Scores were compared with intra-class correlation coefficient (ICC) and Bland-Altman plots. The sensitivity and specificity of MRI versus CT were calculated. MRI sensitivity for detecting severe CF bronchiectasis was 0.33 (CI 0.09-0.57), while specificity was 100 % (CI 0.88-1). ICCs for bronchiectasis and trapped air were as follows: MRI-bronchiectasis (0.79); CT-bronchiectasis (0.85); MRI-trapped air (0.51); CT-trapped air (0.87). Bland-Altman plots showed an MRI tendency to overestimate the severity of bronchiectasis in mild CF disease and underestimate bronchiectasis in severe disease. Motion correction in PROPELLER MRI does not improve assessment of CF lung disease compared to CT. However, the good inter- and intra-observer agreement and the high specificity suggest that MRI might play a role in the short-term follow-up of CF lung disease (i.e. pulmonary exacerbations). (orig.)
Assessment of CF lung disease using motion corrected PROPELLER MRI: a comparison with CT
International Nuclear Information System (INIS)
Ciet, Pierluigi; Serra, Goffredo; Catalano, Carlo; Bertolo, Silvia; Morana, Giovanni; Spronk, Sandra; Ros, Mirco; Fraioli, Francesco; Quattrucci, Serena; Assael, M.B.; Pomerri, Fabio; Tiddens, Harm A.W.M.
2016-01-01
To date, PROPELLER MRI, a breathing-motion-insensitive technique, has not been assessed for cystic fibrosis (CF) lung disease. We compared this technique to CT for assessing CF lung disease in children and adults. Thirty-eight stable CF patients (median 21 years, range 6-51 years, 22 female) underwent MRI and CT on the same day. Study protocol included respiratory-triggered PROPELLER MRI and volumetric CT end-inspiratory and -expiratory acquisitions. Two observers scored the images using the CF-MRI and CF-CT systems. Scores were compared with intra-class correlation coefficient (ICC) and Bland-Altman plots. The sensitivity and specificity of MRI versus CT were calculated. MRI sensitivity for detecting severe CF bronchiectasis was 0.33 (CI 0.09-0.57), while specificity was 100 % (CI 0.88-1). ICCs for bronchiectasis and trapped air were as follows: MRI-bronchiectasis (0.79); CT-bronchiectasis (0.85); MRI-trapped air (0.51); CT-trapped air (0.87). Bland-Altman plots showed an MRI tendency to overestimate the severity of bronchiectasis in mild CF disease and underestimate bronchiectasis in severe disease. Motion correction in PROPELLER MRI does not improve assessment of CF lung disease compared to CT. However, the good inter- and intra-observer agreement and the high specificity suggest that MRI might play a role in the short-term follow-up of CF lung disease (i.e. pulmonary exacerbations). (orig.)
Neutron Spectra, Fluence and Dose Rates from Bare and Moderated Cf-252 Sources
Energy Technology Data Exchange (ETDEWEB)
Radev, Radoslav P. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-04-01
A new, stronger ^{252}Cf source (serial number SR-CF-3050-OR) was obtained from Oak Ridge National Laboratory (ORNL) in 2014 to supplement the existing ^{252}Cf sources which had significantly decayed. A new instrument positioning track system was designed and installed by Hopewell Designs, Inc. in 2011. The neutron field from the new, stronger ^{252}Cf source in the modified calibration environment needed to be characterized as well as the modified neutron fields produced by the new source and seven different neutron moderators. Comprehensive information about our ^{252}Cf source, its origin, production, and isotopic content and decay characteristics needed to be compiled as well. This technical report is intended to address these issues.
Energy Technology Data Exchange (ETDEWEB)
Zhao, Hang; Lu, Yinxiang, E-mail: yxlu@fudan.edu.cn
2016-01-30
Graphical abstract: - Highlights: • An etchant-free and moderate surface pre-treatment process was studied. • Citric acid, malic acid and oxalic acid were selected as modification agents. • High adhesive nickel coating on cuprammonium fabric was obtained. • The electromagnetic parameters were evaluated from the experimental data. - Abstract: Nickel films were grown on citric acid (CA), malic acid (MA) and oxalic acid (OA) modified cuprammonium fabric (CF) substrates via electroless nickel deposition. The nickel films were examined using scanning electron microscopy (SEM) and X-ray diffraction (XRD). Their individual deposition rate and electromagnetic interference (EMI) shielding effectiveness (SE) were also investigated to compare the properties of electroless nickel films. SEM images illustrated that the nickel film on MA modified CF substrate was smooth and uniform, and the density of nickel nuclei was much higher. Compared with that of CA modified CF, the coverage of nickel nuclei on OA and MA modified CF substrate was very limited and the nickel particles size was too big. XRD analysis showed that the nickel films deposited on the different modified CF substrates had a structure with Ni (1 1 1) preferred orientation. All the nickel coatings via different acid modification were firmly adhered to the CF substrates, as demonstrated by an ultrasonic washing test. The result of tensile test indicated that the electroless nickel plating on CF has ability to strengthen the CF substrate while causes limited effect on tensile elongation. Moreover, the nickel film deposited on MA modified CF substrate showed more predominant in EMI SE than that deposited on CA or OA modified CF.
Real representations of Lie groups and a theorem of H. Pittie
International Nuclear Information System (INIS)
Freitas, R.
1992-01-01
In this paper, we prove a structure theorem of the real representation ring RO(T) as a module over the real representation ring RO(G), where G is a compact, connected and simply connected Lie group and T is a maximal torus of G. This provides a real version to a theorem of H. Pittie. (author). 24 refs
Bell's Theorem and Einstein's "Spooky Actions" from a Simple Thought Experiment
Kuttner, Fred; Rosenblum, Bruce
2010-01-01
In 1964 John Bell proved a theorem allowing the experimental test of whether what Einstein derided as "spooky actions at a distance" actually exist. We will see that they "do". Bell's theorem can be displayed with a simple, nonmathematical thought experiment suitable for a physics course at "any" level. And a simple, semi-classical derivation of…
Directory of Open Access Journals (Sweden)
Badridatt Pant
2014-02-01
Full Text Available In this paper, we prove a common fixed point theorem for finite number of self mappings in Menger probabilistic quasi metric space. Our result improves and extends the results of Rezaiyan et al. [A common fixed point theorem in Menger probabilistic quasi-metric spaces, Chaos, Solitons and Fractals 37 (2008 1153-1157.], Miheţ [A note on a fixed point theorem in Menger probabilistic quasi-metric spaces, Chaos, Solitons and Fractals 40 (2009 2349-2352], Pant and Chauhan [Fixed points theorems in Menger probabilistic quasi metric spaces using weak compatibility, Internat. Math. Forum 5 (6 (2010 283-290] and Sastry et al. [A fixed point theorem in Menger PQM-spaces using weak compatibility, Internat. Math. Forum 5 (52 (2010 2563-2568
A Bayesian perspective on Markovian dynamics and the fluctuation theorem
Virgo, Nathaniel
2013-08-01
One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.
Green-Tao theorem in function fields
Le, Thai Hoang
2009-01-01
We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every $k$, the irreducible polynomials in $\\mathbf{F}_q[t]$ contain configurations of the form $\\{f+ Pg : \\d(P)
On the extension of the Fermi-Watson Theorem to high energy diffraction
International Nuclear Information System (INIS)
Malecki, A.; Istituto Nazionale di Fisica Nucleare, Frascati
1995-12-01
The Fermi-Watson theorem, established for low energy reactions and then applied to high energy collision, is revisited. Its use for the processes of inelastic diffraction is discussed. The theorem turns out to be valid in the case inclusive cross-section of diffractive transition
76 FR 68634 - Airworthiness Directives; General Electric Company (GE) CF6 Turbofan Engines
2011-11-07
... Airworthiness Directives; General Electric Company (GE) CF6 Turbofan Engines AGENCY: Federal Aviation... ``(c) This AD applies to * * * and CF6-80A3 turbofan engines with left-hand links * * *.'' to ``(c) This AD applies to * * * and CF6-80A3 turbofan engines, including engines marked on the engine data...
Supersymmetric extension of the Adler-Bardeen theorem
International Nuclear Information System (INIS)
Novikov, V.A.; Zakharov, V.I.; Shifman, M.A.; Vainshtein, A.I.
1985-01-01
A supersymmetric generalization of the Adler-Bardeen theorem in SUSY gauge theories is given. We show that within the Adler-Bardeen procedure, both the conformal and axial anomalies are exhausted by one loop. (orig.)
Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Ensign, P.W.
1987-01-01
By the Adler-Bardeen theorem, only one-loop Feynman diagrams contribute to the anomalous divergences of quantum axial currents. The anomalous nature of scale transformations is manifested by an anomalous trace of the energy-momentum tensor, T/sup μ//sub μ/. Renormalization group arguments show that the quantum T/sup μ//sub μ/ must be proportional to the β-function. Since the β-function receives contributions at all loop levels, the Adler-Bardeen theorem appears to conflict with supersymmetry. Recently Grisaru, Milewski and Zanon constructed a supersymmetric axial current for pure supersymmetric Yang-Mills theory which satisfies the Adler-Bardeen theorem to two-loops. They used supersymmetric background field theory and regularization by dimensional reduction to maintain manifest supersymmetry and gauge invariance. In this thesis, their construction is extended to supersymmetric Yang-Mills theory coupled to chiral matter fields. The Adler-Bardeen theorem is then proven to all orders in perturbation theory for both the pure and coupled theories. The extension to coupled supersymmetric Yang-Mills supports the general validity of these techniques, and adds considerable insight into the structure of the anomalies. The all orders proof demonstrates that there is no conflict between supersymmetry and the Adler-Bardeen theorem
An existence theorem for a type of functional differential equation with infinite delay
Izsak, F.
We prove an existence theorem for a functional differential equation with infinite delay using the Schauder fixpoint theorem. We extend a result in [19] applying the fixed point procedure in an appropriate function space.
Neutron shielding for a 252 Cf source
International Nuclear Information System (INIS)
Vega C, H.R.; Manzanares A, E.; Hernandez D, V.M.; Eduardo Gallego, Alfredo Lorente
2006-01-01
To determine the neutron shielding features of water-extended polyester a Monte Carlo study was carried out. Materials with low atomic number are predominantly used for neutron shielding because these materials effectively attenuate neutrons, mainly through inelastic collisions and absorption reactions. During the selection of materials to design a neutron shield, prompt gamma production as well as radionuclide production induced by neutron activation must be considered. In this investigation the Monte Carlo method was used to evaluate the performance of a water-extended polyester shield designed for the transportation, storage, and use of a 252 Cf isotopic neutron source. During calculations a detailed model for the 252 Cf and the shield was utilized. To compare the shielding features of water extended polyester, the calculations were also made for the bare 252 Cf in vacuum, air and the shield filled with water. For all cases the calculated neutron spectra was utilized to determine the ambient equivalent neutron dose at four sites around the shielding. In the case of water extended polyester and water shielding the calculations were extended to include the prompt gamma rays produced during neutron interactions, with this information the Kerma in air was calculated at the same locations where the ambient equivalent neutron dose was determined. (Author)
Confusion and Clarification: Albert Einstein and Walther Nernst's Heat Theorem, 1911-1916
Kox, A.J.
2006-01-01
This paper discusses the early history of Walther Nernst's Heat Theorem and the first stages of its development into the Third Law of Thermodynamics. In addition to published papers, informal discussions were important in shaping the understanding of the meaning and validity of the Theorem. Special
Quantum and classical strong direct product theorems and optimal time-space tradeoffs
H. Klauck (Hartmut); R. Spalek (Robert); R. M. de Wolf (Ronald)
2007-01-01
textabstractA strong direct product theorem says that if we want to compute $k$ independent instances of a function, using less than $k$ times the resources needed for one instance, then our overall success probability will be exponentially small in $k$. We establish such theorems for the
A Borsuk-Ulam type generalization of the Leray-Schauder fixed point theorem
International Nuclear Information System (INIS)
Prykarpatsky, A.K.
2007-05-01
A generalization of the classical Leray-Schauder fixed point theorem, based on the infinite-dimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on a weak version of the well known Krein-Milman theorem are presented. (author)
OligoG CF-5/20 normalizes cystic fibrosis mucus by chelating calcium.
