Anti-Bell - Refutation of Bell's theorem
Barukčić, Ilija
2012-12-01
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
Expectation Value in Bell's Theorem
Wang, Zheng-Chuan
2006-01-01
We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell's inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experiments to show the violation of Bell's inequality and then further deny the local hidden-variables theor...
Statistics, Causality and Bell's theorem
Gill, Richard D
2012-01-01
Bell's (1964) theorem is popularly supposed to establish the non-locality of quantum physics as a mathematical-physical theory. Building from this, observed violation of Bell's inequality in experiments such as that of Aspect and coworkers (1982) is popularly supposed to provide empirical proof of non-locality in the real world. This paper reviews recent work on Bell's theorem, linking it to issues in causality as understood by statisticians. The paper starts with a new proof of a strong (finite sample) version of Bell's theorem which relies only on elementary arithmetic and (counting) probability. This proof underscores the fact that Bell's theorem tells us that quantum theory is incompatible with the conjunction of three cherished and formerly uncontroversial physical principles, nicknamed here locality, realism, and freedom. The first, locality, is obviously connected to causality: causal influences need time to propagate spatially. Less obviously, the other two principles, realism and freedom, are also fo...
Concrete incompleteness & Bell's theorem
Geurdes, Han
2014-01-01
For a subset of 2 dimensional unit parameter vectors, Bell's correlation formula with local hidden variables reproduces the quantum correlation. This is unexpected considering a general no-go LHV claim derived from the same function.
Causarum Investigatio and the Two Bell's Theorems of John Bell
Wiseman, Howard M
2015-01-01
"Bell's theorem" can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the joint assumptions of Locality and Predetermination. His 1976 theorem is their incompatibility with the single property of Local Causality. This is contrary to Bell's own later assertions, that his 1964 theorem began with the assumption of Local Causality, even if not by that name. Although the two Bell's theorems are logically equivalent, their assumptions are not. Hence, the earlier and later theorems suggest quite different conclusions, embraced by operationalists and realists, respectively. The key issue is whether Locality or Local Causality is the appropriate notion emanating from Relativistic Causality, and this rests on one's basic notion of causation. For operationalists the appropriate notion is what is here called the Principle of Agent-Causation, while for realists it is Reichenbach's Principle of common cause. By...
Bell on Bell's theorem: The changing face of nonlocality
Brown, Harvey R
2015-01-01
Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates `local causality') became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about the mathematical form of the local causality condition, and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, both in its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz-covariant version of quantum theory, free of action-at-a-distance, can be a...
Causality, Bell's theorem, and Ontic Definiteness
Henson, Joe
2011-01-01
Bell's theorem shows that the reasonable relativistic causal principle known as "local causality" is not compatible with the predictions of quantum mechanics. It is not possible maintain a satisfying causal principle of this type while dropping any of the better-known assumptions of Bell's theorem. However, another assumption of Bell's theorem is the use of classical logic. One part of this assumption is the principle of "ontic definiteness", that is, that it must in principle be possible to assign definite truth values to all propositions treated in the theory. Once the logical setting is clarified somewhat, it can be seen that rejecting this principle does not in any way undermine the type of causal principle used by Bell. Without ontic definiteness, the deterministic causal condition known as Einstein Locality succeeds in banning superluminal influence (including signalling) whilst allowing correlations that violate Bell's inequalities. Objections to altering logic, and the consequences for operational and...
Multideviations: The hidden structure of Bell's theorems
Fogel, Brandon
2015-01-01
Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open problem. Here I provide a new set of tools, which I refer to as "multideviations", for finding and analyzing these inequalities for the fully general case. In Part I, I introduce the multideviation framework and then use it to prove an important theorem: the Bell distributions can be generated from the set of joint distributions over all observables by deeming specific degrees of freedom unobservable. In Part II, I show how the theorem provides a new method for finding tight Bell inequalities. I then specify a set of new tight Bell inequalities for arbitrary event spaces -- the "even/odd" inequalities -- which have a straightforward interpretation when expressed in terms of multideviations. The even/odd inequalities concern degrees of freedom that are independent of those invol...
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
Bell's theorem without inequalities and without alignments
Cabello, A
2003-01-01
A proof of Bell's theorem without inequalities is presented which exhibits three remarkable properties: (a) reduced local states are immune to collective decoherence, (b) local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups, and (c) local measurements require only individual measurements on the qubits. Indeed, it is shown that this proof is essentially the only one which fulfils (a), (b), and (c).
Bell's theorem, inference, and quantum transactions
Garrett, A. J. M.
1990-04-01
Bell's theorem is expounded as an analysis in Bayesian inference. Assuming the result of a spin measurement on a particle is governed by a causal variable internal (hidden, “local”) to the particle, one learns about it by making a spin measurement; thence about the internal variable of a second particle correlated with the first; and from there predicts the probabilistic result of spin measurements on the second particle. Such predictions are violated by experiment: locality/causality fails. The statistical nature of the observations rules out signalling; acausal, superluminal, or otherwise. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of experiment imply that it has a nonlocal/acausal interpretation. Cramer's new transactional interpretation, which incorporates this feature by adapting the Wheeler-Feynman idea of advanced and retarded processes to the quantum laws, is advocated. It leads to an invaluable way of envisaging quantum processes. The usual paradoxes melt before this, and one, the “delayed choice” experiment, is chosen for detailed inspection. Nonlocality implies practical difficulties in influencing hidden variables, which provides a very plausible explanation for why they have not yet been found; from this standpoint, Bell's theorem reinforces arguments in favor of hidden variables.
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...
Bell's theorem without inequalities and without unspeakable information
Cabello, A
2004-01-01
A proof of Bell's theorem without inequalities is presented in which distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups.
Rotationally invariant proof of Bell's theorem without inequalities
Cabello, A
2003-01-01
The singlet state of two spin-/sup 3///sub 2/ particles allows a proof of Bell's theorem without inequalities with two distinguishing features: any local observable can be regarded as an Einstein- Podolsky-Rosen element of reality, and the contradiction with local realism occurs not only for some specific local observables but for any rotation whereof. (19 refs).
A Modest View of Bell's Theorem
Boughn, Stephen
2016-01-01
In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however, many physicists and philosophers of science do harbor this belief. Experts in the field often use the term `nonlocality' to designate particular non-classical aspects of quantum entanglement and do not confuse the term with superluminal interactions. However, many physicists seem to take the term more literally. I endeavor to disabuse the latter of this notion by emphasizing that the correlations of Bell-type entangleme...
Random Numbers Certified by Bell's Theorem
Pironio, S; Massar, S; de la Giroday, A Boyer; Matsukevich, D N; Maunz, P; Olmschenk, S; Hayes, D; Luo, L; Manning, T A; Monroe, C
2009-01-01
Randomness is difficult to characterize mathematically, and its generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, we show that the nonlocal correlations of entangled quantum particles can be used to design a new type of cryptographically secure random number generator without the need for any assumptions on the internal working of the devices. This strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We demonstrate this proposal in a system of two entangled atoms separated by approximately 1 meter. The observed Bell inequality violation, featuring near-perfect detection efficiency, guarantees that 42 new random numbers are generated with 99% confidence. Our results lay the groundwork...
Random numbers certified by Bell's theorem.
Pironio, S; Acín, A; Massar, S; de la Giroday, A Boyer; Matsukevich, D N; Maunz, P; Olmschenk, S; Hayes, D; Luo, L; Manning, T A; Monroe, C
2010-04-15
Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on non-locality-based and device-independent quantum information processing, we show that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device. Such a strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately one metre. The observed Bell inequality violation, featuring near perfect detection efficiency, guarantees that 42 new random numbers are generated with 99 per cent confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory.
Bell's theorem with and without inequalities for all three-qubit entangled states
Cabello, A
2001-01-01
A proof of Bell's theorem without inequalities valid for both inequivalent classes of three-qubit entangled states under local operations assisted by classical communication, namely GHZ and W, is described. This proof leads to a Bell inequality that allows more conclusive tests of Bell's theorem for three-qubit systems. Another Bell inequality involving both tri- and bipartite correlations is introduced which illustrates the different violations of local realism exhibited by the GHZ and W states.
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…
A Bell-type Theorem Without Hidden Variables
Stapp, Henry P
2002-01-01
Bell's theorem rules out local hidden-variable theories. The locality condition is the demand that what an experimenter freely chooses to measure in one space-time region has no influence in a second space-time region that is spacelike separated from the first. The hidden-variable stipulation means that this demand is implemented through requirements on an assumed-to-exist substructure involving hidden variables. The question thus arises whether the locality condition itself fails, or only its implementation by means of the assumed hidden-variable structure. This paper shows that any theory that satisfies two generally accepted features of orthodox quantum theory and that yields certain predictions of quantum theory cannot satisfy the afore-mentioned locality condition. These two features are that the choices made by the experimenters can be treated as localized free variables and that such free choices do not affect outcomes that have already occurred.
Bell's theorem tells us NOT what quantum mechanics IS, but what quantum mechanics IS NOT
Zukowski, Marek
2015-01-01
Non-locality, or quantum-non-locality, are buzzwords in the community of quantum foundation and information scientists, which purportedly describe the implications of Bell's theorem. When such phrases are treated seriously, that is it is claimed that Bell's theorem reveals non-locality as an inherent trait of the quantum description of the micro-world, this leads to logical contradictions, which will be discussed here. In fact, Bell's theorem, understood as violation of Bell inequalities by quantum predictions, is consistent with Bohr's notion of complementarity. Thus, if it points to anything, then it is rather the significance of the principle of Bohr, but even this is not a clear implication. Non-locality is a necessary consequence of Bell's theorem only if we reject complementarity by adopting some form of realism, be it additional hidden variables, additional hidden causes, etc., or counterfactual definiteness. The essay contains two largely independent parts. The first one is addressed to any reader int...
Non-separability does not relieve the problem of Bell's theorem
Henson, Joe
2013-01-01
This paper addresses arguments that "separability" is an assumption of Bell's theorem, and that abandoning this assumption in our interpretation of quantum mechanics (a position sometimes referred to as "holism") will allow us to restore a satisfying locality principle. Separability here means that all events associated to the union of some set of disjoint regions are combinations of events associated to each region taken separately. In this article, it is shown that: (a) localised events can be consistently defined without implying separability; (b) the definition of Bell's locality condition does not rely on separability in any way; (c) the proof of Bell's theorem does not use separability as an assumption. If, inspired by considerations of non-separability, the assumptions of Bell's theorem are weakened, what remains no longer embodies the locality principle. Teller's argument for "relational holism" and Howard's arguments concerning separability are criticised in the light of these results. Howard's claim...
Bringing Bell's theorem back to the domain of Particle Physics & Cosmology
Hiesmayr, Beatrix C
2015-01-01
John St. Bell was a physicist working most of his time at CERN and contributing intensively and sustainably to the development of Particle Physics and Collider Physics. As a hobby he worked on so-called "foundations of quantum theory", that was that time very unpopular, even considered to be scientifically taboo. His 1964-theorem, showing that predictions of local realistic theories are different to those of quantum theory, initiated a new field in quantum physics: quantum information theory. The violation of Bell's theorem, for instance, is a necessary and sufficient criterion for generating a secure key for cryptography at two distant locations. This contribution shows how Bell's theorem can be brought to the realm of high energy physics and presents the first conclusive experimental feasible test for weakly decaying neutral mesons on the market. Strong experimental and theoretical limitations make a Bell test in weakly decaying systems such as mesons and hyperons very challenging, however, these systems sh...
Bell's theorem and the measurement problem: reducing two mysteries to one?
Cavalcanti, Eric G
2016-01-01
In light of a recent reformulation of Bell's theorem from causal principles by Howard Wiseman and the author, I argue that the conflict between quantum theory and relativity brought up by Bell's work can be softened by a revision of our classical notions of causation. I review some recent proposals for a quantum theory of causation that make great strides towards that end, but highlight a property that is shared by all those theories that would not have satisfied Bell's realist inclinations. They require (implicitly or explicitly) agent-centric notions such as "controllables" and "uncontrollables", or "observed" and "unobserved". Thus they relieve the tensions around Bell's theorem by highlighting an issue more often associated with another deep conceptual issue in quantum theory: the measurement problem. Rather than rejecting those terms, however, I argue that we should understand why they seem to be, at least at face-value, needed in order to reach compatibility between quantum theory and relativity. This s...
Does Quantum Nonlocality Exist? Bell's Theorem and the Many-Worlds Interpretation
Tipler, F J
2000-01-01
Quantum nonlocality may be an artifact of the assumption that observers obey the laws of classical mechanics, while observed systems obey quantum mechanics. I show that, at least in the case of Bell's Theorem, locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the Many-Worlds Interpretation. Using the MWI, I shall show that the apparently "non-local" expectation value for the product of the spins of two widely separated particles --- the "quantum" part of Bell's Theorem --- is really due to a series of three purely local measurements. Thus, experiments confirming "nonlocality" are actually confirming the MWI.
Bell Theorem without Inequality for Some Generalized GHZ and W States
Institute of Scientific and Technical Information of China (English)
REN Chang-Liang; SHI Ming-Jun; DU Jiang-Feng
2007-01-01
Bell's theorem without inequalities is applied for some general Greenberger-Horn-Zeilinger (GHZ) states and W states and a wide range of such states can exhibit all-versus-nothing conflict between local realism and quantum theory. The case of standard GHZ state is contained in our proposal. For some generalized GHZ states more intensive violation on local realism is manifested.
Reply to Marinatto's comment on "Bell's theorem without inequalities and without alignments"
Cabello, A
2004-01-01
Marinatto claims that in the proof of Bell's theorem without inequalities and without alignments [A. Cabello, Phys. Rev. Lett. 91, 230403 (2003)], local observables cannot be measured by means of tests on individual qubits. Marinatto's claim is incorrect. To support this, the proof is explicitly rewritten in terms of tests on individual qubits.
Cabello, A
2003-01-01
It is shown that Marinatto's claim [Phys. Rev. Lett. 90, 258901 (2003)] that the proof of "Bell's theorem without inequalities and without probabilities for two observers" [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] requires four spacelike separated observers rather than two is unjustified.
Hidden assumptions in the derivation of the theorem of Bell
Hess, Karl; De Raedt, Hans; Michielsen, Kristel
2012-01-01
John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT an
Bell's theorem and the causal arrow of time
Argaman, Nathan
2010-10-01
Einstein held that the formalism of quantum mechanics involves "spooky actions at a distance." In the 1960s, Bell amplified this by showing that the predictions of quantum mechanics disagree with the results of any locally causal description. It should be appreciated that accepting nonlocal descriptions while retaining causality leads to a clash with relativity. Furthermore, the causal arrow of time by definition contradicts time-reversal symmetry. For these reasons, Wheeler and Feynman, Costa de Beauregard, Cramer, Price, and others have advocated abandoning microscopic causality. In this paper, a simplistic but concrete example of this line of thought is presented, in the form of a retro-causal toy model that is stochastic and provides an appealing description of the quantum correlations discussed by Bell. It is concluded that Einstein's "spooky actions" may occur "in the past" rather than "at a distance," resolving the tension between quantum mechanics and relativity and opening unexplored possibilities for future reformulations of quantum mechanics.
Violation of Locality Beyond Bell's Theorem for Multiparticle Perfect Correlations
Institute of Scientific and Technical Information of China (English)
ZHENG Li; ZHENG Tai-Yu; WU Zhao-Yan; WAN Fan
2005-01-01
We present the analogous inequalities of Bell's inequality for N-qubit system predicted respectively by realistic theory, quantum mechanics, local theory, local realistic theory, and local quantum theory on the same Belltype joint experiment. It is shown that quantum mechanics can be interpreted by hidden-variable theories while being incompatible to any local theory. A necessary condition for the separability of N-qubit system is derived.
Two theorems of Jhon Bell and Communication Complexity
Kar, G
2005-01-01
John Bell taught us that quantum mechanics can not be reproduced by non-contextual and local Hidden variable theory. The impossibility of replacing quantum mechanics by non-contextual Hidden Variable Theory can be turned to a impossible coloring pseudo-telepathy game to be played by two distant players. The game can not be won without communication in the classical world. But if the players share entangled state (quantum correlation) the game can be won deterministically using no communication. This again shows that though quantum correlation can not be used for communication, two parties can not simulate quantum correlation without classical communication. The motivation of the article is to present the earlier works on Hidden Variable Theory and recently developed pseudo-telepathy problem in a simpler way, which may be helpful for the beginners in this area.
Recursive proof of the Bell-Kochen-Specker theorem in any dimension $n>3$
Cabello, A; García-Alcaine, G; Cabello, Adan; Estebaranz, Jose M.; Garcia-Alcaine, Guillermo
2005-01-01
We present a method to obtain sets of vectors proving the Bell-Kochen-Specker theorem in dimension $n$ from a similar set in dimension $d$ ($3\\leq d
Bell's theorem and quantum realism. Reassessment in light of the Schroedinger paradox
Energy Technology Data Exchange (ETDEWEB)
Shakur, Asif M. [Salisbury Univ., MD (United States). Dept. of Physics; Hemmick, Douglas L.
2012-07-01
Quantum theory presents a strange picture of the world, offering no real account of physical properties apart from observation. Neils Bohr felt that this reflected a core truth of nature: ''There is no quantum world. There is only an abstract mathematical description.'' Among the most significant developments since Bohr's day has been the theorem of John S. Bell. It is important to consider whether Bell's analysis supports such a denial of microrealism. In this book, we evaluate the situation in terms of an early work of Erwin Schroedinger. Doing so, we see how Bell's theorem is conceptually related to the Conway and Kochen Free Will theorem and also to all the major anti-realism efforts. It is easy to show that none of these analyses imply the impossibility of objective realism. We find that Schroedinger's work leads to the derivation of a new series of theoretical proofs and potential experiments, each involving ''entanglement,'' the link between particles in some quantum systems. (orig.)
Leffler, Warren
2011-01-01
This paper implements in a simple but rigorous fashion a model of particle interaction involving all paths within a quantum system, both for configuration space and for spin. The model, which we call the space of all paths, leads to a locally explicable conceptual framework for quantum mechanics. Using it we present two counterexamples to Bell's theorem. Moreover, we show that the result places severe constraints on possible viable interpretations of quantum mechanics: Either an interpretation must in some form represent a quantum system in terms of all paths within the system or, alternatively, the interpretation must harbor "action at a distance." We take action-at-a-distance as a reductio ad absurdum argument for our framework for quantum foundations, since any mechanism in which causal effects can operate instantaneously across vast distances would be completely unknown and magical, a near absurdity.
Simple refutation of Joy Christian's simple refutation of Bell's simple theorem
Gill, Richard D
2012-01-01
I point out a simple algebraic error in Joy Christian's refutation of Bell's theorem. In substituting the result of multiplying some derived bivectors with one another by consultation of their multiplication table, he confuses the generic vectors which he used to define the table, with other specific vectors having a special role in the paper, which had been introduced earlier. The result should be expressed in terms of the derived bivectors which indeed do follow this multiplication table. When correcting this calculation, the result is not the singlet correlation any more. Moreover, curiously, his normalized correlations are independent of the number of measurements and certainly do not require letting n converge to infinity. On the other hand his unnormalized or raw correlations are identically equal to -1, independently of the number of measurements too. Correctly computed, his standardized correlations are the bivectors - a . b - a x b, and they find their origin entirely in his normalization or standard...
Quantum [un]speakables II half a century of Bell's theorem
Zeilinger, Anton
2017-01-01
This self-contained essay collection is published to commemorate half a century of Bell’s theorem. Like its much acclaimed predecessor “Quantum [Un]Speakables: From Bell to Quantum Information” (published 2002), it comprises essays by many of the worlds leading quantum physicists and philosophers. These revisit the foundations of quantum theory as well as elucidating the remarkable progress in quantum technologies achieved in the last couple of decades. Fundamental concepts such as entanglement, nonlocality and contextuality are described in an accessible manner and, alongside lively descriptions of the various theoretical and experimental approaches, the book also delivers interesting philosophical insights. The collection as a whole will serve as a broad introduction for students and newcomers as well as delighting the scientifically literate general reader.
Sica, Louis
2012-01-01
The usual interpretation of the Greenberger, Horne, Zeilinger (GHZ) theorem is that only nonlocal hidden variables are consistent with quantum mechanics. This conclusion is reasoned from the fact that combinations of results of unperformed non-commutative measurement procedures (counterfactuals) do not agree with quantum mechanical predictions taking non-commutation into account. However, it is shown from simple counter-examples, that combinations of such counterfactuals are inconsistent with classical non-commutative measurement sequences as well. There is thus no regime in which the validity of combined non-commutative counterfactuals may be depended upon. As a consequence, negative conclusions regarding local hidden variables do not follow from the GHZ and Bell theorems as historically reasoned.
Nonlocality, No-Signalling and Bell's Theorem investigated by Weyl's Conformal Differential Geometry
De Martini, Francesco; Santamato, Enrico
2014-01-01
The principles and methods of the Conformal Quantum Geometrodynamics (CQG) based on the Weyl's differential geometry are presented. The theory applied to the case of the relativistic single quantum spin 1/2 leads a novel and unconventional derivation of Dirac's equation. The further extension of the theory to the case of two spins 1/2 in EPR entangled state and to the related violation of Bell's inequalities leads, by an exact albeit non relativistic analysis, to an insightful resolution of a...
An entangled web of crime: Bell's theorem as a short story
Jacobs, Kurt; Wiseman, Howard M.
2005-10-01
Nonlocality of the type first elucidated by Bell in 1964 is a difficult concept to explain to nonspecialists and undergraduates. We attempt to do so by showing how nonlocality can be used to solve a problem in which someone might find themselves as the result of a series of normal, even if somewhat unlikely, events. Our story is told in the style of a Sherlock Holmes mystery, and is based on Mermin's formulation of the "paradoxical" illustration of quantum nonlocality discovered by Greenberger, Horne, and Zeilinger.
An Entangled Web of Crime: Bell's Theorem as a Short Story
Jacobs, K; Jacobs, Kurt; Wiseman, Howard
2005-01-01
Non-locality of the type first elucidated by Bell in 1964 is a difficult concept to explain to non-specialists and undergraduates. Here we attempt this by showing how such non-locality can be used to solve a problem in which someone might find themselves as the result of a collection of normal, even if somewhat unlikely, events. Our story is told in the style of a Sherlock Holmes mystery, and is based on Mermin's formulation of the "paradoxical" illustration of quantum non-locality discovered by Greenberger, Horne and Zeilinger.
Relational interpretation of the wave function and a possible way around Bell's theorem
Filk, T
2006-01-01
The famous ``spooky action at a distance'' in the EPR-szenario is shown to be a local interaction, once entanglement is interpreted as a kind of ``nearest neighbor'' relation among quantum systems. Furthermore, the wave function itself is interpreted as encoding the ``nearest neighbor'' relations between a quantum system and spatial points. This interpretation becomes natural, if we view space and distance in terms of relations among spatial points. Therefore, ``position'' becomes a purely relational concept. This relational picture leads to a new perspective onto the quantum mechanical formalism, where many of the ``weird'' aspects, like the particle-wave duality, the non-locality of entanglement, or the ``mystery'' of the double-slit experiment, disappear. Furthermore, this picture cirumvents the restrictions set by Bell's inequalities, i.e., a possible (realistic) hidden variable theory based on these concepts can be local and at the same time reproduce the results of quantum mechanics.
De Raedt, Hans; Hess, Karl
2016-01-01
John Bell is generally credited to have accomplished the remarkable "proof" that any theory of physics, which is both Einstein-local and "realistic" (counterfactually definite), results in a strong upper bound to the correlations that are measured in space and time. He thus predicts that Einstein-Podolsky-Rosen experiments cannot violate Bell- type inequalities. We present a counterexample to this claim, based on discrete-event computer simulations. Our model-results fully agree with the predictions of quantum theory for Einstein-Podolsky-Rosen-Bohm experiments and are free of the detection- or a coincidence-loophole.
Hirota, O; Sohma, M; Li Ming Wei; Tang, Z L; Liao, C C
2002-01-01
In this report, we simulate practical feature of Yuen-Kim protocol for quantum key distribution with unconditional secure. In order to demonstrate them experimentally by intensity modulation/direct detection(IMDD) optical fiber communication system, we use simplified encoding scheme to guarantee security for key information(1 or 0). That is, pairwise M-ary intensity modulation scheme is employed. Furthermore, we give an experimental implementation of YK protocol based on IMDD. A proof of Bell's theorem without inequalities for two maximally entangled particles is proposed using the technique of quantum teleportation. It follows Hardy's arguments for a non-maximally entangled state with the help of two auxiliary particles without correlation. The present proof can be tested by measurements with 100% probability.
Alexander, G. P.; Yeomans, J. M.
2008-01-01
We investigate the way in which oscillating dumb-bells, a simple microscopic model of apolar swimmers, move at low Reynold's number. In accordance with Purcell's Scallop Theorem a single dumb-bell cannot swim because its stroke is reciprocal in time. However the motion of two or more dumb-bells, with mutual phase differences, is not time reversal invariant, and hence swimming is possible. We use analytical and numerical solutions of the Stokes equations to calculate the hydrodynamic interacti...
Alexander, G. P.; Yeomans, J. M.
2008-08-01
We investigate the way in which oscillating dumb-bells, a simple microscopic model of apolar swimmers, move at low Reynold's number. In accordance with Purcell's Scallop Theorem a single dumb-bell cannot swim because its stroke is reciprocal in time. However the motion of two or more dumb-bells, with mutual phase differences, is not time reversal invariant, and hence swimming is possible. We use analytical and numerical solutions of the Stokes equations to calculate the hydrodynamic interaction between two dumb-bell swimmers and to discuss their relative motion. The cooperative effect of interactions between swimmers is explored by considering first regular, and then random arrays of dumb-bells. We find that a square array acts as a micropump. The long-time behaviour of suspensions of dumb-bells is investigated and compared to that of model polar swimmers.
Simplest proof of Bell's inequality
Maccone, Lorenzo
2013-01-01
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an extremely simple proof of Bell's inequality: a single figure suffices. This simplicity may be useful in the unending debate of what exactly the Bell inequality means, since the hypothesis at the basis of the proof become extremely transparent. It is also a useful didactic tool, as the Bell inequality can be explained in a single intuitive lecture.
Correlations for a new Bell's inequality experiment
Sica, L
2002-01-01
Proofs of Bell's theorem and the data analysis used to show its violation have commonly assumed a spatially stationary underlying process. However, it has been shown recently that the appropriate Bell's inequality holds identically for cross correlations of three or four lists of + or - 1's, independently of statistical assumptions. When data consistent with its derivation are analyzed without imposition of the stationarity assumption, the resulting correlations satisfy the Bell inequality.
... Palsy? Bell's palsy is a form of temporary facial paralysis resulting from damage or trauma to the facial ... to stroke, is the most common cause of facial paralysis. Generally, Bell's palsy affects only one of the ...
A simple proof of Bell's inequality
Maccone, Lorenzo
2013-11-01
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an extremely simple proof of Bell's inequality; a single figure suffices. This simplicity may be useful in the unending debate over what exactly the Bell inequality means, because the hypotheses underlying the proof become transparent. It is also a useful didactic tool, as the Bell inequality can be explained in a single intuitive lecture.
... Bell's palsy, some people with the condition may benefit from the following: Relaxation techniques. Relaxing by using techniques such as meditation and yoga may relieve muscle tension and chronic pain. Acupuncture. ...
A Bell inequality with local violation
Cabello, Adan
2009-01-01
We introduce a Bell-like inequality for testing the Kochen-Specker with locality theorem and the free will theorem. Remarkably, quantum mechanics violates this inequality even though the quantum correlations between the distant systems admit a local description. The violation is due to the correlations between successive compatible measurements on one of the local systems. The violation is robust against imperfections, and can be observed in actual experiments.
Khrennikov, Andrei
2016-01-01
We analyze foundational consequences of recently announced loophole free tests of violation of Bell's inequality. We consider two interpretations of these remarkable experiments. By the conventional one "Einstein was wrong and Bohr was right, there is spooky action at a distance, quantum realism is incompatible with locality." However, we show that it is still possible to treat quantum mechanics without appealing to nonlocality or denying realism. We hope that this note will attract attention of the experts in quantum foundations and convince them to come with their own comments on the final Bell's test.
Time, Finite Statistics, and Bell's Fifth Position
Gill, R D
2003-01-01
I discuss three issues connected to Bell's theorem and Bell-CHSH-type experiments: time and the memory loophole, finite statistics (how wide are the error bars Under Local Realism), and the question of whether a loophole-free experiment is feasible, a surprising omission on Bell's list of four positions to hold in the light of his results. Levy's (1935) theory of martingales, and Fisher's (1935) theory of randomization in experimental design, take care of time and of finite statistics. I exploit a (classical) computer network metaphor for local realism to argue that Bell's conclusions are independent of how one likes to interpret probability, and give a critique of some recent anti-Bellist literature.
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
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
Mathematical and physical meaning of the Bell inequalities
Santos, Emilio
2016-09-01
It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values \\{0,1\\}. A hidden variables model may be defined as a mapping between a set of quantum projection operators and a set of random variables. The model is noncontextual if there is a joint probability distribution. The Bell inequalities are necessary conditions for its existence. The inequalities are most relevant when measurements are performed at space-like separation, thus showing a conflict between quantum mechanics and local realism (Bell's theorem). The relations of the Bell inequalities with contextuality, the Kochen-Specker theorem, and quantum entanglement are briefly discussed.
Classical probabilistic realization of “Random Numbers Certified by Bell's Theorem”
Khrennikov, Andrei
2015-07-01
We question the commonly accepted statement that random numbers certified by Bell's theorem carry some special sort of randomness, so to say, quantum randomness or intrinsic randomness. We show that such numbers can be easily generated by classical random generators.
John Stewart Bell and twentieth century physics vision and integrity
Whitaker, Andrew
2016-01-01
John Stewart Bell (1928-1990) was one of the most important figures in twentieth-century physics, famous for his work on the fundamental aspects of the century's most important theory, quantum mechanics. While the debate over quantum theory between the supremely famous physicists, Albert Einstein and Niels Bohr, appeared to have become sterile in the 1930s, Bell was able to revive it and to make crucial advances - Bell's Theorem or Bell's Inequalities. He was able to demonstrate a contradiction between quantum theory and essential elements of pre-quantum theory - locality and causality. The book gives a non-mathematical account of Bell's relatively impoverished upbringing in Belfast and his education. It describes his major contributions to quantum theory, but also his important work in the physics of accelerators, and nuclear and elementary particle physics.
Calabrese, Edward J
2010-04-01
This paper introduces an issue of the BELLE Newsletter that is designed to reflect on the role of BELLE in affecting how the concept of hormesis is perceived and accepted by the biomedical and toxicological communities. A brief overview of how BELLE was created is provided.
Bell inequalities for quantum optical fields
Żukowski, Marek; Wieśniak, Marcin; Laskowski, Wiesław
2016-08-01
The commonly used "practical" Bell inequalities for quantum optical fields, which use intensities as the observables, are derivable only if specific additional assumptions hold. This limits the range of local hidden variable theories, which are invalidated by their violation. We present alternative Bell inequalities, which do not suffer from any (theoretical) loophole. The inequalities are for correlations of averaged products of local rates. By rates we mean ratios of the measured intensity in the given local output channel to the total local measured intensity, in the given run of the experiment. Bell inequalities of this type detect entanglement in situations in which the "practical" ones fail. Thus, we have full consistency with Bell's theorem, and better device-independent entanglement indicators. Strongly driven type-II parametric down conversion (bright squeezed vacuum) is our working example. The approach can be used to modify many types of standard Bell inequalities, to the case of undefined particle numbers. The rule is to replace the usual probabilities by rates.
Particle Identification with BELLE
Satpathy, A
1999-01-01
The working principle and performance of the BELLE particle identification device (PID), based on a hybrid system consisting of an array of high precision scintillator Time of Flight and silica Aerogel Counters, is discussed. The performances achieved in the beam tests are satisfactory and Monte Carlo tests of meeting physics objectives of BELLE are promising. Prior to the real experiment which is expected to commence in spring 1999, the BELLE PID is taking cosmic ray data for calibration and fine tuning.
Wagner, Tom
2010-01-01
The ceremonial copper and iron bells at the Smithsonian's National Museum of African Art were the author's inspiration for an interdisciplinary unit with a focus on the contributions various cultures make toward the richness of a community. The author of this article describes an Edo bell-inspired ceramic project incorporating slab-building…
On Generalized Bell Polynomials
Directory of Open Access Journals (Sweden)
Roberto B. Corcino
2011-01-01
Full Text Available It is shown that the sequence of the generalized Bell polynomials Sn(x is convex under some restrictions of the parameters involved. A kind of recurrence relation for Sn(x is established, and some numbers related to the generalized Bell numbers and their properties are investigated.
On local-hidden-variable no-go theorems
Methot, A. A.
2006-06-01
The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow.
Energy Technology Data Exchange (ETDEWEB)
Liu Chunping
2003-06-02
Using a direct algebraic method, more new exact solutions of the Kolmogorov-Petrovskii-Piskunov equation are presented by formula form. Then a theorem concerning the relation between the kink-type solution and the kink-bell-type solution of nonlinear evolution equations is given. Finally, the applications of the theorem to several well-known equations in physics are also discussed.
Indian Academy of Sciences (India)
Kazuo Abe
2003-02-01
The Belle experiment continues to explore the origin of CP violation and test all aspects of standard model in meson decays. Recent results on CP violating paramter sin 21 and other measurements are presented.
Institute of Scientific and Technical Information of China (English)
孔雪伟
2004-01-01
A tiny, two-year-old blonde, recovering from surgical removal (外科切除) of her cancerous left eye, discovers in her mailbox a brightly colored package with a big sticker of hugging bears under a rainbow. Tearing open the box, Belle cries "Mama, look, it's teddy bears! " The bears (and the goodie package of gifts) bring about something that hadn't happened in quite a while: Belle smiles!
