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Sample records for bell theorem

  1. The Two Bell's Theorems of John Bell

    CERN Document Server

    Wiseman, Howard M

    2014-01-01

    Many of the heated arguments about the meaning of "Bell's theorem" arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the dual assumptions of locality and determinism. His 1976 theorem is the incompatibility of quantum phenomena with the unitary property of local causality. This is contrary to Bell's own later assertions, that his 1964 theorem began with that single, and indivisible, assumption of local causality (even if not by that name). While there are other forms of Bell's theorems --- which I present to explain the relation between Jarrett-completeness, "weak locality", and EPR-completeness --- I maintain that Bell's two versions are the essential ones. Although the two Bell's theorems are logically equivalent, their assumptions are not, and the different versions of the theorem suggest quite different conclusions, which are embraced by different communities. For ...

  2. Anti-Bell - Refutation of Bell's theorem

    Science.gov (United States)

    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.

  3. The two Bell's theorems of John Bell

    International Nuclear Information System (INIS)

    Many of the heated arguments about the meaning of ‘Bell's theorem’ arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the dual assumptions of locality and determinism. His 1976 theorem is the incompatibility of quantum phenomena with the unitary property of local causality. This is contrary to Bell's own later assertions, that his 1964 theorem began with that single, and indivisible, assumption of local causality (even if not by that name). While there are other forms of Bell's theorems—which I present to explain the relation between Jarrett-completeness, ‘fragile locality’, and EPR-completeness—I maintain that Bell's two versions are the essential ones. Although the two Bell's theorems are logically equivalent, their assumptions are not, and the different versions of the theorem suggest quite different conclusions, which are embraced by different communities. For realists, the notion of local causality, ruled out by Bell's 1976 theorem, is motivated implicitly by Reichenbach's principle of common cause and explicitly by the principle of relativistic causality, and it is the latter which must be forgone. Operationalists pay no heed to Reichenbach's principle, but wish to keep the principle of relativistic causality, which, bolstered by an implicit ‘principle of agent-causation’, implies their notion of locality. Thus for operationalists, Bell's theorem is the 1964 one, and implies that it is determinism that must be forgone. I discuss why the two ‘camps’ are drawn to these different conclusions, and what can be done to increase mutual understanding. (review article)

  4. Statistics, Causality and Bell's theorem

    CERN Document Server

    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...

  5. Concrete incompleteness & Bell's theorem

    CERN Document Server

    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.

  6. Bell's theorem, accountability and nonlocality

    International Nuclear Information System (INIS)

    Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner (2011 Nature Commun. 2 411), we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)

  7. Causarum Investigatio and the Two Bell's Theorems of John Bell

    CERN Document Server

    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...

  8. Bell on Bell's theorem: The changing face of nonlocality

    CERN Document Server

    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...

  9. Causality, Bell's theorem, and Ontic Definiteness

    CERN Document Server

    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...

  10. On the failure of Bell's theorem

    OpenAIRE

    Bene, Gyula

    1997-01-01

    Using a new approach to quantum mechanics we revisit Hardy's proof for Bell's theorem and point out a loophole in it. We also demonstrate on this example that quantum mechanics is a local realistic theory.

  11. Multideviations: The hidden structure of Bell's theorems

    CERN Document Server

    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...

  12. Extending Bell's Theorem: Ruling out Paramater Independent Hidden Variable Theories

    Science.gov (United States)

    Leegwater, G. J.

    2016-03-01

    Bell's Theorem may well be the best known result in the foundations of quantum mechanics. Here, it is presented as stating that for any hidden variable theory the combination of the conditions Parameter Independence, Outcome Independence, Source Independence and Compatibility with Quantum Theory leads to a contradiction. Based on work by Roger Colbeck and Renato Renner, an extension of Bell's Theorem is considered. In this extension the theorem is strengthened by replacing Outcome Independence by a strictly weaker condition.

  13. Quantum nonlocality and reality 50 years of Bell's theorem

    CERN Document Server

    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...

  14. Classical probabilistic realization of "Random Numbers Certified by Bell's Theorem"

    OpenAIRE

    Khrennikov, Andrei

    2015-01-01

    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.

  15. A Modest View of Bell's Theorem

    CERN Document Server

    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...

  16. Bell's Theorem and Einstein's "Spooky Actions" from a Simple Thought Experiment

    Science.gov (United States)

    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…

  17. A Bell-type Theorem Without Hidden Variables

    CERN Document Server

    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.

  18. State-Independent Proofs of Bell's Theorem Without Inequalities and Bell Inequality for Four-Qubit System

    Institute of Scientific and Technical Information of China (English)

    CHEN Chang-Yong; GAO Ke-Lin

    2005-01-01

    A state-dependent proof of Bell's theorem without inequalities using the product state of any two maximally entangled states (Bell states) of two qubits for two observers in an ideal condition, each of which possesses two qubits,is proposed. It is different from the other proofs in which there exists a fundamental requirement that certain specific suitable Bell states have been chosen. Moreover, in any non-ideal situation, a common Bell inequality independent of the choices of the 16-product states is derived, which is used to test the contradiction between quantum mechanics and local reality theory in the reach of current experimental technology.

  19. Bell's theorem tells us NOT what quantum mechanics IS, but what quantum mechanics IS NOT

    CERN Document Server

    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...

  20. Non-separability does not relieve the problem of Bell's theorem

    CERN Document Server

    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...

  1. Bringing Bell's theorem back to the domain of Particle Physics & Cosmology

    CERN Document Server

    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...

  2. 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.

  3. Hidden assumptions in the derivation of the theorem of Bell

    NARCIS (Netherlands)

    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

  4. Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons.

    Science.gov (United States)

    Giustina, Marissa; Versteegh, Marijn A M; Wengerowsky, Sören; Handsteiner, Johannes; Hochrainer, Armin; Phelan, Kevin; Steinlechner, Fabian; Kofler, Johannes; Larsson, Jan-Åke; Abellán, Carlos; Amaya, Waldimar; Pruneri, Valerio; Mitchell, Morgan W; Beyer, Jörn; Gerrits, Thomas; Lita, Adriana E; Shalm, Lynden K; Nam, Sae Woo; Scheidl, Thomas; Ursin, Rupert; Wittmann, Bernhard; Zeilinger, Anton

    2015-12-18

    Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem states that this worldview is incompatible with the predictions of quantum mechanics, as is expressed in Bell's inequalities. Previous experiments convincingly supported the quantum predictions. Yet, every experiment requires assumptions that provide loopholes for a local realist explanation. Here, we report a Bell test that closes the most significant of these loopholes simultaneously. Using a well-optimized source of entangled photons, rapid setting generation, and highly efficient superconducting detectors, we observe a violation of a Bell inequality with high statistical significance. The purely statistical probability of our results to occur under local realism does not exceed 3.74×10^{-31}, corresponding to an 11.5 standard deviation effect. PMID:26722905

  5. Bell's theorem and the causal arrow of time

    Science.gov (United States)

    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.

  6. 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.

  7. Bell's Theorem, Many Worlds and Backwards-Time Physics: Not Just a Matter of Interpretation

    CERN Document Server

    Werbos, Paul J

    2008-01-01

    The classic "Bell's Theorem" of Clauser, Holt, Shimony and Horne tells us that we must give up at least one of: (1) objective reality (aka "hidden variables"); (2) locality; or (3) time-forwards macroscopic statistics (aka "causality"). The orthodox Copenhagen version of physics gives up the first. The many-worlds theory of Everett and Wheeler gives up the second. The backwards-time theory of physics (BTP) gives up the third. Contrary to conventional wisdom, empirical evidence strongly favors Everett-Wheeler over orthodox Copenhagen. BTP has two major variations -- a many-worlds version, and a neoclassical version of partial differential equations (PDE) in the spirit of Einstein. Section 2 discusses quantum measurement according to BTP, focusing on how we represent condensed matter objects like polarizers in a Bell's Theorem experiment or in tests of Hawking's cosmology. The Backwards Time Telegraph, though speculative, is discussed.

  8. Non-separability does not relieve the problem of Bell's theorem

    OpenAIRE

    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...

  9. 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.)

  10. A new look at Bell's inequalities and Nelson's theorem

    Energy Technology Data Exchange (ETDEWEB)

    Schulz, B.

    2009-04-15

    In 1985, Edward Nelson, who formulated the theory of stochastic mechanics, made an interesting remark about Bell's theorem. Nelson analysed the latter in the light of classical fields that behave randomly. He found that if a stochastic hidden variable theory fulfils certain conditions, the inequality of Bell can be violated. Moreover, Nelson was able to prove that this may happen without any instantaneous communication between the two spatially separated measurement stations. Since Nelson's article got almost overlooked by physicists, we try to review his comments on the theorem. We argue that a modification of stochastic mechanics published recently by Fritsche and Haugk can be extended to a theory which fulfils the requirements of Nelson's analysis. The article proceeds to derive the quantum mechanical formalism of spinning particles and the Pauli equation from this version of stochastic mechanics. Then, we investigate Bohm's version of the EPR experiment. Additionally, other setups, like entanglement swapping or time and position correlations, are shortly explained from the viewpoint of our local hidden-variable model. Finally, we mention that this theory could perhaps be relativistically extended and useful for the formulation of quantum mechanics in curved space-times. (Abstract Copyright [2009], Wiley Periodicals, Inc.)

  11. Limits to quantum mechanics as a source of magic tricks: Retrodiction and the Bell-Kochen-Specker theorem

    International Nuclear Information System (INIS)

    A trick discovered by Vaidman, Aharanov, and Albert permitting retrodiction of the outcomes of more measurements than one would naively have thought possible is extended to a case in which the retrodicted observables are forbidden all to have values by a Bell-Kochen-Specker theorem. A rather peculiar analysis shows that an even better trick that retrodicts the outcomes of more informative measurements of these same observables is impossible

  12. A Mathematician's Viewpoint to Bell's theorem: In Memory of Walter Philipp

    OpenAIRE

    Khrennikov, Andrei

    2006-01-01

    In this paper dedicated to the memory of Walter Philipp, we formalize the rules of classical$\\to$ quantum correspondence and perform a rigorous mathematical analysis of the assumptions in Bell's NO-GO arguments.

  13. Nonlocality, No-Signalling and Bell's Theorem investigated by Weyl's Conformal Differential Geometry

    OpenAIRE

    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...

  14. An Entangled Web of Crime: Bell's Theorem as a Short Story

    CERN Document Server

    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.

  15. An Entangled Web of Crime: Bell's Theorem as a Short Story

    OpenAIRE

    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...

  16. Relational interpretation of the wave function and a possible way around Bell's theorem

    CERN Document Server

    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.

  17. Irrelevance of Bell's Theorem for experiments involving correlations in space and time: a specific loophole-free computer-example

    CERN Document Server

    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.

  18. Bell's Theorem and Entangled Solitons

    Science.gov (United States)

    Rybakov, Yu. P.; Kamalov, T. F.

    2016-09-01

    Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein—Podolsky—Rosen (EPR) spin correlation is calculated and shown to coincide with the quantum mechanical one for the 1/2-spin particles.

  19. Polynomial Bell Inequalities

    Science.gov (United States)

    Chaves, Rafael

    2016-01-01

    It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell's theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell networks.

  20. John Bell and the Nature of the Quantum World

    CERN Document Server

    Bertlmann, Reinhold A

    2014-01-01

    I present my encounter with John Bell at CERN, our collaboration and joint work in particle physics. I also will recall our quantum debates and give my personal view on Bell's fundamental work on quantum theory, in particular, on contextuality and nonlocality of quantum physics. Some mathematical and geometric aspects of entanglement are discussed as influence of Bell's Theorem. Finally, I make some historical comments on the experimental side of Bell inequalities.

  1. Bell's inequality violation with spins in silicon.

    Science.gov (United States)

    Dehollain, Juan P; Simmons, Stephanie; Muhonen, Juha T; Kalra, Rachpon; Laucht, Arne; Hudson, Fay; Itoh, Kohei M; Jamieson, David N; McCallum, Jeffrey C; Dzurak, Andrew S; Morello, Andrea

    2016-03-01

    Bell's theorem proves the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states, and provides a single-number benchmark for the performance of devices that use such states for quantum computing. We demonstrate a Bell/ Clauser-Horne-Shimony-Holt inequality violation with Bell signals up to 2.70(9), using the electron and the nuclear spins of a single phosphorus atom embedded in a silicon nanoelectronic device. Two-qubit state tomography reveals that our prepared states match the target maximally entangled Bell states with >96% fidelity. These experiments demonstrate complete control of the two-qubit Hilbert space of a phosphorus atom and highlight the important function of the nuclear qubit to expand the computational basis and maximize the readout fidelity. PMID:26571006

  2. After Bell

    CERN Document Server

    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.

  3. John Bell and the nature of the quantum world

    Science.gov (United States)

    Bertlmann, Reinhold A.

    2014-10-01

    I present my encounter with John Bell at CERN, our collaboration and joint work in particle physics. I also recall our quantum debates and give my personal view on Bell's fundamental work on quantum theory, in particular, on contextuality and nonlocality of quantum physics. Some mathematical and geometric aspects of entanglement are discussed as influence of Bell's theorem. Finally, I make some historical comments on the experimental side of Bell inequalities. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.

  4. Waldhausen's Theorem

    OpenAIRE

    Schleimer, Saul

    2009-01-01

    This note is an exposition of Waldhausen's proof of Waldhausen's Theorem: the three-sphere has a single Heegaard splitting, up to isotopy, in every genus. As a necessary step we also give a sketch of the Reidemeister-Singer Theorem.

  5. Frege's theorem

    CERN Document Server

    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

  6. Mathematical and physical meaning of the Bell inequalities

    Science.gov (United States)

    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.

  7. John Stewart Bell and twentieth century physics vision and integrity

    CERN Document Server

    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.

  8. All Pure Entangled States of Three-Qubit System Violate a Bell Inequality For Probabilities

    CERN Document Server

    Chen, J L; Kwek, L C; Oh, C H; Chen, Jing-Ling; Wu, Chun-Feng

    2003-01-01

    We present a Theorem that all generalized GHZ states of three-qubit system violation a Bell inequality in terms of probabilities. We also show that all pure entangled states of three-qubit system violate a Bell inequality for probabilities.

  9. On the Analysis of Bell's 1964 Paper by Wiseman, Cavalcanti, and Rieffel

    CERN Document Server

    Gillis, Edward J

    2015-01-01

    In a recent series of papers Wiseman, Cavalcanti, and Rieffel have outlined and contrasted the operationalist and realist views about what we now call Bell's theorem. They also assert that Bell presented these two different versions at different times. A careful examination of the historic 1964 paper and of the writings of Bell and others that preceded it shows clearly that their interpretation of that paper is incorrect.

  10. Bell inequalities for quantum optical fields

    Science.gov (United States)

    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.

  11. Belle II production system

    Science.gov (United States)

    Miyake, Hideki; Grzymkowski, Rafal; Ludacka, Radek; Schram, Malachi

    2015-12-01

    The Belle II experiment will record a similar quantity of data to LHC experiments and will acquire it at similar rates. This requires considerable computing, storage and network resources to handle not only data created by the experiment but also considerable amounts of simulated data. Consequently Belle II employs a distributed computing system to provide the resources coordinated by the the DIRAC interware. DIRAC is a general software framework that provides a unified interface among heterogeneous computing resources. In addition to the well proven DIRAC software stack, Belle II is developing its own extension called BelleDIRAC. BelleDIRAC provides a transparent user experience for the Belle II analysis framework (basf2) on various environments and gives access to file information managed by LFC and AMGA metadata catalog. By unifying DIRAC and BelleDIRAC functionalities, Belle II plans to operate an automated mass data processing framework named a “production system”. The Belle II production system enables large-scale raw data transfer from experimental site to raw data centers, followed by massive data processing, and smart data delivery to each remote site. The production system is also utilized for simulated data production and data analysis. Although development of the production system is still on-going, recently Belle II has prepared prototype version and evaluated it with a large scale simulated data production. In this presentation we will report the evaluation of the prototype system and future development plans.

  12. A quantum loophole to Bell nonlocality

    CERN Document Server

    Romero-Rochin, Victor

    2015-01-01

    We argue that the conclusion of Bell theorem, namely, that there must be spatial non-local correlations in certain experimental situations, does not apply to typical individual measurements performed on entangled EPR pairs. Our claim is based on three points, (i) on the notion of quantum {\\it complete measurements}; (ii) on Bell results on local yet distant measurements; and (iii) on the fact that perfect simultaneity is banned by the quantum mechanics. We show that quantum mechanics indicates that, while the measurements of the pair members are indeed space-like separated, the pair measurement is actually a sequence of two complete measurements, the first one terminating the entanglement and, therefore, the second one becoming unrelated to the initial preparation of the entangled pair. The outstanding feature of these measurements is that neither of them violates the principle of locality. We discuss that the present measurement viewpoint appears to run contrary to the usual interpretation of "superposition"...

  13. Why do Bell experiments?

    OpenAIRE

    Percival, Ian C.

    2000-01-01

    Experiments over three decades have been unable to demonstrate weak nonlocality in the sense of Bell unambiguously, without loopholes. The last important loophole remaining is the detection loophole, which is being tackled by at least three experimental groups. This letter counters five common beliefs about Bell experiments, and presents alternative scenarios for future developments.

  14. Selected topics from Belle

    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.

  15. A Smile for Belle

    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!

  16. Vorticity, Stokes' Theorem and the Gauss's Theorem

    Science.gov (United States)

    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

  17. Bell's theorem and the demise of local reality

    CERN Multimedia

    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).

  18. Early History of BELL'S Theorem Theory and Experiment

    Science.gov (United States)

    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.

  19. Open water bells

    Science.gov (United States)

    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.

  20. 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?.

  1. Software Development at Belle II

    Science.gov (United States)

    Kuhr, Thomas; Hauth, Thomas

    2015-12-01

    Belle II is a next generation B-factory experiment that will collect 50 times more data than its predecessor Belle. This requires not only a major upgrade of the detector hardware, but also of the simulation, reconstruction, and analysis software. The challenges of the software development at Belle II and the tools and procedures to address them are reviewed in this article.

  2. Bell's Universe: A Personal Recollection

    CERN Document Server

    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.

  3. Bell's palsy before Bell: Cornelis Stalpart van der Wiel's observation of Bell's palsy in 1683.

    Science.gov (United States)

    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.

  4. Godel's theorem is invalid

    OpenAIRE

    Saa, Diego

    2005-01-01

    Goedel's results have had a great impact in diverse fields such as philosophy, computer sciences and fundamentals of mathematics. The fact that the rule of mathematical induction is contradictory with the rest of clauses used by Goedel to prove his undecidability and incompleteness theorems is proved in this paper. This means that those theorems are invalid.