Ermund, Anna; Recktenwald, Christian V; Skjåk-Braek, Gudmund; Meiss, Lauren N; Onsøyen, Edvar; Rye, Philip D; Dessen, Arne; Myrset, Astrid Hilde; Hansson, Gunnar C
2017-06-01
The goal of this study was to determine whether the guluronate (G) rich alginate OligoG CF-5/20 (OligoG) could detach cystic fibrosis (CF) mucus by calcium chelation, which is also required for normal mucin unfolding. Since bicarbonate secretion is impaired in CF, leading to insufficient mucin unfolding and thereby attached mucus, and since bicarbonate has the ability to bind calcium, we hypothesized that the calcium chelating property of OligoG would lead to detachment of CF mucus. Indeed, OligoG could compete with the N-terminus of the MUC2 mucin for calcium binding as shown by microscale thermophoresis. Further, effects on mucus thickness and attachment induced by OligoG and other alginate fractions of different length and composition were evaluated in explants of CF mouse ileum mounted in horizontal Ussing-type chambers. OligoG at 1.5% caused effective detachment of CF mucus and the most potent alginate fraction tested, the poly-G fraction of about 12 residues, had similar potency compared to OligoG whereas mannuronate-rich (M) polymers had minimal effect. In conclusion, OligoG binds calcium with appropriate affinity without any overt harmful effect on the tissue and can be exploited for treating mucus stagnation. © 2017 John Wiley & Sons Australia, Ltd.
1/4-pinched contact sphere theorem
DEFF Research Database (Denmark)
Ge, Jian; Huang, Yang
2016-01-01
Given a closed contact 3-manifold with a compatible Riemannian metric, we show that if the sectional curvature is 1/4-pinched, then the contact structure is universally tight. This result improves the Contact Sphere Theorem in [EKM12], where a 4/9-pinching constant was imposed. Some tightness...
A general shakedown theorem for elastic/plastic bodies with work hardening
International Nuclear Information System (INIS)
Ponter, A.R.S.
1975-01-01
In recent years the design of metallic structures under variable loading has been assisted by the application of Melan's lower bound theorem for the shakedown on an elastic/perfectly plastic structure. The design codes for both portal frames and pressure vessels have taken account of such calculations. The theory of shakedown suffers from two defects, geometry changes are ignored and the material behaviour is described by a perfectly plastic constitutive relationship which includes neither work hardening nor the Bauschinger effect. This paper is concerned with the latter problem. A very general lower bound shakedown theorem is derived for an arbitrary time-independent material in terms of functional properties of the constitutive relationship. The theorem is then applied to perfect, isotropic and kinematic hardening plasticity. (Auth.)
A DIDACTIC SURVEY OVER MAIN CHARACTERISTICS OF LAGRANGE'S THEOREM IN MATHEMATICS AND IN ECONOMICS
Xhonneux, Sebastian; Henry, Valérie
2011-01-01
Because of its many uses, the constrained optimization problem is presented in most calculus courses for mathematicians but also for economists. Looking at Lagrange's Theorem we are interested in studying the teaching of this theorem in both branches of study, mathematics and economics. This paper faces a twofold objective: first, we show the methodology of our research project concerning the didactic transposition of Lagrange's Theorem in university mathematics courses. Sec...
State-Independent Proof of Kochen—Specker Theorem with Thirty Rank-Two Projectors
International Nuclear Information System (INIS)
Toh, S. P.
2013-01-01
The Kochen—Specker theorem states that noncontextual hidden variable theories are incompatible with quantum mechanics. We provide a state-independent proof of the Kochen—Specker theorem using the smallest number of projectors, i.e., thirty rank-2 projectors, associated with the Mermin pentagram for a three-qubit system
Boers, Sarah N; de Winter-de Groot, Karin M; Noordhoek, Jacquelien; Gulmans, Vincent; van der Ent, Cornelis K; van Delden, Johannes J M; Bredenoord, Annelien L
2018-03-06
Organoid technology enables the cultivation of human tissues in a dish. Its precision medicine potential could revolutionize the Cystic Fibrosis (CF) field. We provide a first thematic exploration of the patient perspective on organoid technology to set the further research agenda, which is necessary for responsible development of this ethically challenging technology. 23 semi-structured qualitative interviews with 14 Dutch adult CF patients and 12 parents of young CF patients to examine their experiences, opinions, and attitudes regarding organoid technology. Four themes emerged: (1) Respondents express a close as well as a distant relationship to organoids; (2) the open-endedness of organoid technology sparks hopes and concerns, (3) commercial use evokes cautiousness. (4) Respondents mention the importance of sound consent procedures, long-term patient engagement, responsible stewardship, and stringent conditions for commercial use. The precision medicine potential of organoid technology can only be realized if the patient perspective is taken adequately into account. Copyright © 2018 European Cystic Fibrosis Society. Published by Elsevier B.V. All rights reserved.
Strong-Weak CP Hierarchy from Non-Renormalization Theorems
Energy Technology Data Exchange (ETDEWEB)
Hiller, Gudrun
2002-01-28
We point out that the hierarchy between the measured values of the CKM phase and the strong CP phase has a natural origin in supersymmetry with spontaneous CP violation and low energy supersymmetry breaking. The underlying reason is simple and elegant: in supersymmetry the strong CP phase is protected by an exact non-renormalization theorem while the CKM phase is not. We present explicit examples of models which exploit this fact and discuss corrections to the non-renormalization theorem in the presence of supersymmetry breaking. This framework for solving the strong CP problem has generic predictions for the superpartner spectrum, for CP and flavor violation, and predicts a preferred range of values for electric dipole moments.
Entanglement, space-time and the Mayer-Vietoris theorem
Patrascu, Andrei T.
2017-06-01
Entanglement appears to be a fundamental building block of quantum gravity leading to new principles underlying the nature of quantum space-time. One such principle is the ER-EPR duality. While supported by our present intuition, a proof is far from obvious. In this article I present a first step towards such a proof, originating in what is known to algebraic topologists as the Mayer-Vietoris theorem. The main result of this work is the re-interpretation of the various morphisms arising when the Mayer-Vietoris theorem is used to assemble a torus-like topology from more basic subspaces on the torus in terms of quantum information theory resulting in a quantum entangler gate (Hadamard and c-NOT).
On a theorem of Faltings on formal functions
Directory of Open Access Journals (Sweden)
Paola Bonacini
2007-12-01
Full Text Available In 1980, Faltings proved, by deep local algebra methods, a local resultregarding formal functions which has the following global geometric factas a consequence. Theorem. − Let k be an algebraically closed field (ofany characteristic. Let Y be a closed subvariety of a projective irreduciblevariety X defined over k. Assume that X ⊂ P^n , dim(X = d > 2 and Yis the intersection of X with r hyperplanes of P^n , with r ≤ d − 1. Then,every formal rational function on X along Y can be (uniquely extended toa rational function on X . Due to its importance, the aim of this paper is toprovide two elementary global geometric proofs of this theorem.
Modern Thermodynamics Based on the Extended Carnot Theorem
Wang, Jitao
2012-01-01
"Modern Thermodynamics- Based on the Extended Carnot Theorem" provides comprehensive definitions and mathematical expressions of both classical and modern thermodynamics. The goal is to develop the fundamental theory on an extended Carnot theorem without incorporating any extraneous assumptions. In particular, it offers a fundamental thermodynamic and calculational methodology for the synthesis of low-pressure diamonds. It also discusses many "abnormal phenomena", such as spiral reactions, cyclic reactions, chemical oscillations, low-pressure carat-size diamond growth, biological systems, and more. The book is intended for chemists and physicists working in thermodynamics, chemical thermodynamics, phase diagrams, biochemistry and complex systems, as well as graduate students in these fields. Jitao Wang is a professor emeritus at Fudan University, Shanghai, China.
Double soft theorems in gauge and string theories
Energy Technology Data Exchange (ETDEWEB)
Volovich, Anastasia [Brown University Department of Physics,182 Hope St, Providence, RI, 02912 (United States); Wen, Congkao [I.N.F.N. Sezione di Roma “Tor Vergata”,Via della Ricerca Scientifica, 00133 Roma (Italy); Zlotnikov, Michael [Brown University Department of Physics,182 Hope St, Providence, RI, 02912 (United States)
2015-07-20
We investigate the tree-level S-matrix in gauge theories and open superstring theory with several soft particles. We show that scattering amplitudes with two or three soft gluons of non-identical helicities behave universally in the limit, with multi-soft factors which are not the product of individual soft gluon factors. The results are obtained from the BCFW recursion relations in four dimensions, and further extended to arbitrary dimensions using the CHY formula. We also find new soft theorems for double soft limits of scalars and fermions in N=4 and pure N=2 SYM. Finally, we show that the double-soft-scalar theorems can be extended to open superstring theory without receiving any α{sup ′} corrections.
Apatin, V. M.; Lokhman, V. N.; Makarov, G. N.; Ogurok, N.-D. D.; Ryabov, E. A.
2018-02-01
We report the results of research on the experimental control of CF3Br molecule clustering under gas-dynamic expansion of the CF3Br - Ar mixture at a nozzle exit by using IR laser radiation. A cw CO2 laser is used for exciting molecules and clusters in the beam and a time-of-flight mass-spectrometer with laser UV ionisation of particles for their detection. The parameters of the gas above the nozzle are determined (compositions and pressure) at which intensive molecule clustering occurs. It is found that in the case of the CF3Br gas without carrier when the pressure P0 above the nozzle does not exceed 4 atm, molecular clusters actually are not generated in the beam. If the gas mixture of CF3Br with argon is used at a pressure ratio 1 : N, where N >= 3, and the total pressure above the nozzle is P0 >= 2 atm, then there occurs molecule clustering. We study the dependences of the efficiency of suppressing the molecule clustering on parameters of the exciting pulse, gas parameters above the nozzle, and on a distance of the molecule irradiation zone from the nozzle exit section. It is shown that in the case of resonant vibrational excitation of gas-dynamically cooled CF3Br molecules at the nozzle exit one can realise isotope-selective suppression of molecule clustering with respect to bromine isotopes. With the CF3Br - Ar mixtures having the pressure ratio 1 : 3 and 1 : 15, the enrichment factors obtained with respect to bromine isotopes are kenr ≈ 1.05 ± 0.005 and kenr ≈ 1.06 ± 0.007, respectively, under jet irradiation by laser emission in the 9R(30) line (1084.635 cm-1). The results obtained let us assume that this method can be used to control clustering of molecules comprising heavy element isotopes, which have a small isotopic shift in IR absorption spectra.
Radiation ulcers in patients with cancer of the torgue after 252Cf therapy
International Nuclear Information System (INIS)
Galantseva, G.F.; Guseva, L.I.; Plichko, V.I.
1984-01-01
Interstitial therapy with 252 Cf was conducted for 57 patients with cancer of the tongue. It was established that clinical course of radiation tungue ulcers after interstitial therapy with 252 Cf doesn't differ sufficiently from the course of radiation injuries, occurring after γ-radiation application. Radiation ulcers are often observed in patients after the treatment of recurrent and residual tumors with 252 Cf (in 33% of patients); the ulcers appeared in 15% of cases in patients after the treatment of initial ulcers tumors. Conservative treatment provide the cure of radiation tongUe ulcers after interstitial therapy with 252 Cf
The BRST quantization and the no-ghost theorem for AdS3
International Nuclear Information System (INIS)
Asano, Masako; Natsuume, Makoto
2003-01-01
In our previous papers, we prove the no-ghost theorem without light-cone directions. We point out that our results are valid for more general backgrounds. In particular, we prove the no-ghost theorem for AdS 3 in the context of the BRST quantization (with the standard restriction on the spin). We compare our BRST proof with the OCQ proof and establish the BRST-OCQ equivalence for AdS 3 . The key in both approaches lies in the certain structure of the matter Hilbert space as a product of two Verma modules. We also present the no-ghost theorem in the most general form. (author)
Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces
Directory of Open Access Journals (Sweden)
Sunny Chauhan
2013-05-01
Full Text Available The aim of this paper is to prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space by using the (CLRg property. An example is also furnished which demonstrates the validity of our main result. As an application to our main result, we present a fixed point theorem for two finite families of self mappings in fuzzy metric space by using the notion of pairwise commuting. Our results improve the results of Sedghi, Shobe and Aliouche [A common fixed point theorem for weakly compatible mappings in fuzzy metric spaces, Gen. Math. 18(3 (2010, 3-12 MR2735558].
Improving the care of patients with cystic fibrosis (CF)
Khan, Ahsan Aftab; Nash, Edward F; Whitehouse, Joanna; Rashid, Rifat
2017-01-01
Background The West Midlands Adult Cystic Fibrosis (CF) Centre based at Birmingham Heartlands Hospital provides care for adults with CF in the West Midlands. People with CF are prone to pulmonary exacerbations, which often require inpatient admission for intravenous antibiotics. We observed that the admission process was efficient during working hours (9:00–17:00, Monday–Friday) when the CF team are routinely available, but out-of-working hours, there were delays in these patients being clerked and receiving their first antibiotic dose. We were concerned that this was resulting in quality and potential safety issues by causing delays in starting treatment and prolonging hospital inpatient stays. We therefore undertook a quality improvement project (QIP) aimed at addressing these issues. An initial survey showed median time to clerk of 5 hours, with 60% of patients missing their first dose of antibiotics and mean length of stay of 16 days. Methods We applied the Plan-Do-Study-Act (PDSA) cycle approach, with the first PDSA cycle involving raising awareness of the issue through education to doctors, nurses and patients. Results This led to a reduction of median time to clerk from 5 to 2 hours with 23% of patients missing their first antibiotic dose and mean length of stay reducing to 14 days. The second cycle involved introducing an admissions checklist and displaying education posters around the hospital, resulting in median time to clerk remaining at 2 hours but only 20% of patients missing their first antibiotic dose and the mean length of stay remaining at 14 days. Conclusion This QIP has improved the out-of-hours admissions process for adults with CF in our centre. We plan to review the longer term effects of the project including sustainability, effects on clinical outcomes and patient satisfaction. PMID:28959778
A divergence theorem for pseudo-Finsler spaces
Minguzzi, E.