Wei, Zhang; Jiali, Hou; Wenfang, Yang
2013-01-01
A number of versions of the well-known "bell-in-a-bell-jar" demonstration have been discussed in this journal.1-3 The basic idea is that when a sound source is placed inside an air-tight container, the volume of the sound that's heard decreases dramatically when the container is evacuated. This phenomenon is primarily due to the mismatch that is created between the sound transducer and the surrounding medium.4,5 Here we describe a simple small-scale version of this demonstration, one that may be added to the growing list of examples of how a simple syringe may be used as a tool in physics teaching.6-8
A Cosmic Bell Test with Measurement Settings from Astronomical Sources
Handsteiner, Johannes; Rauch, Dominik; Gallicchio, Jason; Liu, Bo; Hosp, Hannes; Kofler, Johannes; Bricher, David; Fink, Matthias; Leung, Calvin; Mark, Anthony; Nguyen, Hien T; Sanders, Isabella; Steinlechner, Fabian; Ursin, Rupert; Wengerowsky, Sören; Guth, Alan H; Kaiser, David I; Scheidl, Thomas; Zeilinger, Anton
2016-01-01
Bell's theorem states that some predictions of quantum mechanics cannot be reproduced by a local-realist theory. That conflict is expressed by Bell's inequality, which is usually derived under the assumption that there are no statistical correlations between the choices of measurement settings and anything else that can causally affect the measurement outcomes. In previous experiments, this "freedom of choice" was addressed by ensuring that selection of measurement settings via conventional "quantum random number generators" (QRNGs) was space-like separated from the entangled particle creation. This, however, left open the possibility that an unknown cause affected both the setting choices and measurement outcomes as recently as mere microseconds before each experimental trial. Here we report on a new experimental test of Bell's inequality that, for the first time, uses distant astronomical sources as "cosmic setting generators." In our tests with polarization-entangled photons, measurement settings were chos...
Vorticity, Stokes' Theorem and the Gauss's Theorem
Narayanan, M.
2004-12-01
Vorticity is a property of the flow of any fluid and moving fluids acquire properties that allow an engineer to describe that particular flow in greater detail. It is important to recognize that mere motion alone does not guarantee that the air or any fluid has vorticity. Vorticity is one of four important quantities that define the kinematic properties of any fluid flow. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. However, the divergence theorem is a mathematical statement of the physical fact that, in the absence of the creation or destruction of matter, the density within a region of space can change only by having it flow into, or away from the region through its boundary. This is also known as Gauss's Theorem. It should also be noted that there are many useful extensions of Gauss's Theorem, including the extension to include surfaces of discontinuity in V. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. Integral (Surface) [(DEL X V)] . dS = Integral (Contour) [V . dx] In this paper, the author outlines and stresses the importance of studying and teaching these mathematical techniques while developing a course in Hydrology and Fluid Mechanics. References Arfken, G. "Gauss's Theorem." 1.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985. Morse, P. M. and Feshbach, H. "Gauss's Theorem." In Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 37-38, 1953. Eric W. Weisstein. "Divergence Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DivergenceTheorem.html
Paramati, Manjula; Tirumkudulu, Mahesh S.
2016-03-01
A smooth circular moving liquid sheet is formed by the head-on impingement of two equal laminar water jets. We subject such a liquid sheet to uniform laminar air flow from one side such that the direction of air velocity is perpendicular to the liquid sheet. The pressure of the moving air deforms the liquid sheet giving rise to an open water bell. The water bell is symmetric suggesting that the gas flow around the bell is also symmetric and that the gravitational force is negligible. We have captured the shape of the water bells for varying air flow rates and for varying Weber numbers, and compared the measurements with theoretical predictions obtained from a force balance involving liquid inertia, surface tension, and pressure difference across the sheet. The pressure exerted by the gas phase on the front and the rear surface of the deformed liquid sheet is obtained from known results of flow past flat circular discs. The predicted steady state shapes match well with the measurements at low Weber numbers but differences are observed at high Weber numbers, where the sheet flaps and is no longer smooth. Interestingly, the shape predicted by assuming a constant pressure difference equal to the stagnation pressure over the whole of the front face of the sheet and free stream value over the whole of the rear face yields nearly identical results suggesting that an open water bell is similar to a closed water bell in that, to a good approximation, the pressure on either sides of the water bell is homogeneous.
Early History of BELL'S Theorem Theory and Experiment
Clauser, John F.
Before 1980 it was unfashionable for a physicist to admit that he either did not understand and/or doubted the Truth and/or Orthodoxy of Quantum Mechanics (QM). Contemporary wisdom deemed it impossible that it may lead to incorrect predictions. Thus, it was foolish to suggest that it warranted further testing. Said wisdom proclaimed that nothing would ever be gained by any such pursuit. Bohr had won his debates with Einstein. Von Neumann had proven all other interpretations wrong. That was the end to it! Only an iconoclast dared think otherwise. Here I provide a brief history of some of my encounters with a few fellow iconoclasts, past denizens of a QM doubter's subculture.
Bell's theorem and the demise of local reality
McAdam, S
2003-01-01
"The advent of quantum physics led to the insight that the act of observation may affect that which is observed. In fact, it can be argued that the act of observation sometimes actually creates that which is observed. One can consider the possibility that the momentum of a particle does not exist until something happens to cause its momentum to exist" (2 pages).
On the logical structure of Bell theorems without inequalities
Broadbent, A; Méthot, A A; Walgate, J; Broadbent, Anne; Carteret, Hilary A.; Methot, Andre Allan; Walgate, Jonathan
2005-01-01
The goal of `all-versus-nothing' nonlocality proofs is to demonstrate (in theory and experimentally) that quantum mechanics is not locally realistic. Here, we show that a category of these proofs--those that use additional hypotheses based on quantum properties to restrict any classical strategy--do not achieve this goal. This failure is caused by the presence of an additional assumption in these arguments, which allows local realistic interpretations to evade contradiction. Our explanation is clearly presented in terms of logic and should serve to correct misconceptions and avoid future mistakes. We also show how to transform Cabello's proof into a valid nonlocality proof involving four participants, which has interesting theoretical properties.
Ybert, Christophe; Clanet, Christophe; Bocquet, Lyderic; Duez, Cyril
2007-11-01
We study experimentally the situation that consist in a liquid jet impacting normally onto a fixed solid disk. Depending on the experimental conditions, the thin liquid film that spreads onto the solid surface can either pour along the surface, or detach form the disk and form a so-called water bell. The dynamics and the stability of such bells as a function of the hydrodynamic parameters such as the jet and disk diameters or the jet velocity, have already been the object of detailed characterization [1]. This experiment of bell formation appears as the symmetric situation compared to that of a solid body impacting a quiescent liquid. In the latter case, it was recently shown [2] that despite large Re and We numbers, the solid surface characteristics were dramatically influencing the impact scenario. In the present study, we consequently revisit this problem of water bell formation by systematically varying the solid surface characteristics (roughness, surface properties, etc.). It is shown here again that surface parameters strongly influence the domain of bell existence. Our measurements are rationalized by a subtle balance between inertia versus capillary forces and wetting contributions on the liquid film in the ejection region. [1] C. Clanet, J. Fluid Mech., 430, 111-147 (2001) [2] C. Duez et al., Nature Physics, 3, 180-183 (2007)
Lagrange Theorem for polygroups
Directory of Open Access Journals (Sweden)
alireza sedighi
2014-12-01
Full Text Available So far?, ?isomorphism theorems in hyperstructure were proved for different structures of polygroups?, ?hyperrings and etc?. ?In this paper?, ?the polygroups properties is studied with the introduction of a suitable equivalence relation?. ?We show that the above relation is strongly regular?. ?Our main purpose in the paper is investigating Lagrang theorem and other expressing of isomorphism theorems for polygroups?.
Cosmic Bell Test: Measurement Settings from Milky Way Stars
Handsteiner, Johannes; Friedman, Andrew S.; Rauch, Dominik; Gallicchio, Jason; Liu, Bo; Hosp, Hannes; Kofler, Johannes; Bricher, David; Fink, Matthias; Leung, Calvin; Mark, Anthony; Nguyen, Hien T.; Sanders, Isabella; Steinlechner, Fabian; Ursin, Rupert; Wengerowsky, Sören; Guth, Alan H.; Kaiser, David I.; Scheidl, Thomas; Zeilinger, Anton
2017-02-01
Bell's theorem states that some predictions of quantum mechanics cannot be reproduced by a local-realist theory. That conflict is expressed by Bell's inequality, which is usually derived under the assumption that there are no statistical correlations between the choices of measurement settings and anything else that can causally affect the measurement outcomes. In previous experiments, this "freedom of choice" was addressed by ensuring that selection of measurement settings via conventional "quantum random number generators" was spacelike separated from the entangled particle creation. This, however, left open the possibility that an unknown cause affected both the setting choices and measurement outcomes as recently as mere microseconds before each experimental trial. Here we report on a new experimental test of Bell's inequality that, for the first time, uses distant astronomical sources as "cosmic setting generators." In our tests with polarization-entangled photons, measurement settings were chosen using real-time observations of Milky Way stars while simultaneously ensuring locality. Assuming fair sampling for all detected photons, and that each stellar photon's color was set at emission, we observe statistically significant ≳7.31 σ and ≳11.93 σ violations of Bell's inequality with estimated p values of ≲1.8 ×10-13 and ≲4.0 ×10-33, respectively, thereby pushing back by ˜600 years the most recent time by which any local-realist influences could have engineered the observed Bell violation.
Hamilton, Kendra
2009-01-01
The "Bennett Belle." The words conjure an image that is genteel, old-fashioned--hats and gloves, brown-skinned women in flowing white dresses beaming as they take that final walk to graduation. The Bennett College for Women campus certainly reinforces the image, with its broad, tree-shaded lawns and quadrangle and its historic buildings--fully 15…
Bell's Universe: A Personal Recollection
Bertlmann, Reinhold A
2016-01-01
My collaboration and friendship with John Bell is recollected. I will explain his outstanding contributions in particle physics, in accelerator physics, and his joint work with Mary Bell. Mary's work in accelerator physics is also summarized. I recall our quantum debates, mention some personal reminiscences, and give my personal view on Bell's fundamental work on quantum theory, in particular, on the concept of contextuality and nonlocality of quantum physics. Finally, I describe the huge influence Bell had on my own work, in particular on entanglement and Bell inequalities in particle physics and their experimental verification, and on mathematical physics, where some geometric aspects of the quantum states are illustrated.
The asymmetric sandwich theorem
Simons, Stephen
2011-01-01
We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel duality theorem. Most of the results are about affine functions defined on convex subsets of vector spaces, rather than linear functions defined on vector spaces. We consider both results that use a simple boundedness hypothesis (as in Rockafellar's version of the Fenchel duality theorem) and also results that use Baire's theorem (as in the Robinson-Attouch-Brezis version of the Fenchel duality theorem). This paper also contains some new results about metrizable topological vector spaces that are not necessarily locally convex.
Bell's palsy before Bell: Cornelis Stalpart van der Wiel's observation of Bell's palsy in 1683.
van de Graaf, Robert C; Nicolai, Jean-Philippe A
2005-11-01
Bell's palsy is named after Sir Charles Bell (1774-1842), who has long been considered to be the first to describe idiopathic facial paralysis in the early 19th century. However, it was discovered that Nicolaus Anton Friedreich (1761-1836) and James Douglas (1675-1742) preceded him in the 18th century. Recently, an even earlier account of Bell's palsy was found, as observed by Cornelis Stalpart van der Wiel (1620-1702) from The Hague, The Netherlands in 1683. Because our current knowledge of the history of Bell's palsy before Bell is limited to a few documents, it is interesting to discuss Stalpart van der Wiel's description and determine its additional value for the history of Bell's palsy. It is concluded that Cornelis Stalpart van der Wiel was the first to record Bell's palsy in 1683. His manuscript provides clues for future historical research.
New Slant on the EPR-Bell Experiment
Evans, Peter; Wharton, K B
2010-01-01
The best case for thinking that quantum mechanics is nonlocal rests on Bell's Theorem, and later results of the same kind. However, the correlations characteristic of EPR-Bell (EPRB) experiments also arise in familiar cases elsewhere in QM, where the two measurements involved are timelike rather than spacelike separated; and in which the correlations are usually assumed to have a local causal explanation, requiring no action-at-a-distance. It is interesting to ask how this is possible, in the light of Bell's Theorem. We investigate this question, and present two options. Either (i) the new cases are nonlocal, too, in which case action-at-a-distance is more widespread in QM than has previously been appreciated (and does not depend on entanglement, as usually construed); or (ii) the means of avoiding action-at-a-distance in the new cases extends in an obvious way to EPRB, removing action-at-a-distance in these cases, too. There is a third option, viz., to argue that the new cases are strongly disanalogous to EP...
Belle electromagnetic calorimeter
Miyabayashi, K
2002-01-01
We report the performance of the Belle electromagnetic calorimeter for the first three years operation. Good mass resolutions for pi sup 0 and eta are obtained to be 4.8 and 12.1 MeV/c sup 2 , respectively. The degradation of light output due to the radiation damage is small, about 3% for the radiation dose of 40 rad. These performances promise further study of B physics with neutral particle reconstruction.
Reflections on the PBR Theorem: Reality Criteria & Preparation Independence
Directory of Open Access Journals (Sweden)
Shane Mansfield
2014-12-01
Full Text Available This paper contains initial work on attempting to bring recent developments in the foundations of quantum mechanics concerning the nature of the wavefunction within the scope of more logical and structural methods. A first step involves dualising a criterion for the reality of the wavefunction proposed by Harrigan & Spekkens, which was central to the Pusey-Barrett-Rudolph theorem. The resulting criterion has several advantages, including the avoidance of certain technical difficulties relating to sets of measure zero. By considering the 'reality' not of the wavefunction but of the observable properties of any ontological physical theory a new characterisation of non-locality and contextuality is found. Secondly, a careful analysis of preparation independence, one of the key assumptions of the PBR theorem, leads to a precise analogy with the kind of locality prohibited by Bell's theorem. Motivated by this, we propose a weakening of the assumption to something analogous to no-signalling. This amounts to allowing global or non-local correlations in the joint ontic state, which nevertheless do not allow for superluminal signalling. This is, at least, consistent with the Bell and Kochen-Specker theorems. We find a counter-example to the PBR argument, which violates preparation independence, but does satisfy this physically motivated assumption. The question of whether the PBR result can be strengthened to hold under the relaxed assumption is therefore posed.
2011-01-01
Arvanitakis established recently a theorem which is a common generalization of Michael's convex selection theorem and Dugundji's extension theorem. In this note we provide a short proof of a more general version of Arvanitakis' result.
On the BELLE Charmonium States
Arkhipov, A A
2004-01-01
It is shown that newly performed experimental studies by the Belle Collaboration are excellently incorporated in the unified picture for hadron spectra developed early. From our analysis it follows that the measured values for the masses of the BELLE states exactly coincide with the calculated masses of the states living in the corresponding KK towers.
Bell inequalities based on equalities
Cabello, A
2006-01-01
We show that bipartite Bell inequalities based on the Einstein-Podolsky-Rosen criterion for elements of reality and derived from the properties of some hyperentangled states allow feasible experimental verifications of the fact that quantum nonlocality grows exponentially with the size of the subsystems, and Bell loophole-free tests with currently available photo-detection efficiencies.
To string together six theorems of physics by Pythagoras theorem
Cui, H Y
2002-01-01
In this paper, we point out that there are at lest six theorems in physics sharing common virtue of Pythagoras theorem, so that it is possible to string these theorems together with the Pythagoras theorem for physics teaching, the six theorems are Newton's three laws of motion, universal gravitational force, Coulomb's law, and the formula of relativistic dynamics. Knowing the internal relationships between them, which have never been clearly revealed by other author, will benefit the logic of physics teaching.
On the Equivalence of Weyl Theorem and Generalized Weyl Theorem
Institute of Scientific and Technical Information of China (English)
M. BERKANI
2007-01-01
We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theo rem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a similar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.
Trigonometry, Including Snell's Theorem.
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
Bell's palsy before Bell : Cornelis Stalpart van der Wiel's observation of Bell's palsy in 1683
van de Graaf, RC; Nicolai, JPA
2005-01-01
Bell's palsy is named after Sir Charles Bell (1774-1842), who has long been considered to be the first to describe idiopathic facial paralysis in the early 19th century. However, it was discovered that Nicolaus Anton Friedreich (1761-1836) and James Douglas (1675-1742) preceded him in the 18th centu
A Theorem on Grid Access Control
Institute of Scientific and Technical Information of China (English)
XU ZhiWei(徐志伟); BU GuanYing(卜冠英)
2003-01-01
The current grid security research is mainly focused on the authentication of grid systems. A problem to be solved by grid systems is to ensure consistent access control. This problem is complicated because the hosts in a grid computing environment usually span multiple autonomous administrative domains. This paper presents a grid access control model, based on asynchronous automata theory and the classic Bell-LaPadula model. This model is useful to formally study the confidentiality and integrity problems in a grid computing environment. A theorem is proved, which gives the necessary and sufficient conditions to a grid to maintain confidentiality.These conditions are the formalized descriptions of local (node) relations or relationship between grid subjects and node subjects.
Coincidence Point Theorems, Intersection Theorems and Saddle Point Theorems on FC-spaces
Institute of Scientific and Technical Information of China (English)
PIAO YONG-JIE; YIN ZHE
2009-01-01
In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.
Sesia, Sergio
2016-01-01
Background For specific therapy to correct pectus excavatum (PE), conservative treatment with the vacuum bell (VB) was introduced more than 10 years ago in addition to surgical repair. Preliminary results using the VB were encouraging. We report on our 13-year experience with the VB treatment including the intraoperative use during the Nuss procedure and present some technical innovations. Methods A VB with a patient-activated hand pump is used to create a vacuum at the anterior chest wall. Three different sizes of vacuum bells, as well as a model fitted for young women, exist. The appropriate size is selected according to the individual patient’s age and ventral surface. The device should be used at home for a minimum of 30 minutes (twice a day), and may be used up to a maximum of several hours daily. The intensity of the applied negative pressure can be evaluated with an integrated pressure gauge during follow-up visits. A prototype of an electronic model enables us to measure the correlation between the applied negative pressure and the elevation of the anterior chest wall. Results Since 2003, approx. 450 patients between 2 to 61 years of age started the VB therapy. Age and gender specific differences, depth of PE, symmetry or asymmetry, and concomitant malformations such as scoliosis and/or kyphosis influence the clinical course and success of VB therapy. According to our experience, we see three different groups of patients. Immediate elevation of the sternum was confirmed thoracoscopically during the Nuss procedure in every patient. Conclusions The VB therapy has been established as an alternative therapeutic option in selected patients suffering from PE. The initial results up to now are encouraging, but long-term results comprising more than 15 years are so far lacking, and further evaluation and follow-up studies are necessary. PMID:27747177
Bansal, Vikas
2015-01-01
The Belle II experiment at the SuperKEKB collider in Tsukuba, Japan, will start physics data taking in 2018 and will accumulate 50 ab$^{-1}$ of e$^{+}$e$^{-}$ collision data, about 50 times larger than the data set of the earlier Belle experiment. The computing requirements of Belle II are comparable to those of a run I high-p$_T$ LHC experiment. Computing will make full use of such grids in North America, Asia, Europe, and Australia, and high speed networking. Results of an initial MC simulation campaign with 3 ab$^{-1}$ equivalent luminosity will be described
The most elementary Bell inequalities
Sadiq, Muhamad; Bourennane, Mohamed; Cabello, Adan
2011-01-01
Every nontrivial Bell inequality can be associated to a graph with some special properties. The simplest of these graphs is the pentagon. In this sense, any Bell inequality associated to a pentagon can be regarded as elementary. We show that there are three of them: one is a primitive Bell inequality inside the Clauser-Horne-Shimony-Holt inequality and, surprisingly, it is not maximally violated by maximally entangled states. The other two are maximally violated by maximally entangled states and are related to the Clauser-Horne inequality and the I3322 inequality, respectively. We report experimental violations of the three inequalities with pairs of photons entangled in polarization.
Belle II Technical Design Report
Abe, T; Adamczyk, K; Ahn, S; Aihara, H; Akai, K; Aloi, M; Andricek, L; Aoki, K; Arai, Y; Arefiev, A; Arinstein, K; Arita, Y; Asner, D M; Aulchenko, V; Aushev, T; Aziz, T; Bakich, A M; Balagura, V; Ban, Y; Barberio, E; Barvich, T; Belous, K; Bergauer, T; Bhardwaj, V; Bhuyan, B; Blyth, S; Bondar, A; Bonvicini, G; Bozek, A; Bracko, M; Brodzicka, J; Brovchenko, O; Browder, T E; Cao, G; Chang, M -C; Chang, P; Chao, Y; Chekelian, V; Chen, A; Chen, K -F; Chen, P; Cheon, B G; Chiang, C -C; Chistov, R; Cho, K; Choi, S -K; Chung, K; Comerma, A; Cooney, M; Cowley, D E; Critchlow, T; Dalseno, J; Danilov, M; Dieguez, A; Dierlamm, A; Dillon, M; Dingfelder, J; Dolenec, R; Dolezal, Z; Drasal, Z; Drutskoy, A; Dungel, W; Dutta, D; Eidelman, S; Enomoto, A; Epifanov, D; Esen, S; Fast, J E; Feindt, M; Garcia, M Fernandez; Fifield, T; Fischer, P; Flanagan, J; Fourletov, S; Fourletova, J; Freixas, L; Frey, A; Friedl, M; Fruehwirth, R; Fujii, H; Fujikawa, M; Fukuma, Y; Funakoshi, Y; Furukawa, K; Fuster, J; Gabyshev, N; Cueto, A Gaspar de Valenzuela; Garmash, A; Garrido, L; Geisler, Ch; Gfall, I; Goh, Y M; Golob, B; Gorton, I; Grzymkowski, R; Guo, H; Ha, H; Haba, J; Hara, K; Hara, T; Haruyama, T; Hayasaka, K; Hayashi, K; Hayashii, H; Heck, M; Heindl, S; Heller, C; Hemperek, T; Higuchi, T; Horii, Y; Hou, W -S; Hsiung, Y B; Huang, C -H; Hwang, S; Hyun, H J; Igarashi, Y; Iglesias, C; Iida, Y; Iijima, T; Imamura, M; Inami, K; Irmler, C; Ishizuka, M; Itagaki, K; Itoh, R; Iwabuchi, M; Iwai, G; Iwai, M; Iwasaki, M; Iwasaki, M; Iwasaki, Y; Iwashita, T; Iwata, S; Jang, H; Ji, X; Jinno, T; Jones, M; Julius, T; Kageyama, T; Kah, D H; Kakuno, H; Kamitani, T; Kanazawa, K; Kapusta, P; Kataoka, S U; Katayama, N; Kawai, M; Kawai, Y; Kawasaki, T; Kennedy, J; Kichimi, H; Kikuchi, M; Kiesling, C; Kim, B K; Kim, G N; Kim, H J; Kim, H O; Kim, J -B; Kim, J H; Kim, M J; Kim, S K; Kim, K T; Kim, T Y; Kinoshita, K; Kishi, K; Kisielewski, B; van Dam, K Kleese; Knopf, J; Ko, B R; Koch, M; Kodys, P; Koffmane, C; Koga, Y; Kohriki, T; Koike, S; Koiso, H; Kondo, Y; Korpar, S; Kouzes, R T; Kreidl, Ch; Kreps, M; Krizan, P; Krokovny, P; Krueger, H; Kruth, A; Kuhn, W; Kuhr, T; Kumar, R; Kumita, T; Kupper, S; Kuzmin, A; Kvasnicka, P; Kwon, Y -J; Lacasta, C; Lange, J S; Lee, I -S; Lee, M J; Lee, M W; Lee, S -H; Lemarenko, M; Li, J; Li, W D; Li, Y; Libby, J; Limosani, A; Liu, C; Liu, H; Liu, Y; Liu, Z; Liventsev, D; Virto, A Lopez; Makida, Y; Mao, Z P; Marinas, C; Masuzawa, M; Matvienko, D; Mitaroff, W; Miyabayashi, K; Miyata, H; Miyazaki, Y; Miyoshi, T; Mizuk, R; Mohanty, G B; Mohapatra, D; Moll, A; Mori, T; Morita, A; Morita, Y; Moser, H -G; Martin, D Moya; Mueller, T; Muenchow, D; Murakami, J; Myung, S S; Nagamine, T; Nakamura, I; Nakamura, T T; Nakano, E; Nakano, H; Nakao, M; Nakazawa, H; Nam, S -H; Natkaniec, Z; Nedelkovska, E; Negishi, K; Neubauer, S; Ng, C; Ninkovic, J; Nishida, S; Nishimura, K; Novikov, E; Nozaki, T; Ogawa, S; Ohmi, K; Ohnishi, Y; Ohshima, T; Ohuchi, N; Oide, K; Olsen, S L; Ono, M; Ono, Y; Onuki, Y; Ostrowicz, W; Ozaki, H; Pakhlov, P; Pakhlova, G; Palka, H; Park, H; Park, H K; Peak, L S; Peng, T; Peric, I; Pernicka, M; Pestotnik, R; Petric, M; Piilonen, L E; Poluektov, A; Prim, M; Prothmann, K; Regimbal, K; Reisert, B; Richter, R H; Riera-Babures, J; Ritter, A; Ritter, A; Ritter, M; Roehrken, M; Rorie, J; Rosen, M; Rozanska, M; Ruckman, L; Rummel, S; Rusinov, V; Russell, R M; Ryu, S; Sahoo, H; Sakai, K; Sakai, Y; Santelj, L; Sasaki, T; Sato, N; Sato, Y; Scheirich, J; Schieck, J; Schwanda, C; Schwartz, A J; Schwenker, B; Seljak, A; Senyo, K; Seon, O -S; Sevior, M E; Shapkin, M; Shebalin, V; Shen, C P; Shibuya, H; Shiizuka, S; Shiu, J -G; Shwartz, B; Simon, F; Simonis, H J; Singh, J B; Sinha, R; Sitarz, M; Smerkol, P; Sokolov, A; Solovieva, E; Stanic, S; Staric, M; Stypula, J; Suetsugu, Y; Sugihara, S; Sugimura, T; Sumisawa, K; Sumiyoshi, T; Suzuki, K; Suzuki, S Y; Takagaki, H; Takasaki, F; Takeichi, H; Takubo, Y; Tanaka, M; Tanaka, S; Taniguchi, N; Tarkovsky, E; Tatishvili, G; Tawada, M; Taylor, G N; Teramoto, Y; Tikhomirov, I; Trabelsi, K; Tsuboyama, T; Tsunada, K; Tu, Y -C; Uchida, T; Uehara, S; Ueno, K; Uglov, T; Unno, Y; Uno, S; Urquijo, P; Ushiroda, Y; Usov, Y; Vahsen, S; Valentan, M; Vanhoefer, P; Varner, G; Varvell, K E; Vazquez, P; Vila, I; Vilella, E; Vinokurova, A; Visniakov, J; Vos, M; Wang, C H; Wang, J; Wang, M -Z; Wang, P; Wassatch, A; Watanabe, M; Watase, Y; Weiler, T; Wermes, N; Wescott, R E; White, E; Wicht, J; Widhalm, L; Williams, K M; Won, E; Xu, H; Yabsley, B D; Yamamoto, H; Yamaoka, H; Yamaoka, Y; Yamauchi, M; Yin, Y; Yoon, H; Yu, J; Yuan, C Z; Yusa, Y; Zander, D; Zdybal, M; Zhang, Z P; Zhao, J; Zhao, L; Zhao, Z; Zhilich, V; Zhou, P; Zhulanov, V; Zivko, T; Zupanc, A; Zyukova, O
2010-01-01
The Belle detector at the KEKB electron-positron collider has collected almost 1 billion Y(4S) events in its decade of operation. Super-KEKB, an upgrade of KEKB is under construction, to increase the luminosity by two orders of magnitude during a three-year shutdown, with an ultimate goal of 8E35 /cm^2 /s luminosity. To exploit the increased luminosity, an upgrade of the Belle detector has been proposed. A new international collaboration Belle-II, is being formed. The Technical Design Report presents physics motivation, basic methods of the accelerator upgrade, as well as key improvements of the detector.
Energy Technology Data Exchange (ETDEWEB)
Bertlmann, Reinhold A.
2015-07-15
John Bell, with whom I had a fruitful collaboration and warm friendship, is best known for his seminal work on the foundations of quantum physics, but he also made outstanding contributions to particle physics and accelerator physics.
Bell Numbers, Determinants and Series
Indian Academy of Sciences (India)
P K Saikia; Deepak Subedi
2013-05-01
In this article, we study Bell numbers and Uppuluri Carpenter numbers. We obtain various expressions and relations between them. These include polynomial recurrences and expressions as determinants of certain matrices of binomial coefficients.
Bell's inequalities and Kolmogorov's axioms
Atkinson, D
2001-01-01
After recalling proofs of the Bell inequality based on the assumptions of separability and of noncontextuality, the most general noncontextual contrapositive conditional probabilities consistent with the Aspect experiment are constructed. In general these probabilities are not all positive.
ON RANGE DECOMPOSITION THEOREMS
Institute of Scientific and Technical Information of China (English)
吴利生
1990-01-01
We prove the following theorems.Theorem 1.Suppose f:X→Y is a closed map.X is a ωγ and β space,then Y=Y0∪(∪n=1∞Yn),where f-1(y) is countably compact for each y ∈Y0 and Yn is closed discrete in Y for each n≥1,Theorem 2-3:Suppose f:X→Y is a closed map,X is stratifable space,then Y=Y0 ∪(∪n=1∞Yn),where f-1(y) is compact for each y∈Y0 and Yn is closed discrete in Y for each n≥1.
D'Agostini, G
2005-01-01
It is curious to learn that Enrico Fermi knew how to base probabilistic inference on Bayes theorem, and that some influential notes on statistics for physicists stem from what the author calls elsewhere, but never in these notes, {\\it the Bayes Theorem of Fermi}. The fact is curious because the large majority of living physicists, educated in the second half of last century -- a kind of middle age in the statistical reasoning -- never heard of Bayes theorem during their studies, though they have been constantly using an intuitive reasoning quite Bayesian in spirit. This paper is based on recollections and notes by Jay Orear and on Gauss' ``Theoria motus corporum coelestium'', being the {\\it Princeps mathematicorum} remembered by Orear as source of Fermi's Bayesian reasoning.
Kartavtsev, Alexander
2014-01-01
According to the Goldstone theorem a scalar theory with a spontaneously broken global symmetry contains strictly massless states. In this letter we identify a loophole in the current-algebra proof of the theorem. Therefore, the question whether in models with Mexican hat potential the tangential excitations are strictly massless or are just almost massless as compared to the radial ones remains open. We also argue that mass of the tangential excitations approaches zero even if the symmetry is not spontaneously broken but a combination of the field components invariant under the symmetry transformations acquires a large vacuum expectation value.
Pérez-Espigares, Carlos; Redig, Frank; Giardinà, Cristian
2015-08-01
For non-equilibrium systems of interacting particles and for interacting diffusions in d-dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current values in different spatial directions. The result is a consequence of spatial symmetries of the microscopic dynamics, generalizing in this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal symmetry. This new perspective opens up the possibility of direct experimental measurements of fluctuation relations of vectorial observables.
Francesco Poppi
2010-01-01
During the Nobel prize-winning UA1 experiment, scientists in the control room used to ring a bell if a particularly interesting event had occurred. Today, the “CMS Exotica hotline” routine produces a daily report that lists the exotic events that were recorded the day before. Display of an event selected by the Exotica routine. Take just a very small fraction of the available data (max. 5%); define the events that you want to keep and set the parameters accordingly; run the Exotica routine and only look at the very few images that the system has selected for you. This is the recipe that a small team of CMS researchers has developed to identify the signals coming from possible new physics processes. “This approach does not replace the accurate data analysis on the whole set of data. However, it is a very fast and effective way to focus on just a few events that are potentially very interesting”, explains Maurizio Pierini (CERN), who developed the...
Reply to Gillis's "On the Analysis of Bell's 1964 Paper by Wiseman, Cavalcanti, and Rieffel"
Wiseman, Howard M; Cavalcanti, Eric G
2016-01-01
We address Gillis' recent criticism [arXiv:1506.05795] of a series of papers (by different combinations of the present authors) on formulations of Bell's theorem. Those papers intended to address an unfortunate gap of communication between two broad camps in the quantum foundations community that we identify as "operationalists" and "realists". Here, we once again urge the readers to approach the question from an unbiased standpoint, and explain that Gillis' criticism draws too heavily on the philosophical inclinations of one side of that debate -- the realist camp. As part of that explanation we discuss intuition versus proof, look again at Bell's formalizations of locality, and correct misstatements by Gillis of our views, and those of Bell and Einstein.
Virial Theorem and Scale Transformations.
Kleban, Peter
1979-01-01
Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)
Teleman, Nicolae
2011-01-01
$Local^{3}$ Index Theorem means $Local(Local(Local \\;Index \\; Theorem)))$. $Local \\; Index \\; Theorem$ is the Connes-Moscovici local index theorem \\cite{Connes-Moscovici1}, \\cite{Connes-Moscovici2}. The second "Local" refers to the cyclic homology localised to a certain separable subring of the ground algebra, while the last one refers to Alexander-Spanier type cyclic homology. The Connes-Moscovici work is based on the operator $R(A) = \\mathbf{P} - \\mathbf{e}$ associated to the elliptic pseudo-differential operator $A$ on the smooth manifold $M$, where $\\mathbf{P}$, $\\mathbf{e}$ are idempotents, see \\cite{Connes-Moscovici1}, Pg. 353. The operator $R(A)$ has two main merits: it is a smoothing operator and its distributional kernel is situated in an arbitrarily small neighbourhood of the diagonal in $M \\times M$. The operator $R(A)$ has also two setbacks: -i) it is not an idempotent (and therefore it does not have a genuine Connes-Chern character); -ii) even if it were an idempotent, its Connes-Chern character ...