  5. Teleportation, Bell's inequalities and inseparability

    International Nuclear Information System (INIS)

    Relations between teleportation, Bell's inequalities and inseparability are investigated. It is shown that any mixed two spin-1/2 state which violates the Bell-CHSH inequality is useful for teleportation. The result is extended to any Bell's inequalities constructed from the expectation values of products of spin operators. It is also shown that there exist inseparable states which are not useful for teleportation within the standard scheme. (orig.)

  6. Bell's Universe: A Personal Recollection

    OpenAIRE

    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 inf...

  7. Acoustics of old Asian bells

    Science.gov (United States)

    Rossing, Thomas D.

    2001-05-01

    The art of casting bronze bells developed to a high level of sophistication in China during the Shang dynasty (1766-1123 BC). Many chimes of two-tone bells remain from the Western and Eastern Zhou dynasties (1122-249 BC). With the spread of Buddhism from the third century, large round temple bells developed in China and later in Korea, Japan, and other Asian countries. Vibrational modes of some of these bells have been studied by means of holographic interferometry and experimental modal testing. Their musical as well as acoustical properties are discussed.

  8. To string together six theorems of physics by Pythagoras theorem

    OpenAIRE

    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...

  9. To string together six theorems of physics by Pythagoras theorem

    CERN Document Server

    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.

  10. 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.

  11. Virial Theorem and Hypervirial Theorem in a spherical geometry

    OpenAIRE

    Li, Yan; Zhang, Fu-Lin; Chen, Jing-Ling

    2010-01-01

    The Virial Theorem in the one- and two-dimensional spherical geometry are presented, in both classical and quantum mechanics. Choosing a special class of Hypervirial operators, the quantum Hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman Theorem, these relations can be used to formulate a \\emph{perturbation theorem without wave functions}, corresponding to the Hypervirial-Hellmann-Feynman Theorem perturbation theorem of Euclidean geometry. The o...

  12. Automated theorem proving.

    Science.gov (United States)

    Plaisted, David A

    2014-03-01

    Automated theorem proving is the use of computers to prove or disprove mathematical or logical statements. Such statements can express properties of hardware or software systems, or facts about the world that are relevant for applications such as natural language processing and planning. A brief introduction to propositional and first-order logic is given, along with some of the main methods of automated theorem proving in these logics. These methods of theorem proving include resolution, Davis and Putnam-style approaches, and others. Methods for handling the equality axioms are also presented. Methods of theorem proving in propositional logic are presented first, and then methods for first-order logic. WIREs Cogn Sci 2014, 5:115-128. doi: 10.1002/wcs.1269 CONFLICT OF INTEREST: The authors has declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website. PMID:26304304

  13. Trigonometry, Including Snell's Theorem.

    Science.gov (United States)

    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)

  14. Two preservation theorems

    OpenAIRE

    Zapletal, Jindrich

    2005-01-01

    I prove preservation theorems for countable support iteration of proper forcing concerning certain classes of capacities and submeasures. New examples of forcing notions and connections with measure theory are included.

  15. 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.

  16. Bell's palsy before Bell : Cornelis Stalpart van der Wiel's observation of Bell's palsy in 1683

    NARCIS (Netherlands)

    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

  17. All the Bell inequalities

    CERN Document Server

    Peres, A

    1999-01-01

    Bell inequalities are derived for any number of observers, any number of alternative setups for each one of them, and any number of distinct outcomes for each experiment. It is shown that if a physical system consists of several distant subsystems, and if the results of tests performed on the latter are determined by local variables with objective values, then the joint probabilities for triggering any given set of distant detectors are convex combinations of a finite number of Boolean arrays, whose components are either 0 or 1 according to a simple rule. This convexity property is both necessary and sufficient for the existence of local objective variables. It leads to a simple graphical method which produces a large number of generalized Clauser-Horne inequalities corresponding to the faces of a convex polytope. It is plausible that quantum systems whose density matrix has a positive partial transposition satisfy all these inequalities, and therefore are compatible with local objective variables, even if th...

  18. Belle II Technical Design Report

    CERN Document Server

    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.

  19. 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.

  20. The Fermi's Bayes Theorem

    CERN Document Server

    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.

  1. Deterministically distinguishing a remote Bell state

    Institute of Scientific and Technical Information of China (English)

    Zhao Zhi-Guo; Peng Wei-Min; Tan Yong-Gang

    2011-01-01

    It has been proven that, with a single copy provided, the four Bell states cannot be distinguished by local operations and classical communications (LOCC). Traditionally, a Bell basis projective measurement is needed to distinguish the four Bell states, which is usually carried out with a local interference between two particles. This paper presents an interesting protocol that allows two remote parties to distinguish four Bell states deterministically. We prove that our protocol of distinguishing remote Bell states is beyond LOCC.

  2. Converse Barrier Certificate Theorem

    DEFF Research Database (Denmark)

    Wisniewski, Rafael; Sloth, Christoffer

    2013-01-01

    This paper presents a converse barrier certificate theorem for a generic dynamical system.We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold. Other authors have developed a related result, by assuming that the dynamical system has no singular...... points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work by...

  3. Goldstone theorem revisited

    CERN Document Server

    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.

  4. Formality theorem for gerbes

    DEFF Research Database (Denmark)

    Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard;

    2015-01-01

    The main result of the present paper is an analogue of Kontsevich formality theorem in the context of the deformation theory of gerbes. We construct an L∞L∞ deformation of the Schouten algebra of multi-vectors which controls the deformation theory of a gerbe.......The main result of the present paper is an analogue of Kontsevich formality theorem in the context of the deformation theory of gerbes. We construct an L∞L∞ deformation of the Schouten algebra of multi-vectors which controls the deformation theory of a gerbe....

  5. Bell's inequalities and Kolmogorov's axioms

    NARCIS (Netherlands)

    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.

  6. Magic moments with John Bell

    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.

  7. 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.

  8. Bell's Palsy (Beyond the Basics)

    Science.gov (United States)

    ... changes caused by Bell's palsy will affect the appearance of your face, including how you smile. These ... are comfortable with some medical jargon. Patient information: Genital herpes (Beyond the Basics) Patient information: Shingles (Beyond ...

  9. Magic moments with John Bell

    International Nuclear Information System (INIS)

    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

  10. Virial Theorem and Scale Transformations.

    Science.gov (United States)

    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)

  11. Gödel's Theorem

    NARCIS (Netherlands)

    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

  12. An order drop theorem

    Directory of Open Access Journals (Sweden)

    Mihai Turinici

    2006-11-01

    Full Text Available A drop theorem on ordered metric spaces is established from the (pre order version of Ekeland’s variational principle in Turinici [An St UAIC Ia (Math, 36 (1990, 329-352]. The logical equivalence between these results is also discussed.

  13. An order drop theorem

    OpenAIRE

    Mihai Turinici

    2006-01-01

    A drop theorem on ordered metric spaces is established from the (pre) order version of Ekeland’s variational principle in Turinici [An St UAIC Ia (Math), 36 (1990), 329-352]. The logical equivalence between these results is also discussed.

  14. Gödel's Theorem

    OpenAIRE

    Dalen, D. van

    2008-01-01

    The following pages make form a new chapter for the book Logic and Structure. This chapter deals with the incompleteness theorem, and contains enough basic material for the treatment of the required notions of computability, representability and the like. This chapter will appear in the next edition of Logic and Structure. Comments are welcome.

  15. Multivariate irregular sampling theorem

    Institute of Scientific and Technical Information of China (English)

    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.

  16. Discovering the Theorem of Pythagoras

    Science.gov (United States)

    Lattanzio, Robert (Editor)

    1988-01-01

    In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.

  17. An Improved Subadditive Ergodic Theorem

    OpenAIRE

    Liggett, Thomas M.

    1985-01-01

    A new version of Kingman's subadditive ergodic theorem is presented, in which the subadditivity and stationarity assumptions are relaxed without weakening the conclusions. This result applies to a number of situations that were not covered by Kingman's original theorem. The proof involves a rather simple reduction to the additive case, where Birkhoff's ergodic theorem can be applied.

  18. How to Understand a Theorem?

    Science.gov (United States)

    Abramovitz, Buma; Berezina, Miryam; Berman, Abraham; Shvartsman, Ludmila

    2009-01-01

    In this article we describe the process of studying the assumptions and the conclusion of a theorem. We tried to provide the students with exercises and problems where we discuss the following questions: What are the assumptions of a theorem and what are the conclusions? What is the geometrical meaning of a theorem? What happens when one or more…

  19. An Extension of Sobolev's Theorem

    Institute of Scientific and Technical Information of China (English)

    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.

  20. 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)

  1. Is the bell ringing?

    CERN Multimedia

    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...

  2. Reply to Gillis's "On the Analysis of Bell's 1964 Paper by Wiseman, Cavalcanti, and Rieffel"

    CERN Document Server

    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.

  3. Some Approximation Theorems

    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.

  4. The holographic F theorem

    CERN Document Server

    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.

  5. Negishi's Theorem and Method

    OpenAIRE

    Vela Velupillai, K.

    2011-01-01

    Takashi Negishi's remarkable youthful contribution to welfare economics, general equilibrium theory and, with the benefit of hindsight, also to one strand of computable general equilibrium theory, all within the span of six pages in one article, has become one of the modern classics of general equilibrium theory and mathematical economics. Negishi's celebrated theorem and what has been called Negishi's Method have formed one foundation for computable general equilibrium theory. In this paper ...

  6. The Recovery Theorem

    OpenAIRE

    Stephen A. Ross

    2011-01-01

    We can only estimate the distribution of stock returns but we observe the distribution of risk neutral state prices. Risk neutral state prices are the product of risk aversion - the pricing kernel - and the natural probability distribution. The Recovery Theorem enables us to separate these and to determine the market's forecast of returns and the market's risk aversion from state prices alone. Among other things, this allows us to determine the pricing kernel, the market risk premium, the pro...

  7. Sandwich classification theorem

    Directory of Open Access Journals (Sweden)

    Alexey Stepanov

    2015-09-01

    Full Text Available The present note arises from the author's talk at the conference ``Ischia Group Theory 2014''. For subgroups FleN of a group G denote by Lat(F,N the set of all subgroups of N , containing F . Let D be a subgroup of G . In this note we study the lattice LL=Lat(D,G and the lattice LL ′ of subgroups of G , normalized by D . We say that LL satisfies sandwich classification theorem if LL splits into a disjoint union of sandwiches Lat(F,N G (F over all subgroups F such that the normal closure of D in F coincides with F . Here N G (F denotes the normalizer of F in G . A similar notion of sandwich classification is introduced for the lattice LL ′ . If D is perfect, i.,e. coincides with its commutator subgroup, then it turns out that sandwich classification theorem for LL and LL ′ are equivalent. We also show how to find basic subroup F of sandwiches for LL ′ and review sandwich classification theorems in algebraic groups over rings.

  8. Bourgain's discretization theorem

    CERN Document Server

    Giladi, Ohad; Schechtman, Gideon

    2011-01-01

    Bourgain's discretization theorem asserts that there exists a universal constant $C\\in (0,\\infty)$ with the following property. Let $X,Y$ be Banach spaces with $\\dim X=n$. Fix $D\\in (1,\\infty)$ and set $\\d= e^{-n^{Cn}}$. Assume that $\\mathcal N$ is a $\\d$-net in the unit ball of $X$ and that $\\mathcal N$ admits a bi-Lipschitz embedding into $Y$ with distortion at most $D$. Then the entire space $X$ admits a bi-Lipschitz embedding into $Y$ with distortion at most $CD$. This mostly expository article is devoted to a detailed presentation of a proof of Bourgain's theorem. We also obtain an improvement of Bourgain's theorem in the important case when $Y=L_p$ for some $p\\in [1,\\infty)$: in this case it suffices to take $\\delta= C^{-1}n^{-5/2}$ for the same conclusion to hold true. The case $p=1$ of this improved discretization result has the following consequence. For arbitrarily large $n\\in \\N$ there exists a family $\\mathscr Y$ of $n$-point subsets of ${1,...,n}^2\\subseteq \\R^2$ such that if we write $|\\mathscr ...

  9. Charmonium and exotics from Belle

    CERN Document Server

    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 $B\\to K\\pi + X(\\to\\pi^+\\pi^-J/\\psi)$.

  10. Bell violation in the Sky

    CERN Document Server

    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...

  11. Optical Bell Measurement by Fock Filtering

    CERN Document Server

    Paris, M G A; Jonathan, D; Bose, S; D'Ariano, G M; Paris, MGA

    2000-01-01

    We describe a nonlinear interferometric setup to perform a complete optical Bell measurement, i.e. to unambigously discriminate the four polarization entangled EPR-Bell photon pairs. The scheme is robust against detector inefficiency.

  12. John Bell and the Identical Twins

    CERN Multimedia

    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.

  13. Belle Physics at Wayne State

    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.

  14. Nonlocality, Bell's Ansatz and Probability

    CERN Document Server

    Kracklauer, A F

    2006-01-01

    Quantum Mechanics lacks an intuitive interpretation, which is the cause of a generally formalistic approach to its use. This in turn has led to a certain insensitivity to the actual meaning of many words used in its description and interpretation. Herein, we analyze carefully the possible meanings of those terms used in analysis of EPR's contention, that Quantum Mechanics is incomplete, as well as Bell's work descendant therefrom. As a result, many inconsistencies and errors in contemporary discussions of nonlocality, as well as in Bell's Ansatz with respect to the laws of probability, are identified. Evading these errors precludes serious conflicts between Quantum Mechanics and Special Relativity and Philosophy.

  15. 33 CFR 117.424 - Belle River.

    Science.gov (United States)

    2010-07-01

    ... 33 Navigation and Navigable Waters 1 2010-07-01 2010-07-01 false Belle River. 117.424 Section 117... OPERATION REGULATIONS Specific Requirements Louisiana § 117.424 Belle River. The draw of the S70 bridge, mile 23.8 (Landside Route) near Belle River, shall open on signal; except that, from 10 p.m. to 6...

  16. 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.……

  17. Bells: the past and the present

    Institute of Scientific and Technical Information of China (English)

    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.

  18. 27 CFR 9.55 - Bell Mountain.

    Science.gov (United States)

    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...

  19. A theorem in relativistic electronics

    Science.gov (United States)

    Yongjian, Yu

    1990-04-01

    This paper presents a theorem that connects the dispersion relation of the Electron Cyclotron Maser' and the oscillation equation of the Gyromonotron. This theorem gives us a simple way of obtaining the osscillating characteristics of the Gyromonotron provided that dispersion relation of the ECRM is given. Though the theorem is proved only with the case of ECRM and Gyromonotron, it holds for other kinds of Electron Masers, FEL4etc. and corresponding osscillators.

  20. For Whom the Bell Tolls.

    Science.gov (United States)

    Houston, Paul

    1996-01-01

    Selfishness has spawned a new breed of racism, driven by fear, fed by scarcity, and manifested through economic imperatives. California's Proposition 187 and Herrnstein and Murray's book "The Bell Curve" are built on racist foundations. Our current obsession with race is driven by an economy and an elitist social system that is dismantling the…

  1. A-Browder's Theorem and Generalized a-Weyl's Theorem

    Institute of Scientific and Technical Information of China (English)

    Xiao Hong CAO

    2007-01-01

    Two variants of the essential approximate point spectrum are discussed. We find for example that if one of them coincides with the left Drazin spectrum then the generalized a-Weyl's theorem holds, and conversely for a-isoloid operators. We also study the generalized a-Weyl's theorem for Class A operators.

  2. 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

  3. Geometry of the Adiabatic Theorem

    Science.gov (United States)

    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.…

  4. 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.

  5. Andreev's Theorem on hyperbolic polyhedra

    CERN Document Server

    Roeder, R K W; Dunbar, W D; Roeder, Roland K. W.; Hubbard, John H.; Dunbar, William D.

    2004-01-01

    In 1970, E. M. Andreev published a classification of all three-dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, $C$, Andreev's Theorem provides five classes of linear inequalities, depending on $C$, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing $C$ with the assigned dihedral angles. Andreev's Theorem also shows that the resulting polyhedron is unique, up to hyperbolic isometry. Andreev's Theorem is both an interesting statement about the geometry of hyperbolic 3-dimensional space, as well as a fundamental tool used in the proof for Thurston's Hyperbolization Theorem for 3-dimensional Haken manifolds. It is also remarkable to what level the proof of Andreev's Theorem resembles (in a simpler way) the proof of Thurston. We correct a fundamental error in Andreev's proof of existence and also provide a readable new proof of the other parts of the proof of And...

  6. 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.

  7. Herbrand's Fundamental Theorem - an encyclopedia article

    OpenAIRE

    Wirth, Claus-Peter

    2015-01-01

    Herbrand's Fundamental Theorem provides a constructive characterization of derivability in first-order predicate logic by means of sentential logic. Sometimes it is simply called "Herbrand's Theorem", but the longer name is preferable as there are other important "Herbrand theorems" and Herbrand himself called it "Th\\'eor\\`eme fondamental". It was ranked by Bernays [1957] as follows: "In its proof-theoretic form, Herbrand's Theorem can be seen as the central theorem of predicate logic. It exp...

  8. Combinatorial Reciprocity Theorems

    CERN Document Server

    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.

  9. Bell Palsy and Acupuncture Treatment

    Directory of Open Access Journals (Sweden)

    Betul Battaloglu Ižnanc

    2013-08-01

    A 22-year-old female patient, a midwifery student, had treatment with corticosteroid and antiviral agents as soon as Bell Palsy (BP was diagnosed (House-Breckman stage 6. Six weeks later, patient didn’t recover, while in House-Breckman stage 3, acupuncture was perfomed and local and distal acupoints were used with ears, body and face. Ear acupuncture point was used two times with detection. In the course of six sessions body and face points were stimulated by electroacupuncture. After ten acupuncture treatments, the subjective symptoms and the facial motion on the affected side improved. There was an spotting ecchymosis the ST2 points on. The symmetry of the face is a determinant of facial charm and influences interpersonal attraction for adults, children and pregnant women. Medical options for the sequelae of BP are limited. Acupuncture’s effectively in Bell palsy patients’ should be shown with more clinical and electrophysiological studies.

  10. Belle II Silicon Vertex Detector

    CERN Document Server

    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.