2015-01-01
We study the divergence theorem on pseudo-Finsler spaces and obtain a completely Finslerian version for spaces having a vanishing mean Cartan torsion. This result helps to clarify the problem of energy-momentum conservation in Finsler gravity theories.
Divergence theorem for symmetric (0,2)-tensor fields on a semi-Riemannian manifold with boundary
International Nuclear Information System (INIS)
Ezin, J.P.; Mouhamadou Hassirou; Tossa, J.
2005-08-01
We prove in this paper a divergence theorem for symmetric (0,2)-tensors on a semi-Riemannian manifold with boundary. As a consequence we establish the complete divergence theorem on a semi-Riemannian manifold with any kinds of smooth boundaries. This result contains the previous attempts to write this theorem on a semi-Riemannian manifold as Unal results. A vanishing theorem for gradient timelike Killing vector fields on Einstein semi-Riemannian manifolds is obtained. As a tool, an induced volume form is defined for a degenerate boundary by using a star like operator that we define on degenerate submanifolds. (author)
Corrosion of Continuous Fiber Reinforced Aluminum Metal Matrix Composites (CF-AMCs)
Tiwari, Shruti
The first objective of this research is to study the atmospheric corrosion behavior of continuous reinforced aluminum matrix composites (CF-AMCs). The materials used for this research were alumina (Al2O3) and nickel (Ni) coated carbon (C) fibers reinforced AMCs. The major focus is to identify the correlation between atmospheric parameters and the corrosion rates of CF-AMCs in the multitude of microclimates and environments in Hawai'i. The micro-structures of CF-AMCs were obtained to correlate the microstructures with their corrosion performances. Also electrochemical polarization experiments were conducted in the laboratory to explain the corrosion mechanism of CF-AMCs. In addition, CF-AMCs were exposed to seven different test sites for three exposure periods. The various climatic conditions like temperature (T), relative humidity (RH), rainfall (RF), time of wetness (TOW), chloride (Cl- ) and sulfate (SO42-) deposition rate, and pH were monitored for three exposure period. Likewise, mass losses of CF-AMCs at each test site for three exposure periods were determined. The microstructure of the CF-AMCS showed that Al/C/50f MMCs contained a Ni-rich phase in the matrix, indicating that the Ni coating on the C fiber dissolved in the matrix. The intermetallic phases obtained in Al-2wt% Cu/Al 2O3/50f-T6 MMC and Al-2wt%-T6 monolith were rich in Cu and Fe. The intermetallic phases obtained in Al 7075/Al2O3/50f-T6 MMC and Al 7075-T6 monolith also contained traces of Mg, Zn, Ni, and Si. Electrochemical polarization experiment indicated that the Al/Al 2O3/50f Al-2wt% Cu/Al2O3/50f-T6 and Al 7075/Al2O3/50f-T6 MMC showed similar corrosion trends as their respective monoliths pure Al, Al-2wt%-T6 and Al 7075-T6 in both aerated and deaerated condition. Al2O3 fiber, being an insulator, did not have a great effect on the polarization behavior of the composites. Al/C/50f MMCs corroded at a much faster rate as compared to pure Al monolith due to the galvanic effect between C and Al
Dispersive approach to the axial anomaly and nonrenormalization theorem
International Nuclear Information System (INIS)
Pasechnik, R.S.; Teryaev, O.V.
2006-01-01
Anomalous triangle graphs for the divergence of the axial-vector current are studied using the dispersive approach generalized for the case of higher orders of perturbation theory. The validity of this procedure is proved up to the two-loop level. By direct calculation in the framework of dispersive approach we have obtained that the two-loop axial-vector-vector (AVV) amplitude is equal to zero. According to the Vainshtein's theorem, the transversal part of the anomalous triangle is not renormalized in the chiral limit. We generalize this theorem for the case of finite fermion mass in the triangle loop
Testing subleading multiple soft graviton theorem for CHY prescription
Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay
2018-01-01
In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.
A generalized integral fluctuation theorem for general jump processes
International Nuclear Information System (INIS)
Liu Fei; Ouyang Zhongcan; Luo Yupin; Huang Mingchang
2009-01-01
Using the Feynman-Kac and Cameron-Martin-Girsanov formulae, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Unlike the latter approach that has been extensively employed in the existing literature, our approach can naturally bring out the definition of a time reversal of a Markovian stochastic system. Additionally, we find that the robust GIFT usually does not result in a detailed fluctuation theorem. (fast track communication)
Role of excited CF_{3}CFHO radicals in the atmospheric chemistry of HFC-134a
DEFF Research Database (Denmark)
Wallington, T.J.; Hurley, M.D.; Fracheboud, J.M.
1996-01-01
with Oz, CF3CFHO + O-2 --> CF3C(O)F + HO2, and decomposition via C-C bond scission, CF3CFHO + M --> CS3 + HC(O)F + M. CF3CFHO radicals were produced by two different reactions: either via the self-reaction of CF3CFHO2 radicals or via the CF3CFHO2 + NO reaction. It was found that decomposition was much...
Reciprocity theorem in high-temperature superconductors
Czech Academy of Sciences Publication Activity Database
Janeček, I.; Vašek, Petr
2003-01-01
Roč. 390, - (2003), s. 330-340 ISSN 0921-4534 R&D Projects: GA ČR GA202/00/1602; GA AV ČR IAA1010919 Institutional research plan: CEZ:AV0Z1010914 Keywords : transport properties * reciprocity theorem Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.192, year: 2003
On the first case of Fermat's theorem for cyclotomic fields
International Nuclear Information System (INIS)
Kolyvagin, V A
1999-01-01
The classical criteria of Kummer, Mirimanov and Vandiver for the validity of the first case of Fermat's theorem for the field Q of rationals and prime exponent l are generalized to the field Q( l √1) and exponent l. As a consequence, some simpler criteria are established. For example, the validity of the first case of Fermat's theorem is proved for the field Q( l √1) and exponent l on condition that l 2 does not divide 2 l -2
CF3SF5 : a ‘super’ greenhouse gas
Tuckett, R. P.
2008-01-01
One molecule of the anthropogenic pollutant trifluoromethyl sulphur pentafluoride (CF\\(_3\\)SF\\(_5\\)), an adduct of the CF\\(_3\\) and SF\\(_5\\) free radicals, causes more global warming than one molecule of any other greenhouse gas yet detected in the Earth’s atmosphere. That is, it has the highest per molecule radiative forcing of any greenhouse pollutant, and the value of its global warming potential is only exceeded by that of SF\\(_6\\). First, the greenhouse effect is described, the propertie...
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.
Lectures on Fermat's last theorem
International Nuclear Information System (INIS)
Sury, B.
1993-09-01
The report presents the main ideas involved in the approach towards the so-called Fermat's last theorem (FLT). The discussion leads to the point where recent work of A. Wiles starts and his work is not discussed. After a short history of the FLT and of the present approach, are discussed the elliptic curves and the modular forms with their relations, the Taniyama-Shimura-Well conjecture and the FLT
Study of the 249-251Cf + 48Ca reactions: recent results and outlook
Voinov, A. A.; Oganessian, Yu Ts; Abdullin, F. Sh; Brewer, N. T.; Dmitriev, S. N.; Grzywacz, R. K.; Hamilton, J. H.; Itkis, M. G.; Miernik, K.; Polyakov, A. N.; Roberto, J. B.; Rykaczewski, K. P.; Sabelnikov, A. V.; Sagaidak, R. N.; Shirokovsky, I. V.; Shumeiko, M. V.; Stoyer, M. A.; Subbotin, V. G.; Sukhov, A. M.; Tsyganov, Yu S.; Utyonkov, V. K.; Vostokin, G. K.
2018-02-01
Experiment aiming at the synthesis of heavy isotopes of Z=118 (Og) using beam of 48Ca and a target of 249-251Cf was undertaken in October 2015 - April 2016 employing the Dubna Gas-Filled Recoil Separator (FLNR JINR). The target of mixed isotopes of 249-251Cf (50.7% of 249Cf, 12.9% of 250Cf, and 36.4% of 251Cf) was irradiated by 48Ca ions at two beam energies of 252 and 258 MeV with the corresponding accumulated beam doses of 1.6×1019 and 1.1×1019. A single event observed at lower beam energy was assigned to the isotope 294Og, the product of the reaction 249Cf(48Ca, 3n); its decay pattern and the observed radioactive properties of the nuclides in the decay chain reproduce in full those observed for 294Og in our earlier experiments of 2002-2005 and 2012. At higher beam energy we observed no decay chains that could be attributed to the isotopes of Og. The possibility of renewal of this experiment in the future is discussed.
Mean value theorem in topological vector spaces
International Nuclear Information System (INIS)
Khan, L.A.
1994-08-01
The aim of this note is to give shorter proofs of the mean value theorem, the mean value inequality, and the mean value inclusion for the class of Gateaux differentiable functions having values in a topological vector space. (author). 6 refs
Yields of fission products produced by thermal-neutron fission of 249Cf
International Nuclear Information System (INIS)
Dickens, J.K.; McConnell, J.W.
1981-01-01
Absolute yields have been determined for 107 gamma rays emitted in the decay of 97 fission products representing 54 mass chains created during thermal-neutron fission of 249 Cf. These results include 14 mass chains for which no prior yield data exist. Using a Ge(Li) detector, spectra were obtained of gamma rays emanating from a 0.4 μg sample of 249 Cf between 45 s and 0.4 yr after very short irradiations of the 249 Cf by thermal neutrons. On the basis of measured gamma-ray yields and known nuclear data, total chain mass yields and relative uncertainties were obtained for 51 masses between 89 and 156. The absolute overall normalization uncertainty is approx.8%. The measured A-chain cumulative yields make up 77% of the total light mass (A 249 Cf
The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project
Robiette, Alan G.
1975-01-01
Describes a student project which requires limited knowledge of Fortran and only minimal computing resources. The results illustrate such important principles of quantum mechanics as the variation theorem and the virial theorem. Presents sample calculations and the subprogram for energy calculations. (GS)
235Cf anti ν discrepancy and the sulfur discrepancy
International Nuclear Information System (INIS)
Smith, J.R.
1979-01-01
The cantankerous discrepancy among measured values of anti ν for 235 Cf appears at last to be nearing a final resolution. A recent review has summarized the progress that has been achieved through revaluation upward by 0.5% of two manganese bath values anti ν and the performance of a new liquid scintillator measurement. A new manganese bath measurement at INEL is in reasonably good agreement with previous manganese bath values of 235 Cf anti ν. It now appears that the manganese bath values could still be systematically low by as much as 0.4% because the BNL-325 thermal absorption cross section for sulfur may be as much as 10% low. There is a bona fide discrepancy between measurements of the sulfur cross section by pile oscillators and the values derived from transmission measurements. The resolution of this discrepancy is a prerequisite to the final resolution of the 235 Cf anti ν discrepancy. 22 references
Student Research Project: Goursat's Other Theorem
Petrillo, Joseph
2009-01-01
In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…
A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process
International Nuclear Information System (INIS)
Okabe, Y.
1985-01-01
The [α,β,γ]-Langevin equation describes the time evolution of a real stationary process with T-positivity (reflection positivity) originating in the axiomatic quantum field theory. For this [α,β,γ]-Langevin equation a generalized fluctuation-dissipation theorem is proved. We shall obtain, as its application, a generalized fluctuation-dissipation theorem for the one-dimensional non-linear diffusion process, which presents one solution of Ryogo Kubo's problem in physics. (orig.)
Berezhkovskii, Alexander M; Bezrukov, Sergey M
2008-05-15
In this paper, we discuss the fluctuation theorem for channel-facilitated transport of solutes through a membrane separating two reservoirs. The transport is characterized by the probability, P(n)(t), that n solute particles have been transported from one reservoir to the other in time t. The fluctuation theorem establishes a relation between P(n)(t) and P-(n)(t): The ratio P(n)(t)/P-(n)(t) is independent of time and equal to exp(nbetaA), where betaA is the affinity measured in the thermal energy units. We show that the same fluctuation theorem is true for both single- and multichannel transport of noninteracting particles and particles which strongly repel each other.
Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Ensign, P.; Mahanthappa, K.T.
1987-01-01
We construct the supercurrent and a supersymmetric current which satisfies the Adler-Bardeen theorem in supersymmetric Yang-Mills theory coupled to non-self-interacting chiral matter. Using the formulation recently developed by Grisaru, Milewski, and Zanon, supersymmetry and gauge invariance are maintained with supersymmetric background-field theory and regularization by dimensional reduction. We verify the finiteness of the supercurrent to one loop, and the Adler-Bardeen theorem to two loops by explicit calculations in the minimal-subtraction scheme. We then demonstrate the subtraction-scheme independence of the one-loop Adler-Bardeen anomaly and prove the existence of a subtraction scheme in which the Adler-Bardeen theorem is satisfied to all orders in perturbation theory
State Prices and Implementation of the Recovery Theorem
Directory of Open Access Journals (Sweden)
Alex Backwell
2015-01-01
Full Text Available It is generally held that derivative prices do not contain useful predictive information, that is, information relating to the distribution of future financial variables under the real-world measure. This is because the market’s implicit forecast of the future becomes entangled with market risk preferences during derivative price formation. A result derived by Ross [1], however, recovers the real-world distribution of an equity index, requiring only current prices and mild restrictions on risk preferences. In addition to being of great interest to the theorist, the potential practical value of the result is considerable. This paper addresses implementation of the Ross Recovery Theorem. The theorem is formalised, extended, proved and discussed. Obstacles to application are identified and a workable implementation methodology is developed.
Modern thermodynamics. Based on the extended Carnot theorem
Energy Technology Data Exchange (ETDEWEB)
Wang, Jitao [Fudan Univ., Shanghai (China). Microelectronics Dept.
2011-07-01
''Modern Thermodynamics- Based on the Extended Carnot Theorem'' provides comprehensive definitions and mathematical expressions of both classical and modern thermodynamics. The goal is to develop the fundamental theory on an extended Carnot theorem without incorporating any extraneous assumptions. In particular, it offers a fundamental thermodynamic and calculational methodology for the synthesis of low-pressure diamonds. It also discusses many ''abnormal phenomena'', such as spiral reactions, cyclic reactions, chemical oscillations, low-pressure carat-size diamond growth, biological systems, and more. The book is intended for chemists and physicists working in thermodynamics, chemical thermodynamics, phase diagrams, biochemistry and complex systems, as well as graduate students in these fields. Jitao Wang is a professor emeritus at Fudan University, Shanghai, China. (orig.)
Fixed point theorems in locally convex spacesÃ¢Â€Â”the Schauder mapping method
Directory of Open Access Journals (Sweden)
S. Cobzaş
2006-03-01
Full Text Available In the appendix to the book by F. F. Bonsal, Lectures on Some Fixed Point Theorems of Functional Analysis (Tata Institute, Bombay, 1962 a proof by Singbal of the Schauder-Tychonoff fixed point theorem, based on a locally convex variant of Schauder mapping method, is included. The aim of this note is to show that this method can be adapted to yield a proof of Kakutani fixed point theorem in the locally convex case. For the sake of completeness we include also the proof of Schauder-Tychonoff theorem based on this method. As applications, one proves a theorem of von Neumann and a minimax result in game theory.
Etching properties of BLT films in CF4/Ar plasma
International Nuclear Information System (INIS)
Kim, Dong Pyo; Kim, Kyoung Tae; Kim, Chang Il
2003-01-01
CF 4 /Ar plasma mass content and etching rate behavior of BLT thin films were investigated in inductively coupled plasma (ICP) reactor as functions of CF 4 /Ar gas mixing ratio, rf power, and dc bias voltage. The variation of relative volume densities for F and Ar atoms were measured by the optical emission spectroscopy (OES). The etching rate as functions of Ar content showed the maximum of 803 A/min at 80 % Ar addition into CF 4 plasma. The presence of maximum etch rate may be explained by the concurrence of two etching mechanisms such as physical sputtering and chemical reaction. The role of Ar ion bombardment includes destruction of metal (Bi, La, Ti)-O bonds as well as support of chemical reaction of metals with fluorine atoms
Radionuclide 252Cf neutron source
International Nuclear Information System (INIS)
Kolevatov, Yu.I.; Trykov, L.A.
1979-01-01
Characteristics of radionuclide neutron sourses of 252 Cf base with the activity from 10 6 to 10 9 n/s have been investigated. Energetic distributions of neutrons and gamma-radiation have been presented. The results obtained have been compared with other data available. The hardness parameter of the neutron spectrum for the energy range from 3 to 15 MeV is 1.4 +- 0.02 MeV
On Callan's proof of the BPHZ theorem
International Nuclear Information System (INIS)
Lesniewski, A.
1984-01-01
The author gives an elementary proof of the BPHZ theorem in the case of the Euclidean lambdaphi 4 theory. The method of proof relies on a detailed analysis of the skeleton structure of graphs and estimates based on the Callan-Symanzik equations. (Auth.)
Gladstone-Dale constant for CF4. [experimental design
Burner, A. W., Jr.; Goad, W. K.
1980-01-01
The Gladstone-Dale constant, which relates the refractive index to density, was measured for CF4 by counting fringes of a two-beam interferometer, one beam of which passes through a cell containing the test gas. The experimental approach and sources of systematic and imprecision errors are discussed. The constant for CF4 was measured at several wavelengths in the visible region of the spectrum. A value of 0.122 cu cm/g with an uncertainty of plus or minus 0.001 cu cm/g was determined for use in the visible region. A procedure for noting the departure of the gas density from the ideal-gas law is discussed.
Theorem of comparative sensitivity of fibre sensors
Belovolov, M. I.; Paramonov, V. M.; Belovolov, M. M.
2017-12-01
We report an analysis of sensitivity of fibre sensors of physical quantities based on different types of interferometers. We formulate and prove the following theorem: under the time-dependent external physical perturbations at nonzero frequencies (i.e., except the static and low-frequency ones) on the sensitive arms of an interferometer in the form of multiturn elements (coils), there exist such lengths L of the measuring arms of the fibre interferometers at which the sensitivity of sensors based on the Sagnac fibre interferometers can be comparable with the sensitivity of sensors based on Michelson, Mach - Zehnder, or Fabry - Perot fibre interferometers, as well as exceed it under similar other conditions (similar-type perturbations, similar arm lengths and single-mode fibre types). The consequences that follow from the theorem, important for practical implementation of arrays of fibre sensors for measurement purposes and the devices with stable metrological properties, are discussed.
Pengembangan Perangkat Pembelajaran Geometri Ruang dengan Model Proving Theorem
Directory of Open Access Journals (Sweden)
Bambang Eko Susilo
2016-03-01
Full Text Available Kemampuan berpikir kritis dan kreatif mahasiswa masih lemah. Hal ini ditemukan pada mahasiswa yang mengambil mata kuliah Geometri Ruang yaitu dalam membuktikan soal-soal pembuktian (problem to proof. Mahasiswa masih menyelesaikan secara algoritmik atau prosedural sehingga diperlukan pengembangan perangkat pembelajaran Geometri Ruang berbasis kompetensi dan konservasi dengan model Proving Theorem. Dalam penelitian ini perangkat perkuliahan yang dikembangkan yaitu Silabus, Satuan Acara Perkuliahan (SAP, Kontrak Perkuliahan, Media Pembelajaran, Bahan Ajar, Tes UTS dan UAS serta Angket Karakter Konservasi telah dilaksanakan dengan baik dengan kriteria (1 validasi perangkat pembelajaran mata kuliah Geometri ruang berbasis kompetensi dan konservasi dengan model proving theorem berkategori baik dan layak digunakan dan (2 keterlaksanaan RPP pada pembelajaran yang dikembangkan secara keseluruhan berkategori baik.Critical and creative thinking abilities of students still weak. It is found in students who take Space Geometry subjects that is in solving problems to to prove. Students still finish in algorithmic or procedural so that the required the development of Space Geometry learning tools based on competency and conservation with Proving Theorem models. This is a research development which refers to the 4-D models that have been modified for the Space Geometry learning tools, second semester academic year 2014/2015. Instruments used include validation sheet, learning tools and character assessment questionnaire. In this research, the learning tools are developed, namely Syllabus, Lesson Plan, Lecture Contract, Learning Media, Teaching Material, Tests, and Character Conservation Questionnaire had been properly implemented with the criteria (1 validation of Space Geometry learning tools based on competency and conservation with Proving Theorem models categorized good and feasible to use, and (2 the implementation of Lesson Plan on learning categorized
Kochen-Specker theorem as a precondition for secure quantum key distribution
International Nuclear Information System (INIS)
Nagata, Koji
2005-01-01
We show that (1) the violation of the Ekert 1991 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 1992 (BBM92) inequality is, also, a sufficient condition for certification of the KS theorem. Therefore the success in each quantum key distribution protocol reveals the nonclassical feature of quantum theory, in the sense that the KS realism is violated. Further, it turned out that the Ekert inequality and the BBM inequality are depictured by distillable entanglement witness inequalities. Here, we connect the success in these two key distribution processes into the no-hidden-variables theorem and into witness on distillable entanglement. We also discuss the explicit difference between the KS realism and Bell's local realism in the Hilbert space formalism of quantum theory
A non linear ergodic theorem and application to a theorem of A. Pazy
International Nuclear Information System (INIS)
Djafari Rouhani, B.
1989-07-01
We prove that if (y n )n≥1 is a sequence in a real Hilbert space H such that for every non negative integer m the sequence (parallelΣ l =0 m y i +l parallel) i≥1 is non increasing, then: s n = 1/n Σ i=1 n y i converges strongly in H to the element of minimum norm in the closed convex hull of the sequence (y n ) n≥1 . We deduce a direct proof of a result containing a theorem of A. Pazy. (author). 27 refs
Tereshchenko, D. S.; Morozov, I. V.; Boltalin, A. I.; Karpova, E. V.; Glazunova, T. Yu.; Troyanov, S. I.
2013-01-01
A series of fluoro(trifluoroacetato)metallates were synthesized by crystallization from solutions in trifluoroacetic acid containing nickel(II) or cobalt(II) nitrate hydrates and alkali metal or ammonium fluorides: Li[Ni3(μ3-F)(CF3COO)6(CF3COOH)3](CF3COOH)3 ( I), M'[Ni3(μ3-F)(CF3COO)6(CF3COOH)3] ( M' = Na ( II), NH4 ( IV), Rb ( V), and Cs ( VI)), NH4[Co3(μ3-F) (CF3COO)6(CF3COOH)3] ( III), and Cs[Ni3(μ3-F)(CF3COO)6(CF3COOH)3](CF3COOH)0.5 ( VII). The crystal structures of these compounds were determined by single-crystal X-ray diffraction. All structures contain triangular trinuclear complex anions [ M 3″(μ3-F)(CF3COO)6(CF3COOH)3]- ( M″ = Ni, Co) structurally similar to trinuclear 3d metal oxo carboxylate complexes. The three-coordinated F atom is located at the center of the triangle formed by Ni(II) or Co(II) atoms. The metal atoms are linked in pairs by six bridging trifluoroacetate groups located above and below the plane of the [ M″3 F] triangle. The oxygen atoms of the axial CF3COOH molecules complete the coordination environment of M″ atoms to an octahedron.
Testing ground for fluctuation theorems: The one-dimensional Ising model
Lemos, C. G. O.; Santos, M.; Ferreira, A. L.; Figueiredo, W.
2018-04-01
In this paper we determine the nonequilibrium magnetic work performed on a Ising model and relate it to the fluctuation theorem derived some years ago by Jarzynski. The basic idea behind this theorem is the relationship connecting the free energy difference between two thermodynamic states of a system and the average work performed by an external agent, in a finite time, through nonequilibrium paths between the same thermodynamic states. We test the validity of this theorem by considering the one-dimensional Ising model where the free energy is exactly determined as a function of temperature and magnetic field. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field applied to the system. We have also determined the probability distribution function for the work performed on the system for the forward and reverse processes and verified that predictions based on the Crooks relation are equally correct. We also propose a method to calculate the lag between the current state of the system and that of the equilibrium based on macroscopic variables. We have shown that the lag increases with the sweeping rate of the field at its final value for the reverse process, while it decreases in the case of the forward process. The lag increases linearly with the size of the chain and with a slope decreasing with the inverse of the rate of variation of the field.
A restructuring of CF package for MIDAS computer code
International Nuclear Information System (INIS)
Park, S. H.; Kim, K. R.; Kim, D. H.; Cho, S. W.