Multivariate irregular sampling theorem
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.
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. © Instytut Matematyczny PAN, 2009....
Certified Kruskal's Tree Theorem
Directory of Open Access Journals (Sweden)
Christian Sternagel
2014-07-01
Full Text Available This article presents the first formalization of Kurskal's tree theorem in aproof assistant. The Isabelle/HOL development is along the lines of Nash-Williams' original minimal bad sequence argument for proving the treetheorem. Along the way, proofs of Dickson's lemma and Higman's lemma, as well as some technical details of the formalization are discussed.
Rediscovering Schreinemakers' Theorem.
Bathurst, Bruce
1983-01-01
Schreinemakers' theorem (arrangement of curves around an invariant point), derived from La Chatelier's principle, can be rediscovered by students asked to use the principle when solving a natural problem such as "How does diluting a mineral/fluid alter shape of a pressure/temperature diagram?" Background information and instructional…
Multivariate irregular sampling theorem
Institute of Scientific and Technical Information of China (English)
CHEN GuangGui; FANG GenSun
2009-01-01
In this paper, we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result, we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.
DEFF Research Database (Denmark)
Thomassen, Carsten
2004-01-01
We present a short proof of the theorem of Tutte that every planar 3-connected graph has a drawing in the plane such that every vertex which is not on the outer cycle is the barycenter of its neighbors. Moreover, this holds for any prescribed representation of the outer cycle. (C) 2004 Wiley Peri...
Dalen, D. van
2008-01-01
The following pages make form a new chapter for the book Logic and Structure. This chapter deals with the incompleteness theorem, and contains enough basic material for the treatment of the required notions of computability, representability and the like. This chapter will appear in the next edition
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 sing...
Automated Discovery of Inductive Theorems
McCasland, Roy; Bundy, Alan; Serge, Autexier
2007-01-01
Inductive mathematical theorems have, as a rule, historically been quite difficult to prove – both for mathematics students and for auto- mated theorem provers. That said, there has been considerable progress over the past several years, within the automated reasoning community, towards proving some of these theorems. However, little work has been done thus far towards automatically discovering them. In this paper we present our methods of discovering (as well as proving) inductive theorems, ...
The Second Noether Theorem on Time Scales
Malinowska, Agnieszka B.; Natália Martins
2013-01-01
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.
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
An Extension of Sobolev's Theorem
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Sobolev's Theorem is the most fundamental theorem in the theory of Invariant Cubature Formulas (ICFs). In this paper, a quantitative structure is established for the classical ICFs. Enlightened by this structure, the author generalizes the concept of ICFs and extends the Sobolev's Theorem to the case of generalized ICFs. Several illustrative examples are given.
Generalized no-broadcasting theorem.
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
2007-12-14
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with "superquantum" correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
Virial theorem and hypervirial theorem in a spherical geometry
Energy Technology Data Exchange (ETDEWEB)
Li Yan; Chen Jingling [Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Zhang Fulin, E-mail: flzhang@tju.edu.cn, E-mail: chenjl@nankai.edu.cn [Physics Department, School of Science, Tianjin University, Tianjin 300072 (China)
2011-09-09
The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)
Improved Bell-in-a-Bell-Jar Demonstration
Han, Dejun
2003-05-01
It is well understood in acoustics that a medium is required to conduct sound. Stated in another way, sound is not transmitted through a vacuum. The earliest person to test this experimentally was the Irish physicist Robert Boyle (1627-1691). In his experiment, he put a ringing bell under a glass cover called a bell jar. After the air was pumped out, the ringing disappeared. This convinced him that sound cannot be conducted in vacuum. Here we describe an improved version of this demonstration.
John Bell and the Identical Twins
1984-01-01
A biographical profile of John S.Bell is presented based on extensive interviews the author had with Bell. Bell’s vierws on the quantum theory are presented along with a simple explanation of his idenity.
Choudhury, Sayantan; Singh, Rajeev
2016-01-01
In this work, we have studied the possibility of setting up Bell's inequality violating experiment in the context of cosmology, based on the basic principles of quantum mechanics. First we start with the physical motivation of implementing the Bell's inequality violation in the context of cosmology. Then to set up the cosmological Bell violating test experiment we introduce a model independent theoretical framework using which we have studied the creation of new massive particles by implementing the WKB approximation method for the scalar fluctuations in presence of additional time dependent mass contribution. Next using the background scalar fluctuation in presence of new time dependent mass contribution, we explicitly compute the expression for the one point and two point correlation functions. Furthermore, using the results for one point function we introduce a new theoretical cosmological parameter which can be expressed in terms of the other known inflationary observables and can also be treated as a fut...
Charmonium and exotics from Belle
Wang, Xiaolong
2015-01-01
The recent results on charmonium and charmoniumlike states from Belle experiment are reviewed. We summarise searches in $B$ decays for possible $X$-like states in final states containing $\\eta_c$. The new measurement of $e^+e^-\\to\\pi^+\\pi^-\\psi(2S)$ improves the determination of the properties of $Y(4360)$ and $Y(4660)$. The fits including $Y(4260)$ are performed. Evidence for a charged charmoniumlike structure at $4.05~{\\rm GeV}/c^2$ is observed in the $\\pi^{\\pm}\\psi(2S)$ intermediate state in the $Y(4360)$ decays. Belle also updates the measurement on $e^+e^-\\to KKJ/\\psi$ via initial state radiation using the full data sample. Finally, Belle observed $X(3872)$ in $B\\to K\\pi + X(\\to\\pi^+\\pi^-J/\\psi)$.
Taylor, Marika
2016-01-01
The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension $3/2 < \\Delta < 5/2$. Therefore the strongest version of the F theorem is in general violated.
Indian Academy of Sciences (India)
N V Rao
2003-02-01
The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose is a compact set in the complex plane and 0 belongs to the boundary . Let $\\mathcal{A}(K)$ denote the space of all functions on such that is holomorphic in a neighborhood of and (0) = 0. Also for any given positive integer , let $\\mathcal{A}(m, K)$ denote the space of all such that is holomorphic in a neighborhood of and $f(0) = f'(0) = \\cdots = f^{(m)}(0) = 0$. Then $\\mathcal{A}(m, K)$ is dense in $\\mathcal{A}(K)$ under the supremum norm on provided that there exists a sector $W = \\{re^{i}; 0 ≤ r ≤ , ≤ ≤ \\}$ such that $W \\cap K = \\{0\\}$. (This is the well-known Poincare's external cone condition).} We present various generalizations of this result in the context of higher dimensions replacing holomorphic with harmonic.
Energy Technology Data Exchange (ETDEWEB)
Cinabro, David [Wayne State Univ., Detroit, MI (United States)
2016-01-01
The major goals of our work on Belle II were to complete our contributions, a 64 channel PIN diode based radiation monitor, to the precursor detector called Beast II and the electronics for the endcap K-Long/Muon (E-KLM) detector. This was done by Professor Cinabro, Technician Gutierrez, and undergraduate labor supported by US-Japan funds. Professor Bonvicini through US-Japan funds led the development and installation of a beamstrahlung monitor system in the Belle II interaction region. Graduate students Farhat and DiCarlo worked on this. We also worked on charm physics analysis.
Bell's inequality without alternative settings
Cabello, A
2003-01-01
A suitable generalized measurement described by a four-element positive operator valued measure (POVM) on each particle of a two-qubit system in the singlet state is, from the point of view of Einstein, Podolsky, and Rosen's (EPR's) criterion of elements of reality, equivalent to a random selection between two alternative projective measurements. It is shown that an EPR-experiment with a fixed POVM on each particle provides a violation of Bell's inequality without requiring local observers to choose between the alternatives. This approach could be useful for designing a loophole-free test of Bell's inequality.
Gouin, Henri
2015-01-01
Comments on Archimedes' theorem about sphere and cylinder; In his treatise addressed to Dositheus of Pelusium, Archimedes of Syracuse obtained the result of which he was the most proud: a sphere has two-thirds the volume of its circumscribing cylinder. At his request a sculpted sphere and cylinder were placed on his tomb near Syracuse. Usually, it is admitted that to find this formula, Archimedes used a half polygon inscribed in a semicircle; then he performed rotations of these two figures t...
1987-03-20
with standard expressions of spherical trigonometry is sinr)0 = cos0 sini//0 (4.37) which is consistent with the results obtained previously with...theorems for discrete transforms. However, sampling questions inlroduce difficult obstacles in the develop- ment of a discrete theory. First, sampling...additional obstacle to discrete represen- tations of the CT. An example of qualitative predication of the shape of silhouettes with the Silhouette-Slice
The geometry of violation of Bell's inequality
Institute of Scientific and Technical Information of China (English)
Weihan Tan(谭维翰); Qizhi Guo(郭奇志)
2003-01-01
The purpose of this paper is to deduce an analytical expression for the violation of Bell's inequality by quantum theory and plane trigonometry, and expound the violation and maximal violation of the first,second type Bell's inequality in detail. Further, we find out the sufficient conditions for the region in which Bell's inequalities are violated.
Bells: the past and the present
Institute of Scientific and Technical Information of China (English)
Smirnova; O.; G.; Lisovskaya; O.; B.; Lisovskiy; V.; A.
2005-01-01
Bell is a part of history of Russia, a work of founding craft and art, a musical instrument. Myths and legends that arose around the bell casting craft and its ‘material base' the bell alloy are of considerable research interest.……
Bells: the past and the present
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
@@ Bell is a part of history of Russia, a work of founding craft and art, a musical instrument. Myths and legends that arose around the bell casting craft and its ‘material base' the bell alloy are of considerable research interest.
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Bell Mountain. 9.55... Mountain. (a) Name. The name of the viticultural area described in this section is “Bell Mountain.” (b) Approved map. The appropriate map for determining the boundaries of the Bell Mountain viticultural area...
Sandwich classification theorem
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Alexey Stepanov
2015-09-01
Full Text Available The present note arises from the author's talk at the conference ``Ischia Group Theory 2014''. For subgroups FleN of a group G denote by Lat(F,N the set of all subgroups of N , containing F . Let D be a subgroup of G . In this note we study the lattice LL=Lat(D,G and the lattice LL ′ of subgroups of G , normalized by D . We say that LL satisfies sandwich classification theorem if LL splits into a disjoint union of sandwiches Lat(F,N G (F over all subgroups F such that the normal closure of D in F coincides with F . Here N G (F denotes the normalizer of F in G . A similar notion of sandwich classification is introduced for the lattice LL ′ . If D is perfect, i.,e. coincides with its commutator subgroup, then it turns out that sandwich classification theorem for LL and LL ′ are equivalent. We also show how to find basic subroup F of sandwiches for LL ′ and review sandwich classification theorems in algebraic groups over rings.
Cosmic Bell Test: Measurement Settings from Milky Way Stars.
Handsteiner, Johannes; Friedman, Andrew S; Rauch, Dominik; Gallicchio, Jason; Liu, Bo; Hosp, Hannes; Kofler, Johannes; Bricher, David; Fink, Matthias; Leung, Calvin; Mark, Anthony; Nguyen, Hien T; Sanders, Isabella; Steinlechner, Fabian; Ursin, Rupert; Wengerowsky, Sören; Guth, Alan H; Kaiser, David I; Scheidl, Thomas; Zeilinger, Anton
2017-02-10
Bell's theorem states that some predictions of quantum mechanics cannot be reproduced by a local-realist theory. That conflict is expressed by Bell's inequality, which is usually derived under the assumption that there are no statistical correlations between the choices of measurement settings and anything else that can causally affect the measurement outcomes. In previous experiments, this "freedom of choice" was addressed by ensuring that selection of measurement settings via conventional "quantum random number generators" was spacelike separated from the entangled particle creation. This, however, left open the possibility that an unknown cause affected both the setting choices and measurement outcomes as recently as mere microseconds before each experimental trial. Here we report on a new experimental test of Bell's inequality that, for the first time, uses distant astronomical sources as "cosmic setting generators." In our tests with polarization-entangled photons, measurement settings were chosen using real-time observations of Milky Way stars while simultaneously ensuring locality. Assuming fair sampling for all detected photons, and that each stellar photon's color was set at emission, we observe statistically significant ≳7.31σ and ≳11.93σ violations of Bell's inequality with estimated p values of ≲1.8×10^{-13} and ≲4.0×10^{-33}, respectively, thereby pushing back by ∼600 years the most recent time by which any local-realist influences could have engineered the observed Bell violation.
Experimental design of a loophole-free Bell test with spin qubits in diamond
Hensen, Bas; Bernien, Hannes; Dréau, Anaïs; Reiserer, Andreas; Ruitenberg, Just; Blok, Machiel; Wehner, Stephanie; Markham, M.; Twitchen, D.; Hanson, Ronald
2015-03-01
50 years ago, John Bell formulated his famous theorem. The outcomes of independent measurements on entangled objects can reveal strong correlations that violate Bell's inequality. Until now, all experimental implementations of Bell's test required additional assumptions, that open the door for so-called loopholes. These loopholes are particularly important in a cryptography setting where Bell violations enable fully device-independent protocols for quantum key distribution and certified generation of randomness. Here we will present the experimental design of a Bell test, aimed at closing the detection loophole and addressing the locality and free-will loopholes in a single experiment. We use two qubits associated with the electronic spin of the nitrogen-vacancy (NV) center in diamond, separated far enough to allow space-like separation between the two qubits during their measurement. The heralded nature of our remote entanglement protocol and efficient qubit readout allow us to use all entangled pairs, avoiding the fair-sampling assumption. Finally, the free-will loophole is addressed by the use of fast random number generators.
On local-hidden-variable no-go theorems
Méthot, A A
2005-01-01
The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimatly doomed in 1964 with the work of Bell Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus we will discuss here the three principal fo...
Vibrational Modes of Trumpet Bells
MOORE, T. R.; KAPLON, J. D.; MCDOWALL, G. D.; MARTIN, K. A.
2002-07-01
We report on an investigation of the normal modes of vibration of the bells of several modern trumpets. We describe the results of experiments using electronic speckle-pattern interferometry to visualize the modal structure and we show that the mode frequencies follow a generalized version of Chladni's law.
Bells, Motels and Permutation Groups
McGuire, Gary
2012-01-01
This article is about the mathematics of ringing the changes. We describe the mathematics which arises from a real-world activity, that of ringing the changes on bells. We present Rankin's solution of one of the famous old problems in the subject. This article was written in 2003.
Clusters of Bell's palsy "Surtos" da paralisia de Bell
Directory of Open Access Journals (Sweden)
Thiago D. Gonçalves-Coêlho
1997-01-01
Full Text Available The idiopathic facial paralysis or Bell's palsy installs abruptly or within a few hours, without any apparent cause. It corresponds to approximately 75% of all peripheral facial palsies. Three theories try to explain its pathogenecity: vascular-ischemic, viral and auto-immune. We reviewed the records of the EMG Sector, Hospital do Servidor Público Estadual (São Paulo, Brazil, from 1985 to 1995 and found 239 cases of Bell's palsy. Data were analysed according to age, gender, seasonal distribution of cases. There was a predominance of cases in the 31 - 60 age bracket (40.59 %. The female gender was responsible to 70.71 % of cases. There was a predominance of cases in winter (31.38 % and autumn (30.13 %, which was statiscally significant. These findings let us to suppose that Bell's palsy predominates in females, in 41-60 years age bracket, and occurs predominantly in cold months. There are groups of clusters throughout temporal distribution of cases and cases are dependent on one each other or on factors affecting them all, which reinforces the infectious hypothesis (there is a rise in the incidence of viral upper respiratory tract infection during cold months.A paralisia facial idiopática ou paralisia de Bell se instala abruptamente ou em algumas horas, sem causa aparente. Corresponde a aproximadamente 75% de todos os casos de paralisia facial. Três teorias tentam explicar sua patogenia: vásculo-isquêmica, autoimune e viral. Nós revisamos os arquivos do Setor de Eletromiografia do Hospital do Servidor Público Estadual (São Paulo de 1985 a 1995, encontrando 239 casos de paralisia de Bell. Dados foram analisados quanto a idade, sexo, distribuição sazonal. Houve predominância dos casos na faixa etária de 31 a 60 anos (40,59 %. O sexo feminino foi responsável por 70,71 % dos casos. Houve predominância de casos no inverno (31,38 % e outono (30,13 %, estatisticamente sigmficante. Estes achados levam-nos a supor que a paralisia de Bell
Transfinite Approximation of Hindman's Theorem
Beiglböck, Mathias
2010-01-01
Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the corresponding finite form, stating that in any finite coloring of the integers there are arbitrarily long finite sets with the same property. We extend the finite form of Hindman's Theorem to a "transfinite" version for each countable ordinal, and show that Hindman's Theorem is equivalent to the appropriate transfinite approximation holding for every countable ordinal. We then give a proof of Hindman's Theorem by directly proving these transfinite approximations.
Belle II silicon vertex detector
Adamczyk, K.; Aihara, H.; Angelini, C.; Aziz, T.; Babu, V.; Bacher, S.; Bahinipati, S.; Barberio, E.; Baroncelli, Ti.; Baroncelli, To.; Basith, A. K.; Batignani, G.; Bauer, A.; Behera, P. K.; Bergauer, T.; Bettarini, S.; Bhuyan, B.; Bilka, T.; Bosi, F.; Bosisio, L.; Bozek, A.; Buchsteiner, F.; Casarosa, G.; Ceccanti, M.; Červenkov, D.; Chendvankar, S. R.; Dash, N.; Divekar, S. T.; Doležal, Z.; Dutta, D.; Enami, K.; Forti, F.; Friedl, M.; Hara, K.; Higuchi, T.; Horiguchi, T.; Irmler, C.; Ishikawa, A.; Jeon, H. B.; Joo, C. W.; Kandra, J.; Kang, K. H.; Kato, E.; Kawasaki, T.; Kodyš, P.; Kohriki, T.; Koike, S.; Kolwalkar, M. M.; Kvasnička, P.; Lanceri, L.; Lettenbicher, J.; Maki, M.; Mammini, P.; Mayekar, S. N.; Mohanty, G. B.; Mohanty, S.; Morii, T.; Nakamura, K. R.; Natkaniec, Z.; Negishi, K.; Nisar, N. K.; Onuki, Y.; Ostrowicz, W.; Paladino, A.; Paoloni, E.; Park, H.; Pilo, F.; Profeti, A.; Rashevskaya, I.; Rao, K. K.; Rizzo, G.; Rozanska, M.; Sandilya, S.; Sasaki, J.; Sato, N.; Schultschik, S.; Schwanda, C.; Seino, Y.; Shimizu, N.; Stypula, J.; Suzuki, J.; Tanaka, S.; Tanida, K.; Taylor, G. N.; Thalmeier, R.; Thomas, R.; Tsuboyama, T.; Uozumi, S.; Urquijo, P.; Vitale, L.; Volpi, M.; Watanuki, S.; Watson, I. J.; Webb, J.; Wiechczynski, J.; Williams, S.; Würkner, B.; Yamamoto, H.; Yin, H.; Yoshinobu, T.
2016-09-01
The Belle II experiment at the SuperKEKB collider in Japan is designed to indirectly probe new physics using approximately 50 times the data recorded by its predecessor. An accurate determination of the decay-point position of subatomic particles such as beauty and charm hadrons as well as a precise measurement of low-momentum charged particles will play a key role in this pursuit. These will be accomplished by an inner tracking device comprising two layers of pixelated silicon detector and four layers of silicon vertex detector based on double-sided microstrip sensors. We describe herein the design, prototyping and construction efforts of the Belle-II silicon vertex detector.
Belle II Silicon Vertex Detector
Mohanty, Gagan B
2015-01-01
The Belle II experiment at the SuperKEKB collider in Japan is designed to indirectly probe new physics using approximately 50 times the data recorded by its predecessor. An accurate determination of the decay-point position of subatomic particles such as beauty and charm hadrons as well as a precise measurement of low-momentum charged particles will play a key role in this pursuit. These will be accomplished by a vertex detector, which comprises two layers of pixelated silicon detector and four layers of silicon vertex detector. We describe herein the design, prototyping and construction efforts of the Belle-II silicon vertex detector that is aimed to be commissioned towards the middle of 2017.
Belle II silicon vertex detector
Energy Technology Data Exchange (ETDEWEB)
Adamczyk, K. [H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342 (Poland); Aihara, H. [Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan); Angelini, C. [Dipartimento di Fisica, Università di Pisa, I-56127 Pisa (Italy); INFN Sezione di Pisa, I-56127 Pisa (Italy); Aziz, T.; Babu, V. [Tata Institute of Fundamental Research, Mumbai 400005 (India); Bacher, S. [H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342 (Poland); Bahinipati, S. [Indian Institute of Technology Bhubaneswar, Satya Nagar (India); Barberio, E.; Baroncelli, Ti.; Baroncelli, To. [School of Physics, University of Melbourne, Melbourne, Victoria 3010 (Australia); Basith, A.K. [Indian Institute of Technology Madras, Chennai 600036 (India); Batignani, G. [Dipartimento di Fisica, Università di Pisa, I-56127 Pisa (Italy); INFN Sezione di Pisa, I-56127 Pisa (Italy); Bauer, A. [Institute of High Energy Physics, Austrian Academy of Sciences, 1050 Vienna (Austria); Behera, P.K. [Indian Institute of Technology Madras, Chennai 600036 (India); Bergauer, T. [Institute of High Energy Physics, Austrian Academy of Sciences, 1050 Vienna (Austria); Bettarini, S. [Dipartimento di Fisica, Università di Pisa, I-56127 Pisa (Italy); INFN Sezione di Pisa, I-56127 Pisa (Italy); Bhuyan, B. [Indian Institute of Technology Guwahati, Assam 781039 (India); Bilka, T. [Faculty of Mathematics and Physics, Charles University, 121 16 Prague (Czech Republic); Bosi, F. [INFN Sezione di Pisa, I-56127 Pisa (Italy); Bosisio, L. [Dipartimento di Fisica, Università di Trieste, I-34127 Trieste (Italy); INFN Sezione di Trieste, I-34127 Trieste (Italy); and others
2016-09-21
The Belle II experiment at the SuperKEKB collider in Japan is designed to indirectly probe new physics using approximately 50 times the data recorded by its predecessor. An accurate determination of the decay-point position of subatomic particles such as beauty and charm hadrons as well as a precise measurement of low-momentum charged particles will play a key role in this pursuit. These will be accomplished by an inner tracking device comprising two layers of pixelated silicon detector and four layers of silicon vertex detector based on double-sided microstrip sensors. We describe herein the design, prototyping and construction efforts of the Belle-II silicon vertex detector.
Particle Identification at Belle II
Sandilya, S
2016-01-01
We report on the charged particle identification (PID) systems for the upcoming Belle II experiment. The time of propagation counter in the central region and the proximity focusing ring imaging Cherenkov counters with aerogel radiator in the forward region will be used as the PID devices. They are expected to provide a kaon identification efficiency of more than 94% at a low pion misidentification probability of 4%. The motivation for the upgrade, method, and status of both systems are discussed.
Electromagnetic calorimeter trigger at Belle
Cheon, B G; Lee, S H; Won, E; Park, I C; Hur, T W; Park, C S; Kim, S K; Kim, H J; Kim, H O; Chu, T H; Usov, Y V; Aulchenko, V M; Kuzmin, A S; Bondar, A E; Shwartz, B A; Eidelman, S; Krokovnyi, P P; Hayashii, H; Sagawa, H; Fukushima, M
2002-01-01
The performance of CsI(Tl) electromagnetic calorimeter trigger system in the Belle experiment is described. Two kinds of trigger schemes have been taken into account, namely a total energy trigger and a cluster counting trigger which are complementary to each other. In addition, the system has provided the online/offline luminosity information using the Bhabha event trigger scheme. An upgrade of the trigger is discussed.
1988-03-01
to Orley Ashenfelter, the editor of the American Economic Review . to inform him that ample opportunities were being provided to Evans and Heckman for...matter. Readers should also refer to the nearly three pages of errata and corrigenda published by Evans and Heckman (1986) in The American Economic Review which...Errors in the Evans and Heckman Bell System Breakup Studies," American Economic Review , (submitted, October 1986). Sueyoshi, T. and P.C. Anselmo, "The
Bell Inequalities for Complex Networks
2015-10-26
AFRL-AFOSR-VA-TR-2015-0355 YIP Bell Inequalities for Complex Networks Greg Ver Steeg UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES Final Report 10/26...Period: 1 August 2012 to 31 July 2015 Information Sciences Institute University of Southern California, 4676 Admiralty Way Marina del Rey, CA 90292...Machine Intelligence and Autonomy ” in 2014. Besides these Air Force affiliated interactions, I disseminated results of this effort in standard academic
Abelian theorems for Whittaker transforms
Directory of Open Access Journals (Sweden)
Richard D. Carmichael
1987-01-01
Full Text Available Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches 0 or ∞ in absolute value inside a wedge region in the right half plane.
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].
A Time scales Noether's theorem
Anerot, Baptiste; Cresson, Jacky; Pierret, Frédéric
2016-01-01
We prove a time scales version of the Noether's theorem relating group of symmetries and conservation laws. Our result extends the continuous version of the Noether's theorem as well as the discrete one and corrects a previous statement of Bartosiewicz and Torres in \\cite{BT}.
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.…
Lopez-Real, Francis
2008-01-01
While the author was searching the web, he came across an article by Michael Keyton of IMSA (Illinois Mathematics and Science Academy) called "Theorems of mystery". The phrase is Keyton's own, and he defines such a theorem as "a result that has considerable structure with minimal hypotheses." The simplest of his 10 examples is one that many…
Peripheral facial weakness (Bell's palsy).
Basić-Kes, Vanja; Dobrota, Vesna Dermanović; Cesarik, Marijan; Matovina, Lucija Zadro; Madzar, Zrinko; Zavoreo, Iris; Demarin, Vida
2013-06-01
Peripheral facial weakness is a facial nerve damage that results in muscle weakness on one side of the face. It may be idiopathic (Bell's palsy) or may have a detectable cause. Almost 80% of peripheral facial weakness cases are primary and the rest of them are secondary. The most frequent causes of secondary peripheral facial weakness are systemic viral infections, trauma, surgery, diabetes, local infections, tumor, immune disorders, drugs, degenerative diseases of the central nervous system, etc. The diagnosis relies upon the presence of typical signs and symptoms, blood chemistry tests, cerebrospinal fluid investigations, nerve conduction studies and neuroimaging methods (cerebral MRI, x-ray of the skull and mastoid). Treatment of secondary peripheral facial weakness is based on therapy for the underlying disorder, unlike the treatment of Bell's palsy that is controversial due to the lack of large, randomized, controlled, prospective studies. There are some indications that steroids or antiviral agents are beneficial but there are also studies that show no beneficial effect. Additional treatments include eye protection, physiotherapy, acupuncture, botulinum toxin, or surgery. Bell's palsy has a benign prognosis with complete recovery in about 80% of patients, 15% experience some mode of permanent nerve damage and severe consequences remain in 5% of patients.
Common questions about Bell palsy.
Albers, Janet R; Tamang, Stephen
2014-02-01
Bell palsy is an acute affliction of the facial nerve, resulting in sudden paralysis or weakness of the muscles on one side of the face. Testing patients with unilateral facial paralysis for diabetes mellitus or Lyme disease is not routinely recommended. Patients with Lyme disease typically present with additional manifestations, such as arthritis, rash, or facial swelling. Diabetes may be a comorbidity of Bell palsy, but testing is not needed in the absence of other indications, such as hypertension. In patients with atypical symptoms, magnetic resonance imaging with contrast enhancement can be used to rule out cranial mass effect and to add prognostic value. Steroids improve resolution of symptoms in patients with Bell palsy and remain the preferred treatment. Antiviral agents have a limited role, and may improve outcomes when combined with steroids in patients with severe symptoms. When facial paralysis is prolonged, surgery may be indicated to prevent ocular desiccation secondary to incomplete eyelid closure. Facial nerve decompression is rarely indicated or performed. Physical therapy modalities, including electrostimulation, exercise, and massage, are neither beneficial nor harmful.
Some Theorems on Generalized Basic Hypergeometric Series
Directory of Open Access Journals (Sweden)
A. D. Wadhwa
1972-07-01
Full Text Available In an earlier paper the author has established two theorems on generalized hypergeometric functions. In each theorem a numerator differs from a denominator by a positive integer. These theorems were further used to prove some theorems on the sums of Kampe de Feriet functions. Here, we have established the theorems which are the basic analogues of the theorems proved in the earlier paper.
Combinatorial Reciprocity Theorems
Beck, Matthias
2012-01-01
A common theme of enumerative combinatorics is formed by counting functions that are polynomials evaluated at positive integers. In this expository paper, we focus on four families of such counting functions connected to hyperplane arrangements, lattice points in polyhedra, proper colorings of graphs, and $P$-partitions. We will see that in each instance we get interesting information out of a counting function when we evaluate it at a \\emph{negative} integer (and so, a priori the counting function does not make sense at this number). Our goals are to convey some of the charm these "alternative" evaluations of counting functions exhibit, and to weave a unifying thread through various combinatorial reciprocity theorems by looking at them through the lens of geometry, which will include some scenic detours through other combinatorial concepts.
Towards the Carpenter's Theorem
Argerami, Martin
2008-01-01
Let M be a II_1 factor, A a masa in M and E the unique conditional expectation on A. Under some technical assumptions on the inclusion of A in M, which hold true for any semiregular masa of a separable factor, we show that for every discrete a in the positive part of the unit ball of A it is possible to find a projection p in M such that E(p)=a$. We also show an example of a diffuse operator x in A such that there exists a projection q in M with E(q)=x. These results show a new family of instances of a conjecture by Kadison, the so-called ``Carpenter's Theorem''.
Choudhury, Sayantan; Panda, Sudhakar; Singh, Rajeev
2017-02-01
In this work, we have studied the possibility of setting up Bell's inequality violating experiment in the context of cosmology, based on the basic principles of quantum mechanics. First we start with the physical motivation of implementing the Bell inequality violation in the context of cosmology. Then to set up the cosmological Bell violating test experiment we introduce a model independent theoretical framework using which we have studied the creation of new massive particles by implementing the WKB approximation method for the scalar fluctuations in the presence of additional time-dependent mass contribution in the cosmological perturbation theory. Here for completeness we compute the total number density and the energy density of the newly created particles in terms of the Bogoliubov coefficients using the WKB approximation method. Next using the background scalar fluctuation in the presence of a new time-dependent mass contribution, we explicitly compute the expression for the one point and two point correlation functions. Furthermore, using the results for a one point function we introduce a new theoretical cosmological parameter which can be expressed in terms of the other known inflationary observables and can also be treated as a future theoretical probe to break the degeneracy amongst various models of inflation. Additionally, we also fix the scale of inflation in a model-independent way without any prior knowledge of primordial gravitational waves. Also using the input from a newly introduced cosmological parameter, we finally give a theoretical estimate for the tensor-to-scalar ratio in a model-independent way. Next, we also comment on the technicalities of measurements from isospin breaking interactions and the future prospects of newly introduced massive particles in a cosmological Bell violating test experiment. Further, we cite a precise example of this setup applicable in the context of string theory motivated axion monodromy model. Then we comment
Quantum Bell Inequalities from Macroscopic Locality
Yang, Tzyh Haur; Sheridan, Lana; Scarani, Valerio
2010-01-01
We propose a method to generate analytical quantum Bell inequalities based on the principle of Macroscopic Locality. By imposing locality over binary processings of virtual macroscopic intensities, we establish a correspondence between Bell inequalities and quantum Bell inequalities in bipartite scenarios with dichotomic observables. We discuss how to improve the latter approximation and how to extend our ideas to scenarios with more than two outcomes per setting.
Do resonating bells increase jellyfish swimming performance?
Hoover, Alexander; Miller, Laura
2013-11-01
A current question in swimming and flight is whether or not driving flexible appendages at their resonant frequency results in faster or more efficient locomotion. It has been suggested that jellyfish swim faster and/or more efficiently when the bell is driven at its resonant frequency. Previous work has modeled the jellyfish bell as a damped harmonic oscillator, and this simplified model suggests that work done by the bell is maximized when force is applied at the resonant frequency of the bell. We extend the idea of resonance phenomena of the jellyfish bell to a fluid structure interaction framework using the immersed boundary method. We first examine the effects of the bending stiffness of the bell on its resonant frequency. We then further our model with the inclusion of a ``muscular'' spring that connects the two sides of a 2D bell and drives it near its resonant frequency. We use this muscular spring to force the bell at varying frequencies and examine the work done by these springs and the resulting swimming speed. We finally augment our model with a flexible, passive bell margin to examine its role in propulsive efficiency.
-Dimensional Fractional Lagrange's Inversion Theorem
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F. A. Abd El-Salam
2013-01-01
Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.
Complex integration and Cauchy's theorem
Watson, GN
2012-01-01
This brief monograph by one of the great mathematicians of the early twentieth century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.Author G. N. Watson begins by reviewing various propositions of Poincaré's Analysis Situs, upon which proof of the theorem's most general form depends. Subsequent chapters examine the calculus of residues, calculus optimization, the
Limit theorem and uniqueness theorem of backward stochastic differential equations
Institute of Scientific and Technical Information of China (English)
JIANG; Long
2006-01-01
This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0)≡0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectation εg; this paper also proves that if a filtration consistent expectation ε can be represented as a g-expectation εg, then the corresponding generator g must be unique.