  11. Time-Continuous Bell Measurements

    CERN Document Server

    Hofer, Sebastian G; Aspelmeyer, Markus; Hammerer, Klemens

    2013-01-01

    We combine the concept of Bell measurements, in which two systems are projected into maximally entangled states, with the concept of continuous measurements, which concerns the evolution of a continuously monitored quantum system. For time continuous Bell measurements based on homodyne detection of light we derive the corresponding stochastic Schr\\"odinger equations, as well as the unconditional feedback master equations. Our results cover in particular the two scenarios of time-continuous quantum teleportation and entanglement swapping. We apply our results to show that (i) two two-level systems can be deterministically entangled via homodyne detection of light, even including photon loss approaching the fundamental limit of 50%, and (ii) a quantum state of light can be continuously teleported to a mechanical oscillator. This time-continuous remote quantum state preparation works under the same conditions as are required for optomechanical ground state cooling.

  12. Belle II silicon vertex detector

    Science.gov (United States)

    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.

  13. A loophole-free Bell test with spin quits in diamond

    Science.gov (United States)

    Dreau, Anais; Hensen, Bas; Bernien, Hannes; Reiserer, Andreas; Ruitenberg, Just; Blok, Machiel; Markham, Matthew; Twitchen, Daniel; Wehner, Stephanie; Hanson, Ronald; Element 6 Team

    2015-03-01

    One of the most intriguing phenomena in quantum physics is the entanglement of spatially separated objects. The benchmark to prove the fundamental non-locality of remote entanglement is provided by the famous Bell's theorem. Nevertheless, all its experimental implementations to date open the door to loopholes that restrict the practical validity of this theorem., we present our latest experimental results towards the realization of a Bell test, aimed to close the detection loophole and address the locality and free-will loopholes in a single experiment. Our qubits consist of the electronic spin associated with single NV center defects in diamond. An efficient remote entanglement protocol allows us to generate entangled qubit pairs between two labs separated by 1.3 km on the TU Delft campus. The moderate time (99%) qubit rotations and efficient (>97%) readout make our setup a good candidate to allow the experimental violation of Bell's inequalities between two space-like separated entangled spins without relying on the fair sampling assumption. FOM, NWO, ERC, Kavli Institute of Nanoscience Delft, QUTech, STW.

  14. Particle Identification at Belle II

    CERN Document Server

    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.

  15. Bell inequality and complementarity loophole

    OpenAIRE

    Czachor, Marek

    1997-01-01

    A simple classical, deterministic, local situation violating the Bell inequality is described. The detectors used in the experiment are ideal and the observers who decide which pair of measuring devices to choose for a given pair of particles have free will. The construction uses random variables which are not jointly measurable in a single run of an experiment and the hidden variables have a nonsymmetric probability density. Such random variables are complementary but still fully classical. ...

  16. Bell inequalities and incompatible measurements

    OpenAIRE

    Morgan, Peter

    2003-01-01

    Bell inequalities are a consequence of measurement incompatibility (not, as generally thought, of nonlocality). In classical terms, this is equivalent to contextuality -- measurement devices do have a significant effect. Contextual models are reasonable in classical physics, which always took the view that we ignore measurement devices whenever possible, but if that isn't good enough then we do have to model measurement devices. It is also argued that quantum theory should only be taken with ...

  17. Common questions about Bell palsy.

    Science.gov (United States)

    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.

  18. Complex integration and Cauchy's theorem

    CERN Document Server

    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

  19. -Dimensional Fractional Lagrange's Inversion Theorem

    Directory of Open Access Journals (Sweden)

    F. A. Abd El-Salam

    2013-01-01

    Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.

  20. KAM Theorem and Renormalization Group

    OpenAIRE

    E. Simone; Kupiainen, A.

    2007-01-01

    We give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a PDE with quadratic nonlinearity, the so called Polchinski renormalization group equation studied in quantum field theory.

  1. 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.

  2. The Kolmogorov-Riesz compactness theorem

    CERN Document Server

    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.

  3. Noether theorems and higher derivatives

    OpenAIRE

    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...

  4. Complex extension of Wigner's theorem

    CERN Document Server

    Brody, Dorje C

    2013-01-01

    Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed, we obtain the following complex generalisation of Wigner's theorem: a holomorphically projective (complex geodesic-curves preserving) transformation on a quantum state space must be generated by a Hamiltonian that is not necessarily Hermitian.

  5. Local virial and tensor theorems.

    Science.gov (United States)

    Cohen, Leon

    2011-11-17

    We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem. PMID:21863837

  6. Local virial and tensor theorems.

    Science.gov (United States)

    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.

  7. Acceptable Complexity Measures of Theorems

    OpenAIRE

    Grenet, Bruno

    2009-01-01

    In 1931, G\\"odel presented in K\\"onigsberg his famous Incompleteness Theorem, stating that some true mathematical statements are unprovable. Yet, this result gives us no idea about those independent (that is, true and unprovable) statements, about their frequency, the reason they are unprovable, and so on. Calude and J\\"urgensen proved in 2005 Chaitin's "heuristic principle" for an appropriate measure: the theorems of a finitely-specified theory cannot be significantly more complex than the t...

  8. Goedel's Incompleteness Theorems hold vacuously

    OpenAIRE

    Anand, Bhupinder Singh

    2002-01-01

    In an earlier paper, "Omega-inconsistency in Goedel's formal system: a constructive proof of the Entscheidungsproblem" (math/0206302), I argued that a constructive interpretation of Goedel's reasoning establishes any formal system of Arithmetic as omega-inconsistent. It follows from this that Goedel's Theorem VI holds vacuously. In this paper I show that Goedel's Theorem XI essentially states that, if we assume there is a P-formula [Con(P)] whose standard interpretation is equivalent to the a...

  9. Bell Canyon test summary report

    International Nuclear Information System (INIS)

    The Bell Canyon Test was an in situ evaluation of the ability of a cement grout plug to seal boreholes. It consisted of a 2-m-long, 20-cm-diameter grout plug in an anhydrite formation at a depth of 1370 m, directly above an aquifer that provided a 12.4 MPa (1800 psi) differential pressure. The aquifer had a production capability of 38,000 l/day (240 bbl/day, 104 gal/day). The observed leakage after plug installation was 0.6 l/day, which is equivalent to a 50 microdarcy flow path assuming all flow occurred through the plug cross-sectional area. Laboratory results and analysis of field data indicate that the bulk of the flow occurred through a microstructure at the interface between the plug and the host rock. The Bell Canyon Test demonstrated that a plug could be formulated, emplaced, and tested under actual conditions and provide acceptable performance. When these results are related to the WIPP performance assessment models, they provide additional confidence that borehole plugging can be accomplished satisfactorily. The Bell Canyon results can also be used as basis for future activities in the generic repository sealing program for similar emplacements and performance assessment evaluations. If the observed leakage rates are not acceptable at other sites, the BCT results would indicate that the first step in improving such emplacements should deal with improved bonding of the plug to the rock at these sites. The results obtained from the BCT, when coupled with results from long-term durability assessments, form a plug performance data basis for repository designers at other proposed waste repository sites

  10. Contemporary management of Bell palsy.

    Science.gov (United States)

    Jowett, Nate; Hadlock, Tessa A

    2015-04-01

    Bell palsy (BP) is the most common diagnosis in acute and chronic facial palsy. Although most patients fully recover, more than one-quarter will have residual dysfunction. Of these, nearly half will demonstrate severe limitations in facial expression. Though significant attention has been paid to acute management and prognosis, a paucity of literature exists addressing management of the long-term sequelae of BP. This article describes contemporary use of physical therapy, injectables, and static and dynamic surgical procedures in facial reanimation of acute and chronic BP. PMID:25958893

  11. 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 dijikstra’s 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.

  12. A model with cosmological Bell inequalities

    CERN Document Server

    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.

  13. 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.

  14. George Boole and the Bell inequalities

    CERN Document Server

    Rosinger, E E

    2004-01-01

    As shown by Pitowsky, the Bell inequalities are related to certain classes of probabilistic inequalities dealt with by George Boole, back in the 1850s. Here a short presentation of this relationship is given. Consequently, the Bell inequalities can be obtained without any assumptions of physical nature, and merely through mathematical argument.

  15. Belle-II Experiment Network Requirements

    Energy Technology Data Exchange (ETDEWEB)

    Asner, David; Bell, Greg; Carlson, Tim; Cowley, David; Dart, Eli; Erwin, Brock; Godang, Romulus; Hara, Takanori; Johnson, Jerry; Johnson, Ron; Johnston, Bill; Dam, Kerstin Kleese-van; Kaneko, Toshiaki; Kubota, Yoshihiro; Kuhr, Thomas; McCoy, John; Miyake, Hideki; Monga, Inder; Nakamura, Motonori; Piilonen, Leo; Pordes, Ruth; Ray, Douglas; Russell, Richard; Schram, Malachi; Schroeder, Jim; Sevior, Martin; Singh, Surya; Suzuki, Soh; Sasaki, Takashi; Williams, Jim

    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.

  16. Physics Achievements from the Belle Experiment

    CERN Document Server

    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.

  17. The design of bells with harmonic overtones.

    Science.gov (United States)

    McLachlan, Neil; Nigjeh, Behzad Keramati; Hasell, Anton

    2003-07-01

    Musical bells have had limited application due to the presence of inharmonic partials in the lower part of their acoustic spectra. A series of bells has been designed that contains up to seven partial frequencies in the harmonic series beginning at the fundamental frequency. This was achieved by choosing geometries for finite-element analysis models in which as many purely circumferential bending modes as possible occurred at frequencies below any mode with an axial ring node. The bell models were then fine tuned using gradient projection method shape optimization and the resulting profiles were cast in silicon bronze. A range of bell geometries and timbres is analyzed using psycho-acoustic models and is discussed in relation to European carillon bells. PMID:12880061

  18. Research News -- Quantum Mechanical Entanglement and Tests of CPT Theorem with Neutral Mesons at e+ e- Colliders

    CERN Document Server

    Ananthanarayan, B

    2007-01-01

    We review the recent confirmation of quantum entanglement in e+ e- collisions at the BELLE experiment at KEK-B in Japan with neutral B- mesons, and at the KLOE experiment at the DAFNE in Italy with neutral K- mesons. Such effects in the latter system seen already in proton-antiproton collisions by the CPLEAR experiment are also reviewed for purposes of comparison. In addition, the KLOE experiment provides new tests of the CPT theorem and are briefly discussed.

  19. Nambu-Goldstone theorem and spin-statistics theorem

    Science.gov (United States)

    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.

  20. Fluctuation theorems for quantum processes

    CERN Document Server

    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.

  1. New Double Soft Emission Theorems

    CERN Document Server

    Cachazo, Freddy; Yuan, Ellis Ye

    2015-01-01

    We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, DBI, Einstein-Maxwell-Scalar, NLSM and Yang-Mills-Scalar. We use the recently found CHY representation of these theories in order to give a simple proof of the leading order part of all these theorems

  2. Noether theorems and higher derivatives

    CERN Document Server

    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.

  3. 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.

  4. Nonperturbative Adler-Bardeen theorem

    International Nuclear Information System (INIS)

    The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions

  5. A Stokes theorem for everyone

    CERN Document Server

    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.

  6. Violating a Bell inequality with classical states

    CERN Document Server

    Liu, Qin; Lamas-Linares, Antía; Skaar, Johannes; Makarov, Vadim; Kurtsiefer, Christian

    2011-01-01

    A strong probe for limits of classical physics is the Bell inequality between measurements of separated particles. Its violation can be used to secure a shared secret between two parties, but a fair-sampling assumption has to be made for limited detection efficiencies. Here, we present an experimental violation of a Bell inequality by classical states, exploiting imperfections in common photodetectors. We also propose measurements to obtain violations exceeding those allowed by quantum physics for ideal Bell tests. This exploit demonstrates that device-independent quantum cryptography requires the detection loophole be closed.

  7. A normal form theorem around symplectic leaves

    NARCIS (Netherlands)

    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.

  8. Interpolation theorems on weighted Lorentz martingale spaces

    Institute of Scientific and Technical Information of China (English)

    Yong JIAO; Li-ping FAN; Pei-de LIU

    2007-01-01

    In this paper several interpolation theorems on martingale Lorentz spaces are given. The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces. Applying the interpolation theorems, we obtain some inequalities on martingale transform operator.

  9. Von Laue's theorem and its applications

    CERN Document Server

    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.

  10. On the Putnam-Fuglede theorem

    Directory of Open Access Journals (Sweden)

    Yin Chen

    2004-01-01

    Full Text Available We extend the Putnam-Fuglede theorem and the second-degree Putnam-Fuglede theorem to the nonnormal operators and to an elementary operator under perturbation by quasinilpotents. Some asymptotic results are also given.

  11. 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....

  12. 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.

  13. Angle Defect and Descartes' Theorem

    Science.gov (United States)

    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.)

  14. Discovering the Inscribed Angle Theorem

    Science.gov (United States)

    Roscoe, Matt B.

    2012-01-01

    Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…

  15. Illustrating the Central Limit Theorem

    Science.gov (United States)

    Corcoran, Mimi

    2016-01-01

    Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…

  16. Microwave electronics Slater's perturbation theorem

    International Nuclear Information System (INIS)

    Slater's perturbation theorem is one of the most useful for both experiments and theories of microwave electronics. In particular, this is applied to measurements of the field strengths in standing-wave systems. Since a traveling wave can be represented by a linear combination of two standing waves, the field measurement is also possible in a traveling-wave system. The theorem tells us the amount of the shift in a resonant frequency arising from a metallic body. Since the amount is dependent upon the square of the electric and magnetic field strengths at the metallic body, one can obtain the field strengths at the metallic body from the measured frequency shift. First the theorem is derived in Sec. 2. We then discuss the implications of the theorem by deriving it intuitively in Sec. 3. The perturbation of the field due to a metallic body is described in Sec. 4, where the frequency shift is actually related to the field strengths. In Sec. 5, we describe how to determine the impedance by using the data thus measured. Examples of field measurement are shown in Sec. 6 together with the impedance measurement. (author)

  17. Almost Subadditive Extensions of Kingman's Ergodic Theorem

    OpenAIRE

    Schurger, Klaus

    1991-01-01

    Based on two notions of almost subadditivity which were introduced by Derriennic and Schurger, two a.s. limit theorems are proved which both generalize Kingman's subadditive ergodic theorem. These results, being valid under weak moment conditions, are obtained by short proofs. One of these proofs is completely elementary and does not even make use of Birkhoff's ergodic theorem which, instead, is obtained as a by-product. Finally, an improvement of Liggett's a.s. limit theorem is given.

  18. 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.

  19. Herpes Simplex Virus-1 and Bell's Palsy

    Directory of Open Access Journals (Sweden)

    J Gordon Millichap

    2008-05-01

    Full Text Available The association between herpes simplex virus-1 (HSV-1 infection and Bell palsy was determined in 47 children studied at Children's Hospital at Montefiore, Bronx, NY. Swabs of saliva and conjunctiva were taken for PCR testing.

  20. Helicopter attempts tow of Liberty Bell 7

    Science.gov (United States)

    1961-01-01

    Marine helicopter appears to have Liberty Bell 7 in tow after Virgil I. Grissom's successful flight of 305 miles down the Atlantic Missile Range. Minutes after 'Gus' Grissom got out of the spacecraft, it sank.

  1. A generalized no-broadcasting theorem

    OpenAIRE

    Barnum, H.; Barrett, J; Leifer, M.; Wilce, A.

    2007-01-01

    We prove a generalized version of the no-broadcasting theorem, applicable to essentially \\emph{any} nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with ``super-quantum'' correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.

  2. Pythagorean Theorem Proofs: Connecting Interactive Websites

    Science.gov (United States)

    Lin, Cheng-Yao

    2007-01-01

    There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)

  3. An Algebraic Identity Leading to Wilson Theorem

    OpenAIRE

    Ruiz, Sebastian Martin

    2004-01-01

    In most text books on number theory Wilson Theorem is proved by applying Lagrange theorem concerning polynomial congruences.Hardy and Wright also give a proof using cuadratic residues. In this article Wilson theorem is derived as a corollary to an algebraic identity.

  4. On Brayton and Moser's missing stability theorem

    NARCIS (Netherlands)

    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

  5. 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.

  6. 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.

  7. Reality or Locality? - Proposed test to decide \\textit{how} Nature breaks Bell's inequality

    CERN Document Server

    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...

  8. 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.

  9. Three experimental tests of Bell's inequalities by measurement of polarization correlation of photons

    International Nuclear Information System (INIS)

    We have performed three experimental tests of Bell's inequalities by measuring the linear-polarization correlation of photons emitted by pairs in the 4p21S0 → 4s4p 1P1 → 4s21S0 radiative cascade of calcium. The first part of this dissertation reminds the theoretical background (Bell's theorem), and the experimental situation (previous experiments). We then describe our apparatus: the source (calcium atomic beam selectively excited by two-photon absorption), the optics, the photon coincidence-counting system. Our first experiment, analogous to previous ones (but more precise) involves one-channel polarizers. Our second experiment, based on a conceptually simpler scheme, uses two-channel polarizers. The third experiment involves acousto-optical switches followed by two linear polarizers: these devices act as time-varying polarizers, the orientation of which is changed during the time of flight of photons. In the three experiments, the results are in good agreement with the Quantum mechanical predictions, and they distinctly violate the relevant Bell's inequalities

  10. Bell's palsy before Bell : Evert Jan Thomassen a Thuessink and idiopathic peripheral facial paralysis

    NARCIS (Netherlands)

    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

  11. The relativistic virial theorem and scale invariance

    CERN Document Server

    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.

  12. The Classical Version of Stokes' Theorem Revisited

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    2005-01-01

    Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we prove that the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly that this latter fact usually does not get within reach for students in first year calculus courses and secondly that calculus textbooks in general only just hint at the correspondence alluded...

  13. The classical version of Stokes' Theorem revisited

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    2008-01-01

    Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we show how the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly...... that this latter fact usually does not get within reach for students in first year calculus courses and secondly that calculus textbooks in general only just hint at the correspondence alluded to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used...

  14. Navier Stokes Theorem in Hydrology

    Science.gov (United States)

    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

  15. Bell tests with optimal local hidden variable models

    CERN Document Server

    Wang, Fuming

    2014-01-01

    An alternative method for detection-loophole-free Bell test is proposed using local hidden variable (LHV) models with optimal detection efficiencies. A framework for constructing such optimal LHV models is presented. Optimal LHV models for maximally and non-maximally entangled twopartite states are constructed and compared with Bell inequalities. The equivalence between Bell tests based on Bell inequalities and on optimal models is demonstrated. Testable LHV models with detection efficiencies lower than that of the Bell inequalities are demonstrated for the first time. Applications in Bell tests and in device-independent quantum information processing are discussed.

  16. Lectures on Fermat's last theorem

    International Nuclear Information System (INIS)

    The report presents the main ideas involved in the approach towards the so-called Fermat's last theorem (FLT). The discussion leads to the point where recent work of A. Wiles starts and his work is not discussed. After a short history of the FLT and of the present approach, are discussed the elliptic curves and the modular forms with their relations, the Taniyama-Shimura-Well conjecture and the FLT

  17. Pythagoras Theorem and Relativistic Kinematics

    Science.gov (United States)

    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.