2004-01-01
CF package, which evaluates user-specified 'control functions' and applies them to define or control various aspects of computation, has been restructured for the MIDAS computer code. MIDAS is being developed as an integrated severe accident analysis code with a user-friendly graphical user interface and modernized data structure. To do this, data transferring methods of current MELCOR code are modified and adopted into the CF package. The data structure of the current MELCOR code using FORTRAN77 causes a difficult grasping of meaning of the variables as well as waste of memory, difficulty is more over because its data is location information of other package's data due to characteristics of CF package. New features of FORTRAN90 make it possible to allocate the storage dynamically and to use the user-defined data type, which lead to an efficient memory treatment and an easy understanding of the code. Restructuring of the CF package addressed in this paper includes module development, subroutine modification, and treats MELGEN, which generates data file, as well as MELCOR, which is processing a calculation. The verification has been done by comparing the results of the modified code with those from the existing code. As the trends are similar to each other, it hints that the same approach could be extended to the entire code package. It is expected that code restructuring will accelerate the code domestication thanks to direct understanding of each variable and easy implementation of modified or newly developed models
Watson's theorem and resonant pion photoproduction amplitude in the delta channel
International Nuclear Information System (INIS)
Wittman, R.; Davidson, R.; Mukhopadhyay, N.C.
1984-01-01
The CGLN and BL theories of the pion photoproduction on nucleons, used in nuclear calculations, are examined regarding their predictions of the resonant M 1 + and E 1 + multipoles. The nonunitary BL approach violates Watson's theorem, and predicts these multipoles porly. In the static limit, the CGLN multipoles satisfy Watson's theorem and are in fine agreement with data. The unitarized BL multipoles agree with those from the Olsson theory and data. (orig.)
Thermodynamical and Green function many-body Wick theorems
International Nuclear Information System (INIS)
Westwanski, B.
1987-01-01
The thermodynamical and Green function many-body reduction theorems of Wick type are proved for the arbitrary mixtures of the fermion, boson and spin systems. ''Many-body'' means that the operators used are the products of the arbitrary number of one-body standard basis operators [of the fermion or (and) spin types] with different site (wave vector) indices, but having the same ''time'' (in the interaction representation). The method of proving is based on'' 1) the first-order differential equation of Schwinger type for: 1a) anti T-product of operators; 1b) its average value; 2) KMS boundary conditions for this average. It is shown that the fermion, boson and spin systems can be unified in the many-body formulation (bosonification of the fermion systems). It is impossible in the one-body approach. Both of the many-body versions of the Wick theorem have the recurrent feature: nth order moment diagrams for the free energy or Green functions can be expressed by the (n-1)th order ones. This property corresponds to the automatic realization of: (i) summations over Bose-Einstein or (and) Fermi-Dirac frequencies; (ii) elimination of Bose-Einstein or (and) Fermi-Dirac distributions. The procedures (i) and (ii), being the results of using the Green function one-body reduction theorem, have constituted the significant difficulty up to now in the treatment of quantum systems. (orig.)
General Correlation Theorem for Trinion Fourier Transform
Bahri, Mawardi
2017-01-01
- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.
Bell's theorem based on a generalized EPR criterion of reality
International Nuclear Information System (INIS)
Eberhard, P.H.; Rosselet, P.
1995-01-01
First, the demonstration of Bell's theorem, i.e., of the nonlocal character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedanken experiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almost with certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future
The a theorem for Gauge-Yukawa theories beyond Banks-Zaks
DEFF Research Database (Denmark)
Antipin, Oleg; Gillioz, Marc; Mølgaard, Esben
2013-01-01
We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including the pres......We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including...
A survey of weighted substitution operators and generalizations of Banach-stone theorem
R. K. Singh
2005-01-01
The classical Banach-Stone theorem characterizes linear surjective isometries between C(K)-spaces. The main aim of this paper is to present a survey of Banach-Stone-theorem-type results between some function spaces. The weighted substitution operators play an important role in characterization of isometries, disjointness preserving operators, and lattice homomorphisms. Some open problems are given for further investigation.
Virial theorem and the Born-Oppenheimer approximation at different orders of perturbation
International Nuclear Information System (INIS)
Olivier, Gabriel; Weislinger, Edmond
1977-01-01
The link between the virial theorem and the adiabatic approximation is studied for a few orders of perturbation. It is shown that the total energy of the system is distributed between the mean values of kinetic and potential energy of the nuclei and the electrons in each order of perturbation. No static approximation connected with the Hellmann-Feynman theorem is made [fr
Stupel, Moshe; Ben-Chaim, David
2013-01-01
Based on Steiner's fascinating theorem for trapezium, seven geometrical constructions using straight-edge alone are described. These constructions provide an excellent base for teaching theorems and the properties of geometrical shapes, as well as challenging thought and inspiring deeper insight into the world of geometry. In particular, this…
Reactions of CF3O radicals with selected alkenes and aromatics under atmospheric conditions
DEFF Research Database (Denmark)
Kelly, C.; Sidebottom, H.W.; Treacy, J.
1994-01-01
Rate data for the reactions of CF3O radicals with alkenes and aromatic compounds have been determined at 298 K using a relative rate method. The data are analyzed in terms of structure-reactivity relationships, and their importance to the atmospheric chemistry of CF3O discussed.......Rate data for the reactions of CF3O radicals with alkenes and aromatic compounds have been determined at 298 K using a relative rate method. The data are analyzed in terms of structure-reactivity relationships, and their importance to the atmospheric chemistry of CF3O discussed....
Magnetic susceptibility of 244Cm metal and 249Cf metal
International Nuclear Information System (INIS)
Fujita, D.K.; Parsons, T.C.; Edelstein, N.; Noe, M.; Peterson, J.R.
1975-07-01
The first magnetic susceptibility measurements made on the expanded fcc phase of 249 Cf metal are reported. Further measurements are needed on other Cf metal phases. Another measurement of the magnetic susceptibility of 244 Cm metal in a limited temperature range has been reported. The result does not agree with previously reported values. Further work is continuing on the synthesis of 244 Cm metal and 248 Cm metal and magnetic measurements on these samples. (auth)
Graph-like continua, augmenting arcs, and Menger's theorem
DEFF Research Database (Denmark)
Thomassen, Carsten; Vella, Antoine
2008-01-01
We show that an adaptation of the augmenting path method for graphs proves Menger's Theorem for wide classes of topological spaces. For example, it holds for locally compact, locally connected, metric spaces, as already known. The method lends itself particularly well to another class of spaces......, connected graph. While closed subsets of such a space behave nicely in that they are compact and locally connected (and therefore locally arcwise connected), the general subspaces do not: They may be connected without being arcwise connected. Nevertheless, they satisfy Menger's Theorem......., namely the locally arcwise connected, hereditarily locally connected, metric spaces. Finally, it applies to every space where every point can be separated from every closed set not containing it by a finite set, in particular to every subspace of the Freudenthal compactification of a locally finite...
Short distance modification of the quantum virial theorem
Zhao, Qin; Faizal, Mir; Zaz, Zaid
2017-07-01
In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.
Fluctuation-dissipation theorem for frequency-dependent specific heat
DEFF Research Database (Denmark)
Dyre, Jeppe; Nielsen, Johannes K.
1996-01-01
A derivation of the fluctuation-dissipation (FD) theorem for the frequency-dependent specific heat of a system described by a master equation is presented. The FD theorem is illustrated by a number of simple examples, including a system described by a linear Langevin equation, a two-level system......, and a system described by the energy master equation. It is shown that for two quite different models with low-energy cutoffsa collection of two-level systems and a system described by the energy master equationthe frequency-dependent specific heat in dimensionless units becomes universal at low temperatures......, i.e., independent of both energy distribution and temperature. These two models give almost the same universal frequency-dependent specific heat, which compares favorably to experiments on supercooled alcohols....
A local inverse spectral theorem for Hamiltonian systems
International Nuclear Information System (INIS)
Langer, Matthias; Woracek, Harald
2011-01-01
We consider (2 × 2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x in [s − , s + ). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q H . The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q H . In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q H 1 and q H 2 corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H 1 and H 2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients
The status of low dose rate and future of high dose rate Cf-252 brachytherapy
International Nuclear Information System (INIS)
Rivard, M.J.; Wierzbicki, J.G.; Van den Heuvel, F.; Chuba, P.J.; Fontanesi, J.
1997-12-01
This work describes the current status of the US low dose rate (LDR) Cf-252 brachytherapy program. The efforts undertaken towards development of a high dose rate (HDR) remotely after loaded Cf-252 source, which can accommodate 1 mg or greater Cf-252, are also described. This HDR effort is a collaboration between Oak Ridge National Laboratory (ORNL), commercial remote after loader manufactures, the Gershenson Radiation Oncology Center (ROC), and Wayne State University. To achieve this goal, several advances in isotope chemistry and source preparation at ORNL must be achieved to yield a specific material source loading of greater than or equal 1 mg Cf-252 per mm3. Development work with both radioactive and non-radioactive stand-ins for Cf-252 have indicated the feasibility of fabricating such sources. As a result, the decreased catheter diameter and computer controlled source placement will permit additional sites (e.g. brain, breast, prostate, lung, parotid, etc.) to be treated effectively with Cf-252 sources. Additional work at the Radiochemical Engineering and Development Center (REDC) remains in source fabrication, after loader modification, and safe design. The current LDR Cf-252 Treatment Suite at the ROC is shielded and licensed to hold up to 1 mg of Cf-252. This was designed to maintain cumulative personnel exposure, both external to the room and in direct isotope handling, at less than 20 microSv/hr. However, cumulative exposure may be greatly decreased if a Cf-252 HDR unit is employed which would eliminate direct isotope handling and decrease treatment times from tilde 3 hours to an expected range of 3 to 15 minutes. Such a Cf-252 HDR source will also demonstrate improved dose distributions over current LDR treatments due to the ability to step the point-like source throughout the target volume and weight the dwell time accordingly
Generalized Friedland's theorem for C0-semigroups
Cichon, Dariusz; Jung, Il Bong; Stochel, Jan
2008-07-01
Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.
A note on the Pfaffian integration theorem
International Nuclear Information System (INIS)
Borodin, Alexei; Kanzieper, Eugene
2007-01-01
Two alternative, fairly compact proofs are presented of the Pfaffian integration theorem that surfaced in the recent studies of spectral properties of Ginibre's Orthogonal Ensemble. The first proof is based on a concept of the Fredholm Pfaffian; the second proof is purely linear algebraic. (fast track communication)
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 landing theorem for entire functions with bounded post-singular sets
Benini, Anna Miriam; Rempe-Gillen, Lasse
2017-01-01
The Douady-Hubbard landing theorem for periodic external rays is one of the cornerstones of the study of polynomial dynamics. It states that, for a complex polynomial with bounded postcritical set, every periodic external ray lands at a repelling or parabolic periodic point, and conversely every repelling or parabolic point is the landing point of at least one periodic external ray. We prove an analogue of this theorem for an entire function with bounded postsingular set: every periodic dread...
On Viviani's Theorem and Its Extensions
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
Highly preferential association of NonF508del CF mutations with the M470 allele.
Ciminelli, B M; Bonizzato, A; Bombieri, C; Pompei, F; Gabaldo, M; Ciccacci, C; Begnini, A; Holubova, A; Zorzi, P; Piskackova, T; Macek, M; Castellani, C; Modiano, G; Pignatti, P F
2007-01-01
On the basis of previous findings on random individuals, we hypothesized a preferential association of CF causing mutations with the M allele of the M470V polymorphic site of the CFTR gene. We have determined the M/V-CF mutation haplotype in a series of 201 North East Italian and 73 Czech CF patients who were not F508del homozygotes, as F508del was already known to be fully associated with the M allele. Out of 358 not F508del CF genes, 84 carried the V allele and 274 the less common M allele. In the N-E Italian population, MM subjects have a risk of carrying a CF causing mutation 6.9x greater than VV subjects when F508del is excluded and 15.4x when F508del is included. In the Czech population a similar, although less pronounced, association is observed. Besides the possible biological significance of this association, the possibility of exploiting it for a pilot screening program has been explored in a local North East Italian population for which CF patients were characterized for their CF mutation. General M470V genotyping followed by common CF mutation screening limited to couples in which each partner carries at least one M allele would need testing only 39% of the couples, which contribute 89% of the total risk, with a cost benefit.