Belle II and Hadron spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Križan, Peter, E-mail: peter.krizan@ijs.si [J. Stefan Institute and University of Ljubljana (Slovenia)
2015-08-15
Asymmetric B factories, PEP-II with BaBar and KEKB with Belle, made a decisive contribution to flavour physics. In addition, they also observed a long list of new hadrons, some of which do not fit into the standard meson and baryon schemes. The next generation of B factories, the so called Super B factory will search for departures from the Standard model. For this task, a 50 times larger data sample is needed, corresponding to an integrated luminosity of 50 ab{sup −1}. With such a large data sample there are many more topics to explore, including searches for new and exotic hadrons, and investigation of their properties.
Cardioids and Morley's Trisector Theorem
J. Brinkhuis (Jan); van de Craats, J.
2017-01-01
textabstractA self-contained account of Morley's own proof of his celebrated trisector theorem is given. This makes this elegant and almost forgotten fragment of analytic Euclidean geometry more accessible to modern readers
Belle-II Experiment Network Requirements
Energy Technology Data Exchange (ETDEWEB)
Asner, David [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Bell, Greg [ESnet; Carlson, Tim [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Cowley, David [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Dart, Eli [ESnet; Erwin, Brock [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Godang, Romulus [Univ. of South Alabama, Mobile, AL (United States); Hara, Takanori [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Johnson, Jerry [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Johnson, Ron [Univ. of Washington, Seattle, WA (United States); Johnston, Bill [ESnet; Dam, Kerstin Kleese-van [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Kaneko, Toshiaki [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Kubota, Yoshihiro [NII; Kuhr, Thomas [Karlsruhe Inst. of Technology (KIT) (Germany); McCoy, John [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Miyake, Hideki [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Monga, Inder [ESnet; Nakamura, Motonori [NII; Piilonen, Leo [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Pordes, Ruth [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Ray, Douglas [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Russell, Richard [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Schram, Malachi [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Schroeder, Jim [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Sevior, Martin [Univ. of Melbourne (Australia); Singh, Surya [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Suzuki, Soh [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Sasaki, Takashi [High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Williams, Jim [Indiana Univ., Bloomington, IN (United States)
2013-05-28
The Belle experiment, part of a broad-based search for new physics, is a collaboration of ~400 physicists from 55 institutions across four continents. The Belle detector is located at the KEKB accelerator in Tsukuba, Japan. The Belle detector was operated at the asymmetric electron-positron collider KEKB from 1999-2010. The detector accumulated more than 1 ab-1 of integrated luminosity, corresponding to more than 2 PB of data near 10 GeV center-of-mass energy. Recently, KEK has initiated a $400 million accelerator upgrade to be called SuperKEKB, designed to produce instantaneous and integrated luminosity two orders of magnitude greater than KEKB. The new international collaboration at SuperKEKB is called Belle II. The first data from Belle II/SuperKEKB is expected in 2015. In October 2012, senior members of the Belle-II collaboration gathered at PNNL to discuss the computing and neworking requirements of the Belle-II experiment with ESnet staff and other computing and networking experts. The day-and-a-half-long workshop characterized the instruments and facilities used in the experiment, the process of science for Belle-II, and the computing and networking equipment and configuration requirements to realize the full scientific potential of the collaboration's work.
Physics Achievements from the Belle Experiment
Brodzicka, Jolanta; Chang, Paoti; Eidelman, Simon; Golob, Bostjan; Hayasaka, Kiyoshi; Hayashii, Hisaki; Iijima, Toru; Inami, Kenji; Kinoshita, Kay; Kwon, Youngjoon; Miyabayashi, Kenkichi; Mohanty, Gagan; Nakao, Mikihiko; Nakazawa, Hideyuki; Olsen, Stephen; Sakai, Yoshihide; Schwanda, Christoph; Schwartz, Alan; Trabelsi, Karim; Uehara, Sadaharu; Uno, Shoji; Watanabe, Yasushi; Zupanc, Anze
2012-01-01
The Belle experiment, running at the KEKB e+e- asymmetric energy collider during the first decade of the century, achieved its original objective of measuring precisely differences between particles and anti-particles in the B system. After collecting 1000 fb-1 of data at various Upsilon resonances, Belle also obtained the many other physics results described in this article.
Arditti, D.
2008-12-01
The Dumb-bell Nebula (M27) and the Little Dumb-bell (M76) imaged on October 24?25 by David Arditti. David writes: 'These images were recorded on the same night with the same equipment, so they show the true relationship of sizes.'
Clinical practice guideline: Bell's Palsy executive summary.
Baugh, Reginald F; Basura, Gregory J; Ishii, Lisa E; Schwartz, Seth R; Drumheller, Caitlin Murray; Burkholder, Rebecca; Deckard, Nathan A; Dawson, Cindy; Driscoll, Colin; Gillespie, M Boyd; Gurgel, Richard K; Halperin, John; Khalid, Ayesha N; Kumar, Kaparaboyna Ashok; Micco, Alan; Munsell, Debra; Rosenbaum, Steven; Vaughan, William
2013-11-01
The American Academy of Otolaryngology-Head and Neck Surgery Foundation (AAO-HNSF) has published a supplement to this issue featuring the new Clinical Practice Guideline: Bell's Palsy. To assist in implementing the guideline recommendations, this article summarizes the rationale, purpose, and key action statements. The 11 recommendations developed encourage accurate and efficient diagnosis and treatment and, when applicable, facilitate patient follow-up to address the management of long-term sequelae or evaluation of new or worsening symptoms not indicative of Bell's palsy. There are myriad treatment options for Bell's palsy; some controversy exists regarding the effectiveness of several of these options, and there are consequent variations in care. In addition, there are numerous diagnostic tests available that are used in the evaluation of patients with Bell's palsy. Many of these tests are of questionable benefit in Bell's palsy. Furthermore, while patients with Bell's palsy enter the health care system with facial paresis/paralysis as a primary complaint, not all patients with facial paresis/paralysis have Bell's palsy. It is a concern that patients with alternative underlying etiologies may be misdiagnosed or have an unnecessary delay in diagnosis. All of these quality concerns provide an important opportunity for improvement in the diagnosis and management of patients with Bell's palsy.
A model with cosmological Bell inequalities
Maldacena, Juan
2015-01-01
We discuss the possibility of devising cosmological observables which violate Bell's inequalities. Such observables could be used to argue that cosmic scale features were produced by quantum mechanical effects in the very early universe. As a proof of principle, we propose a somewhat elaborate inflationary model where a Bell inequality violating observable can be constructed.
Minimax discrimination of quasi-Bell states
Energy Technology Data Exchange (ETDEWEB)
Kato, Kentaro [Quantum ICT Research Institute, Tamagawa University, 6-1-1 Tamagawa-gakuen, Machida, Tokyo 194-8610 (Japan)
2014-12-04
An optimal quantum measurement is considered for the so-called quasi-Bell states under the quantum minimax criterion. It is shown that the minimax-optimal POVM for the quasi-Bell states is given by its square-root measurement and is applicable to the teleportation of a superposition of two coherent states.
The Second Noether Theorem on Time Scales
Directory of Open Access Journals (Sweden)
Agnieszka B. Malinowska
2013-01-01
Full Text Available We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus.
The second Noether theorem on time scale
Malinowska, Agnieszka B.; Martins, Natália
2014-01-01
We extend the second Noether theorem to variational problems on time scales. Our result provides as corollaries the classical second Noether theorem, the second Noether theorem for the $h$-calculus and the second Noether theorem for the $q$-calculus.
The Kolmogorov-Riesz compactness theorem
Hanche-Olsen, Harald
2009-01-01
We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.
Local virial and tensor theorems.
Cohen, Leon
2011-11-17
We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem.
SECURING MOBILE ANT AGENT USING CHINESE REMAINDER THEOREM
Directory of Open Access Journals (Sweden)
Srinath Doss
2013-01-01
Full Text Available Recent days, research in wireless network becomes major area for the past few decades. In wireless routing many routing methods such as table driven, source driven; many characteristics such as reactive routing, proactive routing; many routing algorithms such as dijikstraâs shortest path, distributed bell-man ford algorithm are proposed in the literature. For effective wireless routing, the recent ant colony optimization proves better result than the existing methodologies. The ant colony optimization is a swarm intelligence technique which widely used for combinatorial optimization problems such as travelling salesman, network routing, clustering. The ant colony optimization is a real time routing protocol which offers highly reliable and optimal routing for both single path and multi path routing. As the ant is a small tiny mobile agent, providing security is critical issue. In this study, a secured ant colony optimization using Chinese remainder theorem is proposed.
Fixed-point-like theorems on subspaces
Directory of Open Access Journals (Sweden)
Bernard Cornet
2004-08-01
Full Text Available We prove a fixed-point-like theorem for multivalued mappings defined on the finite Cartesian product of Grassmannian manifolds and convex sets. Our result generalizes two different kinds of theorems: the fixed-point-like theorem by Hirsch et al. (1990 or Husseini et al. (1990 and the fixed-point theorem by Gale and Mas-Colell (1975 (which generalizes Kakutani's theorem (1941.
Construction of Bell inequalities based on the CHSH structure
Liu, Binbin; Wang, Jing; Li, Ming; Shen, Shuqian; Chen, Dongmeng
2017-04-01
It is a computationally hard task to find all Bell inequalities for a given number of parties, measurement settings, and measurement outcomes. We investigate the construction of the Clauser-Horne-Shimony-Holt Bell inequalities, based on which we present a set of new Bell inequalities. The maximal violations of the constructed Bell inequalities are analysed, and computable formulas are derived.
Ferromagnetism beyond Lieb's theorem
Costa, Natanael C.; Mendes-Santos, Tiago; Paiva, Thereza; Santos, Raimundo R. dos; Scalettar, Richard T.
2016-10-01
The noninteracting electronic structures of tight-binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a uniform on-site Hubbard interaction U is turned on, Lieb proved rigorously that at half-filling (ρ =1 ) the ground state has a nonzero spin. In this paper we consider a "CuO2 lattice" (also known as "Lieb lattice," or as a decorated square lattice), in which "d orbitals" occupy the vertices of the squares, while "p orbitals" lie halfway between two d orbitals; both d and p orbitals can accommodate only up to two electrons. We use exact determinant quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of U and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case, Ud=Up , originally considered by Lieb, and the inhomogeneous (IH) case, Ud≠Up . For the H case at half-filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all U . For the IH system at half-filling, we argue that the case Up≠Ud falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases Up=0 ,Ud=U and Up=U ,Ud=0 . We found that the different environments of d and p sites lead to a ferromagnetic insulator when Ud=0 ; by contrast, Up=0 leads to to a metal without any magnetic ordering. In addition, we have also established that at density ρ =1 /3 , strong antiferromagnetic correlations set in, caused by the presence of one fermion on each
Nambu-Goldstone theorem and spin-statistics theorem
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
Belle II Physics Prospects, Status and Schedule
Bennett, J.
2016-11-01
The second generation B-factory at the SuperKEKB facility in Tsukuba, Japan is beginning to take shape. The highly anticipated Belle II experiment will have a rich physics program at the intensity frontier, in complement to existing experiments in the energy frontier. Accelerator commissioning has been making good progress, as has the construction and installation of the Belle II detector. An overview of the physics prospects at Belle II, as well as the status and schedule of the experiment, is presented.
Fluctuation theorems for quantum processes
Albash, Tameem; Marvian, Milad; Zanardi, Paolo
2013-01-01
We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that unitality replaces micro-reversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.
Pasicki, Lech
2011-01-01
Many versions of the Stokes theorem are known. More advanced of them require complicated mathematical machinery to be formulated which discourages the users. Our theorem is sufficiently simple to suit the handbooks and yet it is pretty general, as we assume the differential form to be continuous on a compact set F(A) and C1 "inside" while F(A) is built of "bricks" and its inner part is a C1 manifold. There is no problem of orientability and the integrals under consideration are convergent. The proof is based on integration by parts and inner approximation.
Noether theorems and higher derivatives
Townsend, Paul K
2016-01-01
A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\\epsilon$ to an arbitrary function of time; the Noether charge $Q$ is then the coefficient of $\\dot\\epsilon$ in the variation of the action. Here we examine the validity of this proof for Lagrangian mechanics with arbitrarily-high time derivatives, in which context "higher-level" analogs of Noether's theorem can be similarly proved, and "Noetherian charges" read off from, e.g. the coefficient of $\\ddot \\epsilon$ in the variation of the action. While $Q=0$ implies a restricted gauge invariance, an unrestricted gauge invariance requires zero Noetherian charges too. Some illustrative examples are considered.
Improvement of Hartman's linearization theorem
Institute of Scientific and Technical Information of China (English)
SHI; Jinlin(史金麟)
2003-01-01
Hartman's linearization theorem tells us that if matrix A has no zero real part and f(x) isbounded and satisfies Lipchitz condition with small Lipchitzian constant, then there exists a homeomorphismof Rn sending the solutions of nonlinear system x' = Ax + f(x) onto the solutions of linear system x' = Ax.In this paper, some components of the nonlinear item f(x) are permitted to be unbounded and we provethe result of global topological linearization without any special limitation and adding any condition. Thus,Hartman's linearization theorem is improved essentially.
Louis M. Houston
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...
The truncated Second Main Theorem and uniqueness theorems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we first establish a truncated Second Main Theorem for algebraically nondegenerate holomorphic mappings from the complex plane into a complex projective variety V intersecting hypersurfaces. We then prove some uniqueness results for meromorphic mappings. The result of Demailly about a partial solution to the Fujita’s conjecture is used.
Hyperentanglement-assisted Bell-state analysis
Walborn, S P; Monken, C H
2003-01-01
We propose a simple scheme for complete Bell-state measurement of photons using hyperentangled states - entangled in multiple degrees of freedom. In addition to hyperentanglement, our scheme requires only linear optics and single photon detectors, and is realizable with current technology. At the cost of additional classical communication, our Bell-state measurement can be implemented non-locally. We discuss the possible application of these results to quantum dense coding and quantum teleportation.
A systemic "dumb-bell" haemangiopericytoma.
Tancioni, F; Gaetani, P; Tartara, F; Villani, L; Martelli, A; Rodriguez y Baena, R
1996-01-01
Systemic haemangiopericytoma is a rare soft tissue tumour originating from pericytes which are contractile pericapillary cells, and represents less than one percent of all vascular neoplasms. The most common site of involvement is the thigh followed by the retroperitoneum, while the paraspinal location is very rare. We report the first case of systemic "dumb-bell" haemangiopericytoma illustrated radiologically, which mimick, a dorsal "dumb-bell" neurinoma.
Overview of flavor physics results at Belle
Directory of Open Access Journals (Sweden)
Yusa Yosuke
2015-01-01
Full Text Available We will present recent topics of the flavor physics in decays of the heavy mesons at the Belle experiment. Most of the results are based on a full data set which corresponds to 772 million BB̄ pairs collected at the ϒ(4S resonance with the Belle detector at the KEKB asymmetric energy e+e− collider. We also discuss about prospects of the studies in the future B-factory experiment.
Analysis of bell materials: Tin bronzes
Institute of Scientific and Technical Information of China (English)
Jaromir Audy; Katarina Audy
2008-01-01
The present study was set up to examine the effect of alloying elements (including harmful elements) on metallurgical features (material properties and qualitative parameters) of tin bronzes, with particular reference to church bells from Middle Ages to Current times. A driving force of this study was to identify and demonstrate features related to the quality of church bells made in different centuries. The findings have been derived via metallographic and chemical analysis of specimens of bells from various parts of Australasia and Europe. The bell materials consisted of a mixture of the a phase and the (α+β) eutectoid essentially, in proportions determined by tin content and mould materials during casting. The samples from the 15th century to the one from the 20th century showed a progressive increase in hardness, ranging from the minimum of -280 VHM20g to a maximum of -470 VHM20g for the (α+β) eutectoid, and -160 VHM20g to -230 VHM20g for the a phase. The investigation also shows that the sound decay of the bell decreased with lowering the wt.% of tin and increasing the wt.% of lead and silver. This information is expected to provide an additional interesting knowledge into manufacturing practices and their significance in the quality of church bells over past centuries.
BELLE progress report. 1995 April - 1996 March
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-03-01
The scientific goals of the BELLE experiment continue to be of great interest. The large number of papers during the past year that identify measurements that can be done with BELLE reflects the considerable interest in the theoretical community in these physics issues. This is also demonstrated by the approval during the past year of two major B physics projects: the BaBar experiment at SLAC and the HERAB experiment at DESY. Both projects have schedules that put them into direct competition with BELLE for the important goal of testing the KM predictions for CP violations in B meson decays. Other projects addressing this physics are planned for the Tevatron collider and have been proposed both for the LHC and RHIC. The BELLE collaboration remains committed to its goal of being the first group to provide conclusive evidence either confirming or refuting the KM model. The year 1995 was an exciting time for the BELLE experiment. All of the major technology choices were finalized and a final detector configuration has been established. Continued R and D has resulted in improved performance expectations for a number of detector subsystems. The procurement of materials for major subsystems is underway and construction of long leadtime items has started. A construction schedule has been established and an integration strategy is being developed. This report describes the status of BELLE with an emphasis on progress since the last LCPAC meeting in January 1995. (J.P.N.). 90 refs.
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...
Von Laue's theorem and its applications
Wang, Changbiao
2012-01-01
Von Laue's theorem is strictly proved in detail to clarify confusions in textbook and literature. This theorem is used to analyze the classical electron and the static electric field confined in a finite region of space.
A normal form theorem around symplectic leaves
Crainic, M.N.; Marcut, I.T.
2012-01-01
We prove the Poisson geometric version of the Local Reeb Stability (from foliation theory) and of the Slice Theorem (from equivariant geometry), which is also a generalization of Conn’s linearization theorem.
Reality or Locality? - Proposed test to decide \\textit{how} Nature breaks Bell's inequality
Hansson, Johan
2011-01-01
Bell's theorem, and its experimental tests, has shown that the two premises for Bell's inequality - locality and objective reality - cannot both hold in nature, as Bell's inequality is broken. A simple test is proposed, which for the first time may decide which alternative nature actually prefers on the fundamental, quantum level. If each microscopic event is truly random (e.g. as assumed in orthodox quantum mechanics) objective reality is not valid, whereas if each event is described by an unknown but deterministic mechanism ("hidden variables") locality is not valid. This may be analyzed and decided by the well-known reconstruction method of Ruelle and Takens; in the former case no structure should be discerned, in the latter a reconstructed structure should be visible. This could in principle be tested by comparing individual "hits" in a double slit experiment, but in practice a single fluorescent atom, and its (seemingly random) temporal switching between active/inactive states would possibly be better/mo...
Reality or Locality? Proposed Test to Decide How Nature Breaks Bell's Inequality
Directory of Open Access Journals (Sweden)
Johan Hansson
2012-01-01
Full Text Available Bell's theorem, and its experimental tests, has shown that the two premises for Bell's inequality—locality and objective reality—cannot both hold in nature, as Bell's inequality is broken. A simple test is proposed, which for the first time may decide which alternative nature actually prefers on the fundamental, quantum level. If each microscopic event is truly random (e.g., as assumed in orthodox quantum mechanics objective reality is not valid whereas if each event is described by an unknown but deterministic mechanism (“hidden variables” locality is not valid. This may be analyzed and decided by the well-known reconstruction method of Ruelle and Takens; in the former case no structure should be discerned, in the latter a reconstructed structure should be visible. This could in principle be tested by comparing individual “hits” in a double-slit experiment, but in practice a single fluorescent atom, and its (seemingly random temporal switching between active/inactive states would possibly be better/more practical, easier to set up, observe, and analyze. However, only imagination limits the list of possible experimental setups.
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.)
JACKSON'S THEOREM FOR COMPACT GROUPS
Institute of Scientific and Technical Information of China (English)
H. Vaezi; S. F. Rzaev
2002-01-01
In this article we consider the generalized shift operator defined by(Sh.f)(g) = ∫Gf (tut-1g)dton compact group G and by help of this operator we define "Spherical" modulus of continuity. So we proveStechkin and Jackson type theorems.
LUROTH'S THEOREM IN DIFFERENTIAL FIELDS
Institute of Scientific and Technical Information of China (English)
GAO Xiaoshan; XU Tao
2002-01-01
In this paper, we present a constructive proof of Liroth's theorem in differentialcase. We also give a method to find the inversion maps for general differential rationalparametric equations. As a consequence, we prove that a differential rational curve alwayshas a set of proper parametric equations.
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....
GENERALIZED RECIPROCAL THEOREMS AND THEIR APPLICATIONS
Institute of Scientific and Technical Information of China (English)
付宝连
2002-01-01
Generalized reciprocal theorems of non-coupled and coupled systems , which are valid for two deformed bodies with different constitutive relations are established by generalizing the idea of Betti ' s reciprocal theorem. When the constitutive relations of the two deformed bodies are all alike and linear elastic, the generalized reciprocal theorem of non-coupled systems just becomes Betti' s . Meanwhile, the generalized reciprocal theorems are applied to simulate calculations in elasticity.
Ordering in mechanical geometry theorem proving
Institute of Scientific and Technical Information of China (English)
李洪波￥
1997-01-01
Ordering in mechanical geometry theorem proving is studied from geometric viewpoint and some new ideas are proposed. For Thebault’s theorem which is the most difficult theorem that has ever been proved by Wu’ s method, a very simple proof using Wu’s method under a linear order is discovered.
A definability theorem for first order logic
Butz, C.; Moerdijk, I.
2001-01-01
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
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.
On Brayton and Moser's missing stability theorem
Jeltsema, D.; Scherpen, J. M. A.
2005-01-01
In the early 1960s, Brayton and Moser proved three theorems concerning the stability of nonlinear electrical circuits. The applicability of each theorem depends on three different conditions on the type of admissible nonlinearities in circuit. Roughly speaking, this means that the theorems apply to
van de Graaf, R. C.; IJpma, F. F. A.; Nicolai, J-P A.; Werker, P. M. N.
2009-01-01
Bell's palsy is the eponym for idiopathic peripheral facial paralysis. It is named after Sir Charles Bell (1774-1842), who, in the first half of the nineteenth century, discovered the function of the facial nerve and attracted the attention of the medical world to facial paralysis. Our knowledge of
78 FR 65178 - Airworthiness Directives; Bell Helicopter Textron Canada (Bell) Helicopters
2013-10-31
... not require you to provide an affected cap for rework to Bell Tennessee nor require the original cap... rework has been done. Related Service Information Bell has issued ASB No. 206L-04-129 for the Model 206L... missing channel. (4) If the channel is missing, replace or rework the cap assembly by following...
The de Finetti theorem for test spaces
Barrett, Jonathan; Leifer, Matthew
2009-03-01
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.
The de Finetti theorem for test spaces
Energy Technology Data Exchange (ETDEWEB)
Barrett, Jonathan [H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL (United Kingdom); Leifer, Matthew [Institute for Quantum Computing, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1 (Canada)], E-mail: j.barrett@bristol.ac.uk, E-mail: matt@mattleifer.info
2009-03-15
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.
Multiwavelet sampling theorem in Sobolev spaces
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper is to establish the multiwavelet sampling theorem in Sobolev spaces. Sampling theorem plays a very important role in digital signal communication. The most classical sampling theorem is Shannon sampling theorem, which works for bandlimited signals. Recently, sampling theorems in wavelets or multiwavelets subspaces are extensively studied in the literature. In this paper, we firstly propose the concept of dual multiwavelet frames in dual Sobolev spaces (H s (R) , H-s (R)). Then we construct a special class of dual multiwavelet frames, from which the multiwavelet sampling theorem in Sobolev spaces is obtained. That is, for any f ∈ H s (R) with s > 1/2, it can be exactly recovered by its samples. Especially, the sampling theorem works for continuous signals in L 2 (R), whose Sobolev exponents are greater than 1 /2.
The relativistic virial theorem and scale invariance
Gaite, Jose
2013-01-01
The virial theorem is related to the dilatation properties of bound states. This is realized, in particular, by the Landau-Lifshitz formulation of the relativistic virial theorem, in terms of the trace of the energy-momentum tensor. We construct a Hamiltonian formulation of dilatations in which the relativistic virial theorem naturally arises as the condition of stability against dilatations. A bound state becomes scale invariant in the ultrarelativistic limit, in which its energy vanishes. However, for very relativistic bound states, scale invariance is broken by quantum effects and the virial theorem must include the energy-momentum tensor trace anomaly. This quantum field theory virial theorem is directly related to the Callan-Symanzik equations. The virial theorem is applied to QED and then to QCD, focusing on the bag model of hadrons. In massless QCD, according to the virial theorem, 3/4 of a hadron mass corresponds to quarks and gluons and 1/4 to the trace anomaly.
Navier Stokes Theorem in Hydrology
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
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.
ANDRAGOGY OF DEVELOPMENT: BASIC THEOREMS
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A. G. Teslinov
2016-01-01
Full Text Available The article presents criticism of the state of scientific knowledge about adult education and provides the reasons for the choice of directions of its development.Methods. The approach to the substantiation of directions of development of andragogy includes aspectual analysis of scientific rhetoric of adult education; summarizing the symptoms and causes of the problems of educational practice examples of education managers; the analysis of the status of andragogy as a scientific paradigm; a conceptual analysis of the key theses of the modern synthesis of andragogy and the provisions for developmental adult education.Results and scientific novelty. Four theorems are formulated that specify the complete set of propositions about a developmental approach to adult education. These theorems are presented as a scientific hypothesis about the features of the approach. The theorems are proved, and the substantiation of the conditions of emergence of the adult education of educational properties is described. The idea of adult education as a developing culture is in the centre of reasoning. It is shown that the assertions of theorems form the conceptual core of the scientific branches in adult education – andragogy of development. The effect of the practical interpretation of its provisions is disclosed.Practical significance. Disclosed meanings and recommendations may be oriented to developers of educational systems and media for adults while creating the developmental components. These references will help to overcome the evident trend information of adult education to the "pulling" them up to continually outdated standards, and to give it the look of a truly developing technology.
An improvement of Papadakis' theorem
Institute of Scientific and Technical Information of China (English)
ZHANG Zhihua; MU Lehua; ZHANG Peixuan
2004-01-01
There exist many orthonormal wavelets which cannot be derived by multiresolution analysis (MRA) with a single scaling function.In 2000,Papadakis announced that any orthonormal wavelet is derived by a generalized MRA with countable scaling functions at most.We improve Papadakis' theorem and find that for any othonormal wavelet,the least number of the corresponding scaling functions is just the essential supremum of the dimension function of the orthonormal wavelet.Moreover,we construct directly the fewest scaling functions.
A Miniaturisation of Ramsey's Theorem
de Smet, Michiel; Weiermann, Andreas
We approximate the strength of the infinite Ramsey Theorem by iterating a finitary version. This density principle, in the style of Paris, together with PA will give rise to a first-order theory which achieves a lot of the strength of ACA0 and the original infinitary version. To prove our result, we use a generalisation of the results by Bigorajska and Kotlarski about partitioning α-large sets.
Compactness theorems of fuzzy semantics
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically. The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.
Software Reliability through Theorem Proving
Directory of Open Access Journals (Sweden)
S.G.K. Murthy
2009-05-01
Full Text Available Improving software reliability of mission-critical systems is widely recognised as one of the major challenges. Early detection of errors in software requirements, designs and implementation, need rigorous verification and validation techniques. Several techniques comprising static and dynamic testing approaches are used to improve reliability of mission critical software; however it is hard to balance development time and budget with software reliability. Particularly using dynamic testing techniques, it is hard to ensure software reliability, as exhaustive testing is not possible. On the other hand, formal verification techniques utilise mathematical logic to prove correctness of the software based on given specifications, which in turn improves the reliability of the software. Theorem proving is a powerful formal verification technique that enhances the software reliability for missioncritical aerospace applications. This paper discusses the issues related to software reliability and theorem proving used to enhance software reliability through formal verification technique, based on the experiences with STeP tool, using the conventional and internationally accepted methodologies, models, theorem proving techniques available in the tool without proposing a new model.Defence Science Journal, 2009, 59(3, pp.314-317, DOI:http://dx.doi.org/10.14429/dsj.59.1527
A class of Bell diagonal states and entanglement witnesses
Chruscinski, D; Mlodawski, K; Matsuoka, T
2010-01-01
We analyze special class of bipartite states - so called Bell diagonal states. In particular we provide new examples of bound entangled Bell diagonal states and construct the class of entanglement witnesses diagonal in the magic basis.
The Bell states in noncommutative algebraic geometry
Beil, Charlie
2014-10-01
We introduce new mathematical aspects of the Bell states using matrix factorizations, non-noetherian singularities, and noncommutative blowups. A matrix factorization of a polynomial p consists of two matrices ϕ1, ϕ2 such that ϕ1ϕ2 = ϕ2ϕ1 = p id. Using this notion, we show how the Bell states emerge from the separable product of two mixtures, by defining pure states over complex matrices rather than just the complex numbers. We then show in an idealized algebraic setting that pure states are supported on non-noetherian singularities. Moreover, we find that the collapse of a Bell state is intimately related to the representation theory of the noncommutative blowup along its singular support. This presents an exchange in geometry: the nonlocal commutative spacetime of the entangled state emerges from an underlying local noncommutative spacetime.
Clinical Practice Guideline of Acupuncture for Bell's Palsy
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Xi Wu
2016-10-01
Full Text Available Backgroud: Acupuncture is common used for Bell's palsy in clinic, however, recent systematic reviews all shows that there is no sufficient evidence to support the effectiveness of acupuncture for Bell's palsy because ofthe poor quality and heterogeneity. It's urgently necessary to develop a guideline of acupuncture for Bell's palsy based on principles of evidence-based medicine to optimize acupuncture treating, standardize outcomes evaluating and to improve the quality of acupuncture for patients with Bell's palsy under general circumstances.
Software and Physics Simulation at Belle II
Kim, Doris Yangsoo
2015-01-01
The Belle II experiment at the SuperKEKB collider in Tsukuba, Japan, will start physics data taking in 2018. It is planned to accumulate an e+ e- collision data set of 50 /ab, about 50 times larger than that of the earlier Belle experiment. The software library for the new detector will use GEANT4 for Monte Carlo simulation and is an entirely new software and reconstruction system based on modern computing tools. Examples of physics simulation including beam background overlays will be described.
The Real "Toll" of A. G. Bell: Lessons about Eugenics
Greenwald, Brian H.
2009-01-01
Historian Brian Greenwald offers a revisionist interpretation of Bell. He reviews Bell's role and influence within the American eugenics movement and shows that Bell had the respect of the most prominent American eugenicists. His intimate knowledge of deafness, from personal experience with his mother and wife and from his studies of deaf people…
Bell inequality and CP violation in the neutral kaon system
Bertlmann, Reinhold A; Hiesmayr, B C
2001-01-01
For the entangled neutral kaon system we formulate a Bell inequality sensitive to CP violation in mixing. Via this Bell inequality we obtain a bound on the leptonic CP asymmetry which is violated by experimental data. Furthermore, we connect the Bell inequality with a decoherence approach and find a lower bound on the decoherence parameter which practically corresponds to Furry's hypothesis.
On λ-Bell polynomials associated with umbral calculus
Kim, T.; Kim, D. S.
2017-01-01
In this paper, we introduce some new λ-Bell polynomials and Bell polynomials of the second kind and investigate properties of these polynomials. Using our investigation, we derive some new identities for the two kinds of λ-Bell polynomials arising from umbral calculus.
46 CFR 169.730 - General alarm bell switch.
2010-10-01
... 46 Shipping 7 2010-10-01 2010-10-01 false General alarm bell switch. 169.730 Section 169.730... Vessel Control, Miscellaneous Systems, and Equipment Markings § 169.730 General alarm bell switch. On vessels of 100 gross tons and over there must be a general alarm bell switch in the pilothouse,...
46 CFR 108.623 - General alarm bell switch.
2010-10-01
... 46 Shipping 4 2010-10-01 2010-10-01 false General alarm bell switch. 108.623 Section 108.623... AND EQUIPMENT Equipment Markings and Instructions § 108.623 General alarm bell switch. Each general alarm bell switch must be marked “GENERAL ALARM” on a plate or other firm noncorrosive backing....
2012-06-15
... COMMISSION PPL Bell Bend, LLC; Bell Bend Nuclear Power Plant Combined License Application; Notice of Intent... its Bell Bend Nuclear Power Plant (BBNPP) site, located west of the existing Susquehanna Steam... by relocating the power block footprint and other plant components. For purposes of developing...
2013-01-22
... COMMISSION PPL Bell Bend, LLC; Combined License Application for Bell Bend Nuclear Power Plant; Exemption 1.0... Approvals for Nuclear Power Plants.'' This reactor is to be identified as Bell Bend Nuclear Power Plant... (RCOL) application for UniStar's Calvert Cliffs Nuclear Power Plant, Unit 3 (CCNPP3). The......
2011-12-29
... COMMISSION PPL Bell Bend, LLC; Combined License Application for Bell Bend Nuclear Power Plant; Exemption 1.0..., Certifications, and Approvals for Nuclear Power Plants.'' This reactor is to be identified as Bell Bend Nuclear Power Plant (BBNPP), in Salem County, Pennsylvania. The BBNPP COL application incorporates by...
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.
The classical version of Stokes' Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we show how the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly...... 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....
The Helmholtz theorem and retarded fields
Heras, Ricardo
2016-01-01
Textbooks frequently use the Helmholtz theorem to derive expressions for the electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for the time-dependent electric and magnetic fields, even when there is no formal objection to doing so because the proof of the theorem does not involve time derivatives but only spatial derivatives. Here we address the question as to whether the Helmholtz theorem is useful to derive expressions for the fields of Maxwell's equations. We show that when this theorem is applied to Maxwell's equations we obtain instantaneous expressions of the electric and magnetic fields, which are formally correct but of little practical usefulness. We then discuss two generalizations of the theorem which are shown to be useful to derive the retarded fields.