  18. A Miniaturisation of Ramsey's Theorem

    Science.gov (United States)

    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.

  19. Dynamic Newton-Puiseux Theorem

    OpenAIRE

    Mannaa, Bassel; Coquand, Thierry

    2013-01-01

    A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization algorithm of polynomials over the base field is not needed. The extensions obtained are a type of regular algebras over the base field and the expansions are given as formal power series over these algebras.

  20. Compactness theorems of fuzzy semantics

    Institute of Scientific and Technical Information of China (English)

    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.

  1. 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.

  2. On Harnack's theorem and extensions

    Science.gov (United States)

    Costa, Antonio F.; Parlier, Hugo

    Harnack's theorem states that the fixed points of an orientation reversing involution of a compact orientable surface of genus g are a set of k disjoint simple closed geodesic where 0≤ k≤ g+1 . The first goal of this article is to give a purely geometric, complete and self-contained proof of this fact. In the case where the fixed curves of the involution do not separate the surface, we prove an extension of this theorem, by exhibiting the existence of auxiliary invariant curves with interesting properties. Although this type of extension is well known (see, for instance, Comment. Math. Helv. 57(4): 603-626 (1982) and Transl. Math. Monogr., vol. 225, Amer. Math. Soc., Providence, RI, 2004), our method also extends the theorem in the case where the surface has boundary. As a byproduct, we obtain a geometric method on how to obtain these auxiliary curves. As a consequence of these constructions, we obtain results concerning presentations of Non-Euclidean crystallographic groups and a new proof of a result on the set of points corresponding to real algebraic curves in the compactification of the Moduli space of complex curves of genus g , overline{M_{g}} . More concretely, we establish that given two real curves there is a path in overline{M_{g}} which passes through at most two singular curves, a result of M. Seppaelae (Ann. Sci. Ecole Norm. Sup. (4), 24(5), 519-544 (1991)).

  3. In AppreciationThe Depth and Breadth of John Bell's Physics

    Science.gov (United States)

    Jackiw, Roman; Shimony, Abner

    This essay surveys the work of John Stewart Bell, one of the great physicists of the twentieth century. Section 1 is a brief biography, tracing his career from working-class origins and undergraduate training in Belfast, Northern Ireland, to research in accelerator and nuclear physics in the British national laboratories at Harwell and Malvern, to his profound research on elementary particle physics as a member of the Theory Group at CERN and his equally profound ``hobby'' of investigating the foundations of quantum mechanics. Section 2 concerns this hobby, which began in his discontent with Bohr's and Heisenberg's analyses of the measurement process. He was attracted to the program of hidden variables interpretations, but he revolutionized the foundations of quantum mechanics by a powerful negative result: that no hidden variables theory that is ``local'' (in a clear and well-motivated sense) can agree with all the correlations predicted by quantum mechanics regarding well-separated systems. He further deepened the foundations of quantum mechanics by penetrating conceptual analyses of results concerning measurement theory of von Neumann, de Broglie and Bohm, Gleason, Jauch and Piron, Everett, and Ghirardi-Rimini-Weber. Bell's work in particle theory (Section 3) began with a proof of the CPT theorem in his doctoral dissertation, followed by investigations of the phenomenology of CP-violating experiments. At CERN Bell investigated the commutation relations in current algebras from various standpoints. The failure of current algebra combined with partially conserved current algebra to permit the experimentally observed decay of the neutral pi-meson into two photons stimulated the discovery by Bell and Jackiw of anomalous or quantal symmetry breaking, which has numerous implications for elementary particle phenomena. Other late investigations of Bell on elementary particle physics were bound states in quantum chromodynamics (in collaboration with Bertlmann) and

  4. Generalized Bell Inequality Experiments and Computation

    CERN Document Server

    Hoban, Matty J; Browne, Dan E

    2011-01-01

    We consider general settings of Bell inequality experiments with many parties, where each party chooses from a finite number of measurement settings each with a finite number of outcomes. We investigate the constraints that Bell inequalities place upon the correlations possible in a local hidden variable theories using a geometrical picture of correlations. We show that local hidden variable theories can be characterized in terms of limited computational expressiveness, which allows us to characterize families of Bell inequalities. The limited computational expressiveness for many settings (each with many outcomes) generalizes previous results about the many-party situation each with a choice of two possible measurements (each with two outcomes). Using this computational picture we present generalizations of the Popescu-Rohrlich non-local box for many parties and non-binary inputs and outputs at each site. Finally, we comment on the effect of pre-processing on measurement data in our generalized setting and s...

  5. The Helmholtz theorem and retarded fields

    CERN Document Server

    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.

  6. The Helmholtz theorem and retarded fields

    Science.gov (United States)

    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.

  7. Clinical Practice Guideline of Acupuncture for Bell's Palsy

    Directory of Open Access Journals (Sweden)

    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.

  8. Software and Physics Simulation at Belle II

    CERN Document Server

    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.

  9. Orientation entanglement and temporal Bell inequalities

    CERN Document Server

    Milman, P; Charron, E; Keller, A; Atabek, Osman; Charron, Eric; Keller, Arne; Milman, Perola

    2006-01-01

    We introduce Bell-type inequalities detecting correlations between spatial orientations of two quantum angular momenta. In such inequalities, measurements are performed on each subsystem at different times. These times play the role of the polarizer angles in Bell tests realized with photons. In a first inequality, orientation correlations are the relevant observables. Orientation is then dichotomized by distinguishing "positively" and "negatively" oriented subsystems. We show that the proposed inequalities are violated by a large set of entangled states. The experimental realisation of such proposals can be performed using atoms or molecules. These results open new ways for practical entanglement tests in N-level and continuous variables quantum systems.

  10. Symbolic logic and mechanical theorem proving

    CERN Document Server

    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.

  11. Counterexamples To Bertini Theorems for Test Ideals

    OpenAIRE

    Bydlon, Andrew

    2016-01-01

    In algebraic geometry, Bertini theorems are an extremely important tool. A generalization of the classical theorem to multiplier ideals show that multiplier ideals restrict to a general hyperplane section. In characteristic $p > 0$, the test ideal can be seen to be the characteristic $p > 0$ analog of the multiplier ideal. However, in this paper it is shown that the same type of Bertini type theorem does not hold for test ideals.

  12. The relativistic virial theorem and scale invariance

    OpenAIRE

    Gaite, Jose

    2013-01-01

    The virial theorem is related to the dilatation properties of bound states. This is realized, in particular, by the Landau-Lifshitz formulation of the relativistic virial theorem, in terms of the trace of the energy-momentum tensor. We construct a Hamiltonian formulation of dilatations in which the relativistic virial theorem naturally arises as the condition of stability against dilatations. A bound state becomes scale invariant in the ultrarelativistic limit, in which its energy vanishes. H...

  13. Bringing Theorem Proving to the (sonic) Masses

    OpenAIRE

    Gallego Arias, Emilio Jesús; Pin, Benoît; Jouvelot, Pierre,

    2015-01-01

    We explore the intersection of interactive theorem proving and digital signal processing through the use of web-based, rich interfaces. Traditionally, the barrier to entry to interactive theorem proving has been high.Provers are complex systems using obscure programming languages, and libraries may be underdocumented and use formalisms and notations far from the standard domain-specific practice. Thus, it doesn't come at a surprise that interactive theorem proving has seldom been explored in ...

  14. Expanding the Interaction Equivalency Theorem

    Directory of Open Access Journals (Sweden)

    Brenda Cecilia Padilla Rodriguez

    2015-06-01

    Full Text Available Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner is present at a high level. This study sought to apply this theorem to the corporate sector, and to expand it to include other indicators of course effectiveness: satisfaction, knowledge transfer, business results and return on expectations. A large Mexican organisation participated in this research, with 146 learners, 30 teachers and 3 academic assistants. Three versions of an online course were designed, each emphasising a different type of interaction. Data were collected through surveys, exams, observations, activity logs, think aloud protocols and sales records. All course versions yielded high levels of effectiveness, in terms of satisfaction, learning and return on expectations. Yet, course design did not dictate the types of interactions in which students engaged within the courses. Findings suggest that the interaction equivalency theorem can be reformulated as follows: In corporate settings, an online course can be effective in terms of satisfaction, learning, knowledge transfer, business results and return on expectations, as long as (a at least one of three types of interaction (learner-content, learner-teacher or learner-learner features prominently in the design of the course, and (b course delivery is consistent with the chosen type of interaction. Focusing on only one type of interaction carries a high risk of confusion, disengagement or missed learning opportunities, which can be managed by incorporating other forms of interactions.

  15. The Real "Toll" of A. G. Bell: Lessons about Eugenics

    Science.gov (United States)

    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…

  16. Bell inequality and CP violation in the neutral kaon system

    CERN Document Server

    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.

  17. Bayesian Posteriors Without Bayes' Theorem

    CERN Document Server

    Hill, Theodore P

    2012-01-01

    The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the classical Bayesian posterior is the unique posterior that minimizes the loss of Shannon information in combining the prior and the likelihood distributions. These results, direct corollaries of recent results about conflations of probability distributions, reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics.

  18. Cosmological Perturbations and the Weinberg Theorem

    CERN Document Server

    Akhshik, Mohammad; Jazayeri, Sadra

    2015-01-01

    The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.

  19. 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.

  20. Bit-Blasting ACL2 Theorems

    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.

  1. Constructive and Computable Hahn-Banach Theorems for the (Second) Fundamental Theorem of Welfare Economics

    OpenAIRE

    Vela Velupillai, K.

    2014-01-01

    The Hahn-Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using nonconstructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn-Banach theorems in mathematical economics and advanced general equilibrium theory. The suggested modification would make applied and policy-oriented...

  2. An elementary derivation of the quantum virial theorem from Hellmann-Feynman theorem

    Science.gov (United States)

    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.

  3. "All that palsies is not Bell's" - The need to define Bell's palsy as an adverse event following immunization

    NARCIS (Netherlands)

    Rath, Barbara; Linder, Thomas; Cornblath, David; Hudson, Michael; Fernandopulle, Rohini; Hartmann, Katharina; Heininger, Ulrich; Izurieta, Hector; Killion, Leslie; Kokotis, Pangiotis; Oleske, James; Vajdy, Michael; Wong, Virginia

    2007-01-01

    Bell's palsy has been reported as an adverse event following immunization (AEFI). Review of the published literature reveals that several characteristics have been used to describe Bell's palsy, which differ significantly from author to author. Evidently, the definition of "Bell's palsy" remains con

  4. 76 FR 81992 - PPL Bell Bend, LLC; Combined License Application for Bell Bend Nuclear Power Plant; Exemption

    Science.gov (United States)

    2011-12-29

    ... From the Federal Register Online via the Government Publishing Office NUCLEAR REGULATORY 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...

  5. A Poncelet theorem for lines

    CERN Document Server

    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.

  6. Freiman's theorem for solvable groups

    CERN Document Server

    Tao, Terence

    2009-01-01

    Freiman's theorem asserts, roughly speaking, if that a finite set in a torsion-free abelian group has small doubling, then it can be efficiently contained in (or controlled by) a generalised arithmetic progression. This was generalised by Green and Ruzsa to arbitrary abelian groups, where the controlling object is now a coset progression. We extend these results further to solvable groups of bounded derived length, in which the coset progressions are replaced by the more complicated notion of a ``coset nilprogression''. As one consequence of this result, any subset of such a solvable group of small doubling is is controlled by a set whose iterated products grow polynomially, and which are contained inside a virtually nilpotent group. As another application we establish a strengthening of the Milnor-Wolf theorem that all solvable groups of polynomial growth are virtually nilpotent, in which only one large ball needs to be of polynomial size. This result complements recent work of Breulliard-Green, Fisher-Katz-...

  7. Generalized Bell States and Quantum Teleportation

    OpenAIRE

    Fujii, Kazuyuki

    2001-01-01

    We make a brief comment on measurement of quantum operators with degenerate eigenstates and apply to quantum teleportation. We also try extending the quantum teleportation by Bennett et al [5] to more general situation by making use of generalized Bell states.

  8. Mouthpiece and Bell Effects on Trombone Resonance

    Science.gov (United States)

    LoPresto, Michael C.

    2014-01-01

    The effects of the mouthpiece and bell on the frequencies of the vibrating air column in a trombone can be demonstrated quite readily by first calculating the expected resonant frequencies of a piece of PVC pipe that is the same length as a trombone, then replacing portions of the PVC pipe of the same length with first a cup-shaped mouthpiece and…

  9. The Cultural Contradictions of Daniel Bell.

    Science.gov (United States)

    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)

  10. 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.

  11. MIDAS™ DEMONSTRATION PLOTS IN BELL PEPPER

    Science.gov (United States)

    A demonstration trial comparing MIDAS™ (methyl iodide:chloropicrin 50:50) to methyl bromide:chloropicrin (67:33) was conducted in Saint Lucie County, FL on a commercial bell pepper production farm. Methyl bromide:chloropicrin was shank injected into performed beds at 392 kg/ha using three 25 cm dee...

  12. Detection loophole in asymmetric Bell experiments

    OpenAIRE

    Brunner, Nicolas; Gisin, Nicolas; Scarani, Valerio; Simon, Christoph

    2007-01-01

    The problem of closing the detection loophole with asymmetric systems, such as entangled atom-photon pairs, is addressed. We show that, for the Bell inequality I_3322, a minimal detection efficiency of 43% can be tolerated for one of the particles, if the other one is always detected. We also study the influence of noise and discuss the prospects of experimental implementation.

  13. Bell-inequality violation with "thermal" radiation

    OpenAIRE

    Filip, Radim; Dusek, Miloslav; Fiurasek, Jaromir; Mista, Ladislav

    2001-01-01

    The model of a quantum-optical device for a conditional preparation of entangled states from input mixed states is presented. It is demonstrated that even thermal or pseudo-thermal radiation can be entangled in such a way, that Bell-inequalities are violated.

  14. Violation of Bell's inequalities in quantum optics

    Science.gov (United States)

    Reid, M. D.; Walls, D. F.

    1984-01-01

    An optical field produced by intracavity four-wave mixing is shown to exhibit the following nonclassical features: photon antibunching, squeezing, and violation of Cauchy-Schwarz and Bell's inequalities. These intrinsic quantum mechanical effects are shown to be associated with the nonexistence of a positive normalizable Glauber-Sudarshan P function.

  15. 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?

  16. Baby Bell Libraries?--An Update.

    Science.gov (United States)

    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)

  17. An impossibility theorem for parameter independent hidden variable theories

    Science.gov (United States)

    Leegwater, Gijs

    2016-05-01

    Recently, Roger Colbeck and Renato Renner (C&R) have claimed that '[n]o extension of quantum theory can have improved predictive power' (Colbeck & Renner, 2011, 2012b). If correct, this is a spectacular impossibility theorem for hidden variable theories, which is more general than the theorems of Bell (1964) and Leggett (2003). Also, C&R have used their claim in attempt to prove that a system's quantum-mechanical wave function is in a one-to-one correspondence with its 'ontic' state (Colbeck & Renner, 2012a). C&R's claim essentially means that in any hidden variable theory that is compatible with quantum-mechanical predictions, probabilities of measurement outcomes are independent of these hidden variables. This makes such variables otiose. On closer inspection, however, the generality and validity of the claim can be contested. First, it is based on an assumption called 'Freedom of Choice'. As the name suggests, this assumption involves the independence of an experimenter's choice of measurement settings. But in the way C&R define this assumption, a no-signalling condition is surreptitiously presupposed, making the assumption less innocent than it sounds. When using this definition, any hidden variable theory violating parameter independence, such as Bohmian Mechanics, is immediately shown to be incompatible with quantum-mechanical predictions. Also, the argument of C&R is hard to follow and their mathematical derivation contains several gaps, some of which cannot be closed in the way they suggest. We shall show that these gaps can be filled. The issue with the 'Freedom of Choice' assumption can be circumvented by explicitly assuming parameter independence. This makes the result less general, but better founded. We then obtain an impossibility theorem for hidden variable theories satisfying parameter independence only. As stated above, such hidden variable theories are impossible in the sense that any supplemental variables have no bearing on outcome probabilities

  18. Visualizing the Central Limit Theorem through Simulation

    Science.gov (United States)

    Ruggieri, Eric

    2016-01-01

    The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…

  19. 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.

  20. Euler and the Fundamental Theorem of Algebra.

    Science.gov (United States)

    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)

  1. Anisotropic weak Hardy spaces and interpolation theorems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper, the authors establish the anisotropic weak Hardy spaces associated with very general discrete groups of dilations. Moreover, the atomic decomposition theorem of the anisotropic weak Hardy spaces is also given. As some applications of the above results, the authors prove some interpolation theorems and obtain the boundedness of the singular integral operators on these Hardy spaces.

  2. Boundary contributions to the hypervirial theorem

    OpenAIRE

    Esteve, J. G.; Falceto, F.; Giri, Pulak Ranjan

    2012-01-01

    It is shown that under certain boundary conditions the virial theorem has to be modified. We analyze the origin of the extra term and compute it in particular examples. The Coulomb and harmonic oscillator with point interaction have been studied in the light of this generalization of the virial theorem.

  3. A Generalization of the Prime Number Theorem

    Science.gov (United States)

    Bruckman, Paul S.

    2008-01-01

    In this article, the author begins with the prime number theorem (PNT), and then develops this into a more general theorem, of which many well-known number theoretic results are special cases, including PNT. He arrives at an asymptotic relation that allows the replacement of certain discrete sums involving primes into corresponding differentiable…

  4. Generalized Fibonacci Numbers and Blackwell's Renewal Theorem

    OpenAIRE

    Christensen, Sören

    2010-01-01

    We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers. With the help of error estimates in the renewal theorem we figure out an explicit representation.

  5. The Ahlfors lemma and Picard's theorems

    OpenAIRE

    Simonič, Aleksander

    2015-01-01

    The article introduces Ahlfors' generalization of the Schwarz lemma. With this powerful geometric tool of complex functions in one variable, we are able to prove some theorems concerning the size of images under holomorphic mappings, including the celebrated Picard's theorems. The article concludes with a brief insight into the theory of Kobayashi hyperbolic complex manifolds.

  6. No-cloning theorem in thermofield dynamics

    CERN Document Server

    Prudencio, Thiago

    2011-01-01

    Here we apply the no-cloning theorem from quantum information in the thermofield dynamics (TFD) scenario, relating the doubling procedure of TFD to a cloning machine process. As a consequence we use the no-cloning theorem to demonstrate that the thermal vaccuum state defined in TFD is necessarilly a mixed state.