The effect of CF4 addition on Ru etching with inductively coupled plasma
International Nuclear Information System (INIS)
Lim, Kyu Tae; Kim, Dong Pyo; Kim, Kyoung Tae; Kim, Chang Il
2003-01-01
Ru thin films were etched in CF 4 /O 2 plasma using an ICP (inductively coupled plasma etching) system. The etch rate of Ru thin films was examined as a function of gas mixing ratio. The maximum etch rate of Ru thin films was 168 nm/min at a CF 4 /O 2 gas mixing ratio of 10 %. The selectivity of Ru over SiO 2 was 1.3. From the OES (optical emission spectroscopy), the optical emission intensity of the O radical had a maximum value at 10 % of CF 4 gas concentration and decrease with further addition of CF 4 gas. From XPS (x-ray photoelectron spectroscopy) analysis, Ru-F bonds by the chemical reaction of Ru and F appeared in the surface of the etched Ru thin film in CF 4 /O 2 chemistry. RuF 3-4 compounds were suggested as a surface passivation layer that reduces the chemical reactions between Ru and O radicals. In a FE-SEM (field emission scanning electron microscope) micrograph, we had an almost perpendicular taper angle of 89 .deg.
Neutron shielding for a {sup 252} Cf source
Energy Technology Data Exchange (ETDEWEB)
Vega C, H.R.; Manzanares A, E.; Hernandez D, V.M. [Unidades Academicas de Estudios Nucleares e Ingenieria Electrica, Universidad Autonoma de Zacatecas, C. Cipres 10, Fracc. La Penuela, 98068 Zacatecas (Mexico); Eduardo Gallego, Alfredo Lorente [Depto. de Ingenieria Nuclear, ETS Ingenieros Industriales, Universidad Politecnica de Madrid, C. Jose Gutierrez Abascal 2, 28006 Madrid (Spain)]. e-mail: fermineutron@yahoo.com
2006-07-01
To determine the neutron shielding features of water-extended polyester a Monte Carlo study was carried out. Materials with low atomic number are predominantly used for neutron shielding because these materials effectively attenuate neutrons, mainly through inelastic collisions and absorption reactions. During the selection of materials to design a neutron shield, prompt gamma production as well as radionuclide production induced by neutron activation must be considered. In this investigation the Monte Carlo method was used to evaluate the performance of a water-extended polyester shield designed for the transportation, storage, and use of a {sup 252}Cf isotopic neutron source. During calculations a detailed model for the {sup 252}Cf and the shield was utilized. To compare the shielding features of water extended polyester, the calculations were also made for the bare {sup 252}Cf in vacuum, air and the shield filled with water. For all cases the calculated neutron spectra was utilized to determine the ambient equivalent neutron dose at four sites around the shielding. In the case of water extended polyester and water shielding the calculations were extended to include the prompt gamma rays produced during neutron interactions, with this information the Kerma in air was calculated at the same locations where the ambient equivalent neutron dose was determined. (Author)
A Coordinate-Based Proof of the Scallop Theorem
Ishimoto, Kenta; Yamada, Michio
2012-01-01
We reconsider fluid dynamics for a self-propulsive swimmer in Stokes flow. With an exact definition of deformation of a swimmer, a coordinate-based proof is first given to Purcell's scallop theorem including the body rotation.
A priori knowledge and the Kochen-Specker theorem
International Nuclear Information System (INIS)
Brunet, Olivier
2007-01-01
We introduce and formalize a notion of 'a priori knowledge' about a quantum system, and show some properties about this form of knowledge. Finally, we show that the Kochen-Specker theorem follows directly from this study
Kohn's theorem in a superfluid Fermi gas with a Feshbach resonance
International Nuclear Information System (INIS)
Ohashi, Y.
2004-01-01
We investigate the dipole mode in a superfluid gas of Fermi atoms trapped in a harmonic potential. According to Kohn's theorem, the frequency of this collective mode is not affected by an interaction between the atoms and is always equal to the trap frequency. This remarkable property, however, does not necessarily hold in an approximate theory. We explicitly prove that the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA), including a coupling between fluctuations in the density and Cooper channels, is consistent with both Kohn's theorem as well as Goldstone's theorem. This proof can be immediately extended to the strong-coupling superfluid theory developed by Nozieres and Schmitt-Rink (NSR), where the effect of superfluid fluctuations is included within the Gaussian level. As a result, the NSR-GRPA formalism can be used to study collective modes in the BCS-BEC crossover region in a manner which is consistent with Kohn's theorem. We also include the effect of a Feshbach resonance and a condensate of the associated molecular bound states. A detailed discussion is given of the unusual nature of the Kohn mode eigenfunctions in a Fermi superfluid, in the presence and absence of a Feshbach resonance. When the molecular bosons feel a different trap frequency from the Fermi atoms, the dipole frequency is shown to depend on the strength of effective interaction associated with the Feshbach resonance
Another look at the second incompleteness theorem
Visser, A.
2017-01-01
In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is xed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the interpretation
Another look at the second incompleteness theorem
Visser, Albert
2017-01-01
In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is fixed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the
A pneumatic transfer system for special form 252Cf
International Nuclear Information System (INIS)
Gehrke, R.J.; Berry, S.M.; Grafwallner, E.G.; Hoggan, J.M.
1996-09-01
A pneumatic transfer system has been developed for use with series 100 Special Form 252 Cf. It was developed to reduce the exposure to personnel handling sources of 252 Cf with masses up to 150 microg by permitting remotely activated two-way transfer between the storage container and the irradiation position. The pneumatic transfer system also permits transfers for reproducible repetitive irradiation periods. In addition to the storage container equipped with quick-release fittings, the transfer system consists of an irradiation station, a control box with momentary contact switches to activate the air-pressure control valves and indicators to identify the location of the source, and connecting air hose and electrical wire. A source of 20 psig air and 110 volt electrical power are required for operation of the transfer system which can be easily moved and set up by one individual in 5 to 10 minutes. Tests have shown that rarely does a source become lodged in the transfer tubing, but two methods have been developed to handle incomplete transfers of the 252 Cf source. The first method consists of closing one air vent to allow a pressure impulse to propel the source to the opposite side. The second method applies to those 252 Cf capsules with a threaded or tapped end to which a small ferromagnetic piece can be attached; an incompletely transferred source in the transfer tube can then be guided to a position of safety by surrounding the transfer tubing containing the capsule with a horseshoe magnet attached to the end of a long pole
Atmospheric chemistry of Z- and E-CF3CH=CHCF3
DEFF Research Database (Denmark)
Østerstrøm, Freja From; Andersen, Simone Thirstrup; Sølling, Theis Ivan
2017-01-01
radicals. The atmospheric lifetimes of Z- and E-CF3CH[double bond, length as m-dash]CHCF3 are estimated as 27 and 67 days, respectively. IR absorption cross sections are reported and the global warming potentials (GWPs) of Z- and E-CF3CH[double bond, length as m-dash]CHCF3 for the 100 year time horizon...
A General No-Cloning Theorem for an infinite Multiverse
Gauthier, Yvon
2013-10-01
In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics.
The luminosity function for different morphological types in the CfA Redshift Survey
Marzke, Ronald O.; Geller, Margaret J.; Huchra, John P.; Corwin, Harold G., Jr.
1994-01-01
We derive the luminosity function for different morphological types in the original CfA Redshift Survey (CfA1) and in the first two slices of the CfA Redshift Survey Extension (CfA2). CfA1 is a complete sample containing 2397 galaxies distributed over 2.7 steradians with m(sub z) less than or equal 14.5. The first two complete slices of CfA2 contain 1862 galaxies distributed over 0.42 steradians with m(sub z)=15.5. The shapes of the E-S0 and spiral luminosity functions (LF) are indistinguishable. We do not confirm the steeply decreasing faint end in the E-S0 luminosity function found by Loveday et al. for an independent sample in the southern hemisphere. We demonstrate that incomplete classification in deep redshift surveys can lead to underestimates of the faint end of the elliptical luminosity function and could be partially responsible for the difference between the CfA survey and other local field surveys. The faint end of the LF for the Magellanic spirals and irregulars is very steep. The Sm-Im luminosity function is well fit by a Schechter function with M*=-18.79, alpha=-1.87, and phi*=0.6x10(exp -3) for M(sub z) less than or equal to -13. These galaxies are largely responsible for the excess at the faint end of the general CfA luminosity function. The abundance of intrinsically faint, blue galaxies nearby affects the interpretation of deep number counts. The dwarf population increases the expected counts at B=25 in a no-evolution, q(sub 0)=0.05 model by a factor of two over standard no-evolution estimates. These dwarfs change the expected median redshift in deep redshift surveys by less than 10 percent . Thus the steep Sm-Im LF may contribute to the reconciliation of deep number counts with deep redshift surveys.
Radiation ulcers in patients with cancer of the tongue after /sup 252/Cf therapy
Energy Technology Data Exchange (ETDEWEB)
Galantseva, G.F.; Guseva, L.I.; Plichko, V.I. (Akademiya Meditsinskikh Nauk SSSR, Obninsk. Nauchno-Issledovatel' skij Inst. Meditsinskoj Radiologii)
1984-01-01
Interstitial therapy with /sup 252/Cf was conducted for 57 patients with cancer of the tongue. It was established that clinical course of radiation tungue ulcers after interstitial therapy with /sup 252/Cf doesn't differ sufficiently from the course of radiation injuries, occurring after ..gamma..-radiation application. Radiation ulcers are often observed in patients after the treatment of recurrent and residual tumors with /sup 252/Cf (in 33% of patients); the ulcers appeared in 15% of cases in patients after the treatment of initial ulcers tumors. Conservative treatment provide the cure of radiation tongue ulcers after interstitial therapy with /sup 252/Cf.
Magnetostatic fields computed using an integral equation derived from Green's theorems
International Nuclear Information System (INIS)
Simkin, J.; Trowbridge, C.W.
1976-04-01
A method of computing magnetostatic fields is described that is based on a numerical solution of the integral equation obtained from Green's Theorems. The magnetic scalar potential and its normal derivative on the surfaces of volumes are found by solving a set of linear equations. These are obtained from Green's Second Theorem and the continuity conditions at interfaces between volumes. Results from a two-dimensional computer program are presented and these show the method to be accurate and efficient. (author)
Quenching the scintillation in CF4 Cherenkov gas radiator
International Nuclear Information System (INIS)
Blake, T.; D'Ambrosio, C.; Easo, S.; Eisenhardt, S.; Fitzpatrick, C.; Forty, R.; Frei, C.; Gibson, V.; Gys, T.; Harnew, N.; Hunt, P.; Jones, C.R.; Lambert, R.W.; Matteuzzi, C.; Muheim, F.; Papanestis, A.; Perego, D.L.; Piedigrossi, D.; Plackett, R.; Powell, A.
2015-01-01
CF 4 is used as a Cherenkov gas radiator in one of the Ring Imaging Cherenkov detectors at the LHCb experiment at the CERN Large Hadron Collider. CF 4 is well known to have a high scintillation photon yield in the near and far VUV, UV and in the visible wavelength range. A large flux of scintillation photons in our photon detection acceptance between 200 and 800 nm could compromise the particle identification efficiency. We will show that this scintillation photon emission system can be effectively quenched, consistent with radiationless transitions, with no significant impact on the photons resulting from Cherenkov radiation
Thinning and functionalization of few-layer graphene sheets by CF4 plasma treatment
Shen, Chao
2012-05-24
Structural changes of few-layer graphene sheets induced by CF4 plasma treatment are studied by optical microscopy and Raman spectroscopy, together with theoretical simulation. Experimental results suggest a thickness reduction of few-layer graphene sheets subjected to prolonged CF4 plasma treatment while plasma treatment with short time only leads to fluorine functionalization on the surface layer by formation of covalent bonds. Raman spectra reveal an increase in disorder by physical disruption of the graphene lattice as well as functionalization during the plasma treatment. The F/CF3 adsorption and the lattice distortion produced are proved by theoretical simulation using density functional theory, which also predicts p-type doping and Dirac cone splitting in CF4 plasma-treated graphene sheets that may have potential in future graphene-based micro/nanodevices.
Sturm-Picone type theorems for second-order nonlinear differential equations
Directory of Open Access Journals (Sweden)
Aydin Tiryaki
2014-06-01
Full Text Available The aim of this article is to give Sturm-Picone type theorems for the pair of second-order nonlinear differential equations $$\\displaylines{ (p_1(t|x'|^{\\alpha-1}x''+q_1(tf_1(x=0 \\cr (p_2(t|y'|^{\\alpha-1}y''+q_2(tf_2(y=0,\\quad t_1
Reasoning by analogy as an aid to heuristic theorem proving.
Kling, R. E.
1972-01-01
When heuristic problem-solving programs are faced with large data bases that contain numbers of facts far in excess of those needed to solve any particular problem, their performance rapidly deteriorates. In this paper, the correspondence between a new unsolved problem and a previously solved analogous problem is computed and invoked to tailor large data bases to manageable sizes. This paper outlines the design of an algorithm for generating and exploiting analogies between theorems posed to a resolution-logic system. These algorithms are believed to be the first computationally feasible development of reasoning by analogy to be applied to heuristic theorem proving.
Bell's theorem based on a generalized EPR criterion of reality
International Nuclear Information System (INIS)
Eberhard, P.H.; Rosselet, P.