The Helmholtz theorem and retarded fields
Heras, Ricardo
2016-11-01
Textbooks frequently use the Helmholtz theorem to derive expressions for electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for time-dependent electric and magnetic fields, even when there is no formal objection to doing so because the proof of the theorem does not involve time derivatives but only spatial derivatives. Here we address the question as to whether the Helmholtz theorem is useful in deriving expressions for the fields of Maxwell’s equations. We show that when this theorem is applied to Maxwell’s equations we obtain instantaneous expressions of the electric and magnetic fields, which are formally correct but of little practical usefulness. We then discuss two generalizations of the theorem which are shown to be useful in deriving the retarded fields.
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.
Faulkner's Southern belle - myth or reality?
Directory of Open Access Journals (Sweden)
Nataša Intihar Klančar
2011-12-01
Full Text Available The article deals with heroines of William Faulkner's novels Light in August, Absalom, Absalom!, The Sound and the Fury, The Unvanquished, The Town and his short story "A Rose for Emily". The Southern belle features as a recurring character in Faulkner's fiction, her fragility, modesty, weakness yet strength, beauty, sincerity, generous nature, status and her fall from innocence comprise her central characteristics. Confronted with various expectations of Southern society and with the hardships of war, the belle is faced with many obstacles and challenges. Faulkner's heroines face a wide array of problems that prevent them from being and/or remaining a Southern belle. Let us name a few: Lena's inappropriate social status, Joanna's wrong roots, Mrs. Hightower's inability to fulfill her duties as the minister's wife, Ellen's miserable marriage, Judith's sad love life, Rosa's feelings of inferiority and humiliation, Mrs. Compson's failure as a mother, Caddy's weak rebellion against male convention, Drusilla's male characteristics, Linda's unrequited love and Emily's dark secret, to name a few. Through these characters and their destinies Faulkner shows a decaying South whose position has changed considerably over the years. Can the Southern belle save it? Can she save herself?
Edward Bell,My American Brother
Institute of Scientific and Technical Information of China (English)
2002-01-01
ON themorningof April 17th, 2002, at teno’clock, as I was writing an arti-cle, "I and My AmericanFriends" the phone rang. It wasan unexpected call from far awayBrooklyn, on the other side ofthe Pacific Ocean. Lynn, daugh-ter of Edward Bell, sadly told me
Baby Bell Libraries?--An Update.
Kessler, Jack
1993-01-01
Discusses the emerging three-tiered structure (i.e., the "Baby Bells," network nodes, and information marketers) that will assume responsibility for implementing a new national information network and getting networked information to the public. The role of libraries related to networked information is also considered. (EA)
Campbell, Patricia Shehan
1995-01-01
Presents an interview with Bell Yung, a scholar of Chinese music and ethnomusicology. Maintains that world music (music from many nations and cultures) should be taught as early as possible in the schools and at home. Includes two lesson plans for teaching about Chinese music. (CFR)
Peripheral nerve involvement in Bell's palsy
Directory of Open Access Journals (Sweden)
J. A. Bueri
1984-12-01
Full Text Available A group of patients with Bell's palsy were studied in order to disclose the presence of subclinical peripheral nerve involvement. 20 patients, 8 male and 12 female, with recent Bell's palsy as their unique disease were examined, in all cases other causes of polyneuropathy were ruled out. Patients were investigated with CSF examination, facial nerve latencies in the affected and in the sound sides, and maximal motor nerve conduction velocities, as well as motor terminal latencies from the right median and peroneal nerves. CSF laboratory examination was normal in all cases. Facial nerve latencies were abnormal in all patients in the affected side, and they differed significantly from those of control group in the clinically sound side. Half of the patients showed abnormal values in the maximal motor nerve conduction velocities and motor terminal latencies of the right median and peroneal nerves. These results agree with previous reports which have pointed out that other cranial nerves may be affected in Bell's palsy. However, we have found a higher frequency of peripheral nerve involvement in this entity. These findings, support the hypothesis that in some patients Bell's palsy is the component of a more widespread disease, affecting other cranial and peripheral nerves.
The Cultural Contradictions of Daniel Bell.
Chernow, Ron
1979-01-01
Daniel Bell, author and Harvard sociologist, is interviewed. Among the topics discussed are his view of society, his books, ideology, universities and higher education--including Harvard's core curriculum project and the 1968 student revolt at Columbia University, and Israel and the Jewish experience. (JMD)
Inverting the central limit theorem
Navascues, Miguel; Villanueva, Ignacio
2011-01-01
The central limit theorem states that the sum of N independently distributed n-tuples of real variables (subject to appropriate normalization) tends to a multivariate gaussian distribution for large N. Here we propose to invert this argument: given a set of n correlated gaussian variables, we try to infer information about the structure of the discrete microscopic probability distributions whose convolution generated such a macroscopic behavior. The techniques developed along the article are applied to prove that the classical description of certain macroscopic optical experiments is infinitely more complex than the quantum one.
A History of the Central Limit Theorem
Fischer, Hans
2011-01-01
This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical
A generalised Sylvester-Gallai Theorem
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L. M. Pretorius
2007-09-01
Full Text Available We give an algorithmic proof for the contrapositive of the following theorem that has recently been proved by the authors:Let S be a ﬁnite set of points in the plane, with each point coloured red, blue or with both colours. Suppose that for any two distinct points A and B in S sharing a colour k, there is a third point in S which has (inter alia the colour different from k and is collinear with A and B. Then all the points in S are collinear.This theorem is a generalization of both the Sylvester-Gallai Theorem and the Motzkin-Rabin Theorem.
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.
A generalized preimage theorem in global analysis
Institute of Scientific and Technical Information of China (English)
MA; Jipu
2001-01-01
［1］Ma Jipu, (1.2) inverses of operators between Banach spaces and conjugacy theorem, Chinese Annals of Math., B, 1999, 20(1): 57.［2］Ma Jipu, Rank theorem of operators between Banach spaces, Science in China, Ser. A, 2000, 43(1): 1.［3］Ma Jipu, Local conjugacy theorem, rank theorems in advenced calculus and a generalized principle constructing Banach manifolds, Science in China, Ser. A, 2000, 43(12): 1233.［4］Zeidler, A. E., Nonlinear Function Analysis and Its Applications, IV: Applications to Mathematical Physics, New York: Springer-Verlag, 1988.
The matching theorems and coincidence theorems for generalized R-KKM mapping in topological spaces
Huang, Jianhua
2005-12-01
In this paper we present some new matching theorems with open cover and closed cover by using the generalized R-KKM theorems [L. Deng, X. Xia, Generalized R-KKM theorem in topological space and their applications, J. Math. Anal. Appl. 285 (2003) 679-690] in the topological spaces with property (H). As applications, some coincidence theorems are established in topological spaces. Our results extend and generalize some known results.
An elementary derivation of the quantum virial theorem from Hellmann-Feynman theorem
İpekoğlu, Y.; Turgut, S.
2016-07-01
A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann-Feynman theorem produces the final statement of the virial theorem.
Vallès, Jean
2012-01-01
Our aim is to prove a Poncelet type theorem for a line configuration on the complex projective. More precisely, we say that a polygon with 2n sides joining 2n vertices A1, A2,..., A2n is well inscribed in a configuration Ln of n lines if each line of the configuration contains exactly two points among A1, A2, ..., A2n. Then we prove : "Let Ln be a configuration of n lines and D a smooth conic in the complex projective plane. If it exists one polygon with 2n sides well inscribed in Ln and circumscribed around D then there are infinitely many such polygons. In particular a general point in Ln is a vertex of such a polygon." We propose an elementary proof based on Fr\\'egier's involution. We begin by recalling some facts about these involutions. Then we explore the following question : When does the product of involutions correspond to an involution? It leads to Pascal theorem, to its dual version proved by Brianchon, and to its generalization proved by M\\"obius.
A New Type of Singularity Theorem
Senovilla, José M M
2007-01-01
A new type of singularity theorem, based on spatial averages of physical quantities, is presented and discussed. Alternatively, the results inform us of when a spacetime can be singularity-free. This theorem provides a decisive observational difference between singular and non-singular, globally hyperbolic, open cosmological models.
Abel's theorem in the noncommutative case
Leitenberger, Frank
2004-03-01
We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic differentials of the first kind. Following Abel we prove Abel's theorem.
Double soft theorem for perturbative gravity
Saha, Arnab Priya
2016-09-01
Following up on the recent work of Cachazo, He and Yuan [1], we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.
Interpolation theorems on weighted Lorentz martingale spaces
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation theorems,we obtain some inequalities on martingale transform operator.
A note on the tolerated Tverberg theorem
2016-01-01
In this paper we give an asymptotically tight bound for the tolerated Tverberg Theorem when the dimension and the size of the partition are fixed. To achieve this we study certain partitions of order-type homogeneous sets and use a generalization of the Erd\\H{o}s-Szekeres theorem.
A New Fixed Point Theorem and Applications
Directory of Open Access Journals (Sweden)
Min Fang
2013-01-01
Full Text Available A new fixed point theorem is established under the setting of a generalized finitely continuous topological space (GFC-space without the convexity structure. As applications, a weak KKM theorem and a minimax inequalities of Ky Fan type are also obtained under suitable conditions. Our results are different from known results in the literature.
THE EXISTENCE THEOREM OF OPTIMAL GROWTH MODEL
Institute of Scientific and Technical Information of China (English)
Gong Liutang; Peng Xianze
2005-01-01
This paper proves a general existence theorem of optimal growth theory. This theorem is neither restricted to the case of a constant technology progress, nor stated in terms of mathematical conditions which have no direct economic interpretation and moreover, are difficult to apply.
On the Hausdorff-Young theorem
Nasserddine, W
2005-01-01
Let $G_{mn}=ax + b$ be the matricial group of a local field. The Hausdorff-Young theorem for $G_{11}$ was proved by Eymard-Terp in 1978. We will establish here the Hausdorff-Young theorem for $G_{nn}$ for all $n \\in \\mathbb{N}$.
Euler and the Fundamental Theorem of Algebra.
Duham, William
1991-01-01
The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)
The Euler Line and Nine-Point-Circle Theorems.
Eccles, Frank M.
1999-01-01
Introduces the Euler line theorem and the nine-point-circle theorem which emphasize transformations and the power of functions in a geometric concept. Presents definitions and proofs of theorems. (ASK)
Generalized fluctuation theorems for classical systems
Agarwal, G S
2015-01-01
Fluctuation theorems have a very special place in the study of non equilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen Fluctuation Theorem which is in terms of the distribution of the work $p(W)/p(-W)=\\exp(\\alpha W)$. We derive the general form of the fluctuation theorems for an arbitrary Gaussian Markov process and find conditions when the parameter $\\alpha$ becomes a universal parameter $1/kT$. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is non-trivial. The generalized theorems are equally valid for non-equilibrium steady states.
Pointwise ergodic theorems beyond amenable groups
Bowen, Lewis
2011-01-01
We prove pointwise and maximal ergodic theorems for probability measure preserving actions of any countable group, provided it admits an essentially free, weakly mixing amenable action of stable type III_r for some r >0. Our approach is based on the following two principles. First, it is possible to generalize the ergodic theory of measure-preserving actions of amenable groups to include probability-measure-preserving amenable equivalence relations. Second, it is possible to reduce the proof of ergodic theorems for actions of a general group to the proof of ergodic theorems in an associated measure-preserving amenable equivalence relation, provided the group admits an amenable action with the properties stated above. The general ergodic theorems established here are used in a sequel paper to prove mean and pointwise ergodic theorems for arbitrary Gromov-hyperbolic groups.
Ringin' the water bell: dynamic modes of curved fluid sheets
Kolinski, John; Aharoni, Hillel; Fineberg, Jay; Sharon, Eran
2015-11-01
A water bell is formed by fluid flowing in a thin, coherent sheet in the shape of a bell. Experimentally, a water bell is created via the impact of a cylindrical jet on a flat surface. Its shape is set by the splash angle (the separation angle) of the resulting cylindrically symmetric water sheet. The separation angle is altered by adjusting the height of a lip surrounding the impact point, as in a water sprinkler. We drive the lip's height sinusoidally, altering the separation angle, and ringin' the water bell. This forcing generates disturbances on the steady-state water bell that propagate forward and backward in the fluid's reference frame at well-defined velocities, and interact, resulting in the emergence of an interference pattern unique to each steady-state geometry. We analytically model these dynamics by linearizing the amplitude of the bell's response about the underlying curved geometry. This simple model predicts the nodal structure over a wide range of steady-state water bell configurations and driving frequencies. Due to the curved water bell geometry, the nodal structure is quite complex; nevertheless, the predicted nodal structure agrees extremely well with the experimental data. When we drive the bell beyond perturbative separation angles, the nodal locations surprisingly persist, despite the strikingly altered underlying water bell shape. At extreme driving amplitudes the water sheet assumes a rich variety of tortuous, non-convex shapes; nevertheless, the fluid sheet remains intact.
Uniqueness theorems in linear elasticity
Knops, Robin John
1971-01-01
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...
Belle II sensitivity to missing energy decays
Gaur, Vipin; Belle Collaboration, II
2017-01-01
The Belle II experiment at the SuperKEKB collider is a major upgrade of the KEK `` B factory'' facility in Tsukuba, Japan. The machine is designed for an instantaneous luminosity of 8 ×1035 cm-2 s-1, and the experiment is expected to accumulate a data sample of about 50 ab-1 in five years of running. With this amount of data, decays sensitive to physics beyond the Standard Model can be studied with unprecedented precision. One promising set of modes are physics processes with missing energy such as B+ ->τ+ ν , B ->D (*) τν , and B ->K (*) ν ν decays. The Belle II data also allows searches for the dark photon, the gauge mediator of a hypothetical dark sector, which has received much attention in the context of dark matter models.
The Belle II VXD production database
Energy Technology Data Exchange (ETDEWEB)
Valentan, Manfred; Ritter, Martin [Max-Planck-Institut fuer Physik, Muenchen (Germany); Wuerkner, Benedikt; Leitl, Bernhard [Institut fuer Hochenergiephysik, Wien (Austria); Pilo, Federico [Istituto Nazionale di Fisica Nucleare, Pisa (Italy); Collaboration: Belle II-Collaboration
2015-07-01
The construction and commissioning of the Belle II Vertex Detector (VXD) is a huge endeavor involving a large number of valuable components. Both subsystems PXD (Pixel Detector) and SVD (Silicon Vertex Detector) deploy a large number of sensors, readout electronic parts and mechanical elements. These items are scattered around the world at many institutes, where they are built, measured and assembled. One has to keep track of measurement configurations and results, know at any time the location of the sensors, their processing state, quality, where they end up in an assembly, and who is responsible. These requirements call for a flexible and extensive database which is able to reflect the processes in the laboratories and the logistics between the institutes. This talk introduces the database requirements of a physics experiment using the PXD construction workflow as a showcase, and presents an overview of the database ''HephyDb'', which is used by the groups constructing the Belle II VXD.
Global track finder for Belle II experiment
Energy Technology Data Exchange (ETDEWEB)
Trusov, Viktor; Feindt, Michael; Heck, Martin; Kuhr, Thomas; Goldenzweig, Pablo [Karlsruhe Institute of Technology, IEKP (Germany); Collaboration: Belle II-Collaboration
2015-07-01
We present an implementation of a method based on the Legendre transformation for reconstruction charged particle tracks in the central drift chamber of the Belle II experiment. The method is designed for fast track finding and restoring circular patterns of track hits in transverse plane. It is done by searching for common tangents to drift circles of hits in the conformal space. With known transverse trajectories longitudinal momentum estimation performed by assigning stereo hits followed by determination of the track parameters. The method includes algorithms responsible for track quality estimation and reduction of rate of fakes. The work is targeting at increasing the efficiency and reducing the execution time because the computing power available to the experiment is limited. The algorithm is developed within the Belle II software environment with using Monte-Carlo simulation for probing its efficiency.
Posterior Probability and Fluctuation Theorem in Stochastic Processes
Ohkubo, Jun
2009-12-01
A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via Bayes’ theorem. In conventional fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when suitable assumptions are employed.
Bell's Inequalities, Superquantum Correlations, and String Theory
Directory of Open Access Journals (Sweden)
Lay Nam Chang
2011-01-01
We argue that string theory, viewed as a quantum theory with two deformation parameters, the string tension α ' , and the string coupling constant g s , is such a superquantum theory that transgresses the usual quantum violations of Bell's inequalities. We also discuss the ℏ → ∞ limit of quantum mechanics in this context. As a superquantum theory, string theory should display distinct experimentally observable supercorrelations of entangled stringy states.
Radiative and Electroweak Penguins at Belle
Hyun, HyoJung
2010-02-01
Radiative and electroweak penguin decays of B mesons are a sensitive probe of new physics beyond the Standard Model. We study the inclusive and exclusive radiative and electroweak penguin decays of B meson and also search an exotic particle seen by the HyperCP experiment. The measurements are based on a large data sample of 605 fb-1 containing 657 millions BB¯ pairs collected at the Υ(4S) with the Belle detector at the KEKB energy asymmetric e+e- collider.
Radiative/EW penguin decays at Belle
Taniguchi, Nanae
2009-01-01
We present recent results for radiative and electroweak penguin decays of $B$ me son at Belle. Measurements of differential branching fraction, isospin asymmetr y, $K^*$ polarization, and forward-backward asymmetry as functions of $q^2$ for $B \\to K^{(*)}ll$ decays are reported. For the results of the radiative process, we report measurements of branching fractions for inclusive $B\\to X_s \\gamma$ and the exclusive $B\\to K \\eta' \\gamma$ modes.
Bell Inequalities and Pseudo-functional densities
Geurdes, J F
2001-01-01
A local hidden variable model with pseudo-functional density function restricted to a binary probability event space is demonstrated to be able to reproduce the quantum correlation in an Einstein Podolsky Rosen Bohm and Aharonov type of experiment. In the density function use is made of Hadamard's finite part which disables the possibility to derive Bell's inequality from models with such a type of density function.
Bell's inequalities in the tomographic representation
Lupo, C; Marmo, G
2006-01-01
The tomographic approach to quantum mechanics is revisited as a direct tool to investigate violation of Bell-like inequalities. Since quantum tomograms are well defined probability distributions, the tomographic approach is emphasized to be the most natural one to compare the predictions of classical and quantum theory. Examples of inequalities for two qubits an two qutrits are considered in the tomographic probability representation of spin states.
Double dumb-bell calculus in childhood.
Joshi, Prashant; Sarda, Dinesh; Ahmad, Ashraf; Kothari, Paras
2009-01-01
An eight-year old male was admitted with complaints of right scrotal swelling, dysuria and intermittent retention of urine for 10 days. On per-rectal examination, a hard mass was palpable in the posterior urethra. An X-ray (KUB) of the abdomen revealed a double dumb-bell calculus at the base of bladder, extending into the posterior urethra. A cystolithotomy via the suprapubic approach was successfully curative.
Double dumb-bell calculus in childhood
Directory of Open Access Journals (Sweden)
Joshi Prashant
2009-01-01
Full Text Available An eight-year old male was admitted with complaints of right scrotal swelling, dysuria and intermittent retention of urine for 10 days. On per-rectal examination, a hard mass was palpable in the posterior urethra. An X-ray (KUB of the abdomen revealed a double dumb-bell calculus at the base of bladder, extending into the posterior urethra. A cystolithotomy via the suprapubic approach was successfully curative.
Bell inequalities from variable elimination methods
Budroni, Costantino
2011-01-01
Tight Bell inequalities are facets of Pitowsky's correlation polytope and are usually obtained from its extreme points by solving the hull problem. Recently, Avis, Imai, Ito and Sasaki have proposed an alternative method, based on variable elimination, which overcomes some of the computational difficulties of the hull problem. However, this method can only be applied to the bipartite case. Here we present an algebraic derivation of the half-space representation for a family of convex polytopes, from which every correlation polytope can be obtained as a projection. As a result, variable elimination methods, e.g. the Fourier-Motzkin method, can be applied to obtain tight Bell inequalities in an n-party scenario. Similar ideas are shown to be applicable to a different kind of algebraic conditions. In particular, this analysis provides an explanation for the fact that only a finite number of families of Bell inequalities arise in scenarios where one experimenter can choose between an arbitrary number of measureme...
The pointwise Hellmann-Feynman theorem
Directory of Open Access Journals (Sweden)
David Carfì
2010-02-01
Full Text Available In this paper we study from a topological point of view the Hellmann-Feynman theorem of Quantum Mechanics. The goal of the paper is twofold: On one hand we emphasize the role of the strong topology in the classic version of the theorem in Hilbert spaces, for what concerns the kind of convergence required on the space of continuous linear endomorphisms, which contains the space of (continuous observables.On the other hand we state and prove a new pointwise version of the classic Hellmann-Feynman theorem. This new version is not yet present in the literature and follows the idea of A. Bohm concerning the topology which is desiderable to use in Quantum Mechanics. It is indeed out of question that this non-trivial new version of the Hellmann-Feynman theorem is the ideal one - for what concerns the continuous observables on Hilbert spaces, both from a theoretical point of view, since it is the strongest version obtainable in this context - we recall that the pointwise topology is the coarsest one compatible with the linear structure of the space of continuous observables -, and from a practical point of view, because the pointwise topology is the easiest to use among topologies: it brings back the problems to the Hilbert space topology. Moreover, we desire to remark that this basic theorem of Quantum Mechanics, in his most desiderable form, is deeply interlaced with two cornerstones of Functional Analysis: the Banach-Steinhaus theorem and the Baire theorem.
Bell's inequalities II logical loophole in their interpretation
Sica, L
1999-01-01
Assumed data streams from a delayed choice gedanken experiment must satisfy a Bell's identity independently of locality assumptions. The violation of Bell's inequality by assumed correlations of identical form among these data streams implies that they cannot all result from statistically equivalent variables of a homogeneous process. This is consistent with both the requirements of arithmetic and distinctions between commuting and noncommuting observables in quantum mechanics. Neglect of these distinctions implies a logical loophole in the conventional interpretation of Bell's inequalities.
Entanglement Measure and Quantum Violation of Bell-Type Inequality
Ding, Dong; He, Ying-Qiu; Yan, Feng-Li; Gao, Ting
2016-10-01
By calculating entanglement measures and quantum violation of Bell-type inequality, we reveal the relationship between entanglement measure and the amount of quantum violation for a family of four-qubit entangled states. It has been demonstrated that the Bell-type inequality is completely violated by these four-qubit entangled states. The plot of entanglement measure as a function of the expectation value of Bell operator shows that entanglement measure first decreases and then increases smoothly with increasing quantum violation.
Existence theorems for ordinary differential equations
Murray, Francis J
2007-01-01
Theorems stating the existence of an object-such as the solution to a problem or equation-are known as existence theorems. This text examines fundamental and general existence theorems, along with the Picard iterants, and applies them to properties of solutions and linear differential equations.The authors assume a basic knowledge of real function theory, and for certain specialized results, of elementary functions of a complex variable. They do not consider the elementary methods for solving certain special differential equations, nor advanced specialized topics; within these restrictions, th
Haag's theorem in renormalised quantum field theories
Klaczynski, Lutz
2016-01-01
We review a package of no-go results in axiomatic quantum field theory with Haag's theorem at its centre. Since the concept of operator-valued distributions in this framework comes very close to what we believe canonical quantum fields are about, these results are of consequence to quantum field theory: they suggest the seeming absurdity that this highly victorious theory is incapable of describing interactions. We single out unitarity of the interaction picture's intertwiner as the most salient provision of Haag's theorem and critique canonical perturbation theory to argue that renormalisation bypasses Haag's theorem by violating this very assumption.
Effective randomness, strong reductions and Demuth's theorem
Bienvenu, Laurent
2011-01-01
We study generalizations of Demuth's Theorem, which states that the image of a Martin-L\\"of random real under a tt-reduction is either computable or Turing equivalent to a Martin-L\\"of random real. We show that Demuth's Theorem holds for Schnorr randomness and computable randomness (answering a question of Franklin), but that it cannot be strengthened by replacing the Turing equivalence in the statement of the theorem with wtt-equivalence. We also provide some additional results about the Turing and tt-degrees of reals that are random with respect to some computable measure.
Optical Bell-state analysis in the coincidence basis
Walborn, S P; Pádua, S; Monken, C H
2003-01-01
Many quantum information protocols require a Bell-state measurement of entangled systems. Most optical Bell-state measurements utilize two-photon interference at a beam splitter. By creating polarization-entangled photons with spontaneous parametric down-conversion using a first-order Hermite-Gaussian pump beam, we invert the usual interference behavior and perform an incomplete Bell-state measurement in the coincidence basis. We discuss the possibility of a complete Bell-state measurement in the coincidence basis using hyperentangled states [Phys. Rev. A, \\textbf{58}, R2623 (1998)].
Emile Galle ja legendaarne Belle Epoque / Kärt Kross
Kross, Kärt
2008-01-01
1811. aastal rajatud Perrier-Jouet shampanjamajast ja shampanjast Belle Epoque, mille lillemotiividega pudeli disainis prantsuse klaasikunstnik Emile Galle (1846-1904). Kunstniku eluloolisi andmeid, loomingust
2012-05-30
... SECURITY Coast Guard 33 CFR Part 165 RIN 1625-AA00 Safety Zone; Belle Pass Dredge Operations, Belle Pass... operations in specified waters of Belle Pass, Port Fourchon, Louisiana. This action is necessary for the... pipelines along the Gulf Shoreline of Belle Pass. In addition to the dredging equipment described...
DEFF Research Database (Denmark)
Jørgensen, C. Barker
2003-01-01
History of nerves, Bell's Idea, Bell-Magendie law, Bell-Magendie controversy, Charles Bell, Francois Magendie, P.W. Lund, D.F. Eschricht, Herbert Mayo, Johannes Müller, Claude Bernard, spinal nerve roots, cranial nerves, recurrent sensitivity......History of nerves, Bell's Idea, Bell-Magendie law, Bell-Magendie controversy, Charles Bell, Francois Magendie, P.W. Lund, D.F. Eschricht, Herbert Mayo, Johannes Müller, Claude Bernard, spinal nerve roots, cranial nerves, recurrent sensitivity...
Security Theorems via Model Theory
Directory of Open Access Journals (Sweden)
Joshua Guttman
2009-11-01
Full Text Available A model-theoretic approach can establish security theorems for cryptographic protocols. Formulas expressing authentication and non-disclosure properties of protocols have a special form. They are quantified implications for all xs . (phi implies for some ys . psi. Models (interpretations for these formulas are *skeletons*, partially ordered structures consisting of a number of local protocol behaviors. *Realized* skeletons contain enough local sessions to explain all the behavior, when combined with some possible adversary behaviors. We show two results. (1 If phi is the antecedent of a security goal, then there is a skeleton A_phi such that, for every skeleton B, phi is satisfied in B iff there is a homomorphism from A_phi to B. (2 A protocol enforces for all xs . (phi implies for some ys . psi iff every realized homomorphic image of A_phi satisfies psi. Hence, to verify a security goal, one can use the Cryptographic Protocol Shapes Analyzer CPSA (TACAS, 2007 to identify minimal realized skeletons, or "shapes," that are homomorphic images of A_phi. If psi holds in each of these shapes, then the goal holds.
Index theorems for quantum graphs
Fulling, S A; Wilson, J H
2007-01-01
In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher-order differential operators as an intermediary. In this paper, the case of quantum graphs is addressed. A quantum graph is a graph considered as a (singular) one-dimensional variety and equipped with a second-order differential Hamiltonian H (a "Laplacian") with suitable conditions at vertices. For the case of scale-invariant vertex conditions (i.e., conditions that do not mix the values of functions and of their derivatives), the constant term of the heat-kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph. This observation is placed into the index-theory context by factoring the Laplacian into two first-order operators, H =A*A, and relating the constant term to the index of A. An independent consideration provides an index f...
A generalized preimage theorem in global analysis
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The concept of locally fine point and generalized regular valueof a C1 map between Banach spaces were carried over C1 map between Banach manifolds. Hence the preimage theorem, a principle constructing Banach manifolds in global analysis, is generalized.
The virial theorem for nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: paolo.amore@gmail.com, E-mail: fernande@quimica.unlp.edu.ar
2009-09-15
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular, we consider conservative nonlinear oscillators and obtain the same main result derived earlier from the expansion in Chebyshev polynomials. (letters and comments)
Transformation groups and the virial theorem
Kampen, N.G. van
1972-01-01
A generalization of Noether's result for classical mechanics is given, which shows that the virial theorem is related to an invariance property of the Lagrange function. Two examples are discussed in detail.
Rank theorems of operators between Banach spaces
Institute of Scientific and Technical Information of China (English)
2000-01-01
Let E and F be Banach spaces, and B( E, F) all of bounded linear operators on E into F. Let T0 ∈ B( E, F) with an outer inverse T0# ∈ B( F, E). Then a characteristic condition of S= (I + T0# ( T- T0))-1 T0# with T∈ B( E, F) and || T0# ( T- T0) || < 1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.
Rank theorems of operators between Banach spaces
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Let E and F be Banach spaces, and B(E,F) all of bounded linear operators on E into F. Let T0∈B(E,F) with an outer inverse T#0∈B(F,E). Then a characteristic condition of S=(I+T#0(T-T0))-1T#0 with T∈B(E,F) and ‖T#0(T-T0)‖<1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.
Affine and Projective Tree Metric Theorems
Harel, Matan; Pachter, Lior
2011-01-01
The tree metric theorem provides a combinatorial four point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A similar (but weaker) four point condition characterizes dissimilarity maps derived from circular split systems (Kalmanson metrics). The tree metric theorem was first discovered in the context of phylogenetics and forms the basis of many tree reconstruction algorithms, whereas Kalmanson metrics were first considered by computer scientists, and are notable in that they are a non-trivial class of metrics for which the traveling salesman problem is tractable. We present a unifying framework for these theorems based on combinatorial structures that are used for graph planarity testing. These are (projective) PC-trees, and their affine analogs, PQ-trees. In the projective case, we generalize a number of concepts from clustering theory, including hierarchies, pyramids, ultrametrics and Robinsonian matrices, and the theorems that relate them. As with tree metric...
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 ...
Two No-Go Theorems on Superconductivity
Tada, Yasuhiro
2016-01-01
We study lattice superconductors such as attractive Hubbard models. As is well known, Bloch's theorem asserts absence of persistent current in ground states and equilibrium states for general fermion systems. While the statement of the theorem is true, we can show that the theorem cannot exclude possibility of a surface persistent current. Such a current can be stabilized by boundary magnetic fields which do not penetrate into the bulk region of a superconductor, provided emergence of massive photons, i.e., Meissner effect. Therefore, we can expect that a surface persistent current is realized for a ground/equilibrium state in the sense of stability against local perturbations. We also apply Elitzur's theorem to superconductors at finite temperatures. As a result, we prove absence of symmetry breaking of the global U(1) phase of electrons for almost all gauge fixings. These observations suggest that the nature of superconductivity is the emergence of massive photons rather than the symmetry breaking of the U(...
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 o...... we apply the key instrumental concepts and verify the various steps towards this alternative proof of the divergence theorem....
Sahoo- and Wayment-Type Integral Mean Value Theorems
Tiryaki, Aydin; Cakmak, Devrim
2010-01-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…
A New GLKKM Theorem and Its Application to Abstract Economies
Institute of Scientific and Technical Information of China (English)
WEN Kai-ting
2012-01-01
In this paper,a new GLKKM theorem in L-convex spaces is established.As applications,a new fixed point theorem and a maximal element theorem are obtained in Lconvex spaces.Finally,equilibrium existence theorems for abstract economies and qualitative games in L-convex spaces are yielded.
Herbrand's theorem and non-Euclidean geometry
Beeson, Michael; Boutry, Pierre; Narboux, Julien
2014-01-01
International audience; We use Herbrand's theorem to give a new proof that Eu- clid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non- Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions to give a short, simple, and intuitively appealing proof.
Type Theory, Computation and Interactive Theorem Proving
2015-09-01
in type theory . Harper and student Kuen-Bang Hou developed a machine-checked proof of the equivalence of group actions and cov- ering spaces in...Track 2: Interactive theorem proving and au- tomated reasoning 3.1 Homotopy type theory Avigad participated in the Univalent Foundations Program at IAS...AFRL-AFOSR-VA-TR-2016-0071 TYPE THEORY , COMPUTATION AND INTERACTIVE THEOREM PROVING Jeremy Avigad CARNEGIE MELLON UNIVERSITY Final Report 09/01/2015
Transversality theorems for the weak topology
2011-01-01
In his 1979 paper Trotman proves, using the techniques of the Thom transversality theorem, that under some conditions on the dimensions of the manifolds under consideration, openness of the set of maps transverse to a stratification in the strong (Whitney) topology implies that the stratification is $(a)$-regular. Here we first discuss the Thom transversality theorem for the weak topology and then give a similiar kind of result for the weak topology, under very weak hypotheses. Recently sever...
The large deviations theorem and ergodicity
Energy Technology Data Exchange (ETDEWEB)
Gu Rongbao [School of Finance, Nanjing University of Finance and Economics, Nanjing 210046 (China)
2007-12-15
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.
Double Soft Theorem for Perturbative Gravity
Saha, Arnab Priya
2016-01-01
Following up on the recent work of Cachazo, He and Yuan \\cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.
78 FR 56148 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters
2013-09-12
...-2009-32, dated July 24, 2009, issued by Transport Canada Civil Aviation (TCCA), which is the aviation authority for Canada, to correct an unsafe condition for the specified Bell model ] helicopters. TCCA... operation in the United States. Pursuant to our bilateral agreement with Canada, TCCA has notified us of...
78 FR 65200 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters
2013-10-31
... Transport Canada Civil Aviation (TCCA), which is the aviation authority for Canada. TCCA issued AD No. CF-2004-09R1 to correct an unsafe condition for Model 407 helicopters. TCCA advises that several failures... failures have occurred to the 250- C47B engine used by Bell on the Model 407. According to TCCA,...
78 FR 37158 - Airworthiness Directives; Bell Helicopter Textron Canada (Bell) Model Helicopters
2013-06-20
... does the TCAA AD, and we would not require you to provide an affected cap for rework to Bell Tennessee... bearing support assembly, ensuring that the rework has been done. Costs of Compliance We estimate that... remaining freewheel part details for a missing channel. (4) If the channel is missing, replace or rework...