  7. No-cloning theorem in thermofield dynamics

    OpenAIRE

    Prudencio, Thiago

    2011-01-01

    We discuss the relation between the no-cloning theorem from quantum information and the doubling procedure used in the formalism of thermofield dynamics (TFD). We also discuss how to apply the no-cloning theorem in the context of thermofield states defined in TFD. Consequences associated to mixed states, von Neumann entropy and thermofield vacuum are also addressed.

  8. Abel's Theorem in the Noncommutative Case

    OpenAIRE

    Leitenberger, Frank

    2005-01-01

    We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic differentials of the first kind. Following Abel we prove Abel's Theorem.

  9. Convergence theorems for intermediate problems. II

    OpenAIRE

    Beattie, C. A.; Greenlee, W. M.

    2002-01-01

    Convergence theorems for the practical eigenvector free methods of Gay and Goerisch are obtained under a variety of hypotheses, so that our theorems apply to both traditional boundary-value problems and atomic problems. In addition, we prove convergence of the T*T method of Bazley and Fox without an alignment of projections hypothesis required in previous literature.

  10. Non perturbative Adler-Bardeen Theorem

    OpenAIRE

    Mastropietro, Vieri

    2006-01-01

    The Adler-Bardeen theorem has been proved only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in $d=2$ by using recently developed technical tools in the theory of Grassmann integration.

  11. The Classical Version of Stokes' Theorem Revisited

    Science.gov (United States)

    Markvorsen, Steen

    2008-01-01

    Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…

  12. Aspects of the Flavour Expansion Theorem

    CERN Document Server

    Paraskevas, M

    2015-01-01

    The Flavour Expansion Theorem, which has been recently proposed as a more general and elegant algebraic method, for the derivation of the commonly used Mass Insertion Approximation, is revisited. The theorem is reviewed, with respect to its straightforward applications in Flavour physics, and compared against the standard diagrammatic flavour basis techniques, in cases where the latter become inadequate.

  13. A Metrized Duality Theorem for Markov Processes

    DEFF Research Database (Denmark)

    Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash

    2014-01-01

    We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...

  14. Double soft theorem for perturbative gravity

    Science.gov (United States)

    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.

  15. 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.

  16. The Euler Line and Nine-Point-Circle Theorems.

    Science.gov (United States)

    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)

  17. Generalized fluctuation theorems for classical systems

    CERN Document Server

    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.

  18. Uniqueness theorems in linear elasticity

    CERN Document Server

    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...

  19. OTTER, Resolution Style Theorem Prover

    International Nuclear Information System (INIS)

    1 - Description of program or function: OTTER (Other Techniques for Theorem-proving and Effective Research) is a resolution-style theorem-proving program for first-order logic with equality. OTTER includes the inference rules binary resolution, hyper-resolution, UR-resolution, and binary para-modulation. These inference rules take as small set of clauses and infer a clause. If the inferred clause is new and useful, it is stored and may become available for subsequent inferences. Other capabilities are conversion from first-order formulas to clauses, forward and back subsumption, factoring, weighting, answer literals, term ordering, forward and back demodulation, and evaluable functions and predicates. 2 - Method of solution: For its inference process OTTER uses the given-clause algorithm, which can be viewed as a simple implementation of the set of support strategy. OTTER maintains three lists of clauses: axioms, sos (set of support), and demodulators. OTTER is not automatic. Even after the user has encoded a problem into first-order logic or into clauses, the user must choose inference rules, set options to control the processing of inferred clauses, and decide which input formulae or clauses are to be in the initial set of support and which, if any, equalities are to be demodulators. If OTTER fails to find a proof, the user may try again different initial conditions. 3 - Restrictions on the complexity of the problem - Maxima of: 5000 characters in an input string, 64 distinct variables in a clause, 51 characters in any symbol. The maxima can be changed by finding the appropriate definition in the header.h file, increasing the limit, and recompiling OTTER. There are a few constraints on the order of commands

  20. 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.

  1. Quantum cloning, Bell's inequality and teleportation

    International Nuclear Information System (INIS)

    We analyse the possibility of using the two-qubit output state from the Buzek-Hillery quantum copying machine (not necessarily a universal quantum cloning machine) as a teleportation channel. We show that there is a range of values of the machine parameter ξ for which the two-qubit output state is entangled and violates the Bell-CHSH inequality and for a different range it remains entangled but does not violate the Bell-CHSH inequality. Further, we observe that for certain values of the machine parameter the two-qubit mixed state can be used as a teleportation channel. The use of the output state from the Buzek-Hillery cloning machine as a teleportation channel provides an additional appeal to the cloning machine and motivation for our present work

  2. Radiative and Electroweak Penguins at Belle

    Science.gov (United States)

    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.

  3. 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.

  4. Bell Experiments with Random Destination Sources

    OpenAIRE

    Sciarrino, F.; Vallone, G.; Cabello, A.; Mataloni, P.

    2010-01-01

    It is generally assumed that sources sending randomly two particles to one or two different observers, named here random destination sources (RDS), cannot by used for genuine quantum nonlocality tests because of the postselection loophole. We demonstrate that Bell experiments not affected by the postselection loophole may be performed with: (i) RDS and local postselection using perfect detectors, (ii) RDS, local postselection, and fair sampling assumption with any detection efficiency, and (i...

  5. Generalized Bell-inequality experiments and computation

    Energy Technology Data Exchange (ETDEWEB)

    Hoban, Matty J. [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom); Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD (United Kingdom); Wallman, Joel J. [School of Physics, The University of Sydney, Sydney, New South Wales 2006 (Australia); Browne, Dan E. [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom)

    2011-12-15

    We consider general settings of Bell inequality experiments with many parties, where each party chooses from a finite number of measurement settings each with a finite number of outcomes. We investigate the constraints that Bell inequalities place upon the correlations possible in local hidden variable theories using a geometrical picture of correlations. We show that local hidden variable theories can be characterized in terms of limited computational expressiveness, which allows us to characterize families of Bell inequalities. The limited computational expressiveness for many settings (each with many outcomes) generalizes previous results about the many-party situation each with a choice of two possible measurements (each with two outcomes). Using this computational picture we present generalizations of the Popescu-Rohrlich nonlocal box for many parties and nonbinary inputs and outputs at each site. Finally, we comment on the effect of preprocessing on measurement data in our generalized setting and show that it becomes problematic outside of the binary setting, in that it allows local hidden variable theories to simulate maximally nonlocal correlations such as those of these generalized Popescu-Rohrlich nonlocal boxes.

  6. Limit theorems for 2D invasion percolation

    CERN Document Server

    Damron, Michael

    2010-01-01

    We prove limit theorems and variance estimates for quantities related to ponds and outlets for 2D invasion percolation. We first exhibit several properties of a sequence (O(n)) of outlet variables, the n-th of which gives the number of outlets in the box centered at the origin of side length 2^n. The most important of these properties describe the sequence's renewal structure and exponentially fast mixing behavior. We use these to prove a central limit theorem and strong law of large numbers for (O(n)). We then show consequences of these limit theorems for the pond radii and outlet weights.

  7. An algebraic spin and statistics theorem

    CERN Document Server

    Guido, I D

    1994-01-01

    Abstract. A spin-statistics theorem and a PCT theorem are obtained in the context of the superselection sectors in Quantum Field Theory on a 4-dimensional space-time. Our main assumption is the requirement that the modular groups of the von Neumann algebras of local observables associated with wedge regions act geometrically as pure Lorentz transformations. Such a property, satisfied by the local algebras generated by Wightman fields because of the Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.

  8. Linear Sequences and Weighted Ergodic Theorems

    Directory of Open Access Journals (Sweden)

    Tanja Eisner

    2013-01-01

    Full Text Available We present a simple way to produce good weights for several types of ergodic theorem including the Wiener-Wintner type multiple return time theorem and the multiple polynomial ergodic theorem. These weights are deterministic and come from orbits of certain bounded linear operators on Banach spaces. This extends the known results for nilsequences and return time sequences of the form for a measure preserving system and , avoiding in the latter case the problem of finding the full measure set of appropriate points .

  9. Existence theorems for ordinary differential equations

    CERN Document Server

    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

  10. Interval logic. Proof theory and theorem proving

    DEFF Research Database (Denmark)

    Rasmussen, Thomas Marthedal

    2002-01-01

    . By theorem proving we understand the activity of proving theorems of a logic with the assistance of a computer. The goal of this thesis is to improve theorem proving support for interval logics such that larger and more realistic case-studies of real-time systems can be conducted using these formalisms...... of a direction of an interval, and present a sound and complete Hilbert proof system for it. Because of its generality, SIL can conveniently act as a general formalism in which other interval logics can be encoded. We develop proof theory for SIL including both a sequent calculus system and a labelled natural...

  11. Haag's theorem in renormalised quantum field theories

    CERN Document Server

    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.

  12. Bell's palsy: A Case Report and Literature Review

    Directory of Open Access Journals (Sweden)

    Tashika Kushraj

    2014-06-01

    Full Text Available Bell's palsy is considered as a disease of exclusion. It is a form of lower motor neuron paralysis affecting the facial muscles. Rapid onset of paralysis causes panic to the patients. For speedy recovery, correct diagnosis and early treatment are crucial. Here a case of Bell's palsy is reported and the literature on Bell's palsy is reviewed. [Cukurova Med J 2014; 39(3.000: 581-588

  13. Experimental Bell inequality violation without the postselection loophole

    OpenAIRE

    Lima, G.; Vallone, G.; Chiuri, A.; Cabello, A.; Mataloni, P.

    2009-01-01

    We report on an experimental violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality using energy-time entangled photons. The experiment is not free of the locality and detection loopholes, but is the first violation of the Bell-CHSH inequality using energy-time entangled photons which is free of the postselection loophole described by Aerts et al. [Phys. Rev. Lett. 83, 2872 (1999)].

  14. Closing the Detection Loophole in Bell Experiments Using Qudits

    OpenAIRE

    Vértesi, Tamás; Pironio, Stefano; Brunner, Nicolas

    2010-01-01

    We show that the detection efficiencies required for closing the detection loophole in Bell tests can be significantly lowered using quantum systems of dimension larger than two. We introduce a series of asymmetric Bell tests for which an efficiency arbitrarily close to 1/N can be tolerated using N-dimensional systems, and a symmetric Bell test for which the efficiency can be lowered down to 61.8% using four-dimensional systems. Experimental perspectives for our schemes look promising conside...

  15. Bell Inequality Tests with Macroscopic Entangled States of Light

    OpenAIRE

    Stobińska, M.; Sekatski, Pavel; Buraczewski, A.; Gisin, Nicolas; Leuchs, G.

    2011-01-01

    Quantum correlations may violate the Bell inequalities. Most of the experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiment which closes this loophole and the locality loophole simultaneously is highly desirable and remains challenging. A novel approach to a loophole-free Bell tests is based on amplification of the entangled photons, i.e.\\@ on macroscopic entanglement, which optical signal should be easy to...

  16. Entanglement Measure and Quantum Violation of Bell-Type Inequality

    Science.gov (United States)

    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.

  17. Quadratic Goldreich-Levin Theorems

    CERN Document Server

    Tulsiani, Madhur

    2011-01-01

    Decomposition theorems in classical Fourier analysis enable us to express a bounded function in terms of few linear phases with large Fourier coefficients plus a part that is pseudorandom with respect to linear phases. The Goldreich-Levin algorithm can be viewed as an algorithmic analogue of such a decomposition as it gives a way to efficiently find the linear phases associated with large Fourier coefficients. In the study of "quadratic Fourier analysis", higher-degree analogues of such decompositions have been developed in which the pseudorandomness property is stronger but the structured part correspondingly weaker. For example, it has previously been shown that it is possible to express a bounded function as a sum of a few quadratic phases plus a part that is small in the $U^3$ norm, defined by Gowers for the purpose of counting arithmetic progressions of length 4. We give a polynomial time algorithm for computing such a decomposition. A key part of the algorithm is a local self-correction procedure for Re...

  18. 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.

  19. Remarks on the Cayley-Hamilton Theorem

    OpenAIRE

    Gatto, Letterio; Scherbak, Inna

    2015-01-01

    We revisit the classical theorem by Cayley and Hamilton, "{\\em each endomorphism is a root of its own characteristic polynomial}", from the point of view of {\\em Hasse--Schmidt derivations on an exterior algebra}

  20. Affine and Projective Tree Metric Theorems

    CERN Document Server

    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...

  1. Yet another proof of Szemeredi's theorem

    CERN Document Server

    Green, Ben

    2010-01-01

    Using the density-increment strategy of Roth and Gowers, we derive Szemeredi's theorem on arithmetic progressions from the inverse conjectures GI(s) for the Gowers norms, recently established by the authors and Ziegler.

  2. Transformation groups and the virial theorem

    NARCIS (Netherlands)

    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.

  3. TRANSVERSAL SPACES AND FIXED POINT THEOREMS

    OpenAIRE

    Sinia N. Ješić; Milan R. Tasković; Nataša Babačev

    2007-01-01

    In this paper we define Transversal functional probabilistic spaces (upper and lower) as a natural extension of Metric spaces, Probabilistic metric spaces and Fuzzy metric spaces. Also, we formulate and prove some fixed and common fixed point theorems.

  4. Two No-Go Theorems on Superconductivity

    CERN Document Server

    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(...

  5. A generalized preimage theorem in global analysis

    Institute of Scientific and Technical Information of China (English)

    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.

  6. Lambda-mu-calculus and Bohm's theorem

    OpenAIRE

    David, René; Py, Walter

    2001-01-01

    The lambda mu-calculus is an extension of the lambda-calculus that has been introduced by M. Parigot to give an algorithmic content to classical proofs. We show that Bohm's theorem fails in this calculus.

  7. 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)

  8. Stable convergence and stable limit theorems

    CERN Document Server

    Häusler, Erich

    2015-01-01

    The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level...

  9. 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.

  10. Slowly changing potential problems in Quantum Mechanics: Adiabatic theorems, ergodic theorems, and scattering

    Science.gov (United States)

    Fishman, S.; Soffer, A.

    2016-07-01

    We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.

  11. A Converse of Fermat's Little Theorem

    Science.gov (United States)

    Bruckman, P. S.

    2007-01-01

    As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…

  12. A Theorem on Combinatorial Group Theory

    Institute of Scientific and Technical Information of China (English)

    何伯和

    2000-01-01

    Let F= F(X) be a free group of rand n, A be a finite subset of F(X) and x∈X be a generator. The theorem states that x can be denoted as a rotation-inserting word of A if x is in the normal closure of A in F(X). Finally, an application of the theorem in Heegaard splitting of 3manifolds is given.

  13. Integral fluctuation theorem for the housekeeping heat

    International Nuclear Information System (INIS)

    The housekeeping heat Qhk is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states. By analysing the evolution of its probability distribution, we prove an integral fluctuation theorem (exp[-βQhk]) = 1 valid for arbitrary-driven transitions between steady states. We discuss Gaussian limiting cases and the difference between the new theorem and both the Hatano-Sasa and the Jarzynski relation. (letter to the editor)

  14. Integral fluctuation theorem for the housekeeping heat

    OpenAIRE

    Speck, T.; Seifert, U.

    2005-01-01

    The housekeeping heat $Q\\hk$ is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states. By analyzing the evolution of its probability distribution, we prove an integral fluctuation theorem $\\mean{\\exp[-\\beta Q\\hk]}=1$ valid for arbitrary driven transitions between steady states. We discuss Gaussian limiting cases and the difference between the new theorem and both the Hatano-Sasa and the Jarzynski relation.

  15. q-Deformed Dynamics and Virial Theorem

    OpenAIRE

    Zhang, Jian-zu

    2002-01-01

    In the framework of the q-deformed Heisenberg algebra the investigation of $q$-deformation of Virial theorem explores that q-deformed quantum mechanics possesses better dynamical property. It is clarified that in the case of the zero potential the theoretical framework for the q-deformed Virial theorem is self-consistent. In the selfadjoint states the q-deformed uncertainty relation essentially deviates from the Heisenberg one.

  16. Has the Goldstone theorem been revisited?

    CERN Document Server

    Guerrieri, A

    2014-01-01

    A recent paper (arXiv:1404.5619) claimed the presence of a loophole in the current-algebra proof of Goldstone Theorem. The enforcing of manifest covariance would lead to contradictory results also in scalar theory. We show that the argument proposed is not in contradiction with covariance, thus not invalidating the theorem. Moreover, the counterexample proposed of a scalar operator with a non-zero vacuum expectation value in an unbroken theory is ill-defined.

  17. A new proof of Goodstein's Theorem

    OpenAIRE

    Perez, Juan A.

    2009-01-01

    Goodstein sequences are numerical sequences in which a natural number m, expressed as the complete normal form to a given base a, is modified by increasing the value of the base a by one unit and subtracting one unit from the resulting expression. As initially defined, the first term of the Goodstein sequence is the complete normal form of m to base 2. Goodstein's Theorem states that, for all natural numbers, the Goodstein sequence eventually terminates at zero. Goodstein's Theorem was origin...

  18. Epistemological Consequences of the Incompleteness Theorems

    OpenAIRE

    Raguní, Giuseppe

    2016-01-01

    After highlighting the cases in which the semantics of a language cannot be mechanically reproduced (in which case it is called inherent), the main epistemological consequences of the first incompleteness Theorem for the two fundamental arithmetical theories are shown: the non-mechanizability for the truths of the first-order arithmetic and the peculiarities for the model of the second-order arithmetic. Finally, the common epistemological interpretation of the second incompleteness Theorem is...

  19. Virial theorems for trapped cold atoms

    OpenAIRE

    Werner, Félix

    2008-01-01

    A few small corrections We present a general virial theorem for quantum particles with arbitrary zero-range or finite-range interactions in an arbitrary external potential. We deduce virial theorems for several situations relevant to trapped cold atoms: zero-range interactions with and without Efimov effect, hard spheres, narrow Feshbach resonances, and finite-range interactions. If the scattering length $a$ is varied adiabatically in the BEC-BCS crossover, we find that the trapping potent...

  20. Virial theorem for radiating accretion discs

    OpenAIRE

    Mach, Patryk

    2011-01-01

    A continuum version of the virial theorem is derived for a radiating self-gravitating accretion disc around a compact object. The central object is point-like, but we can avoid the regularization of its gravitational potential. This is achieved by applying a modified Pohozaev-Rellich identity to the gravitational potential of the disk only. The theorem holds for general stationary configurations, including discontinuous flows (shock waves, contact discontinuities). It is used to test numerica...