1993-04-01
First, the demonstration of Bell's theorem, i.e. of the non-local character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedanken experiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almost with certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future. (author) 1 fig., 11 refs
Heuristic analogy in Ars Conjectandi: From Archimedes' De Circuli Dimensione to Bernoulli's theorem.
Campos, Daniel G
2018-02-01
This article investigates the way in which Jacob Bernoulli proved the main mathematical theorem that undergirds his art of conjecturing-the theorem that founded, historically, the field of mathematical probability. It aims to contribute a perspective into the question of problem-solving methods in mathematics while also contributing to the comprehension of the historical development of mathematical probability. It argues that Bernoulli proved his theorem by a process of mathematical experimentation in which the central heuristic strategy was analogy. In this context, the analogy functioned as an experimental hypothesis. The article expounds, first, Bernoulli's reasoning for proving his theorem, describing it as a process of experimentation in which hypothesis-making is crucial. Next, it investigates the analogy between his reasoning and Archimedes' approximation of the value of π, by clarifying both Archimedes' own experimental approach to the said approximation and its heuristic influence on Bernoulli's problem-solving strategy. The discussion includes some general considerations about analogy as a heuristic technique to make experimental hypotheses in mathematics. Copyright © 2018 Elsevier Ltd. All rights reserved.
Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs
Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.
2018-04-01
Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.
Generation of the ArCF22+ dication
Czech Academy of Sciences Publication Activity Database
Lockyear, J. F.; Douglas, K.; Price, S. D.; Karwowska, M.; Fijalkowski, K. J.; Grochala, W.; Remeš, M.; Roithová, J.; Schröder, Detlef
-, č. 1 (2010), s. 358-362 ISSN 1948-7185 R&D Projects: GA ČR GA203/09/1223 Institutional research plan: CEZ:AV0Z40550506 Keywords : argon * dications * mass spectrometry * rare-gas compounds * superelectrophiles Subject RIV: CF - Physical ; Theoretical Chemistry
Strong ergodic theorem for commutative semigroup of non ...
Indian Academy of Sciences (India)
M Azhini
2017-08-14
Aug 14, 2017 ... of non-Lipschitzian mappings in multi-Banach space ... to studying nonlinear ergodic theory for (asymptotically) non-expansive ... As we know, Bruck's lemmas are essential tools in the proof of almost all mean ergodic theorem ...
Haloacyl complexes of boron, [(CF3)3BC(O)Hal]- (Hal=F, Cl, Br, I).
Finze, Maik; Bernhardt, Eduard; Willner, Helge; Lehmann, Christian W
2005-11-04
The haloacyltris(trifluoromethyl)borate anions [(CF3)3BC(O)Hal]- (Hal=F, Cl, Br, I) have been synthesized by reacting (CF3)3BCO with either MHal (M=K, Cs; Hal=F) in SO2 or MHal (M=[nBu4N]+, [Et4N]+, [Ph4P]+; Hal=Cl, Br, I) in dichloromethane. Metathesis reactions of the fluoroacyl complex with Me3SiHal (Hal=Cl, Br, I) led to the formation of its higher homologues. The thermal stabilities of the haloacyltris(trifluoromethyl)borates decrease from the fluorine to the iodine derivative. The chemical reactivities decrease in the same order as demonstrated by a series of selected reactions. The new [(CF3)3BC(O)Hal]- (Hal=F, Cl, Br) salts are used as starting materials in the syntheses of novel compounds that contain the (CF3)3B-C fragment. All borate anions [(CF3)3BC(O)Hal]- (Hal=F, Cl, Br, I) have been characterized by multinuclear NMR spectroscopy (11B, 13C, 17O, 19F) and vibrational spectroscopy. [PPh4][(CF3)3BC(O)Br] crystallizes in the monoclinic space group P2/c (no. 13) and the bond parameters are compared with those of (CF3)3BCO and K[(CF3)3BC(O)F]. The interpretation of the spectroscopic and structural data are supported by DFT calculations [B3LYP/6-311+G(d)].
Natural relations and Appelquist-Carazzone decoupling theorem
International Nuclear Information System (INIS)
Grzadkowski, B.; Krawczyk, P.; Pokorski, S.
1984-01-01
It is pointed out that in some cases violation of the Appelquist-Carazzone decoupling theorem in spontaneously broken gauge theories is related to the presence in such theories of the so-called natural zeroth-order relations. In this context heavy-fermion effects in the Glashow-Salam-Weinberg model are discussed
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.
The Embedding Theorems of Whitney and Nash
Indian Academy of Sciences (India)
We begin by briefly motivating the idea of amanifold and then discuss the embedding theorems of Whitney and Nash that allow us toview these objects inside appropriately large Euclidean spaces. Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 4. Current Issue Volume 23 | Issue 4. April 2018.
Impact of enzymatic digestion on bacterial community composition in CF airway samples.
Williamson, Kayla M; Wagner, Brandie D; Robertson, Charles E; Johnson, Emily J; Zemanick, Edith T; Harris, J Kirk
2017-01-01
Previous studies have demonstrated the importance of DNA extraction methods for molecular detection of Staphylococcus, an important bacterial group in cystic fibrosis (CF). We sought to evaluate the effect of enzymatic digestion (EnzD) prior to DNA extraction on bacterial communities identified in sputum and oropharyngeal swab (OP) samples from patients with CF. DNA from 81 samples (39 sputum and 42 OP) collected from 63 patients with CF was extracted in duplicate with and without EnzD. Bacterial communities were determined by rRNA gene sequencing, and measures of alpha and beta diversity were calculated. Principal Coordinate Analysis (PCoA) was used to assess differences at the community level and Wilcoxon Signed Rank tests were used to compare relative abundance (RA) of individual genera for paired samples with and without EnzD. Shannon Diversity Index (alpha-diversity) decreased in sputum and OP samples with the use of EnzD. Larger shifts in community composition were observed for OP samples (beta-diversity, measured by Morisita-Horn), whereas less change in communities was observed for sputum samples. The use of EnzD with OP swabs resulted in significant increase in RA for the genera Gemella ( p microbial community composition. We show that the application of EnzD to CF airway samples, particularly OP swabs, results in differences in microbial communities detected by sequencing. Use of EnzD can result in large changes in bacterial community composition, and is particularly useful for detection of Staphylococcus in CF OP samples. The enhanced identification of Staphylococcus aureus is a strong indication to utilize EnzD in studies that use OP swabs to monitor CF airway communities.
A remark on three-surface theorem
International Nuclear Information System (INIS)
Lu Zhujia
1991-01-01
The three-surface theorem for uniformly elliptic differential inequalities with nonpositive coefficient of zero-order term in some domain D is included in R n becomes trivial if the maximum of u on two separate boundary surface of D is nonpositive. We give a method in this paper for obtaining a nontrivial estimate of the maximum of u on a family of closed surfaces. (author). 2 refs
The self-normalized Donsker theorem revisited
Parczewski, Peter
2016-01-01
We extend the Poincar\\'{e}--Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the self-normalized Donsker theorem in Cs\\"{o}rg\\H{o} et al. (2003). Some notes on spheres with respect to $\\ell_p$-norms are given.
Optical theorem, depolarization and vector tomography
International Nuclear Information System (INIS)
Toperverg, B.P.
2003-01-01
A law of the total flux conservation is formulated in the form of the optical theorem. It is employed to explicitly derive equations for the description of the neutron polarization within the range of the direct beam defined by its angular divergence. General considerations are illustrated by calculations using the Born and Eikonal approximations. Results are briefly discussed as applied to Larmor-Fourier tomography
Applications of Wck's theorem, ch. 17
International Nuclear Information System (INIS)
Brussaard, P.J.; Glaudemans, P.W.M.
1977-01-01
Wick's theorem is introduced and used to write the many-body Hamiltonian in a selfconsistent basis. The terms of a perturbation expansion are evaluated with the use of the second-quantization formalism.The correspondence with Feyman diagrams is demonstrated. For some nuclei a description in terms of particle-hole configurations is quite convenient. The simplest case, i.e. one-particle, one-hole states, is treated
Classification theorem for principal fibre bundles, Berry's phase, and exact cycle evolution
International Nuclear Information System (INIS)
Bohm, A.; Boya, L.J.; Mostafazadeh, A.; Rudolph, G.
1993-03-01
The relation between the two mathematical interpretations of the geometric (Berry) phase is discussed, using either the fibre bundle over parameter space or over projective Hilbert space. It turns out that these two geometric constructions are linked by the classification theorem for vector bundles. The classification theorem provides the means to classify the parameter space bundles for adiabatic evolution and for non-adiabatic cyclic evolution of the statevectors
Electron drift velocities of Ar-CO2-CF4 gas mixtures
International Nuclear Information System (INIS)
Markeloff, R.
1994-11-01
The muon spectrometer for the D0 experiment at Fermi National Accelerator Laboratory uses proportional drift tubes filled with an Ar-CO 2 -CF 4 gas mixture. Measurements of drift velocity as a function of electric field magnitude for 90%-5%-5% and 90%-4%-6% Ar-CO 2 -CF 4 mixtures are presented, and our operational experiences with these gases at D0 is discussed
Dielectric Properties of SiCf/PyC/SiC Composites After Oxidation
Institute of Scientific and Technical Information of China (English)
SONG Huihui; ZHOU Wancheng; LUO Fa; QING Yuchang; CHEN Malin; LI Zhimin
2016-01-01
In this paper, the SiC fiber-reinforced SiC matrix composites with a 0.15mm thick pyrocarbon interphase (notedas SiCf/PyC/SiC) were prepared by chemical vapor infiltration (CVI). The SiCf/PyC/SiC were oxidized in air at 950℃ for 50h. The dielectric properties after this high temperature oxidation were investigated in X-band from room temperature (RT) to 700℃. Results suggested that:e' of the SiCf/PyC/SiC after oxidation increased at first then de-creased with temperature elevating;e" increased with temperature raising in the temperature range studied.
Quality of life in children with CF: Psychometrics and relations with stress and mealtime behaviors.
Driscoll, Kimberly A; Modi, Avani C; Filigno, Stephanie S; Brannon, Erin E; Chamberlin, Leigh Ann; Stark, Lori J; Powers, Scott W
2015-06-01
The purpose of this study was to evaluate the utility of the Cystic Fibrosis Questionnaire-Revised (CFQ-R) with toddlers and preschool-aged children. Clinically relevant relations between health-related quality of life (HRQOL), stress, and mealtime behaviors have not been examined. It was hypothesized that problematic mealtime behaviors and increased stress would be negatively associated with HRQOL. Parents of 73 children (2-6 years) with CF completed questionnaires assessing their children's generic (PedsQL) and CF-specific HRQOL, parenting and CF-specific stress, and mealtime behaviors. CFQ-R Physical, Eating, and Respiratory HRQOL subscales had acceptable to strong reliability (alphas = 0.73-0.86); other scales approached acceptable reliability. Lower CF-specific stress was associated with higher CFQ-R Eating HRQOL (B = -0.84; P < 0.05) scores. Fewer eating problems were associated with higher CFQ-R Eating (B = -1.17; P < 0.0001) and Weight HRQOL (B = -0.78; P < 0.01) scores. As hypothesized, problematic eating and higher CF-specific stress was associated with lower CF-specific HRQOL. The CFQ-R has promise for use in young children with CF, but will need to be modified to exchange items not relevant to preschoolers with items that are more relevant to this age group. © 2014 Wiley Periodicals, Inc.
CfA3: 185 TYPE Ia SUPERNOVA LIGHT CURVES FROM THE CfA
International Nuclear Information System (INIS)
Hicken, Malcolm; Challis, Peter; Kirshner, Robert P.; Bakos, Gaspar; Berlind, Perry; Brown, Warren R.; Caldwell, Nelson; Calkins, Mike; Cho, Richard; Contreras, Maria; Jha, Saurabh; Matheson, Tom; Modjaz, Maryam; Rest, Armin; Michael Wood-Vasey, W.; Barton, Elizabeth J.; Bragg, Ann; Briceno, Cesar; Ciupik, Larry; Dendy, Kristi-Concannon
2009-01-01
We present multiband photometry of 185 type-Ia supernovae (SNe Ia), with over 11,500 observations. These were acquired between 2001 and 2008 at the F. L. Whipple Observatory of the Harvard-Smithsonian Center for Astrophysics (CfA). This sample contains the largest number of homogeneously observed and reduced nearby SNe Ia (z ∼< 0.08) published to date. It more than doubles the nearby sample, bringing SN Ia cosmology to the point where systematic uncertainties dominate. Our natural system photometry has a precision of ∼<0.02 mag in BVRIr'i' and ∼<0.04 mag in U for points brighter than 17.5 mag. We also estimate a systematic uncertainty of 0.03 mag in our SN Ia standard system BVRIr'i' photometry and 0.07 mag for U. Comparisons of our standard system photometry with published SN Ia light curves and comparison stars, where available for the same SN, reveal agreement at the level of a few hundredths mag in most cases. We find that 1991bg-like SNe Ia are sufficiently distinct from other SNe Ia in their color and light-curve-shape/luminosity relation that they should be treated separately in light-curve/distance fitter training samples. The CfA3 sample will contribute to the development of better light-curve/distance fitters, particularly in the few dozen cases where near-infrared photometry has been obtained and, together, can help disentangle host-galaxy reddening from intrinsic supernova color, reducing the systematic uncertainty in SN Ia distances due to dust.