Khare, A; Paranjape, M B; Khare, Avinash; MacKenzie, R; Paranjape, M B
1994-01-01
The Coleman-Hill theorem prohibits the appearance of radiative corrections to the topological mass (more precisely, to the parity-odd part of the vacuum polarization tensor at zero momentum) in a wide class of abelian gauge theories in 2+1 dimensions. We re-express the theorem in terms of the effective action rather than in terms of the vacuum polarization tensor. The theorem so restated becomes somewhat stronger: a known exception to the theorem, spontaneously broken scalar Chern-Simons electrodynamics, obeys the new non-renormalization theorem. Whereas the vacuum polarization {\\sl does} receive a one-loop, parity-odd correction, this does not translate to a radiative contribution to the Chern-Simons term in the effective action. We also point out a new situation, involving scalar fields and parity-odd couplings, which was overlooked in the original analysis, where the conditions of the theorem are satisfied and where the topological mass does, in fact, get a radiative correction.
Mental Constructions for The Group Isomorphism Theorem
Directory of Open Access Journals (Sweden)
Arturo Mena-Lorca
2016-03-01
Full Text Available The group isomorphism theorem is an important subject in any abstract algebra undergraduate course; nevertheless, research shows that it is seldom understood by students. We use APOS theory and propose a genetic decomposition that separates it into two statements: the first one for sets and the second with added structure. We administered a questionnaire to students from top Chilean universities and selected some of these students for interviews to gather information about the viability of our genetic decomposition. The students interviewed were divided in two groups based on their familiarity with equivalence relations and partitions. Students who were able to draw on their intuition of partitions were able to reconstruct the group theorem from the set theorem, while those who stayed on the purely algebraic side could not. Since our approach to learning this theorem was successful, it may be worthwhile to gather data while teaching it the way we propose here in order to check how much the learning of the group isomorphism theorem is improved. This approach could be expanded to other group homomorphism theorems provided further analysis is conducted: going from the general (e.g., sets to the particular (e.g., groups might not always the best strategy, but in some cases we may just be turning to more familiar settings.
The Belle II Silicon Vertex Detector
Energy Technology Data Exchange (ETDEWEB)
Friedl, M., E-mail: markus.friedl@oeaw.ac.at [HEPHY – Institute of High Energy Physics, Nikolsdorfer Gasse 18, 1050 Vienna (Austria); Ackermann, K. [MPI Munich, Föhringer Ring 6, 80805 München (Germany); Aihara, H. [University of Tokyo, Department of Physics, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Aziz, T. [Tata Institute of Fundamental Research, Experimental High Energy Physics Group, Homi Bhabha Road, Mumbai 400 005 (India); Bergauer, T. [HEPHY – Institute of High Energy Physics, Nikolsdorfer Gasse 18, 1050 Vienna (Austria); Bozek, A. [Institute of Nuclear Physics, Division of Particle Physics and Astrophysics, ul. Radzikowskiego 152, 31 342 Krakow (Poland); Campbell, A. [DESY, Notkestrasse 85, 22607 Hamburg (Germany); Dingfelder, J. [University of Bonn, Department of Physics and Astronomy, Nussallee 12, 53115 Bonn (Germany); Drasal, Z. [Charles University, Institute of Particle and Nuclear Physics, Ke Karlovu 3, 121 16 Praha 2 (Czech Republic); Frankenberger, A. [HEPHY – Institute of High Energy Physics, Nikolsdorfer Gasse 18, 1050 Vienna (Austria); Gadow, K. [DESY, Notkestrasse 85, 22607 Hamburg (Germany); Gfall, I. [HEPHY – Institute of High Energy Physics, Nikolsdorfer Gasse 18, 1050 Vienna (Austria); Haba, J.; Hara, K.; Hara, T. [KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Higuchi, T. [University of Tokyo, Kavli Institute for Physics and Mathematics of the Universe, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583 (Japan); Himori, S. [Tohoku University, Department of Physics, Aoba Aramaki Aoba-ku, Sendai 980-8578 (Japan); Irmler, C. [HEPHY – Institute of High Energy Physics, Nikolsdorfer Gasse 18, 1050 Vienna (Austria); Ishikawa, A. [Tohoku University, Department of Physics, Aoba Aramaki Aoba-ku, Sendai 980-8578 (Japan); Joo, C. [Seoul National University, High Energy Physics Laboratory, 25-107 Shinlim-dong, Kwanak-gu, Seoul 151-742 (Korea, Republic of); and others
2013-12-21
The KEKB machine and the Belle experiment in Tsukuba (Japan) are now undergoing an upgrade, leading to an ultimate luminosity of 8×10{sup 35}cm{sup −2}s{sup −1} in order to measure rare decays in the B system with high statistics. The previous vertex detector cannot cope with this 40-fold increase of luminosity and thus needs to be replaced. Belle II will be equipped with a two-layer Pixel Detector surrounding the beam pipe, and four layers of double-sided silicon strip sensors at higher radii than the old detector. The Silicon Vertex Detector (SVD) will have a total sensitive area of 1.13m{sup 2} and 223,744 channels—twice as many as its predecessor. All silicon sensors will be made from 150 mm wafers in order to maximize their size and thus to reduce the relative contribution of the support structure. The forward part has slanted sensors of trapezoidal shape to improve the measurement precision and to minimize the amount of material as seen by particles from the vertex. Fast-shaping front-end amplifiers will be used in conjunction with an online hit time reconstruction algorithm in order to reduce the occupancy to the level of a few percent at most. A novel “Origami” chip-on-sensor scheme is used to minimize both the distance between strips and amplifier (thus reducing the electronic noise) as well as the overall material budget. This report gives an overview on the status of the Belle II SVD and its components, including sensors, front-end detector ladders, mechanics, cooling and the readout electronics.
The modified Poynting theorem and the concept of mutual energy
Zhao, Shuang-ren; Yang, Kang; Yang, Xingang; Yang, Xintie
2015-01-01
The Poynting theorem is generalized to the modified Poynting theorem. In the modified Poynting theorem the electromagnetic field is superimposition of different electromagnetic fields including the field of retarded potential and advanced potential. The media epsilon (permittivity) and mu (permeability) can also be different in the different fields. The concept of mutual energy is introduced which is the difference between the total energy and self-energy. Using the modified Poynting theorem with the concept of the mutual energy the modified mutual energy theorem is derived. Applying time-offset transform and time integral to the modified mutual energy theorem, the time-correlation modified mutual energy theorem is obtained. Assume there are only two fields which are retarded potential, and there is only one media, the modified time-correlation energy theorem becomes the time-correlation energy theorem, which is also referred as the time-correlation reciprocity theorem. Assume there are two electromagnetic fi...
Won, E
2002-01-01
We present a measurement of CP-violating asymmetries in B0 -> pi+pi- decays based on 41.8 fb-1 data sample collected at the Y(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. From the asymmetry in the distribution of the time intervals between the two B meson decay points, we obtain the CP-violating asymmetry parameters S_pipi = -1.21 + 0.38 - 0.27 (stat) + 0.16 - 0.13 (syst) and A_pipi = +0.94 + 0.25 - 0.31 (stat) +- 0.09 (syst).
Directory of Open Access Journals (Sweden)
Sandra Fischer
2000-11-01
Full Text Available This article presents a study of the film Belle de jour, by Luis Buñuel, based on the text “Sobre a poética da carnaval ização em Luis Buñuel” by Eduardo Peñuela Cañizal, on Mikhail Bakhtin’s theoretical conception about carnival, on Gaston Bachelard’s ideas about the oneiric, on Sigmund Freud’s psychoanalysis and on the notion of the frame structure sustained by Groupe p.
The Bell Curve: An Essay Review
Directory of Open Access Journals (Sweden)
John C. Culbertson
1995-02-01
Full Text Available Occasionally a book out of academia will break from scholarly circles and enter into the mainstream market. On even rarer occasions, it will gain considerable notoriety before its initial publication. Richard Herrnstein and Charles Murray's The Bell Curve: Intelligence and Class Structure in American Life is such a book. Currently, it has entered the New York Times best- sellers list and appeared in most academic and mainstream periodical book reviews. Direct publicity for the book has also been strong. Although Herrnstein died September 24 of the past year, Murray has appeared on many popular television and radio talk shows.
Dummett vs Bell on quantum mechanics
Ben-Menahem, Yemima
The purpose of this paper is to cast doubt on the common allegation that quantum mechanics (QM) is incompatible with realism. I argue that the results usually considered inimical to realism, notably the violation of Bells inequality, in fact play the opposite role-they support realism. The argument is not intended, however, to demonstrate realism or refute its alternatives as general metaphysical positions. It is directed specifically at the view that QM differs from classical mechanics in that, unlike classical mechanics, it is not amenable to a realist interpretation.
Institute of Scientific and Technical Information of China (English)
Lei DENG; Ming Ge YANG
2006-01-01
Some new coincidence theorems involving admissible set-valued mappings are proved in general noncompact topological spaces. As applications, some new minimax inequalities, section theorem, best approximation theorem, existence theorems of weighted Nash equilibria and Pareto equilibria for multiobjective games are given in general topological spaces.
Limit Theorems For Closed Queuing Networks With Excess Of Servers
Tsitsiashvili, G.
2013-01-01
In this paper limit theorems for closed queuing networks with excess of servers are formulated and proved. First theorem is a variant of the central limit theorem and is proved using classical results of V.I. Romanovskiy for discrete Markov chains. Second theorem considers a convergence to chi square distribution. These theorems are mainly based on an assumption of servers excess in queuing nodes.
Bell's Nonlocality in a General Nonsignaling Case: Quantitatively and Conceptually
Loubenets, Elena R.
2017-03-01
Quantum violation of Bell inequalities is now used in many quantum information applications and it is important to analyze it both quantitatively and conceptually. In the present paper, we analyze violation of multipartite Bell inequalities via the local probability model—the LqHV (local quasi hidden variable) model (Loubenets in J Math Phys 53:022201, 2012), incorporating the LHV model only as a particular case and correctly reproducing the probabilistic description of every quantum correlation scenario, more generally, every nonsignaling scenario. The LqHV probability framework allows us to construct nonsignaling analogs of Bell inequalities and to specify parameters quantifying violation of Bell inequalities—Bell's nonlocality—in a general nonsignaling case. For quantum correlation scenarios on an N-qudit state, we evaluate these nonlocality parameters analytically in terms of dilation characteristics of an N-qudit state and also, numerically—in d and N. In view of our rigorous mathematical description of Bell's nonlocality in a general nonsignaling case via the local probability model, we argue that violation of Bell inequalities in a quantum case is not due to violation of the Einstein-Podolsky-Rosen (EPR) locality conjectured by Bell but due to the improper HV modelling of "quantum realism".
Eugenics Past and Present: Remembering Buck v. Bell.
Berson, Michael J.; Cruz, Barbara
2001-01-01
Provides background information about the eugenics movement. Focuses on eugenics in the United States detailing the case, Buck v. Bell, and eugenics in Germany. Explores the present eugenic movement, focusing on "The Bell Curve," China's one child policy, and the use of eugenic sterilizations in the United States and Canada. Includes…
46 CFR 197.334 - Open diving bells.
2010-10-01
... 46 Shipping 7 2010-10-01 2010-10-01 false Open diving bells. 197.334 Section 197.334 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) MARINE OCCUPATIONAL SAFETY AND HEALTH STANDARDS GENERAL PROVISIONS Commercial Diving Operations Equipment § 197.334 Open diving bells. Each open...
Aesthetes and Experts: For Whom Does the Bell Toll?
Rosemont, Henry, Jr.; Feinberg, Walter
1972-01-01
The authors outline a perspective on post-modernism and the counter-culture and question Bell's assessment of their socio-political impact (AA 511 929). They suggest that scientific and technical experts' influence is greater than that of artists, and they compare Bell's earlier work with his current thesis. (Authors/JB)
46 CFR 131.805 - General alarm bell, switch.
2010-10-01
... 46 Shipping 4 2010-10-01 2010-10-01 false General alarm bell, switch. 131.805 Section 131.805 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) OFFSHORE SUPPLY VESSELS OPERATIONS Markings for Fire Equipment and Emergency Equipment § 131.805 General alarm bell, switch. The switch in...
Computational Fluid Dynamics Simulation of Dual Bell Nozzle Film Cooling
Braman, Kalen; Garcia, Christian; Ruf, Joseph; Bui, Trong
2015-01-01
Marshall Space Flight Center (MSFC) and Armstrong Flight Research Center (AFRC) are working together to advance the technology readiness level (TRL) of the dual bell nozzle concept. Dual bell nozzles are a form of altitude compensating nozzle that consists of two connecting bell contours. At low altitude the nozzle flows fully in the first, relatively lower area ratio, nozzle. The nozzle flow separates from the wall at the inflection point which joins the two bell contours. This relatively low expansion results in higher nozzle efficiency during the low altitude portion of the launch. As ambient pressure decreases with increasing altitude, the nozzle flow will expand to fill the relatively large area ratio second nozzle. The larger area ratio of the second bell enables higher Isp during the high altitude and vacuum portions of the launch. Despite a long history of theoretical consideration and promise towards improving rocket performance, dual bell nozzles have yet to be developed for practical use and have seen only limited testing. One barrier to use of dual bell nozzles is the lack of control over the nozzle flow transition from the first bell to the second bell during operation. A method that this team is pursuing to enhance the controllability of the nozzle flow transition is manipulation of the film coolant that is injected near the inflection between the two bell contours. Computational fluid dynamics (CFD) analysis is being run to assess the degree of control over nozzle flow transition generated via manipulation of the film injection. A cold flow dual bell nozzle, without film coolant, was tested over a range of simulated altitudes in 2004 in MSFC's nozzle test facility. Both NASA centers have performed a series of simulations of that dual bell to validate their computational models. Those CFD results are compared to the experimental results within this paper. MSFC then proceeded to add film injection to the CFD grid of the dual bell nozzle. A series of
The Belle II experiment: fundamental physics at the flavor frontier
de la Cruz, Ivan Heredia
2016-01-01
After the major success of B-factories to establish the CKM mechanism and its proven potential to search for new physics, the Belle II experiment will continue exploring the physics at the flavor frontier over the next years. Belle II will collect 50 times more data than its predecessor, Belle, and allow for various precision measurements and searches of rare decays and particles. This paper introduces the B-factory concept and the flavor frontier approach to search for new physics. It then describes the SuperKEKB accelerator and the Belle II detector, as well as some of the physics that will be analyzed in Belle II, concluding with the experiment status and schedule.
The Trieste Lecture of John Stewart Bell
Bassi, Angelo; Carlo Ghirardi, Gian
2007-03-01
Delivered at Trieste on the occasion of the 25th Anniversary of the International Centre for Theoretical Physics, 2 November 1989 The video of this lecture is available here. Please see the PDF for the transcript of the lecture. General remarks by Angelo Bassi and GianCarlo Ghirardi During the autumn of 1989 the International Centre for Theoretical Physics, Trieste, celebrated the 25th anniversary of its creation. Among the many prestigious speakers, who delivered extremely interesting lectures on that occasion, was the late John Stewart Bell. All lectures have been recorded on tape. We succeeded in getting a copy of John's lecture. In the lecture, many of the arguments that John had lucidly stressed in his writings appear once more, but there are also extremely interesting new remarks which, to our knowledge, have not been presented elsewhere. In particular he decided, as pointed out by the very choice of the title of his lecture, to call attention to the fact that the theory presents two types of difficulties, which Dirac classified as first and second class. The former are those connected with the so-called macro-objectification problem, the latter with the divergences characterizing relativistic quantum field theories. Bell describes the precise position of Dirac on these problems and he stresses appropriately how, contrary to Dirac's hopes, the steps which have led to a partial overcoming of the second class difficulties have not helped in any way whatsoever to overcome those of the first class. He then proceeds to analyse the origin and development of the Dynamical Reduction Program and draws attention to the problems that still affect it, in particular that of a consistent relativistic generalization. When the two meetings Are there quantum jumps? and On the present status of Quantum Mechanics were organized in Trieste and Losinj (Croatia), on 5 10 September 2005, it occurred to us that this lecture, which has never been published, might represent an
Bell Could Become the Copernicus of Probability
Khrennikov, Andrei
2016-07-01
Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to Lobachevsky and from Kolmogorov to Bell. In probability, Bell could play the same role as Lobachevsky in geometry. In fact, violation of Bell’s inequality can be treated as implying the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena. Thus the quantum probabilistic model (based on Born’s rule) can be considered as the concrete example of the non-Kolmogorovian model of probability, similarly to the Lobachevskian model — the first example of the non-Euclidean model of geometry. This is the “probability model” interpretation of the violation of Bell’s inequality. We also criticize the standard interpretation—an attempt to add to rigorous mathematical probability models additional elements such as (non)locality and (un)realism. Finally, we compare embeddings of non-Euclidean geometries into the Euclidean space with embeddings of the non-Kolmogorovian probabilities (in particular, quantum probability) into the Kolmogorov probability space. As an example, we consider the CHSH-test.
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.
2011-11-02
...-hour intervals and corrosion protection and sealing of the yoke, P/N 204-011-102, of the main rotor hub... holes on yokes installed on Model 212 helicopters. That AD was intended to detect corrosion pitting and...-02, Bell has introduced a replacement stainless steel yoke, P/N 212-011-102. Bell issued...
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: be C1 nonlinear map, where U (x0) is an open set containing point x0∈E. With the locally fine property for Frechet derivatives f′(x) and generalized rank theorem for f′(x), a local conjugacy theorem, i.e. a characteristic condition for f being conjugate to f′(x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
Institute of Scientific and Technical Information of China (English)
马吉溥
2000-01-01
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally fine property for Frechet derivatives f’ (x) and generalized rank theorem for f ’( x), a local conjugacy theorem, i. e. a characteristic condition for f being conjugate to f (x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
Generalized fluctuation theorems for classical systems
Agarwal, G. S.; Dattagupta, Sushanta
2015-11-01
The fluctuation theorem has a very special place in the study of nonequilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen fluctuation theorem which is in terms of the distribution of the work p (W )/p (-W )=exp(α W ) . We derive the general form of the fluctuation theorems for an arbitrary multidimensional Gaussian Markov process. Interestingly, the parameter α is by no means universal, hitherto taken for granted in the case of linear Gaussian processes. As a matter of fact, conditions under which α does become a universal parameter 1 /K T are found to be rather restrictive. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is nontrivial. The generalized theorems are equally valid for nonequilibrium steady states and could be especially important in the presence of anisotropic diffusion.
Ergodic theorem, ergodic theory, and statistical mechanics.
Moore, Calvin C
2015-02-17
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject--namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics.
WEYL'S TYPE THEOREMS AND HYPERCYCLIC OPERATORS
Institute of Scientific and Technical Information of China (English)
M.H. M. Rashid
2012-01-01
For a bounded operator T acting on an infinite dimensional separable Hilbert space H,we prove the following assertions: (i) If T or T* ∈ SC,then generalized aBrowder's theorem holds for f(T) for every f ∈ Hol(σ(T)).(ii) If T or T* ∈ HC has topological uniform descent at all λ ∈ iso(σ(T)),then generalized Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)).(iii) If T ∈ HC has topological uniform descent at all λ ∈ E(T),then T satisfies generalized Weyl's theorem.(iv) Let T ∈ HC.If T satisfies the growth condition Gd(d ≥ 1),then generalized Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)).(v) If T ∈ SC,then,f(σSBF-+ (T)) =σSBF-+ (f(T)) for all f ∈ Hol(σ(T)).(vi) Let T be a-isoloid such that T* ∈ HC.If T - λI has finite ascent at every λ ∈ Ea(T)and if F is of finite rank on H such that TF =FT,then T + F obeys generalized a-Weyl's theorem.
78 FR 34282 - Airworthiness Directives; Bell Helicopter Textron Canada Limited (Bell) Helicopters
2013-06-07
... wheels used in Rolls Royce 250-C30S and 250-C-47B engines. According to TC, Rolls Royce has determined... flight manual. Revision A to ASB was issued to exclude Bell Model 206L-3 and 206L-4 helicopters with 250... citation for part 39 continues to read as follows: Authority: 49 U.S.C. 106(g), 40113, 44701. Sec. 39.13...
Performing CPR on a commercial diver inside the diving bell
Directory of Open Access Journals (Sweden)
Sourabh Bhutani
2015-01-01
Full Text Available CPR in a diving bell is difficult. It is taught by diving companies and training institutes but has not been subjected to the tenets of evidence based medicine. The diving bell lacks space as well as a flat hard surface to lay the patient on and therefore conventional methods of administering CPR are not possible. The diver is hung from a pulley tied to the diver's harness, and the bell flooded with water to reduce pooling of blood. Airway is established using a cervical collar to hyperextend the neck and inserting an appropriate oropharyngeal airway. Cardiac compressions are administered by the bellman using his head or the knee while holding the patient with his arms from behind. The bell can be recovered to surface only when spontaneous breathing and circulation have started. Diving bell offers a unique environment for management of unconscious casualties. Even though the method is at variance with the conventional method of administering CPR, it is the only method possible inside the bell. It is important that the method be scrutinized and refined so as to be more effective and efficacious inside the bell.
Some Limit Theorems in Geometric Processes
Institute of Scientific and Technical Information of China (English)
Yeh Lam; Yao-hui Zheng; Yuan-lin Zhang
2003-01-01
Geometric process (GP) was introduced by Lam[4,5], it is defined as a stochastic process {Xn, n =1, 2,...} for which there exists a real number a > 0, such that {an-1Xn, n = 1, 2,...} forms a renewal process (RP). In this paper, we study some limit theorems in GP. We first derive the Wald equation for GP and then obtain the limit theorems of the age, residual life and the total life at t for a GP. A general limit theorem for Sn with a > 1 is also studied. Furthermore, we make a comparison between GP and RP, including the comparison of their limit distributions of the age, residual life and the total life at t.
Bayes' theorem: scientific assessment of experience
Directory of Open Access Journals (Sweden)
Lex Rutten
2010-10-01
Full Text Available Homeopathy is based on experience and this is a scientific procedure if we follow Bayes' theorem. Unfortunately this is not the case at the moment. Symptoms are added to our materia medica based on absolute occurrence, while Bayes theorem tells us that this should be based on relative occurrence. Bayes theorem can be applied on prospective research, but also on retrospective research and consensus based on a large number of cases. Confirmation bias is an important source of false data in experience based systems like homeopathy. Homeopathic doctors should become more aware of this and longer follow-up of cases could remedy this. The existing system of adding symptoms to our materia medica is obsolete.
van de Graaf, R C; IJpma, F F A; Nicolai, J-P A; Werker, P M N
2009-11-01
Bell's palsy is the eponym for idiopathic peripheral facial paralysis. It is named after Sir Charles Bell (1774-1842), who, in the first half of the nineteenth century, discovered the function of the facial nerve and attracted the attention of the medical world to facial paralysis. Our knowledge of this condition before Bell's landmark publications is very limited and is based on just a few documents. In 1804 and 1805, Evert Jan Thomassen à Thuessink (1762-1832) published what appears to be the first known extensive study on idiopathic peripheral facial paralysis. His description of this condition was quite accurate. He located several other early descriptions and concluded from this literature that, previously, the condition had usually been confused with other afflictions (such as 'spasmus cynicus', central facial paralysis and trigeminal neuralgia). According to Thomassen à Thuessink, idiopathic peripheral facial paralysis and trigeminal neuralgia were related, being different expressions of the same condition. Thomassen à Thuessink believed that idiopathic peripheral facial paralysis was caused by 'rheumatism' or exposure to cold. Many aetiological theories have since been proposed. Despite this, the cold hypothesis persists even today.
Search for B+ ->KSKSh+ decays at Belle
Gaur, Vipin; Belle Collaboration
2017-01-01
We present updated measurements of charmless decays of charged B mesons to the three-body final states of KSKSK+ and KSKSπ+ , based on a data sample containing 770 ×106 B B events. The data were recorded with the Belle detector operating near the ϒ(4 S) resonance at the KEKB asymmetric-energy e+e- collider. The B+ ->KSKSK+ and B+ ->KSKSπ+ decays proceed via the b -> s and b -> d flavor-changing neutral current (FCNC) transitions, respectively, providing a good probe for new physics beyond the standard model (SM). We report the results on the branching fractions and direct CP asymmetries for both the decay channels. Supported by the Department of Energy Office of Science.
Bell Inequalities, Experimental Protocols and Contextuality
Kupczynski, Marian
2014-01-01
The violation of Bell, CHSH and CH inequalities indicates only that the assumption of "conterfactual definiteness" and/or the probabilistic models used in proofs were incorrect. In this paper we discuss in detail an intimate relation between experimental protocols and probabilistic models. In particular we show that local realistic and stochastic hidden variable models are inconsistent with the experimental protocols used in spin polarization correlation experiments. In particular these models neglect a contextual character of quantum theory (QT) and do not describe properly quantum measurements. We argue that the violation of various inequalities gives arguments against the irreducible randomness of act of the measurement. Therefore quantum probabilities are reducible what means that QT is emergent. In this case one could expect to discover in time series of data some unpredicted fine structures proving that QT is not predictably complete what would be a major discovery.
Bell inequalities with continuous angular variables
Borges, Carolina V S; Keller, Arne
2011-01-01
We consider bipartite quantum systems characterized by a continuous angular variable \\theta \\in [-\\pi, \\pi[, representing, for instance, the position of a particle on a circle. We show how to reveal non-locality on this type of system using inequalities similar to CHSH ones, originally derived for bipartite spin 1/2 like systems. Such inequalities involve correlated measurement of continuous angular functions and are equivalent to the continuous superposition of CHSH inequalities acting on bidimensional subspaces of the infinite dimensional Hilbert space. As an example, we discuss in detail one application of our results, and we derive inequalities based on orientation correlation measurements. The introduced Bell-type inequalities open the perspective of new and simpler experiments to test non locality on a variety of quantum systems described by continuous variables.
Bottomonium Results from BABAR and BELLE
Marks, Joerg
2009-01-01
After nine years of operation the BABAR experiment at the B factory PEPII (Standford Linear Accelerator Center) stopped data taking in April 2008. The last three month of data taking were devoted to e+e- collisions at center of mass energies of the Upsilon(2S), Upsilon(3S) and to an energy scan above the Upsilon(4S). Besides the observation of the bottomonium ground state eta_b, the center of mass energy dependent e+e- -> b bbar cross section was measured in the energy range from 10.54 to 11.20 GeV. BELLE observed an enhancement in the production cross section for e+e- -> Upsilon(nS) pi+ pi- -> mu+ mu- pi+ pi- in an energy scan from 10.83 to 11.02 GeV.
Generalizations of the Abstract Boundary singularity theorem
Whale, Ben E; Scott, Susan M
2015-01-01
The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from $C^1$ curves to locally Lipschitz curves.
A Noether Theorem for Markov Processes
Baez, John C
2012-01-01
Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable commutes with the Hamiltonian if and only if its expected value remains constant in time for every state. For Markov processes that no longer holds, but an observable commutes with the Hamiltonian if and only if both its expected value and standard deviation are constant in time for every state.
Spectral mapping theorems a bluffer's guide
Harte, Robin
2014-01-01
Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several and many variables. The basic algebraic systems – semigroups, rings and linear algebras – are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Spectral Mapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory.
Central Limit Theorem for Nonlinear Hawkes Processes
Zhu, Lingjiong
2012-01-01
Hawkes process is a self-exciting point process with clustering effect whose jump rate depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. Linear Hawkes process has an immigration-birth representation and can be computed more or less explicitly. It has been extensively studied in the past and the limit theorems are well understood. On the contrary, nonlinear Hawkes process lacks the immigration-birth representation and is much harder to analyze. In this paper, we obtain a functional central limit theorem for nonlinear Hawkes process.
Limit theorems for fragmentation processes with immigration
Knobloch, Robert
2012-01-01
In this paper we extend two limit theorems which were recently obtained for fragmentation processes to such processes with immigration. More precisely, in the setting with immigration we consider a limit theorem for the process counted with a random characteristic as well as the asymptotic behaviour of an empirical measure associated with the stopping line corresponding to the first blocks, in their respective line of descent, that are smaller than a given size. In addition, we determine the asymptotic decay rate of the size of the largest block in a homogeneous fragmentation process with immigration. The techniques used to proves these results are based on submartingale arguments.
Pauli and the spin-statistics theorem
Duck, Ian M
1997-01-01
This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties. Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that
Jarzynski's theorem for lattice gauge theory
Caselle, Michele; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-01-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium states. In this article, we extend Jarzynski's theorem to lattice gauge theory, and present examples of applications for two challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schroedinger functional and for simulations at finite density using reweighting techniques.
Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
Bastos, Catarina; Bernardini, Alex E.; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2016-05-01
We examine putative corrections to the Bell operator due to the noncommutativity in the phase space. Starting from a Gaussian squeezed envelope whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics, respectively, we conclude that although the time-evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechanics remain as nonlocal as quantum mechanics itself.
Observation of Bell Inequality violation in B mesons
Go, A
2004-01-01
A pair of $B^0\\bar B^0$ mesons from $\\Upsilon(4S)$ decay exhibit EPR type non-local particle-antiparticle (flavor) correlation. It is possible to write down Bell Inequality (in the CHSH form: $S\\le2$) to test the non-locality assumption of EPR. Using semileptonic $B^0$ decays of $\\Upsilon(4S)$ at Belle experiment, a clear violation of Bell Inequality in particle-antiparticle correlation is observed: S=2.725+-0.167(stat)+-0.092(syst)
Improvement of AMGA Python Client Library for Belle II Experiment
Kwak, Jae-Hyuck; Park, Geunchul; Huh, Taesang; Hwang, Soonwook
2015-12-01
This paper describes the recent improvement of the AMGA (ARDA Metadata Grid Application) python client library for the Belle II Experiment. We were drawn to the action items related to library improvement after in-depth discussions with the developer of the Belle II distributed computing system. The improvement includes client-side metadata federation support in python, DIRAC SSL library support as well as API refinement for synchronous operation. Some of the improvements have already been applied to the AMGA python client library as bundled with the Belle II distributed computing software. The recent mass Monte- Carlo (MC) production campaign shows that the AMGA python client library is reliably stable.
Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2015-01-01
One examines putative corrections to the Bell operator due to the noncommutativity in the phase-space. Starting from a Gaussian squeezed envelop whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics respectively, one concludes that, although the time evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechnics remains as non-local as quantum mechanics itself.
Tower bells and time zones, a history of synchronization
Sigismondi, Costantino
2014-01-01
The Astrarium made by Jacopo Dondi dell'Orologio in Padua in 1344 is one of the first public horologia in the World, their public utility is also shown through the history of the tower bell of Our Lady of Suffragio in Turin, made by the mathematician Francesco Fa\\`a di Bruno in 1866. The tower bell of St. Anthony in Lanciano made by Antonio Cibotti was inaugurated by the Pope Paul VI in 1973 through a radio impulse, and now many tower bells are radio synchronized to the Central European Time within a single second of accuracy.
From Bell's inequalities to quantum information: a new quantum revolution
CERN. Geneva
2015-01-01
In 1964, John Stuart Bell discovered that it is possible to settle the debate experimentally, by testing the famous "Bell's inequalities", and to show directly that the revolutionary concept of entanglement is indeed a reality. A long series of experiments closer and closer to the ideal scheme presented by Bell has confirmed that entanglement is indeed "a great quantum mystery", to use the words of Feynman. Based on that concept, a new field of research has emerged, quantum information, where one uses quantum bits, the so-called “qubits”, to encode the information and process it. Entanglement ...
Reluctant genius Alexander Graham Bell and the passion for invention
Gray, Charlotte
2011-01-01
The popular image of Alexander Graham Bell is that of an elderly American patriarch, memorable only for his paunch, his Santa Claus beard, and the invention of the telephone. In this magisterial reassessment based on thorough new research, acclaimed biographer Charlotte Gray reveals Bell's wide-ranging passion for invention and delves into the private life that supported his genius. The child of a speech therapist and a deaf mother, and possessed of superbly acute hearing, Bell developed an early interest in sound. His understanding of how sound waves might relate to electrical waves enabled h
Do bells affect behaviour and heart rate variability in grazing dairy cows?
Directory of Open Access Journals (Sweden)
Julia Johns
Full Text Available In alpine regions cows are often equipped with bells. The present study investigated the impact of wearing a bell on behaviour and heart rate variability in dairy cows. Nineteen non-lactating Brown-Swiss cows with bell experience were assigned to three different treatments. For 3 days each, cows were equipped with no bell (control, with a bell with inactivated clapper (silent bell or with a functional bell (functional bell. The bells weighed 5.5 kg and had frequencies between 532 Hz and 2.8 kHz and amplitudes between 90 and 113 dB at a distance of 20 cm. Data were collected on either the first and third or on all 3 days of each treatment. Whereas duration of rumination was reduced with a functional bell and a silent bell compared with no bell, feeding duration was reduced with a silent bell and was intermediate with a functional bell. Head movements were reduced when wearing a silent bell compared with no bell and tended to be reduced when wearing a functional compared to no bell. With a functional bell, lying duration was reduced by almost 4 hours on the third day of treatment compared with the first day with a functional bell and compared with no bell or a silent bell. All additional behavioural measures are consistent with the hypothesis of a restriction in the behaviour of the cows wearing bells, although this pattern did not reach significance. There was no treatment effect on heart rate variability, suggesting that the bells did not affect vago-sympathetic balance. An effect of experimental day was found for only 1 out of 10 behavioural parameters, as shown by a decrease in lying with a functional bell on day 3. The results indicate behavioural changes in the cows wearing a bell over 3 days, without indication of habituation to the bell. Altogether, the behavioural changes suggest that the behaviour of the cows was disturbed by wearing a bell. If long-lasting, these effects may have implications for animal welfare.