  1. Shafranov's virial theorem and magnetic plasma confinement

    OpenAIRE

    Faddeev, Ludvig; Freyhult, Lisa; Niemi, Antti J.; Rajan, Peter

    2000-01-01

    Shafranov's virial theorem implies that nontrivial magnetohydrodynamical equilibrium configurations must be supported by externally supplied currents. Here we extend the virial theorem to field theory, where it relates to Derrick's scaling argument on soliton stability. We then employ virial arguments to investigate a realistic field theory model of a two-component plasma, and conclude that stable localized solitons can exist in the bulk of a finite density plasma. These solitons entail a non...

  2. Double Soft Theorem for Perturbative Gravity

    CERN Document Server

    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.

  3. Emile Galle ja legendaarne Belle Epoque / Kärt Kross

    Index Scriptorium Estoniae

    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

  4. 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.

  5. Optical theorem detectors for active scatterers

    Science.gov (United States)

    Marengo, Edwin A.; Tu, Jing

    2015-10-01

    We develop a new theory of the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. It applies to arbitrary lossless backgrounds and quite general probing fields. The derived formulation holds for arbitrary passive scatterers, which can be dissipative, as well as for the more general class of active scatterers which are composed of a (passive) scatterer component and an active, radiating (antenna) component. The generalization of the optical theorem to active scatterers is relevant to many applications such as surveillance of active targets including certain cloaks and invisible scatterers and wireless communications. The derived theoretical framework includes the familiar real power optical theorem describing power extinction due to both dissipation and scattering as well as a novel reactive optical theorem related to the reactive power changes. The developed approach naturally leads to three optical theorem indicators or statistics which can be used to detect changes or targets in unknown complex media. The paper includes numerical simulation results that illustrate the application of the derived optical theorem results to change detection in complex and random media.

  6. Combinatorial theorems in sparse random sets

    CERN Document Server

    Conlon, D

    2010-01-01

    We develop a new technique that allows us to show in a unified way that many well-known combinatorial theorems, including Tur\\'an's theorem, Szemer\\'edi's theorem and Ramsey's theorem, hold almost surely inside sparse random sets. For instance, we extend Tur\\'an's theorem to the random setting by showing that for every epsilon > 0 and every positive integer t >= 3 there exists a constant C such that, if G is a random graph on n vertices where each edge is chosen independently with probability at least C n^{-2/(t+1)}, then, with probability tending to 1 as n tends to infinity, every subgraph of G with at least (1 - \\frac{1}{t-1} + epsilon) e(G) edges contains a copy of K_t. This is sharp up to the constant C. We also show how to prove sparse analogues of structural results, giving two main applications, a stability version of the random Tur\\'an theorem stated above and a sparse hypergraph removal lemma. Many similar results have recently been obtained independently in a different way by Schacht and by Friedgut...

  7. A novel sampling theorem on the sphere

    CERN Document Server

    McEwen, J D

    2011-01-01

    We develop a novel sampling theorem on the sphere and corresponding fast algorithms by associating the sphere with the torus through a periodic extension. The fundamental property of any sampling theorem is the number of samples required to represent a band-limited signal. To represent exactly a signal on the sphere band-limited at L, all sampling theorems on the sphere require O(L^2) samples. However, our sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere and an asymptotically identical, but smaller, number of samples than the Gauss-Legendre sampling theorem. The complexity of our algorithms scale as O(L^3), however, the continual use of fast Fourier transforms reduces the constant prefactor associated with the asymptotic scaling considerably, resulting in algorithms that are fast. Furthermore, we do not require any precomputation and our algorithms apply to both scalar and spin functions on the sphere without any change in computational comple...

  8. The modified Poynting theorem and the concept of mutual energy

    CERN Document Server

    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...

  9. Coincidence Theorems with Applications to Minimax Inequalities, Section Theorem, Best Approximation and Multiobjective Games in Topological Spaces

    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.

  10. An Asymptotic Formula for r-Bell Numbers with Real Arguments

    OpenAIRE

    Corcino, Cristina B.; Corcino, Roberto B.

    2013-01-01

    The r-Bell numbers are generalized using the concept of the Hankel contour. Some properties parallel to those of the ordinary Bell numbers are established. Moreover, an asymptotic approximation for r-Bell numbers with real arguments is obtained.

  11. Aspects of the History of the Nerves: Bell's Theory, the Bell-Magendie Law and Controversy, and Two Forgotten Works by P.W. Lund and D.F. Eschricth

    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...

  12. 77 FR 64439 - Airworthiness Directives; Bell Helicopter Textron Canada (Bell) Model Helicopters

    Science.gov (United States)

    2012-10-22

    ... converter, and AFCS air data computer adapter module for each helicopter, assuming 8 work hours for each... Bell Model 430 helicopters, which would require replacing certain components of the air data system... rulemaking by submitting written comments, data, or views. We also invite comments relating to the...

  13. 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.

  14. As molduras de Belle de jour

    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.

  15. Optimal randomness generation from optical Bell experiments

    International Nuclear Information System (INIS)

    Genuine randomness can be certified from Bell tests without any detailed assumptions on the working of the devices with which the test is implemented. An important class of experiments for implementing such tests is optical setups based on polarization measurements of entangled photons distributed from a spontaneous parametric down conversion source. Here we compute the maximal amount of randomness which can be certified in such setups under realistic conditions. We provide relevant yet unexpected numerical values for the physical parameters and achieve four times more randomness than previous methods. (fast track communication)

  16. 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.

  17. Local conjugacy theorem, rank theorems in advanced calculus and a generalized principle for constructing Banach manifolds

    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.

  18. Local conjugacy theorem, rank theorems in advanced calculus and a generalized principle for constructing Banach manifolds

    Institute of Scientific and Technical Information of China (English)

    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.

  19. Eugenics Past and Present: Remembering Buck v. Bell.

    Science.gov (United States)

    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 strategies…

  20. Indistinguishability of orthogonal time-separated bell states

    Institute of Scientific and Technical Information of China (English)

    Tan Yong-Gang; Cai Qing-Yu; Shi Ting-Yun

    2008-01-01

    This paper proves that it is impossible to identify orthogonally time-separated Bell states.If two qubits of a Bell state interact with the measurement apparatus at different time,any attempt to identify this state will disturb it.

  1. Reconciling local realism and quantum physics: a critique to Bell

    International Nuclear Information System (INIS)

    A Metatheoretical Generalized Principle (MGP) is stated that formalizes an operational non-standard way of looking at the laws of physics. In Quantum Physics MGP leads to the invalidation of Bell's Inequality without renouncing to a minimal form of realism or to locality. Therefore the violation of Bell's Inequality predicted by Quantum Physics does not appear paradoxial if MGP is accepted

  2. Bell Inequalities Classifying Bi-separable Three-qubit States

    CERN Document Server

    Sun, B Z; Sun, Bao-Zhi; Fei, Shao-Ming

    2006-01-01

    We present a set of Bell inequalities that gives rise to a finer classification of the entanglement for tripartite systems. These inequalities distinguish three possible bi-separable entanglements for three-qubit states. The three Bell operators we employed constitute an external sphere of the separable cube.

  3. Bell clapper impact dynamics and the voicing of a carillon

    Science.gov (United States)

    Fletcher, N. H.; McGee, W. T.; Tarnopolsky, A. Z.

    2002-03-01

    The periodic re-voicing of the bell clappers of the Australian National Carillon in Canberra provided an opportunity for the study of the acoustic effects of this operation. After prolonged playing, the impact of the pear-shaped clapper on a bell produces a significant flat area on both the clapper and the inside surface of the bell. This deformation significantly decreases the duration of the impact event and has the effect of increasing the relative amplitude of higher modes in the bell sound, making it ``brighter'' or even ``clangy.'' This effect is studied by comparing the spectral envelope of the sounds of several bells before and after voicing. Theoretical analysis shows that the clapper actually strikes the bell and remains in contact with the bell surface until it is ejected by a displacement pulse that has traveled around the complete circumference of the bell. The contact time, typically about 1 ms, is therefore much longer than the effective impact time, which is only a few tenths of a millisecond. Both the impact time and the contact time are reduced by the presence of a flat on the clapper.

  4. Ergodic theorem, ergodic theory, and statistical mechanics.

    Science.gov (United States)

    Moore, Calvin C

    2015-02-17

    This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject--namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697

  5. 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.

  6. Generalized fluctuation theorems for classical systems

    Science.gov (United States)

    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.

  7. The Belle II experiment: fundamental physics at the flavor frontier

    CERN Document Server

    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.

  8. Bell inequality for pairs of superselection rule restricted states

    CERN Document Server

    Heaney, Libby; Jaksch, Dieter

    2010-01-01

    Proposals for Bell inequality tests on systems restricted by superselection rules often require operations that are difficult to implement in practice. In this paper, we derive a new Bell inequality, where pairs of states are used to by-pass the superselection rule. In particular, we focus on mode entanglement of an arbitrary number of massive particles and show that our Bell inequality detects the entanglement in the pair when other inequalities fail. However, as the number of particles in the system increases, the violation of our Bell inequality decreases due to the restriction in the measurement space caused by the superselection rule. This Bell test can be implemented using techniques that are routinely used in current experiments.

  9. Vertexing and Tracking Software at Belle II

    CERN Document Server

    Schlüter, Tobias

    2014-01-01

    Belle II is a $B$ factory experiment aiming to start physics data taking in 2017. It is currently being set up at the SuperKEKB accelerator at the KEK facility in Tsukuba (Japan), an asymmetric $e^+e^-$ collider which aims to achieve an unprecedented instantaneous luminosity of $8\\cdot10^{35} \\textrm{Hz}/\\textrm{cm}^2$. This forty-fold increase over predecessor experiments is achieved by employing a novel nano-beam scheme. Originally developed for the now-defunct SuperB experiment, this scheme allows a significant increase in luminosity at only modest increases of beam currents. Challenges for the vertex detector result from increased data and background rates. At full luminosity, physics data will be recorded at a rate of $30\\,\\textrm{kHz}$. The radiation-hard DEPFET-sensors of the innermost layer of the vertex detector will be read out employing a novel data-reduction scheme using selective detector read out based on online reconstruction of event data. Belle II uses a software framework in which data handl...

  10. The Trieste Lecture of John Stewart Bell

    Science.gov (United States)

    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

  11. Bell Could Become the Copernicus of Probability

    Science.gov (United States)

    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.

  12. The Trieste Lecture of John Stewart Bell

    Energy Technology Data Exchange (ETDEWEB)

    Bassi, Angelo; Ghirardi, GianCarlo

    2007-03-23

    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

  13. 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.

  14. On Bayes' theorem for improper mixtures

    CERN Document Server

    McCullagh, Peter; 10.1214/11-AOS892

    2011-01-01

    Although Bayes's theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes's theorem sometimes generates sensible procedures from improper priors, Pitman's estimator being a good example. However, improper priors may also lead to Bayes procedures that are paradoxical or otherwise unsatisfactory, prompting some authors to insist that all priors be proper. This paper begins with the observation that an improper measure on Theta satisfying Kingman's countability condition is in fact a probability distribution on the power set. We show how to extend a model in such a way that the extended parameter space is the power set. Under an additional finiteness condition, which is needed for the existence of a sampling region, the conditions for Bayes's theorem are satisfied by the extension. Lack of interference ensures that the posterior distribution in the extended space is compatible with the original parameter space. Provided that the key finiteness conditio...

  15. 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.

  16. Explicit results for the anomalous three point function and non-renormalization theorems

    International Nuclear Information System (INIS)

    Two-loop corrections for the correlator of the singlet axial and vector currents in QCD are calculated in the chiral limit for arbitrary momenta. Explicit calculations confirm the non-renormalization theorems derived recently by Vainshtein [A. Vainshtein, Phys. Lett. B 569 (2003) 187] and Knecht et al. [M. Knecht, S. Peris, M. Perrottet, E. de Rafael, JHEP 0403 (2004) 035]. We find that as in the one-loop case also at two loops the correlator has only three independent form-factors instead of four. From the explicit results we observe that the two-loop correction to the correlator is equal to the one-loop result times the constant factor C2(R)αs/π in the MS-bar scheme. This holds for the full correlator, for the anomalous longitudinal as well as for the non-anomalous transversal amplitudes. The finite overall αs dependent constant has to be normalized away by renormalizing the axial current according to Witten's algebraic/geometrical constraint on the anomalous Ward identity [ correlator]. Our observations, together with known facts, suggest that in perturbation theory the correlator is proportional to the one-loop term to all orders and that the non-renormalization theorem of the Adler-Bell-Jackiw anomaly carries over to the full correlator

  17. Explicit results for the anomalous three point function and non-renormalization theorems

    International Nuclear Information System (INIS)

    Two-loop corrections for the left angle VV A right angle correlator of the singlet axial and vector currents in QCD are calculated in the chiral limit for arbitrary momenta. Explicit calculations confirm the non-renormalization theorems derived recently by Vainshtein [Phys. Lett. B 569 (2003) 187] and Knecht et al. (HEP 0403 (2004) 035). We find that as in the one-loop case also at two loops the left angle VV A right angle correlator has only three independent form-factors instead of four. From the explicit results we observe that the two-loop correction to the bare correlator is equal to the one-loop result times the constant factor C2(R)αs/π in the MS scheme. This holds for the full correlator, for the anomalous longitudinal as well as for the non-anomalous transversal amplitudes. The finite overall αs dependent constant has to be normalized away by renormalizing the axial current according to Witten's algebraic/geometrical constraint on the anomalous Ward identity (left angle VV∂A right angle correlator). Our observations, together with known facts, suggest that in perturbation theory the bare left angle VV A right angle correlator is proportional to the one-loop term to all orders and that the non-renormalization theorem of the Adler-Bell-Jackiw anomaly carries over to the full correlator. (orig.)

  18. Generalizations of the Abstract Boundary singularity theorem

    CERN Document Server

    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.

  19. Pauli and the spin-statistics theorem

    CERN Document Server

    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

  20. Jarzynski's theorem for lattice gauge theory

    CERN Document Server

    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.

  1. The aftermath of the intermediate value theorem

    Directory of Open Access Journals (Sweden)

    Morales Claudio H

    2004-01-01

    Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000–300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (1781–1848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.

  2. The aftermath of the intermediate value theorem

    Directory of Open Access Journals (Sweden)

    Claudio H. Morales

    2004-08-01

    Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000–300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (1781–1848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.

  3. Jarzynski's theorem for lattice gauge theory

    Science.gov (United States)

    Caselle, Michele; Costagliola, Gianluca; Nada, Alessandro; Panero, Marco; Toniato, Arianna

    2016-08-01

    Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a nonequilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schrödinger functional and for simulations at finite density using reweighting techniques.

  4. Central Limit Theorem for Nonlinear Hawkes Processes

    CERN Document Server

    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.

  5. Limit theorems for fragmentation processes with immigration

    CERN Document Server

    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.

  6. Asymptotic symmetries and subleading soft graviton theorem

    Science.gov (United States)

    Campiglia, Miguel; Laddha, Alok

    2014-12-01

    Motivated by the equivalence between the soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the Bondi, van der Burg, Metzner and Sachs (BMS) group, we propose a new extension (different from the so-called extended BMS) of the BMS group that is a semidirect product of supertranslations and Diff(S2) . We propose a definition for the canonical generators associated with the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger.

  7. Bell's palsy before Bell: Evert Jan Thomassen à Thuessink and idiopathic peripheral facial paralysis.

    Science.gov (United States)

    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.

  8. Simulating Bell states with classical light

    CERN Document Server

    Shapiro, Jeffrey H

    2011-01-01

    Recently, Chen \\em et al\\rm.\\ [New J. Phys. {\\bf 13} (2011) 083018] presented experimental results, accompanied by quantum-mechanical analysis, showing that the quantum interference behavior of Bell states could be simulated in a modified Mach-Zehnder interferometer whose inputs are pseudothermal light beams obtained by passing laser light through a rotating ground-glass diffuser. Their experiments and their theory presumed low-flux operation in which the simulated quantum interference is observed via photon-coincidence counting. We first show that the Chen \\em et al\\rm.\\ photon-coincidence counting experiments can be fully explained with semiclassical photodetection theory, in which light is taken to be a classical electromagnetic wave, and the discreteness of the electron charge leads to shot noise as the fundamental photodetection noise. We then use semiclassical photodetection theory to show that the \\em same\\rm\\ simulated quantum interference pattern can be observed in high-flux operation, when photocurr...

  9. Bell Inequalities, Experimental Protocols and Contextuality

    CERN Document Server

    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.

  10. 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.

  11. Observation of Bell Inequality violation in B mesons

    CERN Document Server

    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)

  12. Quantum communication complexity advantage implies violation of a Bell inequality

    Science.gov (United States)

    Buhrman, Harry; Czekaj, Łukasz; Grudka, Andrzej; Horodecki, Michał; Horodecki, Paweł; Markiewicz, Marcin; Speelman, Florian; Strelchuk, Sergii

    2016-03-01

    We obtain a general connection between a large quantum advantage in communication complexity and Bell nonlocality. We show that given any protocol offering a sufficiently large quantum advantage in communication complexity, there exists a way of obtaining measurement statistics that violate some Bell inequality. Our main tool is port-based teleportation. If the gap between quantum and classical communication complexity can grow arbitrarily large, the ratio of the quantum value to the classical value of the Bell quantity becomes unbounded with the increase in the number of inputs and outputs.

  13. Progress of Belle II – detector and performance

    International Nuclear Information System (INIS)

    The progress on the detector and accelerator in the Belle II experiment is presented. The B factories have successfully accumulated the experimental data at ϒ(4S) and achieved the world highest sensitivity on the search for lepton flavor violating tau decays and other new physics searches. The Belle II experiment will obtain 50 times larger data samples compared to the Belle experiment and improve the detector sensitivity. The construction of the detector and accelerator is in progress. The commissioning will start in 2014 and the expected integrated luminosity is 50ab−1 by 2022

  14. Improvement of AMGA Python Client Library for Belle II Experiment

    Science.gov (United States)

    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.

  15. Reluctant genius Alexander Graham Bell and the passion for invention

    CERN Document Server

    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

  16. From Bell's inequalities to quantum information: a new quantum revolution

    CERN Document Server

    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 ...

  17. Green's Theorem for Generalized Fractional Derivatives

    OpenAIRE

    Odzijewicz, Tatiana; Malinowska, Agnieszka B.; Delfim F. M. Torres

    2012-01-01

    We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case when the generalized operators are reduced to the standard partial fractional derivatives and fractional integrals in the sense of Riemann-Liouville or Caputo.

  18. Stokes' theorem, volume growth and parabolicity

    CERN Document Server

    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.