Uniqueness theorem for static phantom wormholes in Einstein–Maxwell-dilaton theory
Directory of Open Access Journals (Sweden)
Boian Lazov
2018-03-01
Full Text Available We prove a uniqueness theorem for completely regular traversable electrically charged wormhole solutions in the Einstein–Maxwell-dilaton gravity with a phantom scalar field and a possible phantom electromagnetic field. In a certain region of the parameter space, determined by the asymptotic values of the scalar field and the lapse function, the regular wormholes are completely specified by their mass, scalar charge and electric charge. The argument is based on the positive energy theorem applied on an appropriate conformally transformed Riemannian space.
''Vanishing theorem'' for a positive holomorphic vector bundle of undefined rank
International Nuclear Information System (INIS)
Le Potier, J.
1974-01-01
Let M ba a compact complex manifold of dimension n and let E→M be a holomorphic vector bundle over M. Theorem: If E is positive of rank r and if Hsup(p,q)(M,E) is the cohomology of type (p,q) of M with values in E, then Hsup(p,q)(M,E) = O as soon as p+q >=n+r. If r = 1, this is the ''precise vanishing theorem'' due to Kodaira and Nakano; the present paper contains a proof of the general case
Quasi-gedanken experiment challenging the no-signalling theorem
Indian Academy of Sciences (India)
Keywords. Quantum information; quantum entanglement; no-signalling theorem ... the construction of empirically testable schemes wherein superluminal exchange of information can occur. In light of this thesis,we present a potentially feasible quantum-optical scheme that purports to enable superluminal signalling.
Confinement, diquarks and goldstone's theorem
International Nuclear Information System (INIS)
Roberts, C.D.
1996-01-01
Determinations of the gluon propagator in the continuum and in lattice simulations are compared. A systematic truncation procedure for the quark Dyson-Schwinger and bound state Bethe-Salpeter equations is described. The procedure ensures the flavor-octet axial- vector Ward identity is satisfied order-by-order, thereby guaranteeing the preservation of Goldstone's theorem; and identifies a mechanism that simultaneously ensures the absence of diquarks in QCD and their presence in QCD N c =2 , where the color singlet diquark is the ''baryon'' of the theory
Cyclic graphs and Apery's theorem
International Nuclear Information System (INIS)
Sorokin, V N
2002-01-01
This is a survey of results about the behaviour of Hermite-Pade approximants for graphs of Markov functions, and a survey of interpolation problems leading to Apery's result about the irrationality of the value ζ(3) of the Riemann zeta function. The first example is given of a cyclic graph for which the Hermite-Pade problem leads to Apery's theorem. Explicit formulae for solutions are obtained, namely, Rodrigues' formulae and integral representations. The asymptotic behaviour of the approximants is studied, and recurrence formulae are found
Wang, Fei; Zhu, Na; Chen, Pinhong; Ye, Jinxing; Liu, Guosheng
2015-08-03
A novel method for convenient access to CF3-containing azirines has been developed, and involves a copper-catalyzed trifluoromethylazidation of alkynes and a photocatalyzed rearrangement. Both terminal and internal alkynes are compatible with the mild reaction conditions, thus delivering the CF3-containing azirines in moderate to good yields. The azirines can be converted into various CF3-substituted aziridines. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
An analogue of Wagner's theorem for decompositions of matrix algebras
International Nuclear Information System (INIS)
Ivanov, D N
2004-01-01
Wagner's celebrated theorem states that a finite affine plane whose collineation group is transitive on lines is a translation plane. The notion of an orthogonal decomposition (OD) of a classically semisimple associative algebra introduced by the author allows one to draw an analogy between finite affine planes of order n and ODs of the matrix algebra M n (C) into a sum of subalgebras conjugate to the diagonal subalgebra. These ODs are called WP-decompositions and are equivalent to the well-known ODs of simple Lie algebras of type A n-1 into a sum of Cartan subalgebras. In this paper we give a detailed and improved proof of the analogue of Wagner's theorem for WP-decompositions of the matrix algebra of odd non-square order an outline of which was earlier published in a short note in 'Russian Math. Surveys' in 1994. In addition, in the framework of the theory of ODs of associative algebras, based on the method of idempotent bases, we obtain an elementary proof of the well-known Kostrikin-Tiep theorem on irreducible ODs of Lie algebras of type A n-1 in the case where n is a prime-power.
Gauge Invariance and the Goldstone Theorem
Guralnik, Gerald S.
This paper was originally created for and printed in the "Proceedings of seminar on unified theories of elementary particles" held in Feldafing, Germany from July 5 to 16, 1965 under the auspices of the Max-Planck-Institute for Physics and Astrophysics in Munich. It details and expands upon the 1964 Guralnik, Hagen, and Kibble paper demonstrating that the Goldstone theorem does not require physical zero mass particles in gauge theories.
Special relativity theorem and Pythagoras’s magic
Korkmaz, S. D.; Aybek, E. C.; Örücü, M.
2016-03-01
In the modern physics unit included in the course curriculum of grade 10 physics introduced in the 2007-2008 education year, the aim is that students at this grade level are aware of any developments which constitute modern physics and may be considered new, and interpret whether mass, length and time values of the motions at any velocities close to the speed of light vary or not. One of the scientific concepts and subjects among the final ones to be learned in the unit of modern physics with 12 course hours includes the special relativity theorem and its results. The special relativity theorem, the foundation of which was laid by Einstein in 1905, has three significant predictions proven by experiments and observations: time extension, dimensional shortening and mass relativity. At the first stage of this study, a simple and fast solution that uses the Pythagorean relation for problems and must be treated by using the mathematical expressions of the predictions as specified above is given, and this way of solution was taught while the relativity subject was explained to the secondary education students who are fifteen years old from grade 10 in the 2013-2014 education year. At the second stage of the study, a qualitative study is released together with grade 11 students who are sixteen years old in 2014-2015, who learnt to solve any problems in both methods, while the special relativity subject is discussed in the physics course in grade 10. The findings of the study show that the students have a misconception on the relativity theorem and prefer to solve any relativity-related problems by using the Pythagorean method constituting the first stage of this study.
Stochastic thermodynamics, fluctuation theorems and molecular machines
International Nuclear Information System (INIS)
Seifert, Udo
2012-01-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (review article)
International Nuclear Information System (INIS)
Zhang, Cheng; Zhou, Yang; Shao, Tao; Xie, Qing; Xu, Jiayu; Yang, Wenjin
2014-01-01
Highlights: • Increase in hydrophobicity on PMMA is achieved after the DBD treatment in CF 4 , and the water contact angle can increase from 68° to 100° after treatment. • Nanosecond-pulse DBD is used for the surface treatment and the power density is about 114.8 mW/cm 2 . • The effects of applied voltage, CF 4 flow, and time on plasma treatment are investigated. • Plasma treatment causes morphological change, significantly increases the roughness of the surface, and introduces fluorine-containing groups into the polymethylmethacrylate surface. • Hydrophobic behavior of the treated PMMA surface is slightly affected by the aging effect. - Abstract: Nanosecond-pulse dielectric barrier discharge (DBD) can provide non-thermal plasmas with extremely high energy and high density, which can result in a series of complicated physical and chemical reactions in the surface treatment of polymers. Therefore, in this paper, hydrophobic treatment of polymethylmethacrylate (PMMA) surface is conducted by nanosecond-pulse DBD in carbon tetrafluoride (CF 4 ) at atmospheric pressure. Investigations on surface morphology and chemical composition before and after the DBD treatment in CF 4 are conducted with the contact angle measurement, atomic force microscope, Fourier transform infrared spectroscopy, and X-ray photoelectron spectrometer. The effects of the applied voltage, CF 4 flow rate, and treatment time on the hydrophobic modification are studied. Results show that the contact angles of the treated PMMA surface increases with the applied voltage, and it could be greatly affected by the CF 4 flow rate and the treatment time. The water contact angle can increase from 68° to 100° after the treatment. Furthermore, both surface morphology and chemical composition of the PMMA samples are changed. Both the increase of the surface roughness and the occurrence of fluorine-containing functional groups on the PMMA surface treated by DBD in CF 4 lead to the hydrophobicity
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.…
Limit theorems for functionals of Gaussian vectors
Institute of Scientific and Technical Information of China (English)
Hongshuai DAI; Guangjun SHEN; Lingtao KONG
2017-01-01
Operator self-similar processes,as an extension of self-similar processes,have been studied extensively.In this work,we study limit theorems for functionals of Gaussian vectors.Under some conditions,we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process.
Radon transformation on reductive symmetric spaces: support theorems
Kuit, J.J.|info:eu-repo/dai/nl/313872589
2011-01-01
In this thesis we introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and study some of their properties. In particular we obtain a generalization of Helgason's support theorem for the horospherical transform on a Riemannian symmetric space.
Fermat's Last Theorem for Factional and Irrational Exponents
Morgan, Frank
2010-01-01
Fermat's Last Theorem says that for integers n greater than 2, there are no solutions to x[superscript n] + y[superscript n] = z[superscript n] among positive integers. What about rational exponents? Irrational n? Negative n? See what an undergraduate senior seminar discovered.
On the proof of the first Carnot theorem in thermodynamics
International Nuclear Information System (INIS)
Morad, M R; Momeni, F
2013-01-01
The proof of the first Carnot theorem in classical thermodynamics is revisited in this study. The underlying conditions of a general proof of this principle presented by Senft (1978 Phys. Educ. 13 35–37) are explored and discussed. These conditions are analysed in more detail using a physical description of heat and work to present a simpler proof of the first principle prior to using the violation of the second law of thermodynamics. Finally, a new simple proof is also presented based on Gibbs relation. This discussion will benefit the teaching of classical thermodynamics and promote better understanding of the proof of the first Carnot theorem in general form. (paper)
The supersymmetric Adler-Bardeen theorem and regularization by dimensional reduction
International Nuclear Information System (INIS)
Ensign, P.; Mahanthappa, K.T.
1987-01-01
We examine the subtraction scheme dependence of the anomaly of the supersymmetric, gauge singlet axial current in pure and coupled supersymmetric Yang-Mills theories. Preserving supersymmetry and gauge invariance explicitly by using supersymmetric background field theory and dimensional reduction, we show that only the one-loop value of the axial anomaly is subtraction scheme independent, and that one can always define a subtraction scheme in which the Adler-Bardeen theorem is satisfied to all orders in perturbation theory. In general this subtraction scheme may be non-minimal, but in both the pure and the coupled theories, the Adler-Bardeen theorem is satisfied to two loops in minimal subtraction. (orig.)
Generalization of the Bogoliubov-Zubarev Theorem for Dynamic Pressure to the Case of Compressibility
Rudoi, Yu. G.
2018-01-01
We present the motivation, formulation, and modified proof of the Bogoliubov-Zubarev theorem connecting the pressure of a dynamical object with its energy within the framework of a classical description and obtain a generalization of this theorem to the case of dynamical compressibility. In both cases, we introduce the volume of the object into consideration using a singular addition to the Hamiltonian function of the physical object, which allows using the concept of the Bogoliubov quasiaverage explicitly already on a dynamical level of description. We also discuss the relation to the same result known as the Hellmann-Feynman theorem in the framework of the quantum description of a physical object.
Randomized central limit theorems: A unified theory.
Eliazar, Iddo; Klafter, Joseph
2010-08-01
The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.
Birth of a theorem a mathematical adventure
Villani, Cédric
2015-01-01
This man could plainly do for mathematics what Brian Cox has done for physics" (Sunday Times). What goes on inside the mind of a rock-star mathematician? Where does inspiration come from? With a storyteller's gift, Cedric Villani takes us on a mesmerising journey as he wrestles with a new theorem that will win him the most coveted prize in mathematics. Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, doubt and anxiety, elation and despair. We discover how it feels to be obsessed by a theorem during your child's cello practise and throughout your dreams, why appreciating maths is a bit like watching an episode of Columbo, and how sometimes inspiration only comes from locking yourself away in a dark room to think. Blending science with history, biography with myth, Villani conjures up an inimitable cast of characters including the omnipresent Einstein, mad genius Kurt Godel, and Villani's personal hero, John Nash. Bir...