Lp-inverse theorem for modified beta operators
Directory of Open Access Journals (Sweden)
V. K. Jain
2003-04-01
Full Text Available We obtain a converse theorem for the linear combinations of modified beta operators whose weight function is the Baskakov operators. To prove our inverse theorem, we use the technique of linear approximating method, namely, Steklov mean.
Application of the residue theorem to bilateral hypergeometric series
Directory of Open Access Journals (Sweden)
Wenchang Chu
2007-12-01
Full Text Available The application of the residue theorem to bilateral hypergeometric series identities is systematically reviewed by exemplifying three classes of summation theorems due to Dougall (1907, Jackson (1949, 1952 and Slater-Lakin (1953.
A duality theorem of crossed coproduct for Hopf algebras
Institute of Scientific and Technical Information of China (English)
王栓宏
1995-01-01
A duality theorem for Hopf crossed coproduct is proved. This theorem plays a role similar to that appearing in the work of Koppinen (which generalized the corresponding results of group grraded ring).
An existence theorem for Volterra integrodifferential equations with infinite delay
Directory of Open Access Journals (Sweden)
Ferenc Izsak
2003-01-01
Full Text Available Using Schauder's fixed point theorem, we prove an existence theorem for Volterra integrodifferential equations with infinite delay. As an appplication, we consider an $n$ species Lotka-Volterra competitive system.
A Note on a Broken-Cycle Theorem for Hypergraphs
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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
Adiabatic limits,vanishing theorems and the noncommutative residue
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
A Dual of the Compression-Expansion Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Henderson Johnny
2007-01-01
Full Text Available This paper presents a dual of the fixed point theorems of compression and expansion of functional type as well as the original Leggett-Williams fixed point theorem. The multi-valued situation is also discussed.
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…
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.…
Crum's Theorem for `Discrete' Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2009-01-01
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in `discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schr\\"odinger equation is a difference equation.
Stokes' theorem, volume growth and parabolicity
Valtorta, Daniele
2010-01-01
We present some new Stokes'type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications to comparison and uniqueness results involving the p-Laplacian are deduced.
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.
An extension theorem for conformal gauge singularities
Tod, Paul
2007-01-01
We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem.
Agreement Theorems in Dynamic-Epistemic Logic
Degremont, Cedric; Roy, Oliver
2012-01-01
This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structure
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].
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 res...
Average sampling theorems for shift invariant subspaces
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.
On the Hardy-Littlewood maximal theorem
Directory of Open Access Journals (Sweden)
Shinji Yamashita
1982-01-01
Full Text Available The Hardy-Littlewood maximal theorem is extended to functions of class PL in the sense of E. F. Beckenbach and T. Radó, with a more precise expression of the absolute constant in the inequality. As applications we deduce some results on hyperbolic Hardy classes in terms of the non-Euclidean hyperbolic distance in the unit disk.
The central limit theorem and chaos
Institute of Scientific and Technical Information of China (English)
NIU Ying-xuan
2009-01-01
Let X be a compact metric space and f : X → X be a continuous map. This paper studies some relationships between stochastic and topological properties of dynamical systems.It is shown that if f satisfies the central limit theorem, then f is topologically ergodic and f is sensitively dependent on initial conditions if and only if f is neither minimal nor equicontinuous.
A Generalized Krein-Rutman Theorem
Zhang, Lei
2016-01-01
A generalized Krein-Rutman theorem for a strongly positive bounded linear operator whose spectral radius is larger than essential spectral radius is established: the spectral radius of the operator is an algebraically simple eigenvalue with strongly positive eigenvector and other eigenvalues are less than the spectral radius.
A non-archimedean Montel's theorem
Favre, Charles; Trucco, Eugenio
2011-01-01
We prove a version of Montel's theorem for analytic functions over a non-archimedean complete valued field. We propose a definition of normal family in this context, and give applications of our results to the dynamics of non-archimedean entire functions.
The Fundamental Theorems of Interval Analysis
van Emden, M. H.; Moa, B.
2007-01-01
Expressions are not functions. Confusing the two concepts or failing to define the function that is computed by an expression weakens the rigour of interval arithmetic. We give such a definition and continue with the required re-statements and proofs of the fundamental theorems of interval arithmetic and interval analysis. Revision Feb. 10, 2009: added reference to and acknowledgement of P. Taylor.
A cosmological no-hair theorem
Chambers, C M; Chris M Chambers; Ian G Moss
1994-01-01
A generalisation of Price's theorem is given for application to Inflationary Cosmologies. Namely, we show that on a Schwarzschild--de Sitter background there are no static solutions to the wave or gravitational perturbation equations for modes with angular momentum greater than their intrinsic spin.
Multiplier theorems for special Hermite expansions on
Institute of Scientific and Technical Information of China (English)
张震球; 郑维行
2000-01-01
The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calderon-Zygmund decomposition. Then the multiplier theorem in Lp(1 < p < ω ) is obtained. The special Hermite expansions in twisted Hardy space are also considered. As an application, the multipli-ers for a certain kind of Laguerre expansions are given in Lp space.
JACKSON‘S THEOREM FOR COMPACT GROUPS
Institute of Scientific and Technical Information of China (English)
H.Vaezi; S.F.Rzaev
2002-01-01
In this article we consider the generalized shift operator defined by (Shuf)(g)=∫Gf(tut-1g)dt on compact group G and by help of this operator we define “Spherical” modulus of continuity.So we prove Stechkin and Jackson type theorems.
Green's Theorem for Generalized Fractional Derivatives
Odzijewicz, Tatiana; Torres, Delfim F M
2012-01-01
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case when the generalized operators are reduced to the standard partial fractional derivatives and fractional integrals in the sense of Riemann-Liouville or Caputo.
SOME REFINEMENTS OF ENESTROM-KAKEYA THEOREM
Institute of Scientific and Technical Information of China (English)
A.Aziz; B.A.Zargar
2007-01-01
In this paper we present certain interesting refinements of a well-known Enestrom-Kakeya theorem in the theory of distribution of zeros of polynomials which among other things also improve upon some results of Aziz and Mohammad, Govil and Rehman and others.
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...
Tennis Rackets and the Parallel Axis Theorem
Christie, Derek
2014-01-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
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...
A non-differentiable Noether's theorem
Cresson, Jacky; Greff, Isabelle
2011-02-01
In the framework of the nondifferentiable embedding of Lagrangian systems, defined by Cresson and Greff [non-dierentiable embedding of lagrangian systems and partial dierential equations. Preprint Max-Plank-Institut für Mathematik in den Naturwissenschaften, Leipzig 16, 26 (2010)], we prove a Noether's theorem based on the lifting of one-parameter groups of diffeomorphisms.
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.
Central Limit Theorem for Coloured Hard Dimers
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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.
Generalization of the Hellmann-Feynman theorem
Energy Technology Data Exchange (ETDEWEB)
Esteve, J.G., E-mail: esteve@unizar.e [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y Fisica de Sistemas complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza (Spain); Falceto, Fernando [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y Fisica de Sistemas complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza (Spain); Garcia Canal, C. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata and IFLP-CONICET (Argentina)
2010-01-25
The well-known Hellmann-Feynman theorem of quantum mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition of the Hamiltonian of the system also depends on that parameter.
Generalizations of Brandl's theorem on Engel length
Quek, S. G.; Wong, K. B.; Wong, P. C.
2013-04-01
Let n Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.
A simpler derivation of the coding theorem
Lomnitz, Yuval
2012-01-01
A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information follow naturally in the proof. It may also be applicable to situations where typicality is not natural.
Norton's theorem for batch routing queueing networks
Bause, Falko; Boucherie, Richard J.; Buchholz, Peter
2001-01-01
This paper shows that the aggregation and decomposition result known as Norton’s theorem for queueing networks can be extended to a general class of batch routing queueing networks with product-form solution that allows for multiple components to simultaneously release and receive (batches of) custo
Bell correlations in a Bose-Einstein condensate.
Schmied, Roman; Bancal, Jean-Daniel; Allard, Baptiste; Fadel, Matteo; Scarani, Valerio; Treutlein, Philipp; Sangouard, Nicolas
2016-04-22
Characterizing many-body systems through the quantum correlations between their constituent particles is a major goal of quantum physics. Although entanglement is routinely observed in many systems, we report here the detection of stronger correlations--Bell correlations--between the spins of about 480 atoms in a Bose-Einstein condensate. We derive a Bell correlation witness from a many-particle Bell inequality involving only one- and two-body correlation functions. Our measurement on a spin-squeezed state exceeds the threshold for Bell correlations by 3.8 standard deviations. Our work shows that the strongest possible nonclassical correlations are experimentally accessible in many-body systems and that they can be revealed by collective measurements.
NOAA Ship Bell M. Shimada Underway Meteorological Data, Quality Controlled
National Oceanic and Atmospheric Administration, Department of Commerce — NOAA Ship Bell M. Shimada Underway Meteorological Data (delayed ~10 days for quality control) are from the Shipboard Automated Meteorological and Oceanographic...
Bell's inequalities; 3, Logical loophole in their formulation
Kracklauer, A F
2000-01-01
In a remarkably insightful pair of papers recently, Sica demonstrated that: dichotomic data that violates Bell's inequalities ``cannot represent any data streams that could possibly exist or be imagined'' if it is to be consistent with the derivation of the inequalities. The present writer maintains, however, that because of quirks in the formulation of Bell's analysis, this statement is, strictly speaking, not correct although the thrust of Sica's analysis remains fundamentally true. Moreover, it is argued that the resolution proposed by Sica for the conflict arising from the fact that real data does violate Bell inequalities, namely that the the functional form of the correlations considered by Bell must be amended, is on physical grounds, untenable. Finally, an alternate resolution is proposed.
Iris Murdoch’s The Bell: Tragedy, Love, and Religion
Directory of Open Access Journals (Sweden)
Kenneth Masong
2008-06-01
Full Text Available The novel begins as follows:"Dora Greenfield left her husband because she was afraid of him. She decided six months later to return to him for the same reason. The absent Paul, haunting her with letters and telephone bells and imagined footsteps on the stairs had begun to be the greater torment. Dora suffered from guilt, and with guilt came fear. She decided at last that the persecution of his presence was to be preferred to the persecution of his absence."Murdoch's novel The Bell is about Imber Court. It is a small Anglican religious community of lay people whose lives were transformed, not just by the arrival of a couple of dissimilar visitors, not just by the arrival of a new bell to be installed at Imber Abbey located beyond the lake, but more significantly by the discovery of a centuries-old bell the story of which is engulfed in a terrible legend.
Subtraction of "accidentals" and the validity of Bell tests
Thompson, C H
1999-01-01
In some key Bell experiments, including two of the well-known ones by Alain Aspect, 1981-2, it is only after the subtraction of ``accidentals'' from the coincidence counts that we get violations of Bell tests. The data adjustment, producing increases of up to 60% in the test statistics, has never been adequately justified. Few published experiments give sufficient information for the reader to make a fair assessment. There is a straightforward and well known realist model that fits the unadjusted data very well. In this paper, the logic of this realist model and the reasoning used by experimenters in justification of the data adjustment are discussed. It is concluded that the evidence from all Bell experiments is in urgent need of re-assessment, in the light of all the known ``loopholes''. Invalid Bell tests have frequently been used, neglecting an improved one derived by Clauser and Horne in 1974. ``Local causal'' explanations for the observations have been wrongfully neglected.
Nonempty intersection theorems in topological spaces with applications
Institute of Scientific and Technical Information of China (English)
Min FANG; Nan-jing HUANG
2009-01-01
In this paper,we establish some new nonempty intersection theorems for generalized L-KKM mappings and prove some new fixed point theorems for set-valued mappings under suitable conditions in topological spaces.As applications,an existence theorem for an equilibrium problem with lower and upper bounds and two existence theorems for a quasi-equilibrium problem with lower and upper bounds are obtained in topological spaces.Our results generalize some known results in the literature.
Two Theorems on Calculating the Relative Entropy of Entanglement
Institute of Scientific and Technical Information of China (English)
WU Sheng-Jun; ZHANG Yong-De; WU Qiang
2001-01-01
We present two theorems on calculating the relative entropy of entanglement. Theorem 1 is an extension of Vedral and Plenio's theorem (Phys. Rev. A 57 (1998) 1619) for pure states, which is useful for calculating the relative entropy of entanglement for all pure states as well as for a class of mixed states. Theorem 2 gives the relative entropy of entanglement for any bipartite state whose tripartite purification has two separable reduced bipartite states.
Ehrenfest theorem, Galilean invariance and nonlinear Schr"odinger equations
Kälbermann, G
2003-01-01
Galilean invariant Schr"odinger equations possessing nonlinear terms coupling the amplitude and the phase of the wave function can violate the Ehrenfest theorem. An example of this kind is provided. The example leads to the proof of the theorem: A Galilean invariant Schr"odinger equation derived from a lagrangian density obeys the Ehrenfest theorem. The theorem holds for any linear or nonlinear lagrangian.
Characterization of the Bell-Shaped Vibratory Angular Rate Gyro
Directory of Open Access Journals (Sweden)
Junfang Fan
2013-08-01
Full Text Available The bell-shaped vibratory angular rate gyro (abbreviated as BVG is a novel shell vibratory gyroscope, which is inspired by the Chinese traditional bell. It sensitizes angular velocity through the standing wave precession effect. The bell-shaped resonator is a core component of the BVG and looks like the millimeter-grade Chinese traditional bell, such as QianLong Bell and Yongle Bell. It is made of Ni43CrTi, which is a constant modulus alloy. The exciting element, control element and detection element are uniformly distributed and attached to the resonator, respectively. This work presents the design, analysis and experimentation on the BVG. It is most important to analyze the vibratory character of the bell-shaped resonator. The strain equation, internal force and the resonator's equilibrium differential equation are derived in the orthogonal curvilinear coordinate system. When the input angular velocity is existent on the sensitive axis, an analysis of the vibratory character is performed using the theory of thin shells. On this basis, the mode shape function and the simplified second order normal vibration mode dynamical equation are obtained. The coriolis coupling relationship about the primary mode and secondary mode is established. The methods of the signal processing and control loop are presented. Analyzing the impact resistance property of the bell-shaped resonator, which is compared with other shell resonators using the Finite Element Method, demonstrates that BVG has the advantage of a better impact resistance property. A reasonable means of installation and a prototypal gyro are designed. The gyroscopic effect of the BVG is characterized through experiments. Experimental results show that the BVG has not only the advantages of low cost, low power, long work life, high sensitivity, and so on, but, also, of a simple structure and a better impact resistance property for low and medium angular velocity measurements.
Chladni's law and the modern English church bell
Perrin, R.; Charnley, T.; Banu, H.; Rossing, T. D.
1985-09-01
Extensive previously reported experimental data on the normal modes of an English church bell is analyzed with use of a modified version of Chladni's law. Excellent fits are obtained in almost every case provided certain conditions, for which a theoretical basis is presented, are satisfied. Some conclusions are drawn about the validity of a previously proposed theory of mode production mechanisms for the church bell.
The Effect of Hominis Placenta Herbal Acupuncture on Bell's palsy
2000-01-01
This report was done to observe the effect of Hominis placenta herbal acupuncture on Bell's palsy. The study group comprised 16 patients who arrived at Woo-suk university oriental hospital from January, 1999 till January, 2000 for Bell's palsy. All patients were divided into two group. One was herbal acupunture group, and the other was control group. Acupunture group was done herbal acupuncture therapy on the facial acupuncture points. Followings are achievement and a term of each group. I...
Hugh Blairs Lectures on Rhetoric and Belles Lettres
DEFF Research Database (Denmark)
Schatz-Jakobsen, Claus
1989-01-01
Artiklen nærlæser dekonstruktivt dele af den skotske retorikprofessor Hugh Blairs Lecures on Rhetoric and Belles Lettres (1783) og påviser splittelsen mellem to vidt forskellige retorik- og liltteraturhistoriske interesser, neoklassicistiske vs. romantiske.......Artiklen nærlæser dekonstruktivt dele af den skotske retorikprofessor Hugh Blairs Lecures on Rhetoric and Belles Lettres (1783) og påviser splittelsen mellem to vidt forskellige retorik- og liltteraturhistoriske interesser, neoklassicistiske vs. romantiske....
Bell tests with arbitrarily low photodetection efficiency and homodyne measurements
Araújo, Mateus; Cavalcanti, Daniel; Santos, Marcelo França; Cabello, Adán; Cunha, Marcelo Terra
2011-01-01
We show that hybrid local measurements combining homodyne measurements and photodetection provide violations of a Bell inequality with arbitrarily low photodetection efficiency. This is shown in two different scenarios: when one part receives an atom entangled to the field mode to be measured by the other part and when both parts make similar photonic measurements. Our findings definitely put the hybrid measurement scenario as a strong candidate for the implementation of a loophole-free Bell test.
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.
Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
von Neumann, John
2010-01-01
It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way, the ergodic theorem and the H-theorem are formulated and proven (without "assumptions of disorder"), followed by a discussion of the physical meaning of the mathematical conditions characterizing their domain of validity.
A Simple Geometrical Derivation of the Spatial Averaging Theorem.
Whitaker, Stephen
1985-01-01
The connection between single phase transport phenomena and multiphase transport phenomena is easily accomplished by means of the spatial averaging theorem. Although different routes to the theorem have been used, this paper provides a route to the averaging theorem that can be used in undergraduate classes. (JN)
A remark on Kov\\'acs' vanishing theorem
Fujino, Osamu
2012-01-01
We give an alternative proof of Kov\\'acs' vanishing theorem. Our proof is based on the standard arguments of the minimal model theory. We do not need the notion of Du Bois pairs. We reduce Kov\\'acs' vanishing theorem to the well-known relative Kawamata--Viehweg--Nadel vanishing theorem.
ON COLLECTIVELY FIXED POINT THEOREMS ON FC-SPACES
Institute of Scientific and Technical Information of China (English)
Yongjie Piao
2010-01-01
Based on a KKM type theorem on FC-space,some new fixed point theorems for Fan-Browder type are established,and then some collectively fixed point theorems for a family of Φ-maps defined on product space of FC-spaees are given.These results generalize and improve many corresponding results.
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
Effects of Bell Speed and Flow Rate on Evaporation of Water Spray from a Rotary Bell Atomizer
Directory of Open Access Journals (Sweden)
Rajan Ray
2015-05-01
Full Text Available A phase doppler anemometer (PDA was used to determine the effects of evaporation on water spray for three rotary bell atomizer operational variable parameters: shaping air, bell speed and liquid flow. Shaping air was set at either 200 standard liters per minute (L/min or 300 L/min, bell speed was set to 30, 40 or 50 thousand rotations per minute (krpm and water flow rate was varied between 100, 200 or 300 cubic centimeters per minute (cm3/min. The total evaporation between 22.5 and 37.5 cm from the atomizer (cm3/s was calculated for all the combinations of those variables. Evaporation rate increased with higher flow rate and bell speed but no statistically significant effects were obtained for variable shaping air on interactions between parameters.
The Belle II SVD data readout system
Thalmeier, R.; Adamczyk, K.; Aihara, H.; Angelini, C.; Aziz, T.; Babu, V.; Bacher, S.; Bahinipati, S.; Barberio, E.; Baroncelli, Ti.; Baroncelli, To.; Basith, A. K.; Batignani, G.; Bauer, A.; Behera, P. K.; Bergauer, T.; Bettarini, S.; Bhuyan, B.; Bilka, T.; Bosi, F.; Bosisio, L.; Bozek, A.; Buchsteiner, F.; Bulla, L.; Casarosa, G.; Ceccanti, M.; Cervenkov, D.; Chendvankar, S. R.; Dash, N.; Divekar, S. T.; Doleźal, Z.; Dutta, D.; Forti, F.; Friedl, M.; Hara, K.; Higuchi, T.; Horiguchi, T.; Irmler, C.; Ishikawa, A.; Jeon, H. B.; Joo, C.; Kandra, J.; Kang, K. H.; Kato, E.; Kawasaki, T.; Kodyś, P.; Kohriki, T.; Koike, S.; Kolwalkar, M. M.; Kvasnićka, P.; Lanceri, L.; Lettenbicher, J.; Lueck, T.; Maki, M.; Mammini, P.; Mayekar, S. N.; Mohanty, G. B.; Mohanty, S.; Morii, T.; Nakamura, K. R.; Natkaniec, Z.; Negishi, K.; Nisar, N. K.; Onuki, Y.; Ostrowicz, W.; Paladino, A.; Paoloni, E.; Park, H.; Pilo, F.; Profeti, A.; Rao, K. K.; Rashevskaya, I.; Rizzo, G.; Rozanska, M.; Sasaki, J.; Sato, N.; Schultschik, S.; Schwanda, C.; Seino, Y.; Shimizu, N.; Stypula, J.; Suzuki, J.; Tanaka, S.; Tanida, K.; Taylor, G. N.; Thomas, R.; Tsuboyama, T.; Uozumi, S.; Urquijo, P.; Vitale, L.; Watanuki, S.; Watson, I. J.; Webb, J.; Wiechczynski, J.; Williams, S.; Würkner, B.; Yamamoto, H.; Yin, H.; Yoshinobu, T.
2017-02-01
The Belle II Experiment at the High Energy Accelerator Research Organization (KEK) in Tsukuba, Japan, will explore the asymmetry between matter and antimatter and search for new physics beyond the standard model. 172 double-sided silicon strip detectors are arranged cylindrically in four layers around the collision point to be part of a system which measures the tracks of the collision products of electrons and positrons. A total of 1748 radiation-hard APV25 chips read out 128 silicon strips each and send the analog signals by time-division multiplexing out of the radiation zone to 48 Flash Analog Digital Converter Modules (FADC). Each of them applies processing to the data; for example, it uses a digital finite impulse response filter to compensate line signal distortions, and it extracts the peak timing and amplitude from a set of several data points for each hit, using a neural network. We present an overview of the SVD data readout system, along with front-end electronics, cabling, power supplies and data processing.
Parameterized quantum field theory without Haag's theorem
Seidewitz, Ed
2015-01-01
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that quantum field theory can be formulated, using an invariant, fifth path parameter in addition to the usual four position parameters, in such a way that Haag's theorem no longer applies, but such that the Dyson perturbation expansion for the sc...
De Finetti theorems for easy quantum groups
Banica, Teodor; Speicher, Roland
2009-01-01
We study sequences of noncommutative random variables which are invariant under "quantum transformations" coming from an orthogonal quantum group satisfying the "easiness" condition axiomatized in our previous paper. For 10 easy quantum groups, we obtain de Finetti type theorems characterizing the joint distribution of any infinite, quantum invariant sequence. In particular, we give a new and unified proof of the classical results of de Finetti and Freedman for the easy groups S_n, O_n, which is based on the combinatorial theory of cumulants. We also recover the free de Finetti theorem of K\\"ostler and Speicher, and the characterization of operator-valued free semicircular families due to Curran. We consider also finite sequences, and prove an approximation result in the spirit of Diaconis and Freedman.
A noncommutative extended de Finetti theorem
Köstler, Claus
2008-01-01
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is a noncommutative version of this theorem. In contrast to the classical result of Ryll-Nadzewski, exchangeability turns out to be stronger than spreadability for infinite noncommutative random sequences. Out of our investigations emerges noncommutative conditional independence in terms of a von Neumann algebraic structure closely related to Popa's notion of commuting squares and K\\"ummerer's generalized Bernoulli shifts. Our main result is applicable to classical probability, quantum probability, in particular free probability, braid group representations and Jones subfactors.
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.
2016-09-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
Noether theorem for {mu}-symmetries
Energy Technology Data Exchange (ETDEWEB)
Cicogna, Giampaolo [Dipartimento di Fisica, Universita di Pisa and INFN, Sezione di Pisa, Largo B Pontecorvo 3, 50127 Pisa (Italy); Gaeta, Giuseppe [Dipartimento di Matematica, Universita di Milano, via Saldini 50, 20133 Milano (Italy)
2007-09-28
We give a version of Noether theorem adapted to the framework of {mu}-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of {lambda}-symmetries, and connects {mu}-symmetries of a Lagrangian to a suitably modified conservation law. In some cases this '{mu}-conservation law' actually reduces to a standard one; we also note a relation between {mu}-symmetries and conditional invariants. We also consider the case where the variational principle is itself formulated as requiring vanishing variation under {mu}-prolonged variation fields, leading to modified Euler-Lagrange equations. In this setting, {mu}-symmetries of the Lagrangian correspond to standard conservation laws as in the standard Noether theorem. We finally propose some applications and examples.
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.
Wigner-Eckart theorem for induced symmetries
Energy Technology Data Exchange (ETDEWEB)
Klein, D.J. (Texas A and M University, Galveston (USA). Department of Marine Sciences); Seligman, T.H. (Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Fisica)
1982-01-01
A unified treatment is given for all group-theoretic problems arising from the evaluation of matrix elements involving operators and states of induced symmetries. To achieve this general treatment two group-theoretic theorems are proven, the first characterizing recoupling coefficients between different symmetry adaptation schemes, and the second making a double coset factorization of a group algebraic matrix basis element. A number of problems previously discussed in the literature, including the conventional Wigner-Eckart theorem and more recent double coset expansions of matrix elements, are realized as special cases in the present treatment. These results entail two new types of recoupling coefficients, namely DC coefficients and 3-symmetry symbols, so that some of their properties are indicated.
Locomotion in complex fluids: Integral theorems
Lauga, Eric
2014-01-01
The biological fluids encountered by self-propelled cells display complex microstructures and rheology. We consider here the general problem of low-Reynolds number locomotion in a complex fluid. {Building on classical work on the transport of particles in viscoelastic fluids,} we demonstrate how to mathematically derive three integral theorems relating the arbitrary motion of an isolated organism to its swimming kinematics {in a non-Newtonian fluid}. These theorems correspond to three situations of interest, namely (1) squirming motion in a linear viscoelastic fluid, (2) arbitrary surface deformation in a weakly non-Newtonian fluid, and (3) small-amplitude deformation in an arbitrarily non-Newtonian fluid. Our final results, valid for a wide-class of {swimmer geometry,} surface kinematics and constitutive models, at most require mathematical knowledge of a series of Newtonian flow problems, and will be useful to quantity the locomotion of biological and synthetic swimmers in complex environments.
An Equivalent Gauge and the Equivalence Theorem
Wulzer, Andrea
2014-01-01
I describe a novel covariant formulation of massive gauge theories in which the longitudinal polarization vectors do not grow with the energy. Therefore in the present formalism, differently from the ordinary one, the energy and coupling power-counting is completely transparent at the level of individual Feynman diagrams, with obvious advantages both at the conceptual and practical level. Since power-counting is transparent, the high-energy limit of the amplitudes involving longitudinal particles is immediately taken, and the Equivalence Theorem is easily demonstrated at all orders in perturbation theory. Since the formalism makes the Equivalence Theorem self-evident, and because it is based on a suitable choice of the gauge, we can call it an "Equivalent Gauge".
Generalized Sampling Theorem for Bandpass Signals
Directory of Open Access Journals (Sweden)
Prokes Ales
2006-01-01
Full Text Available The reconstruction of an unknown continuously defined function from the samples of the responses of linear time-invariant (LTI systems sampled by the th Nyquist rate is the aim of the generalized sampling. Papoulis (1977 provided an elegant solution for the case where is a band-limited function with finite energy and the sampling rate is equal to times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.
Generalized Sampling Theorem for Bandpass Signals
Prokes, Ales
2006-12-01
The reconstruction of an unknown continuously defined function[InlineEquation not available: see fulltext.] from the samples of the responses of[InlineEquation not available: see fulltext.] linear time-invariant (LTI) systems sampled by the[InlineEquation not available: see fulltext.]th Nyquist rate is the aim of the generalized sampling. Papoulis (1977) provided an elegant solution for the case where[InlineEquation not available: see fulltext.] is a band-limited function with finite energy and the sampling rate is equal to[InlineEquation not available: see fulltext.] times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST) for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.
Fluctuation theorem for constrained equilibrium systems
Gilbert, Thomas; Dorfman, J. Robert
2006-02-01
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.
Simultaneous DOA estimation based on Kolmogorov's theorem
Nájar Martón, Montserrat; Lagunas Hernandez, Miguel A.
1993-01-01
The design of a new architecture for signal processing, based on the Kolmogorov's theorem (1957), is addressed. This architecture is applied to solve the problem of source separation. Particularly, an adaptive algorithm is proposed to separate simultaneously all the unknown impinging sources on an aperture of sensors. The implemented framework is composed of two different stages: the first one is the inhibition stage, which turns the problem of estimating simultaneous DOAs (directions of arri...
Hildebrandt's theorem for the essential spectrum
Directory of Open Access Journals (Sweden)
Janko Bračič
2015-01-01
Full Text Available We prove a variant of Hildebrandt's theorem which asserts that the convex hull of the essential spectrum of an operator \\(A\\ on a complex Hilbert space is equal to the intersection of the essential numerical ranges of operators which are similar to \\(A\\. As a consequence, it is given a necessary and sufficient condition for zero not being in the convex hull of the essential spectrum of \\(A\\.
A Central Limit Theorem for Repeating Patterns
Abrams, Aaron; Landau, Henry; Landau, Zeph; Pommersheim, James
2012-01-01
This note gives a central limit theorem for the length of the longest subsequence of a random permutation which follows some repeating pattern. This includes the case of any fixed pattern of ups and downs which has at least one of each, such as the alternating case considered by Stanley in [2] and Widom in [3]. In every case considered the convergence in the limit of long permutations is to normal with mean and variance linear in the length of the permutations.
Theorems for Asymptotic Safety of Gauge Theories
Bond, Andrew D
2016-01-01
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasized. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.
Resource Adaptive Agents in Interactive Theorem Proving
Benzmueller, Christoph
2009-01-01
We introduce a resource adaptive agent mechanism which supports the user in interactive theorem proving. The mechanism uses a two layered architecture of agent societies to suggest appropriate commands together with possible command argument instantiations. Experiments with this approach show that its effectiveness can be further improved by introducing a resource concept. In this paper we provide an abstract view on the overall mechanism, motivate the necessity of an appropriate resource concept and discuss its realization within the agent architecture.
Reciprocity Theorems for Ab Initio Force Calculations
Wei, C; Mele, E J; Rappe, A M; Lewis, Steven P.; Rappe, Andrew M.
1996-01-01
We present a method for calculating ab initio interatomic forces which scales quadratically with the size of the system and provides a physically transparent representation of the force in terms of the spatial variation of the electronic charge density. The method is based on a reciprocity theorem for evaluating an effective potential acting on a charged ion in the core of each atom. We illustrate the method with calculations for diatomic molecules.
On the equivalence theorem for integrable systems
Melikyan, A; Rivelles, V O
2014-01-01
We investigate the equivalence theorem for integrable systems using two formulations of the Alday-Arutyunov-Frolov model. We show that the S-matrix is invariant under the field transformation which reduces the non-linear Dirac brackets of one formulation into the standard commutation relations in the second formulation. We also explain how to perform the direct diagonalization of the transformed Hamiltonian by constructing the states corresponding to self-adjoint extensions.
Hyperplane arrangements and Lefschetz's hyperplane section theorem
Yoshinaga, Masahiko
2005-01-01
The Lefschetz hyperplane section theorem asserts that a complex affine variety is homotopy equivalent to a space obtained from its generic hyperplane section by attaching some cells. The purpose of this paper is to give an explicit description of attaching maps of these cells for the complement of a complex hyperplane arrangement defined over real numbers. The cells and attaching maps are described in combinatorial terms of chambers. We also discuss the cellular chain complex with coefficient...
Bezout's theorem and Cohen-Macaulay modules
1999-01-01
We define very proper intersections of modules and projective subschemes. It turns out that equidimensional locally Cohen-Macaulay modules intersect very properly if and only if they intersect properly. We prove a Bezout theorem for modules which meet very properly. Furthermore, we show for equidimensional subschemes $X$ and $Y$: If they intersect properly in an arithmetically Cohen-Macaulay subscheme of positive dimension then $X$ and $Y$ are arithmetically Cohen-Macaulay. The module version...
Carnot's theorem and Szil\\'ard engine
Shu, Liangsuo; Huang, Suyi; Jin, Shiping
2016-01-01
In this work, the relationship between Carnot engine and Szil\\'ard engine was discussed. By defining the available information about the temperature difference between two heat reservoirs, the Carnot engine was found to have a same physical essence with Szil\\'ard engine: lossless conversion of available information. Thus, a generalized Carnot's theorem for wider scope of application can be described as "all the available information is 100% coded into work".
Volume Integral Theorem for Exotic Matter
Nandi, Kamal Kanti; Zhang, Yuan-Zhong; Kumar, K. B. Vijaya
2004-01-01
We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported ...
The "Nernst Theorem" and Black Hole Thermodynamics
Wald, R M
1997-01-01
The Nernst formulation of the third law of ordinary thermodynamics (often referred to as the ``Nernst theorem'') asserts that the entropy, $S$, of a system must go to zero (or a ``universal constant'') as its temperature, $T$, goes to zero. This assertion is commonly considered to be a fundamental law of thermodynamics. As such, it seems to spoil the otherwise perfect analogy between the ordinary laws of thermodynamics and the laws of black hole mechanics, since rotating black holes in general relativity do not satisfy the analog of the ``Nernst theorem''. The main purpose of this paper is to attempt to lay to rest the ``Nernst theorem'' as a law of thermodynamics. We consider a boson (or fermion) ideal gas with its total angular momentum, $J$, as an additional state parameter, and we analyze the conditions on the single particle density of states, $g(\\epsilon,j)$, needed for the Nernst formulation of the third law to hold. (Here, $\\epsilon$ and $j$ denote the single particle energy and angular momentum.) Alt...