  19. On the Non-Abelian Stokes Theorem

    OpenAIRE

    Diakonov, Dmitri; Petrov, Victor

    2000-01-01

    We present the non-Abelian Stokes theorem for the Wilson loop in various forms and discuss its meaning. Its validity has been recently questioned by Faber, Ivanov, Troitskaya and Zach. We demonstrate that all points of their criticism are based on mistakes in mathematics. Finally, we derive a variant of our formula for the Wilson loop in lattice regularization.

  20. 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.

  1. 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.

  2. 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.

  3. Answering Junior Ant's "Why" for Pythagoras' Theorem

    Science.gov (United States)

    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.…

  4. On Noethers theorem in quantum field theory

    International Nuclear Information System (INIS)

    Extending an earlier construction of local generators of symmetries in (S. Doplicher, 1982) to space-time and supersymmetries, we establish a weak form of Noethers theorem in quantum field theory. We also comment on the physical significance of the 'split property', underlying our analysis, and discuss some local aspects of superselection rules following from our results. (orig./HSI)

  5. 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].

  6. 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.

  7. A Bijective Proof For Forest Reciprocity Theorem

    CERN Document Server

    Huang, ShinnYih

    2009-01-01

    In this paper, we study the graph polynomial that counts spanning rooted forests f_g of a given graph. This polynomial has a remarkable reciprocity property. We give a new bijective proof for this theorem which has Prufer coding as a special case.

  8. Kelvin's Canonical Circulation Theorem in Hall Magnetohydrodynamics

    CERN Document Server

    Shivamoggi, B K

    2016-01-01

    The purpose of this paper is to show that, thanks to the restoration of the legitimate connection between the current density and the plasma flow velocity in Hall magnetohydrodynamics (MHD), Kelvin's Circulation Theorem becomes valid in Hall MHD. The ion-flow velocity in the usual circulation integral is now replaced by the canonical ion-flow velocity.

  9. Random fixed point theorems on product spaces

    OpenAIRE

    Ismat Beg; Naseer Shahzad

    1993-01-01

    The existence of random fixed point of a locally contractive random operator in first variable on product spaces is proved. The concept “continuous random height-selection” is discussed. Some random fixed point theorems for nonexpansive self and nonself maps are also obtained in product spaces.

  10. Automated theorem proving theory and practice

    CERN Document Server

    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...

  11. Non-Archimedean Big Picard Theorems

    OpenAIRE

    Cherry, William

    2002-01-01

    A non-Archimedean analog of the classical Big Picard Theorem, which says that a holomorphic map from the punctured disc to a Riemann surface of hyperbolic type extends accross the puncture, is proven using Berkovich's theory of non-Archimedean analytic spaces.

  12. INTERPOLATION THEOREMS FOR SELF-ADJOINT OPERATORS

    Institute of Scientific and Technical Information of China (English)

    Shijun Zheng

    2009-01-01

    We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator L, without assuming the gra-dient estimate for its spectral kernel. The result applies to the cases where L is a uniformly elliptic operator or a Schr(o)dinger operator with electro-magnetic potential.

  13. Donsker-Type Theorem for BSDEs

    OpenAIRE

    Briand, Philippe; Delyon, Bernard; Mémin, Jean

    2001-01-01

    This paper is devoted to the proof of Donsker's theorem for backward stochastic differential equations (BSDEs for short). The main objective is to give a simple method to discretize in time a BSDE. Our approach is based upon the notion of ``convergence of filtrations'' and covers the case of a $(y,z)$-dependent generator.

  14. An extension theorem for conformal gauge singularities

    CERN Document Server

    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.

  15. Tennis Rackets and the Parallel Axis Theorem

    Science.gov (United States)

    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.

  16. Sandwich reactor lattices and Bloch's theorem

    International Nuclear Information System (INIS)

    The study of the neutron flux distribution in repetitive sandwiches of reactor material leads to results analogous to the 1-dimensional form of Bloch's theorem for the electronic structure in crystals. This principle makes it possible to perform analytically accurate homogenisations of sandwich lattices The method has been extended to cover multi group diffusion and transport theory. (author)

  17. Central Limit Theorem for Coloured Hard Dimers

    Directory of Open Access Journals (Sweden)

    Maria Simonetta Bernabei

    2010-01-01

    Full Text Available We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs. The techniques used at arriving this result comprise combinatorics, generating functions, and conditional expectations.

  18. Extended Kelvin theorem in relativistic magnetohydrodynamics

    OpenAIRE

    Bekenstein, Jacob D.; Oron, Asaf

    2000-01-01

    We prove the existence of a generalization of Kelvin's circulation theorem in general relativity which is applicable to perfect isentropic magnetohydrodynamic flow. The argument is based on a new version of the Lagrangian for perfect magnetohydrodynamics. We illustrate the new conserved circulation with the example of a relativistic magnetohydrodynamic flow possessing three symmetries.

  19. The virial theorem and planetary atmospheres

    OpenAIRE

    Toth, Viktor T.

    2010-01-01

    We derive a version of the virial theorem that is applicable to diatomic planetary atmospheres that are in approximate thermal equilibrium at moderate temperatures and pressures and are sufficiently thin such that the gravitational acceleration can be considered constant. We contrast a pedagogically inclined theoretical presentation with the actual measured properties of air.

  20. The virial theorem for nonlinear problems

    OpenAIRE

    Amore, Paolo; Fernández, Francisco M.

    2009-01-01

    We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation problem. In the former case we obtain the same main result derived earlier from the expansion in Chebyshev polynomials.

  1. A coupling approach to Doob's theorem

    OpenAIRE

    Kulik, Alexei; Scheutzow, Michael

    2014-01-01

    We provide a coupling proof of Doob's theorem which says that the transition probabilities of a regular Markov process which has an invariant probability measure $\\mu$ converge to $\\mu$ in the total variation distance. In addition we show that non-singularity (rather than equivalence) of the transition probabilities suffices to ensure convergence of the transition probabilities for $\\mu$-almost all initial conditions.

  2. A strictly-positive mass theorem

    International Nuclear Information System (INIS)

    We show that the ADM 4-momentum of an isolated gravitational system (spatially asymptotically flat spacetime) satisfying the dominant energy condition cannot be null-like unless it is flat. Together with the positive mass theorem, this implies that the ADM 4-momentum of an isolated gravitational system must be strictly time-like. (orig.)

  3. 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.

  4. Crum's Theorem for 'Discrete' Quantum Mechanics

    OpenAIRE

    Odake, Satoru; Sasaki, Ryu

    2009-01-01

    In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem. describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in 'discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schrodinger equation is a difference equation.

  5. Crum's Theorem for `Discrete' Quantum Mechanics

    OpenAIRE

    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.

  6. Average sampling theorems for shift invariant subspaces

    Institute of Scientific and Technical Information of China (English)

    孙文昌; 周性伟

    2000-01-01

    The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.

  7. Pauli and The Spin-Statistics Theorem

    International Nuclear Information System (INIS)

    This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties.Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that 'everyone knows the spin-statistics theorem, but no one understands it'. This book simplifies and clarifies the formal statements of the theorem, and also corrects the invariably flawed intuitive explanations which are frequently put forward. The book will be of interest to many practising physicists in all fields who have long been frustrated by the impenetrable discussions on the subject which have been available until now.It will also be accessible to students at an advanced undergraduate level as an introduction to modern physics based directly on the classical writings of the founders, including Pauli, Dirac, Heisenberg, Einstein and many others

  8. 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.

  9. Theorems of Tarski's Undefinability and Godel's Second Incompleteness - Computationally

    OpenAIRE

    Salehi, Saeed

    2015-01-01

    We show that the existence of a finitely axiomatized theory which can prove all the true $\\Sigma_1$ sentences may imply Godel's Second Incompleteness Theorem, by incorporating some bi-theoretic version of the derivability conditions (first discussed by Detlefsen~2001). We also argue that Tarski's theorem on the undefinability of truth is Godel's first incompleteness theorem relativized to definable oracles; here a unification of these two theorems is shown.

  10. Ehrenfest theorem, Galilean invariance and nonlinear Schr"odinger equations

    CERN Document Server

    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.

  11. Goedel incompleteness theorems and the limits of their applicability. I

    International Nuclear Information System (INIS)

    This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.

  12. The Interpretability of Inconsistency: Feferman's Theorem and Related Results

    NARCIS (Netherlands)

    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

  13. ON GÖDEL'S INCOMPLETENESS THEOREM(S), ARTIFICIAL INTELLIGENCE/LIFE, AND HUMAN MIND

    OpenAIRE

    CHRISTIANTO, V.; FLORENTIN SMARANDACHE

    2015-01-01

    In the present paper we have discussed concerning Gödel’s incompleteness theorem(s) and plausible implications to artificial intelligence/life and human mind. Perhaps we should agree with Sullins III, that the value of this finding is not to discourage certain types of research in AL, but rather to help move us in a direction where we can more clearly define the results of that research.

  14. Applications of square-related theorems

    Science.gov (United States)

    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.

  15. Qubits from Number States and Bell Inequalities for Number Measurements

    OpenAIRE

    Larsson, Jan-Ake

    2002-01-01

    Bell inequalities for number measurements are derived via the observation that the bits of the number indexing a number state are proper qubits. Violations of these inequalities are obtained from the output state of the nondegenerate optical parametric amplifier.

  16. NOAA Ship Bell M. Shimada Underway Meteorological Data, Quality Controlled

    Data.gov (United States)

    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...

  17. 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.

  18. Bell Inequality Tests with Macroscopic Entangled States of Light

    CERN Document Server

    Stobińska, Magdalena; Buraczewski, Adam; Gisin, Nicolas; Leuchs, Gerd; 10.1103/PhysRevA.84.034104

    2011-01-01

    Quantum correlations may violate the Bell inequalities. Most of the experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiment which closes this loophole and the locality loophole simultaneously is highly desirable and remains challenging. A novel approach to a loophole-free Bell tests is based on amplification of the entangled photons, i.e.\\@ on macroscopic entanglement, which optical signal should be easy to detect. However, the macroscopic states are partially indistinguishable by the classical detectors. An interesting idea to overcome these limitations is to replace the postselection by an appropriate preselection immediately after the amplification. This is in the spirit of state preprocessing revealing hidden nonlocality. Here, we examine one of possible preselections, but the presented tools can be used for analysis of other schemes. Filtering methods making the macroscopic entanglement useful for Bell test and quantum...

  19. Bell-inequality tests with macroscopic entangled states of light

    Energy Technology Data Exchange (ETDEWEB)

    Stobinska, M. [Max Planck Institute for the Science of Light, Erlangen (Germany); Institute for Theoretical Physics II, Erlangen-Nuernberg University, Erlangen (Germany); Sekatski, P.; Gisin, N. [Group of Applied Physics, University of Geneva, Geneva (Switzerland); Buraczewski, A. [Faculty of Electronics and Information Technology, Warsaw University of Technology, Warsaw (Poland); Leuchs, G. [Max Planck Institute for the Science of Light, Erlangen (Germany); Institute for Optics, Information and Photonics, Erlangen-Nuernberg University, Erlangen (Germany)

    2011-09-15

    Quantum correlations may violate the Bell inequalities. Most experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiments which simultaneously close this loophole and the locality loophole are highly desirable and remain challenging. An approach to loophole-free Bell tests is based on amplification of the entangled photons (i.e., on macroscopic entanglement), for which an optical signal should be easy to detect. However, the macroscopic states are partially indistinguishable by classical detectors. An interesting idea to overcome these limitations is to replace the postselection by an appropriate preselection immediately after the amplification. This is in the spirit of state preprocessing revealing hidden nonlocality. Here, we examine one of the possible preselections, but the presented tools can be used for analysis of other schemes. Filtering methods making the macroscopic entanglement useful for Bell tests and quantum protocols are the subject of an intensive study in the field nowadays.

  20. On Superselection Rules in Bohm-Bell Theories

    CERN Document Server

    Colin, S; Tumulka, R; Colin, Samuel; Durt, Thomas; Tumulka, Roderich

    2005-01-01

    The meaning of superselection rules in Bohm-Bell theories (i.e., quantum theories with particle trajectories) is different from that in orthodox quantum theory. More precisely, there are two concepts of superselection rule, a weak and a strong one. Weak superselection rules exist both in orthodox quantum theory and in Bohm-Bell theories and represent the conventional understanding of superselection rules. We introduce the concept of strong superselection rule, which does not exist in orthodox quantum theory. It relies on the clear ontology of Bohm-Bell theories and is a sharper and, in the Bohm-Bell context, more fundamental notion. A strong superselection rule for the observable G asserts that one can replace every state vector by a suitable statistical mixture of eigenvectors of G without changing the particle trajectories or their probabilities. A weak superselection rule asserts that every state vector is empirically indistinguishable from a suitable statistical mixture of eigenvectors of G. We establish ...

  1. Bell correlations in a Bose-Einstein condensate.

    Science.gov (United States)

    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. PMID:27102479

  2. Bell correlations in a Bose-Einstein condensate.

    Science.gov (United States)

    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.

  3. Subtraction of "accidentals" and the validity of Bell tests

    CERN Document Server

    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.

  4. 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.

  5. Bell-type inequalities for cold heteronuclear molecules

    OpenAIRE

    Milman, Perola; Keller, Arne; Charron, Eric; Atabek, Osman

    2006-01-01

    We introduce Bell-type inequalities allowing for non-locality and entanglement tests with two cold heteronuclear molecules. The proposed inequalities are based on correlations between each molecule spatial orientation, an observable which can be experimentally measured with present day technology. Orientation measurements are performed on each subsystem at diferent times. These times play the role of the polarizer angles in Bell tests realized with photons. We discuss the experimental impleme...

  6. Statistical practice at the Belle experiment, and some questions

    International Nuclear Information System (INIS)

    The Belle collaboration operates a general-purpose detector at the KEKB asymmetric energy e+e- collider, performing a wide range of measurements in beauty, charm, tau and 2-photon physics. In this paper, the treatment of statistical problems in past and present Belle measurements is reviewed. Some open questions, such as the preferred method for quoting rare decay results, and the statistical treatment of the new B0/B-bar0→π+π- analysis, are discussed. (author)

  7. Partial list of bipartite Bell inequalities with four binary settings

    Energy Technology Data Exchange (ETDEWEB)

    Brunner, Nicolas [Group of Applied Physics, University of Geneva (Switzerland)], E-mail: nicolas.brunner@physics.unige.ch; Gisin, Nicolas [Group of Applied Physics, University of Geneva (Switzerland)

    2008-04-28

    We give a partial list of 26 tight Bell inequalities for the case where Alice and Bob choose among four two-outcome measurements. All tight Bell inequalities with less settings are reviewed as well. For each inequality we compute numerically the maximal quantum violation, the resistance to noise and the minimal detection efficiency required for closing the detection loophole. Surprisingly, most of these inequalities are outperformed by the CHSH inequality.

  8. Bell's inequalities II: logical loophole in their interpretation

    OpenAIRE

    Sica, Louis

    2001-01-01

    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 the...

  9. Bell tests with arbitrarily low photodetection efficiency and homodyne measurements

    CERN Document Server

    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.

  10. 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....

  11. 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.

  12. A Novel Multiparty Quantum Secret Sharing Scheme of Secure Direct Communication Based on Bell States and Bell Measurements

    Institute of Scientific and Technical Information of China (English)

    SHI Run-Hua; HUANG Liu-Sheng; YANG Wei; ZHONG Hong

    2011-01-01

    @@ We present a novel quantum secret sharing scheme of secure direct communication and analyze its security.This scheme takes Einstein-Podolsky-Rosen(EPR) pairs in Bell states as quantum resources.In order to obtain thedirect communication message,all agents only need to perform Bell measurements,not to perform any local unitary operation.The total efficiency in this scheme approaches 100% as the classical information exchanged is unnecessary except for the eavesdropping checks.%We present a novel quantum secret sharing scheme of secure direct communication and analyze its security. This scheme takes Einstein-Podolsky-Rosen (EPR) pairs in Bell states as quantum resources. In order to obtain the direct communication message, all agents only need to perform Bell measurements, not to perform any local unitary operation. The total efficiency in this scheme approaches 100% as the classical information exchanged is unnecessary except for the eavesdropping checks.

  13. Parameterized quantum field theory without Haag's theorem

    CERN Document Server

    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...

  14. H-theorem in quantum physics

    Science.gov (United States)

    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.

  15. H-theorem in quantum physics.

    Science.gov (United States)

    Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M

    2016-01-01

    Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571

  16. Locomotion in complex fluids: Integral theorems

    CERN Document Server

    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.

  17. On c-theorems in arbitrary dimensions

    CERN Document Server

    Bhattacharyya, Arpan; Sen, Kallol; Sinha, Aninda

    2012-01-01

    The dilaton action in 3+1 dimensions plays a crucial role in the proof of the a-theorem. This action arises using Wess-Zumino consistency conditions and crucially relies on the existence of the trace anomaly. Since there are no anomalies in odd dimensions, it is interesting to ask how such an action could arise otherwise. Motivated by this we use the AdS/CFT correspondence to examine both even and odd dimensional CFTs. We find that in even dimensions, by promoting the cut-off to a field, one can get an action for this field which coincides with the WZ action in flat space. In three dimensions, we observe that by finding an exact Hamilton-Jacobi counterterm, one can find a non-polynomial action which is invariant under global Weyl rescalings. We comment on how this finding is tied up with the F-theorem conjectures.

  18. 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.

  19. 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.

  20. A Dirichlet unit theorem for Drinfeld modules

    OpenAIRE

    Taelman, Lenny

    2009-01-01

    We show that the module of integral points on a Drinfeld module satisfies a an analogue of Dirichlet's unit theorem, despite its failure to be finitely generated. As a consequence, we obtain a construction of a canonical finitely generated sub-module of the module of integral points. We use the results to give a precise formulation of a conjectural analogue of the class number formula.

  1. Stability theorems for symplectic and contact pairs

    OpenAIRE

    Bande, G.; Ghiggini, P.; Kotschick, D.

    2004-01-01

    We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the condition that its kernel hyperplane distribution have constant class in the sense of E. Cartan.

  2. A Central Limit Theorem for Punctuated Equilibrium

    OpenAIRE

    Bartoszek, Krzysztof

    2016-01-01

    Current evolutionary biology models usually assume that a phenotype undergoes gradual change. This is in stark contrast to biological intuition, which indicates that change can also be punctuated - the phenotype can jump. Such a jump can especially occur at speciation, i.e. dramatic change occurs that drives the species apart. Here we derive a central limit theorem for punctuated equilibrium. We show that, if adaptation is fast, for weak convergence to hold, dramatic change has to be a rare e...

  3. Limit theorems for sequences of random trees

    OpenAIRE

    Balding, David; Ferrari, Pablo A.; Fraiman, Ricardo; Sued, Mariela

    2004-01-01

    We consider a random tree and introduce a metric in the space of trees to define the ``mean tree'' as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.