Haag's Theorem and Parameterized Quantum Field Theory
Seidewitz, Edwin
2017-01-01
``Haag's theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction''. In traditional quantum field theory (QFT), Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. But the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field, but which must still account for interactions. So, the usual derivation of the scattering matrix in QFT is mathematically ill defined. Nevertheless, perturbative QFT is currently the only practical approach for addressing realistic scattering, and it has been very successful in making empirical predictions. This success can be understood through an alternative derivation of the Dyson series in a covariant formulation of QFT using an invariant, fifth path parameter in addition to the usual four position parameters. The parameterization provides an additional degree of freedom that allows Haag's Theorem to be avoided, permitting the consistent use of a form of interaction picture in deriving the Dyson expansion. The extra symmetry so introduced is then broken by the choice of an interacting vacuum.
Authentication of bell peppers using boron and strontium isotope compositions
Rosner, Martin; Pritzkow, Wolfgang; Vogl, Jochen; Voerkelius, Susanne
2010-05-01
The wrong declaration of food in terms of geographical origin and production method is a major problem for the individual consumer and public regulatory authorities. The authentication of food matrices using H-C-N-O-S isotopic compositions is already well established. However, specific questions require additional isotopic systems, which are more diagonstic for the source reservoires involved or production methods used. Here we present B and Sr isotopic compositions of bell peppers from Europe (Germany, Austria, Netherlands, Spain) and Israel to verfiy their origin. The bell peppers' B isotopic compositions between different locations are highly variable (d11BNISTSRM951 -8 to +35 ‰), whereas the 87Sr/86Sr ratios are all close to modern seawater Sr isotopic composition of about 0.7092 (0.7078 to 0.7107), but still can reliably be distinguished. Distinct isotopically heavy and light B isotopic fingerprints are obtained for bell peppers from Israel and the Netherlands. Samples from Germany, Austria, and Spain display overlapping d11B values between 0 and +12 ‰. Bell peppers from Israel show high d11B values (+28 to +35 ‰) combined with 87Sr/86Sr ratios slightly more unradiogenic than modern seawater (ca 0.7079). Bell peppers from the Netherlands, however, show low d11B values (-8 ‰) combinded with 87Sr/86Sr ratios of modern seawater (approx. 0.7085). Mainly based on diagnostic B isotopic compositions bell peppers from Israel and the Netherlands can be related to a specific geographical growing environment (Israel) or production method (Netherlands). The isotope fingerprints of bell peppers from the Netherlands are consistent with growing conditions in greenhouses typical for the Netherlands vegetable farming. Using optimized production methods crops in greenhouses were supplied with nutritients by liquid fertilizers on artificial substrates. As most fertilizers derive from non-marine salt deposits, fertilization typically imprints invariant d11B values close
A theoretical study of the vibration and acoustics of ancient Chinese bells.
Jing, M
2003-09-01
In this paper, the acoustics of an ancient Chinese bell, which was made some 3000 years B.C., is studied theoretically. In ancient times, a set of the bells was used as a musical instrument. Unlike a western church bell and an ancient Indian bell, an ancient Chinese bell has two interesting acoustics. First, two tones can be heard separately as the bell is struck at two special points. The interval between the two pitches is always a minor or major third. Second, tones of the bell attenuate quickly, which is necessary for a musical instrument. So, an ancient Chinese bell is sometimes called a two-tone bell or a music bell. Although a three-dimensional model should be used to simulate the acoustics of the bell, a simplified model proposed in this paper does give some insight. Based on the lens-shaped cross section of an ancient Chinese bell, two tones of an ancient Chinese bell can be simulated by the vibration of a double-circular arch and the quick attenuation of tones can be simulated by acoustics of a cylinder with the lens-shaped cross section like a double-circular arch. Numerical results on the vibration and acoustics of the models are presented.
The Belle II DEPFET pixel detector
Energy Technology Data Exchange (ETDEWEB)
Moser, Hans-Günther, E-mail: moser@mpp.mpg.de
2016-09-21
The Belle II experiment at KEK (Tsukuba, Japan) will explore heavy flavour physics (B, charm and tau) at the starting of 2018 with unprecedented precision. Charged particles are tracked by a two-layer DEPFET pixel device (PXD), a four-layer silicon strip detector (SVD) and the central drift chamber (CDC). The PXD will consist of two layers at radii of 14 mm and 22 mm with 8 and 12 ladders, respectively. The pixel sizes will vary, between 50 μm×(55–60) μm in the first layer and between 50 μm×(70–85) μm in the second layer, to optimize the charge sharing efficiency. These innermost layers have to cope with high background occupancy, high radiation and must have minimal material to reduce multiple scattering. These challenges are met using the DEPFET technology. Each pixel is a FET integrated on a fully depleted silicon bulk. The signal charge collected in the ‘internal gate’ modulates the FET current resulting in a first stage amplification and therefore very low noise. This allows very thin sensors (75 μm) reducing the overall material budget of the detector (0.21% X{sub 0}). Four fold multiplexing of the column parallel readout allows read out a full frame of the pixel matrix in only 20 μs while keeping the power consumption low enough for air cooling. Only the active electronics outside the detector acceptance has to be cooled actively with a two phase CO{sub 2} system. Furthermore the DEPFET technology offers the unique feature of an electronic shutter which allows the detector to operate efficiently in the continuous injection mode of superKEKB.
How Bell Labs creates star performers.
Kelley, R; Caplan, J
1993-01-01
How can managers increase the productivity of professionals when most of their work goes on inside their heads? Robert Kelley and Janet Caplan believe that defining the difference between star performers and average workers is the answer. Many managers assume that top performers are just smarter. But the authors' research at the Bell Laboratories Switching Systems Business Unit (SSBU) has revealed that the real difference between stars and average workers is not IQ but the ways top performers do their jobs. Their study has led to a training program based on the strategies of star performers. The SSBU training program, known as the Productivity Enhancement Group (PEG), uses an expert model to demystify productivity. The star engineers selected to develop the expert model identified and ranked nine work strategies, such as taking initiative, networking, and self-management. Middle performers were also asked what makes for top-quality work, but their definitions and ranking of the strategies differed significantly from those of the top performers. Taking initiative, for example, meant something very different to an average worker than it did to a star. And for the middle performers, the ability to give good presentations was a core strategy, while it was peripheral for the top engineers. Once PEG got underway, respected engineers ran the training sessions, which included case studies, work-related exercises, and frank discussion. The benefits of the program were striking: participants and managers reported substantial productivity increases in both star and average performers. The PEG program may not be a blueprint for other companies, but its message is clear: managers must focus on people, not on technology, to increase productivity in the knowledge economy.
The Belle II DEPFET pixel detector
Moser, Hans-Günther
2016-09-01
The Belle II experiment at KEK (Tsukuba, Japan) will explore heavy flavour physics (B, charm and tau) at the starting of 2018 with unprecedented precision. Charged particles are tracked by a two-layer DEPFET pixel device (PXD), a four-layer silicon strip detector (SVD) and the central drift chamber (CDC). The PXD will consist of two layers at radii of 14 mm and 22 mm with 8 and 12 ladders, respectively. The pixel sizes will vary, between 50 μm×(55-60) μm in the first layer and between 50 μm×(70-85) μm in the second layer, to optimize the charge sharing efficiency. These innermost layers have to cope with high background occupancy, high radiation and must have minimal material to reduce multiple scattering. These challenges are met using the DEPFET technology. Each pixel is a FET integrated on a fully depleted silicon bulk. The signal charge collected in the 'internal gate' modulates the FET current resulting in a first stage amplification and therefore very low noise. This allows very thin sensors (75 μm) reducing the overall material budget of the detector (0.21% X0). Four fold multiplexing of the column parallel readout allows read out a full frame of the pixel matrix in only 20 μs while keeping the power consumption low enough for air cooling. Only the active electronics outside the detector acceptance has to be cooled actively with a two phase CO2 system. Furthermore the DEPFET technology offers the unique feature of an electronic shutter which allows the detector to operate efficiently in the continuous injection mode of superKEKB.
Chemical reactions modulated by mechanical stress: extended Bell theory.
Konda, Sai Sriharsha M; Brantley, Johnathan N; Bielawski, Christopher W; Makarov, Dmitrii E
2011-10-28
A number of recent studies have shown that mechanical stress can significantly lower or raise the activation barrier of a chemical reaction. Within a common approximation due to Bell [Science 200, 618 (1978)], this barrier is linearly dependent on the applied force. A simple extension of Bell's theory that includes higher order corrections in the force predicts that the force-induced change in the activation energy will be given by -FΔR - ΔχF(2)∕2. Here, ΔR is the change of the distance between the atoms, at which the force F is applied, from the reactant to the transition state, and Δχ is the corresponding change in the mechanical compliance of the molecule. Application of this formula to the electrocyclic ring-opening of cis and trans 1,2-dimethylbenzocyclobutene shows that this extension of Bell's theory essentially recovers the force dependence of the barrier, while the original Bell formula exhibits significant errors. Because the extended Bell theory avoids explicit inclusion of the mechanical stress or strain in electronic structure calculations, it allows a computationally efficient characterization of the effect of mechanical forces on chemical processes. That is, the mechanical susceptibility of any reaction pathway is described in terms of two parameters, ΔR and Δχ, both readily computable at zero force.
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
Belle II early physics program of bottomonium spectroscopy
Ye, Hua
2016-01-01
The Belle II experiment at the SuperKEKB collider is a major upgrade of the KEK "$B$ factory" facility in Tsukuba, Japan. Phase 1 commissioning of the main ring of SuperKEKB has started in February 2016 and first physics data will be recorded in 2017 during the so-called Phase 2 commissioning, when the partial Belle II detector will be operated still without its vertex detector. In 2018, the full Belle II detector will be rolled in and physics run will start. In this proceeding, a possible physics program for this early data run at different center-of-mass energies is described, in particular at the $\\Upsilon(3S)$ and $\\Upsilon(6S)$ resonances, amongst other energy points.
Experimental violation of Bell inequalities for multi-dimensional systems
Lo, Hsin-Pin; Yabushita, Atsushi; Chen, Yueh-Nan; Luo, Chih-Wei; Kobayashi, Takayoshi
2016-01-01
Quantum correlations between spatially separated parts of a $d$-dimensional bipartite system ($d\\geq 2$) have no classical analog. Such correlations, also called entanglements, are not only conceptually important, but also have a profound impact on information science. In theory the violation of Bell inequalities based on local realistic theories for $d$-dimensional systems provides evidence of quantum nonlocality. Experimental verification is required to confirm whether a quantum system of extremely large dimension can possess this feature, however it has never been performed for large dimension (e.g., $d\\geq 1000$). Here, we report that Bell inequalities are experimentally violated for bipartite quantum systems of extremely high dimensionality with the usual ensembles of polarization-entangled photon pairs. Our entanglement source violates Bell inequalities for extremely high dimensionality of $d>4000$. The designed scenario offers a possible new method to investigate the entanglement of multipartite system...
Violation of Bell inequality based on S4 symmetry
Bolonek-Lasoń, Katarzyna
2016-08-01
In two recent papers [Phys. Rev. A 90, 062121 (2014), 10.1103/PhysRevA.90.062121 and Phys. Rev. A, 91, 052110 (2015), 10.1103/PhysRevA.91.052110] an interesting method of analyzing the violation of Bell inequalities has been proposed which is based on the theory of finite group representations. Here we apply this method to more complicated examples of S4 symmetry. We show how the Bell inequality can be related to the symmetries of regular tetrahedron. By choosing the orbits of three-dimensional representations of S4 determined by the geometry of tetrahedron we find that the Bell inequality under consideration is violated in quantum theory. The corresponding nonlocal game is analyzed.
Belle II SVD ladder assembly procedure and electrical qualification
Adamczyk, K.; Aihara, H.; Angelini, C.; Aziz, T.; Babu, Varghese; Bacher, S.; Bahinipati, S.; Barberio, E.; Baroncelli, T.; Basith, A. K.; Batignani, G.; Bauer, A.; Behera, P. K.; Bergauer, T.; Bettarini, S.; Bhuyan, B.; Bilka, T.; Bosi, F.; Bosisio, L.; Bozek, A.; Buchsteiner, F.; Casarosa, G.; Ceccanti, M.; Červenkov, D.; Chendvankar, S. R.; Dash, N.; Divekar, S. T.; Doležal, Z.; Dutta, D.; Forti, F.; Friedl, M.; Hara, K.; Higuchi, T.; Horiguchi, T.; Irmler, C.; Ishikawa, A.; Jeon, H. B.; Joo, C.; Kandra, J.; Kang, K. H.; Kato, E.; Kawasaki, T.; Kodyš, P.; Kohriki, T.; Koike, S.; Kolwalkar, M. M.; Kvasnička, P.; Lanceri, L.; Lettenbicher, J.; Mammini, P.; Mayekar, S. N.; Mohanty, G. B.; Mohanty, S.; Morii, T.; Nakamura, K. R.; Natkaniec, Z.; Negishi, K.; Nisar, N. K.; Onuki, Y.; Ostrowicz, W.; Paladino, A.; Paoloni, E.; Park, H.; Pilo, F.; Profeti, A.; Rao, K. K.; Rashevskaya, I.; Rizzo, G.; Rozanska, M.; Sandilya, S.; Sasaki, J.; Sato, N.; Schultschik, S.; Schwanda, C.; Seino, Y.; Shimizu, N.; Stypula, J.; Tanaka, S.; Tanida, K.; Taylor, G. N.; Thalmeier, R.; Thomas, R.; Tsuboyama, T.; Uozumi, S.; Urquijo, P.; Vitale, L.; Volpi, M.; Watanuki, S.; Watson, I. J.; Webb, J.; Wiechczynski, J.; Williams, S.; Würkner, B.; Yamamoto, H.; Yin, H.; Yoshinobu, T.
2016-07-01
The Belle II experiment at the SuperKEKB asymmetric e+e- collider in Japan will operate at a luminosity approximately 50 times larger than its predecessor (Belle). At its heart lies a six-layer vertex detector comprising two layers of pixelated silicon detectors (PXD) and four layers of double-sided silicon microstrip detectors (SVD). One of the key measurements for Belle II is time-dependent CP violation asymmetry, which hinges on a precise charged-track vertex determination. Towards this goal, a proper assembly of the SVD components with precise alignment ought to be performed and the geometrical tolerances should be checked to fall within the design limits. We present an overview of the assembly procedure that is being followed, which includes the precision gluing of the SVD module components, wire-bonding of the various electrical components, and precision three dimensional coordinate measurements of the jigs used in assembly as well as of the final SVD modules.
Bell's inequalities with realistic noise for polarization-entangled photons
Cabello, A; Lamas-Linares, A; Cabello, Adan; Feito, Alvaro; Lamas-Linares, Antia
2005-01-01
Contrary to the usual assumption that the experimental preparation of pure entangled states can be described by mixed states due to white noise, a more realistic description for polarization-entangled states produced by parametric down-conversion is that they are mixed states due to decoherence in a preferred polarization basis. This distinction between white and colored noise is crucial when we look for maximal violations of Bell's inequalities for two-qubit and two-qutrit entangled states. We find that violations of Bell's inequalities with realistic noise for polarization-entangled photons are extremely robust for colored noise, whereas this is not the case for white noise. In addition, we study the difference between white and colored noise for maximal violations of Bell's inequalities for three and four-qubit entangled states.
Bell-LaPadula模型研究综述%Survey of Bell-LaPadula model
Institute of Scientific and Technical Information of China (English)
刘波; 陈曙晖; 邓劲生
2013-01-01
对BLP(Bell-LaPadula)模型进行了简单的描述,并从完整性、可用性、灵活性等几个方面归纳了该模型的局限性；讨论了目前国内外针对BLP模型这几个方面的不足进行的相关研究和改进,并进行了总结和展望.%This paper firstly discribed the BLP model itself, and summarized the limitaions and problems in its integrity, usability, flexibility, and so on. Then, it discussed the existing research and improvements aimed at these limitations. Finally, this paper concluded the present and the future work in the field of BLP model.
Complete Bell state measurement with controlled photon absorption and quantum interference
Tomita, A.
2000-01-01
A solid state device to discriminate all the four Bell states is proposed. The device is composed of controlled absorption crystals, rotators, and retarders. The controlled absorption, where the state of one photon affects the absorption of the other photon, is realized by two photon absorption in a cubic crystal. The controlled absorption crystal detects a particular Bell state and is transparent for the other Bell states. The rotators and retarders transform a Bell state to another. This de...
Fluctuation theorem for out-of-time-ordered correlator
Halpern, Nicole Yunger
2016-01-01
The out-of-time-ordered correlator (OTOC) diagnoses quantum chaos and the scrambling of quantum information via the spread of entanglement. The OTOC encodes forward and reverse evolutions and has deep connections with the flow of time. So do fluctuation theorems such as Jarzynski's Equality, derived in nonequilibrium statistical mechanics. I unite these two powerful, seemingly disparate tools by deriving a fluctuation theorem for the OTOC. The fluctuation theorem is analogous to Jarzynski's Equality. The theorem's left-hand side equals the OTOC. The right-hand side implies a platform-nonspecific protocol for experimentally measuring the OTOC in an indirect manner fundamentally different from existing proposals. Time evolution need not be reversed in any trial. The theorem opens holography, condensed matter, and quantum information to new insights from fluctuation theorems and vice versa.
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...
When is facial paralysis Bell palsy? Current diagnosis and treatment.
Ahmed, Anwar
2005-05-01
Bell palsy is largely a diagnosis of exclusion, but certain features in the history and physical examination help distinguish it from facial paralysis due to other conditions: eg, abrupt onset with complete, unilateral facial weakness at 24 to 72 hours, and, on the affected side, numbness or pain around the ear, a reduction in taste, and hypersensitivity to sounds. Corticosteroids and antivirals given within 10 days of onset have been shown to help. But Bell palsy resolves spontaneously without treatment in most patients within 6 months.
[Treatment of idiopathic peripheral facial nerve paralysis (Bell's palsy)].
Meyer, Martin Willy; Hahn, Christoffer Holst
2013-01-28
Bell's palsy is defined as an idiopathic peripheral facial nerve paralysis of sudden onset. It affects 11-40 persons per 100,000 per annum. Many patients recover without intervention; however, up to 30% have poor recovery of facial muscle control and experience facial disfigurement. The aim of this study was to make an overview of which pharmacological treatments have been used to improve outcomes. The available evidence from randomized controlled trials shows significant benefit from treating Bell's palsy with corticosteroids but shows no benefit from antivirals.
Experimental Test of Bell inequalities with Six-Qubit Graph States
Gao, Wei-Bo; Xu, Ping; Gühne, Otfried; Cabello, Adán; Lu, Chao-Yang; Yang, Tao; Chen, Zeng-Bing; Pan, Jian-Wei
2009-01-01
We report on the experimental realization of two different Bell inequality tests based on six-qubit linear-type and Y-shape graph states. For each of these states, the Bell inequalities tested are optimal in the sense that they provide the maximum violation among all Bell inequalities with stabilizing observables and possess the maximum resistance to noise.
Inconsistency of Carnot's theorem's proof by R. Clausius
Ihnatovych, V
2013-01-01
R. Clausius proved Carnot's theorem basing on postulate "Heat cannot, of itself, pass from a colder to a hotter body". Alexander Gukhman demonstrated that Carnot's theorem can be proved based on the postulate "Heat cannot, of itself, pass from a hotter to a colder body". He concluded that Carnot's theorem does not follow from Clausius' postulate. The following paper gives a detailed justification of Gukhman's derivation.
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
Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators
Institute of Scientific and Technical Information of China (English)
王雪红; 郭军义; 李艳
2012-01-01
In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ?/?λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.
On the linearization theorem for proper Lie groupoids
Crainic, Marius
2011-01-01
We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the the fixed point case (known as Zung's theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passing to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise conditions needed for the theorem to hold (which often have been misstated in the literature).
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.
Gerlach, Moritz
2011-01-01
We prove that every bounded, positive, irreducible, stochastically continuous semigroup on the space of bounded, measurable functions which is strong Feller, consists of kernel operators and possesses an invariant measure converges pointwise. This differs from Doob's theorem in that we do not require the semigroup to be Markovian and request a fairly weak kind of irreducibility. In addition, we elaborate on the various notions of kernel operators in this context, show the stronger result that the adjoint semigroup converges strongly and discuss as an example diffusion equations on rough domains. The proofs are based on the theory of positive semigroups and do not use probability theory.
Lifespan theorem for constrained surface diffusion flows
McCoy, James; Williams, Graham; 10.1007/s00209-010-0720-7
2012-01-01
We consider closed immersed hypersurfaces in $\\R^{3}$ and $\\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of the concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.
Central limit theorems under special relativity.
McKeague, Ian W
2015-04-01
Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.
Stone's representation theorem in fuzzy topology
Institute of Scientific and Technical Information of China (English)
LIU; Yingming(刘应明); ZHANG; Dexue(张德学)
2003-01-01
In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0 ∈ L is a prime or 1 ∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L-locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L-topological spaces.
Jackson's Theorem on Bounded Symmetric Domains
Institute of Scientific and Technical Information of China (English)
Ming Zhi WANG; Guang Bin REN
2007-01-01
Polynomial approximation is studied on bounded symmetric domain Ω in C n for holo-morphic function spaces X ,such as Bloch-type spaces,Bergman-type spaces,Hardy spaces,Ω algebra and Lipschitz space.We extend the classical Jackson ’s theorem to several complex variables:E k f,X ) ω (1 /k,f,X ),where E k f,X )is the deviation of the best approximation of f ∈X by polynomials of degree at mostk with respect to the X -metric and ω (1/k,f,X )is the corresponding modulus of continuity.
Adiabatic theorems for generators of contracting evolutions
Avron, J E; Graf, G M; Grech, P
2011-01-01
We develop an adiabatic theory for generators of contracting evolution on Banach spaces. This provides a uniform framework for a host of adiabatic theorems ranging from unitary quantum evolutions through quantum evolutions of open systems generated by Lindbladians all the way to classically driven stochastic systems. In all these cases the adiabatic evolution approximates, to lowest order, the natural notion of parallel transport in the manifold of instantaneous stationary states. The dynamics in the manifold of instantaneous stationary states and transversal to it have distinct characteristics: The former is irreversible and the latter is transient in a sense that we explain. Both the gapped and gapless cases are considered. Some applications are discussed.
Godel's Incompleteness Theorems and Platonic Metaphysics
Mikovic, Aleksandar
2015-01-01
We argue by using Godel's incompletness theorems in logic that platonism is the best metaphysics for science. This is based on the fact that a natural law in a platonic metaphysics represents a timeless order in the motion of matter, while a natural law in a materialistic metaphysics can be only defined as a temporary order which appears at random in the chaotic motion of matter. Although a logical possibility, one can argue that this type of metaphysics is highly implausible. Given that mathematics fits naturally within platonism, we conclude that a platonic metaphysics is more preferable than a materialistic metaphysics.
Fixed point theorems in spaces and -trees
Directory of Open Access Journals (Sweden)
Kirk WA
2004-01-01
Full Text Available We show that if is a bounded open set in a complete space , and if is nonexpansive, then always has a fixed point if there exists such that for all . It is also shown that if is a geodesically bounded closed convex subset of a complete -tree with , and if is a continuous mapping for which for some and all , then has a fixed point. It is also noted that a geodesically bounded complete -tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.
Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem
Directory of Open Access Journals (Sweden)
Juliana Bueno-Soler
2016-09-01
Full Text Available This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs. We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes’ theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.
On Clifford's theorem for singular curves
Franciosi, Marco
2011-01-01
Let C be a 2-connected Gorenstein curve either reduced or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim scheme such that the space H^0(C, I_S K_C) contains a generically invertible section). Under some general assumptions on S or C we show that h^0(C, I_S K_C) <= p_a(C) - deg (S)/2 and if equality holds then either S is trivial, or C is honestly hyperelliptic or 3-disconnected. As a corollary we give a generalization of Clifford's theorem for reduced curves.
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
J M M Senovilla
2007-07-01
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating Universes, expanding everywhere with a non-vanishing spatial average of the matter variables, show severe geodesic incompletness in the past. Another way of stating the result is that, under the same conditions, any singularity-free model must have a vanishing spatial average of the energy density (and other physical variables). This is very satisfactory and provides a clear decisive difference between singular and non-singular cosmologies.
Number systems and the Chinese Remainder Theorem
van de Woestijne, Christiaan E
2011-01-01
A well-known generalisation of positional numeration systems is the case where the base is the residue class of $x$ modulo a given polynomial $f(x)$ with coefficients in (for example) the integers, and where we try to construct finite expansions for all residue classes modulo $f(x)$, using a suitably chosen digit set. We give precise conditions under which direct or fibred products of two such polynomial number systems are again of the same form. The main tool is a general form of the Chinese Remainder Theorem. We give applications to simultaneous number systems in the integers.
APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION
Institute of Scientific and Technical Information of China (English)
杨守志; 程正兴; 唐远炎
2003-01-01
An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution. The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation, a piece-wise linear function, and posseses an explicit computation formula. Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function.
Theorem proving support in programming language semantics
Bertot, Yves
2007-01-01
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational semantics, axiomatic semantics, and abstract interpretation. Descriptions as recursive functions are also provided whenever suitable, thus yielding a a verification condition generator and a static analyser that can be run inside the theorem prover for use in reflective proofs. Extraction of an interpreter from the denotational semantics is also described. All different aspects are formally proved sound with respect to the natural semantics specification.
A Formal Proof Of The Riesz Representation Theorem
Directory of Open Access Journals (Sweden)
Anthony Narkawicz
2011-01-01
Full Text Available This paper presents a formal proof of the Riesz representation theorem in the PVS theorem prover. The Riemann Stieltjes integral was defined in PVS, and the theorem relies on this integral. In order to prove the Riesz representation theorem, it was necessary to prove that continuous functions on a closed interval are Riemann Stieltjes integrable with respect to any function of bounded variation. This result follows from the equivalence of the Riemann Stieltjes and Darboux Stieltjes integrals, which would have been a lengthy result to prove in PVS, so a simpler lemma was proved that captures the underlying concept of this integral equivalence. In order to prove the Riesz theorem, the Hahn Banach theorem was proved in the case where the normed linear spaces are the continuous and bounded functions on a closed interval. The proof of the Riesz theorem follows the proof in Haaser and Sullivan's book Real Analysis. The formal proof of this result in PVS revealed an error in textbook's proof. Indeed, the proof of the Riesz representation theorem is constructive, and the function constructed in the textbook does not satisfy a key property. This error illustrates the ability of formal verification to find logical errors. A specific counterexample is given to the proof in the textbook. Finally, a corrected proof of the Riesz representation theorem is presented.
Fluctuation-dissipation theorem and quantum tunneling with dissipation
Fujikawa, K
1998-01-01
We suggest to take the fluctuation-dissipation theorem of Callen and Welton as a basis to study quantum dissipative phenomena (such as macroscopic quantum tunneling) in a manner analogous to the Nambu-Goldstone theorem for spontaneous symmetry breakdown. It is shown that the essential physical contents of the Caldeira-Leggett model such as the suppression of quantum coherence by Ohmic dissipation are derived from general principles only, namely, the fluctuation-dissipation theorem and unitarity and causality (i.e., dispersion relations), without referring to an explicit form of the Lagrangian. An interesting connection between quantum tunneling with Ohmic dissipation and the Anderson's orthogonality theorem is also noted.
Generalizations of the Nash Equilibrium Theorem in the KKM Theory
Directory of Open Access Journals (Sweden)
Park Sehie
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 -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.
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.
Fluctuation theorem in dynamical systems with quenched disorder
Drocco, Jeffrey; Olson Reichhardt, Cynthia; Reichhardt, Charles
2010-03-01
We demonstrate that the fluctuation theorem of Gallavotti and Cohen can be used to characterize far from equilibrium dynamical nonthermal systems in the presence of quenched disorder where strong fluctuations or crackling noise occur. By observing the frequency of entropy-destroying trajectories, we show that the theorem holds in specific dynamical regimes near the threshold for motion, indicating that these systems might be ideal candidates for understanding what types of nonthermal fluctuations could be used in constructing generalized fluctuation theorems. We also discuss how the theorem could be tested with global or local probes in systems such as superconducting vortices, magnetic domain walls, stripe phases, Coulomb glasses and earthquake models.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
Woolgar, Eric; Wylie, William
2016-02-01
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the "pure Bakry-Émery" N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (-∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (-∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
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Woolgar, Eric, E-mail: ewoolgar@ualberta.ca [Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1 (Canada); Wylie, William, E-mail: wwylie@syr.edu [215 Carnegie Building, Department of Mathematics, Syracuse University, Syracuse, New York 13244 (United States)
2016-02-15
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
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Ronghua He
2012-04-01
Full Text Available Let $I$ be any index set. By using some existence theorems of maximal elements for a family of set-valued mappings involving a better admissible set-valued mapping under noncompact setting of $FC$-spaces, we first present some nonempty intersection theorems for a family $\\{G_{i}\\}_{i\\in I}$ in a product space of $FC$-spaces. Next we give a coincidence theorem and a Fan-Browder type fixed point theorem. Finally, as applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems are proved in product $FC$-space, some existence theorems of solutions for a system of Ky Fan type minimax inequalities involving a family of $G_{\\cal B}$-majorized mappings defined on the product space of $FC$-space are also obtained. Our results improve and generalize some recent results.
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...
De Finetti Theorem on the CAR Algebra
Crismale, Vitonofrio; Fidaleo, Francesco
2012-10-01
The symmetric states on a quasi local C*-algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend the De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki-Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self-containing interest.
De Finetti theorem on the CAR algebra
Crismale, Vito
2012-01-01
The symmetric states on a quasi local C*-algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki-Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self--containing interest.
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.
A vector bundle proof of Poncelet theorem
Vallès, Jean
2012-01-01
In the town of Saratov where he was prisonner, Poncelet, continuing the work of Euler and Steiner on polygons simultaneously inscribed in a circle and circumscribed around an other circle, proved the following generalization : "Let C and D be two smooth conics in the projective complex plane. If D passes through the n(n-1)/2 vertices of a complete polygon with n sides tangent to C then D passes through the vertices of infinitely many such polygons." According to Marcel Berger this theorem is the nicest result about the geometry of conics. Even if it is, there are few proofs of it. To my knowledge there are only three. The first proof, published in 1822 and based on infinitesimal deformations, is due to Poncelet. Later, Jacobi proposed a new proof based on finite order points on elliptic curves; his proof, certainly the most famous, is explained in a modern way and in detail by Griffiths and Harris. In 1870 Weyr proved a Poncelet theorem in space (more precisely for two quadrics) that implies the one above whe...
On the inversion of Fueter's theorem
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2016-10-01
The well known Fueter theorem allows to construct quaternionic regular functions or monogenic functions with values in a Clifford algebra defined on open sets of Euclidean space R n + 1, starting from a holomorphic function in one complex variable or, more in general, from a slice hyperholomorphic function. Recently, the inversion of this theorem has been obtained for odd values of the dimension n. The present work extends the result to all dimensions n by using the Fourier multiplier method. More precisely, we show that for any axially monogenic function f defined in a suitable open set in R n + 1, where n is a positive integer, we can find a slice hyperholomorphic function f → such that f =Δ (n - 1) / 2 f →. Both the even and the odd dimensions are treated with the same, viz., the Fourier multiplier, method. For the odd dimensional cases the result obtained by the Fourier multiplier method coincides with the existing result obtained through the pointwise differential method.
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Mônica Alcantara de Oliveira Santos
2010-06-01
Full Text Available Embora a paralisia de Bell seja o tipo mais frequente de paralisia facial periférica,sua causa ainda é objeto de inúmeros questionamentos. A reativação do vírus varicela zoster tem sido considerada uma das principais causas da paralisia de Bell, porém, os poucos trabalhos que estudam a prevalência do VVZ como agente etiológico da PB são japoneses, o que determina características geográficas e populacionais bastante díspares de nossa população. OBJETIVOS: Verificar a frequência do vírus varicela zoster em saliva de indivíduos com PB, pela técnica de PCR. MATERIAL E MÉTODO: Estudo prospectivo com 171 pacientes com PFP, sendo 120 pacientes portadores de paralisia de Bell, com até uma semana de evolução, sem uso prévio de drogas antivirais. O grupo controle foi composto de 20 adultos sadios. Nestes indivíduos foram coletadas três amostras de saliva em semanas consecutivas, para pesquisa de DNA viral pela técnica de PCR. RESULTADOS: O vírus varicela zoster foi encontrado em amostras de saliva de dois pacientes com paralisia de Bell (1,7%. Nenhum vírus foi identificado no grupo controle. CONCLUSÃO: Foi verificada frequência de 1,7% para vírus varicela zoster em amostras de saliva de pacientes com paralisia de Bell, pela técnica de PCR.Although Bell's palsy is the major cause of acute peripheral facial palsy, its pathogenesis remains unknown. Reactivation of the varicella zoster virus has been implicated as one of the main causes of Bell's palsy, however, studies which investigate the varicella zoster virus reactivation in Bell's palsy patients are mostly Japanese and, therefore, personal and geographic characteristics are quite different from our population. AIMS: To determine varicella zoster virus frequency in saliva samples from patients with Bell's palsy, using PCR. MATERIAL AND METHOD: One hundred seventy one patients with acute peripheral facial palsy were prospectively enrolled in this study. One hundred twenty
"The Bell Curve" and Carrie Buck: Eugenics Revisited.
Smith, J. David
1995-01-01
The 1994 publication of "The Bell Curve" by R. Herrnstein and C. Murray is compared to other examples of eugenic principles, including the sterilization of "feebleminded" Carrie Buck, family degeneracy studies focusing on lower class Caucasian families, and other works that view the poorest and least educated members of society…
Angular dependences in inclusive two-hadron production at BELLE
Boer, Daniel
2009-01-01
A collection of results is presented relevant for the analysis of azimuthal asymmetries in inclusive two-hadron production at BELLE. The aim of this overview is to provide theoretical ingredients necessary to extract the Collins effect fragmentation function. The latter arises within the Collins-Sop