  4. A New Extension Theorem for Concave Operators

    OpenAIRE

    Jian-wen Peng; Wei-dong Rong; Jen-Chih Yao

    2009-01-01

    We present a new and interesting extension theorem for concave operators as follows. Let be a real linear space, and let be a real order complete PL space. Let the set be convex. Let be a real linear proper subspace of , with , where for some . Let be a concave operator such that whenever and . Then there exists a concave operator such that (i) is an extension of , that is, for all , and (ii) whenever .

  5. Asymptotic representation theorems for poverty indices

    OpenAIRE

    Lo, Gane Samb; Sall, Serigne Touba

    2010-01-01

    We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotics of the bulk of poverty indices and issues in poverty analysis. Our representation results uniformly hold on a large collection of poverty indices. They enable the continuous measure of poverty with longitudinal data.

  6. From the Goldbach Conjecture to the Theorem

    CERN Document Server

    Pereyra, P H

    2007-01-01

    In the present work we demonstrate that the so called Goldbach conjecture from 1742, All positive even numbers greater than two can be expressed as a sum of two primes, due to Leonhard Euler, is a true statement. This result is partially based on the Wilson theorem, and complementary on our reasoning to cast the problem into a diophantine equation. The latter is the master equation for the conjectures proof.

  7. 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\\.

  8. An isomorphism theorem for random interlacements

    OpenAIRE

    Sznitman, Alain-Sol

    2011-01-01

    We consider continuous-time random interlacements on a transient weighted graph. We prove an identity in law relating the field of occupation times of random interlacements at level u to the Gaussian free field on the weighted graph. This identity is closely linked to the generalized second Ray-Knight theorem, and uniquely determines the law of occupation times of random interlacements at level u.

  9. Voting, Lobbying, and the Decentralization Theorem

    OpenAIRE

    Lockwood, Benjamin

    2007-01-01

    This paper revisits the fiscal "decentralization theorem", by relaxing the role of the assumption that governments are benevolent, while retaining the assumption of policy uniformity. If instead, decisions are made by direct majority voting, (i) centralization can welfare-dominate decentralization even if there are no externalities and regions are heterogenous; (ii) decentralization can welfare-dominate centralization even if there are positive externalities and regions are hom...

  10. A simple proof of Sarkozy's theorem

    CERN Document Server

    Lyall, Neil

    2011-01-01

    It is a striking and elegant fact (proved independently by Furstenberg and Sarkozy) that in any subset of the natural numbers of positive upper density there necessarily exist two distinct elements whose difference is given by a perfect square. In this article we present a new and simple proof of this result by adapting an argument originally developed by Croot and Sisask to give a new proof of Roth's theorem.

  11. Theorems for Asymptotic Safety of Gauge Theories

    CERN Document Server

    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.

  12. Limit theorems for self-similar tilings

    CERN Document Server

    Bufetov, Alexander I

    2012-01-01

    We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic formula is given for ergodic integrals in terms of these finitely-additive measures, and, as a corollary, limit theorems are obtained for dynamical systems given by self-similar tilings.

  13. On the Danilov-Gizatullin Isomorphism Theorem

    OpenAIRE

    Flenner, Hubert; Kaliman, Shulim; ZAIDENBERG, MIKHAIL

    2008-01-01

    A Danilov-Gizatullin surface is a normal affine surface V, which is a complement to an ample section S in a Hirzebruch surface of index d. By a surprising result due to Danilov and Gizatullin, V depends only on the self-intersection number of S and neither on d nor on S. In this note we provide a new and simple proof of this Isomorphism Theorem.

  14. Uniform Zariski's Theorem On Fundamental Groups

    OpenAIRE

    Kaliman, Shulim

    1997-01-01

    The Zariski theorem says that for every hypersurface in a complex projective (resp. affine) space of dimension at least 3 and for every generic plane in the projective (resp. affine) space the natural embedding generates an isomorphism of the fundamental groups of the complements to the hypersurface in the plane and in the space. If a family of hypersurfaces depends algebraically on parameters then it is not true in general that there exists a plane such that the natural embedding generates i...

  15. Stochastic Reynolds theorem and generalized subgrid tensor

    OpenAIRE

    Resseguier, Valentin; Mémin, Etienne; Chapron, Bertrand

    2015-01-01

    International audience We propose a representation that allows decomposing the flow velocity in terms of a smooth component and a highly oscillating random component. This decomposion leads through a stochastic representation of the Reynolds transport theorem to a large-scale expression of the Navier-Stokes equations. In this work we show the benefit of such a representation to construct low order dynamical systems that include naturally a dissipative term related to the action of the smal...

  16. Thermal Tachyons and the "g"-Theorem

    OpenAIRE

    Chaudhuri, Shyamoli

    2002-01-01

    We give a pedagogical introduction to Affleck and Ludwig's g-theorem, distinguishing its applications in field theory vs string theory. We clarify the recent proposal that the vacuum degeneracy $g$ of a noncompact worldsheet sigma model with a continuous spectrum of scaling dimensions is lowered under renormalization group flow while preserving the central charge. As an illustration we argue that the IR stable endpoint of the relevant flow of the worldsheet RG induced by a thermal tachyon in ...

  17. Reciprocity Theorems for Ab Initio Force Calculations

    CERN Document Server

    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.

  18. The Lebesgue decomposition theorem for arbitrary contents

    OpenAIRE

    König, Heinz

    2005-01-01

    The decomposition theorem named after Lebesgue asserts that certain set functions have canonical representations as sums of particular set functions called the absolutely continuous and the singular ones with respect to some fixed set function. The traditional versions are for the bounded measures with respect to some fixed measure on a \\sigma algebra, in final form due to Hahn 1921, and for the bounded contents with respect to some fixed content on an algebra, due to Bochner-Phillips 194...

  19. Virial Theorem in Nonlocal Newtonian Gravity

    OpenAIRE

    Bahram Mashhoon

    2015-01-01

    Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for “isolated” astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in...

  20. Virial theorem for confined universal Fermi gases

    OpenAIRE

    Thomas, J E

    2008-01-01

    Optically-trapped two-component Fermi gases near a broad Feshbach resonance exhibit universal thermodynamics, where the properties of the gas are independent of the details of the two-body scattering interactions. We present a global proof that such a universal gas obeys the virial theorem for {\\it any} trapping potential $U$ and any spin mixture, without assuming either the local density approximation or harmonic confinement. The total energy of the gas is given in scale invariant form by $E...

  1. Degeneracy, the virial theorem, and stellar collapse

    OpenAIRE

    Cardall, Christian Y.

    2008-01-01

    Formulae for the energies of degenerate non-relativistic and ultra-relativistic Fermi gases play multiple roles in simple arguments related to the collapse of a stellar core to a neutron star. These formulae, deployed in conjunction with the virial theorem and a few other basic physical principles, provide surprisingly good estimates of the temperature, mass, and radius (and therefore also density and entropy) of the core at the onset of collapse; the final radius and composition of the cold ...

  2. The untyped stack calculus and Bohm's theorem

    OpenAIRE

    Alberto Carraro

    2013-01-01

    The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We present a simple extension of stack calculus which is for the stack calculus what Saurin's Lambda-mu is for lambda-mu.

  3. Two beautiful proofs of Pick's theorem

    OpenAIRE

    Raman Sundström, Manya; Öhman, Lars-Daniel

    2011-01-01

    We present two different proofs of Pick’s theorem and analyse in what ways might be perceived as beautiful by working mathematicians. In particular, we discuss two concepts, generality and specificity, that appear to contribute to beauty in different ways. We also discuss possible implications on insight into the nature of beauty in mathematics, and how the teaching of mathematics could be impacted, especially in countries in which discussions of beauty and aesthetics are notably absent from...

  4. Soft Theorems from Conformal Field Theory

    CERN Document Server

    Lipstein, Arthur E

    2015-01-01

    Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambitwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.

  5. Soft theorems from conformal field theory

    Science.gov (United States)

    Lipstein, Arthur E.

    2015-06-01

    Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambtwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.

  6. Soft Theorems from Effective Field Theory

    CERN Document Server

    Larkoski, Andrew J; Stewart, Iain W

    2014-01-01

    The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate t...

  7. QUASI-LOCAL CONJUGACY THEOREMS IN BANACH SPACES

    Institute of Scientific and Technical Information of China (English)

    ZHANG WEIRONG; MA JIPU

    2005-01-01

    Let f: U(xo)() E → F be a C1 map and f'(x0) be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties: f'(x0) is double splitting and R(f'(x)) ∩ N(T0+) = {0} near x0. However,in infinite dimensional Banach spaces, f'(x0) is not always double splitting (i.e., the generalized inverse of f'(x0) does not always exist), but its bounded outer inverse of f'(x0) always exists.Only using the C1 map f and the outer inverse T0# of f'(x0), the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if x0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.

  8. The Belle II DEPFET pixel detector

    Science.gov (United States)

    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.

  9. How Bell Labs creates star performers.

    Science.gov (United States)

    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.

  10. Authentication of bell peppers using boron and strontium isotope compositions

    Science.gov (United States)

    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

  11. Generating Bell states in invariant stratification spin networks

    International Nuclear Information System (INIS)

    In this paper, we study the generation of Bell states between distant vertices in a permanently coupled quantum spin network, interacting via invariant stratification graphs. To begin with we establish a class of upper bounds over the achievable entanglement between the reference site and various vertices. We observe that the maximum of these upper bounds is one e-bit. We conclude that the reference site can generate a Bell state with a vertex if the corresponding upper bound of the vertex is one e-bit. Thus for generation of a Bell state this upper bound must be saturated. Taking this into account, we obtain the characteristic constraint of the proper graphs. We introduce a special class of antipodal invariant stratification graphs, which is called reflective, whereas the antipode vertex obeys the characteristic constraint. We also show that the antipodal association scheme graphs are reflective so Bell states can be generated between the antipodal vertices. Moreover, we observe that in such graphs the proper Hamiltonian that enables the creation of a Bell state is the Heisenberg interaction between vertex pairs

  12. Chemical reactions modulated by mechanical stress: extended Bell theory.

    Science.gov (United States)

    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.

  13. The implicit function theorem history, theory, and applications

    CERN Document Server

    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...

  14. Fluctuation theorem for out-of-time-ordered correlator

    CERN Document Server

    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.

  15. Logic for computer science foundations of automatic theorem proving

    CERN Document Server

    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

  16. 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.

  17. Fluctuation theorems for excess and housekeeping heats for underdamped systems

    OpenAIRE

    Lahiri, Sourabh; Jayannavar, A. M.

    2013-01-01

    We present a simple derivation of the integral fluctuation theorems for excess housekeeping heat for an underdamped Langevin system, without using the concept of dual dynamics. In conformity with the earlier results, we find that the fluctuation theorem for housekeeping heat holds when the steady state distributions are symmetric in velocity, whereas there is no such requirement for the excess heat. We first prove the integral fluctuation theorem for the excess heat, and then show that it nat...

  18. A Fundamental Theorem on the Structure of Symplectic Integrators

    OpenAIRE

    Chin, Siu A.

    2005-01-01

    I show that the basic structure of symplectic integrators is governed by a theorem which states {\\it precisely}, how symplectic integrators with positive coefficients cannot be corrected beyond second order. All previous known results can now be derived quantitatively from this theorem. The theorem provided sharp bounds on second-order error coefficients explicitly in terms of factorization coefficients. By saturating these bounds, one can derive fourth-order algorithms analytically with arbi...

  19. Average Kinetic Energy of Heavy Quark and Virial Theorem

    OpenAIRE

    Hwang, Dae Sung; Kim, C. S.; Namgung, Wuk

    1996-01-01

    We derive the virial theorem of the relativistic two-body system for the study of the B-meson physics. It is also shown that the solution of the variational equation always satisfies the virial theorem. From the virial theorem we also obtained $\\mu_\\pi^2 \\equiv -\\lambda_1 \\equiv = 0.40\\sim 0.58$ GeV$^2$, which is consistent with the result of the QCD sum rule calculations of Ball $et$ $al.$

  20. Automated Theorem Proving for Cryptographic Protocols with Automatic Attack Generation

    OpenAIRE

    Jan Juerjens; Thomas A. Kuhn

    2016-01-01

    Automated theorem proving is both automatic and can be quite efficient. When using theorem proving approaches for security protocol analysis, however, the problem is often that absence of a proof of security of a protocol may give little hint as to where the security weakness lies, to enable the protocol designer to improve the protocol. For our approach to verify cryptographic protocols using automated theorem provers for first-order logic (such as e-SETHEO or SPASS), we demonstrate a method...

  1. Inconsistency of Carnot's theorem's proof by R. Clausius

    CERN Document Server

    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.

  2. 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.

  3. Proceedings Workshop on Partiality and Recursion in Interactive Theorem Provers

    CERN Document Server

    Bove, Ana; Niqui, Milad; 10.4204/EPTCS.43

    2010-01-01

    This volume contains the proceedings of the Workshop on Partiality and Recursion in Interactive Theorem Provers (PAR 2010) which took place on July 15 in Edinburgh, UK. This workshop was held as a satellite workshop of the International Conference on Interactive Theorem Proving (ITP 2010), itself part of the Federated Logic Conference 2010 (FLoC 2010). This workshop is a venue for researchers working on new approaches to cope with partial functions and terminating general (co)recursion in theorem provers.

  4. Reflexivity and the diagonal argument in proofs of limitative theorems

    OpenAIRE

    Młynarski, Kajetan

    2011-01-01

    This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\\"odel's theorem). The fact, that a formal system contains a sentence, which introduces reflexitivity, does not imply, that the same system does not contain a sentence or a proof procedure which solves this problem. Second basic method of proof - diagonal argument (i.e. showing non-eqiunumerosity o...

  5. The Interpretability of Inconsistency: Feferman's Theorem and Related Results

    OpenAIRE

    Visser, Albert

    2014-01-01

    This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case that a theory fails to prove its own consistency, but that a theory actively holds its own inconsistency for possible. We first give a careful presentation of the result. Then, we provide two versi...

  6. The Surprise Examination Paradox and the Second Incompleteness Theorem

    OpenAIRE

    Kritchman, Shira; Raz, Ran

    2010-01-01

    We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest that the second incompleteness theorem gives a possible resolution of the surprise examination paradox. Roughly speaking, we argue that the flaw in the derivation of the paradox is that it contains a hidden assumption that one can prove the consistency of the...

  7. Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

    OpenAIRE

    Mawardi Bahri

    2013-01-01

    General convolution theorems for two-dimensional quaternion Fourier transforms(QFTs) are presented. It is shown that these theorems are not only valid for real-valued functions, but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra fr...

  8. Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

    Directory of Open Access Journals (Sweden)

    Mawardi Bahri

    2013-01-01

    Full Text Available General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra framework.

  9. Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

    OpenAIRE

    Mawardi Bahri; Ryuichi Ashino; Rémi Vaillancourt

    2013-01-01

    General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra framework.

  10. Correlates of degree of nerve involvement in early Bell's palsy

    Directory of Open Access Journals (Sweden)

    Hsieh Ru-Lan

    2009-06-01

    Full Text Available Abstract Background This study aimed to evaluate the still unknown factors correlating with the degree of nerve involvement in early Bell's palsy. Methods This retrospective chart review study of newly diagnosed cases of Bell's palsy was conducted over a three-year period. Information on age, sex, day of onset, comorbidities, corticosteroid use, and electroneurographic test results were collected. The electroneurographic quotient (amplitude of compound muscle action potential on the affected side divided by that on the healthy side and expressed in percent was used as an index of nerve involvement, with lower quotient indicating more severe disease. Results Data were collected on 563 patients. The mean electroneurographic quotient varied inversely with age (p vs. 40.3%; p = 0.002. There was no correlation between the degree of nerve involvement and sex, season of onset, hypertension, or diabetes. Conclusion The degree of nerve involvement in early Bell's palsy correlates positively with age and negatively with corticosteroid use.

  11. Testing Bell inequalities with circuit QEDs by joint spectral measurements

    CERN Document Server

    Yuan, Hao; Huang, J S; Wang, X H; Vedral, Vlatko

    2011-01-01

    We propose a feasible approach to test Bell's inequality with the experimentally-demonstrated circuit QED system, consisting of two well-separated superconducting charge qubits (SCQs) dispersively coupled to a common one-dimensional transmission line resonator (TLR). Our proposal is based on the joint spectral measurements of the two SCQs, i.e., their quantum states in the computational basis $\\{|kl>,\\,k,l=0,1\\}$ can be measured by detecting the transmission spectra of the driven TLR: each peak marks one of the computational basis and its relative height corresponds to the probability superposed. With these joint spectral measurements, the generated Bell states of the two SCQs can be robustly confirmed without the standard tomographic technique. Furthermore, the statistical nonlocal-correlations between these two distant qubits can be directly read out by the joint spectral measurements, and consequently the Bell's inequality can be tested by sequentially measuring the relevant correlations related to the sui...

  12. Experimental violation of Bell inequalities for multi-dimensional systems

    CERN Document Server

    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...

  13. Belle II SVD ladder assembly procedure and electrical qualification

    Science.gov (United States)

    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.

  14. Belle II early physics program of bottomonium spectroscopy

    CERN Document Server

    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.

  15. Two-player conflicting interest Bayesian games and Bell nonlocality

    Science.gov (United States)

    Situ, Haozhen

    2016-01-01

    Nonlocality, one of the most remarkable aspects of quantum mechanics, is closely related to Bayesian game theory. Quantum mechanics can offer advantages to some Bayesian games, if the payoff functions are related to Bell inequalities in some way, most of these Bayesian games that have been discussed are common interest games. Recently, the first conflicting interest Bayesian game is proposed in Phys. Rev. Lett. 114, 020401 (2015). In the present paper, we present three new conflicting interest Bayesian games where quantum mechanics offers advantages. The first game is linked with Cereceda inequalities, the second game is linked with a generalized Bell inequality with three possible measurement outcomes, and the third game is linked with a generalized Bell inequality with three possible measurement settings.

  16. On the Debossing, Annealing and Mounting of Bells

    Science.gov (United States)

    PERRIN, R.; SWALLOWE, G. M.; CHARNLEY, T.; MARSHALL, C.

    1999-10-01

    Changes in the frequencies of the musical partials of various types of bells following debossing dismounting/mounting and annealing/quench annealing are reported. Debossing, dismounting and quench annealing lead to frequency drops, while mounting gives rises. Annealing can lead to frequency increases or decreases depending upon the maximum temperature employed and the initial residual stress. Qualitative explanations of these phenomena are given in terms of changes in crown stiffness, internal stress and alloy phase structure. These are supported by the results of X-ray diffraction measurements. Although the effects are all small they can be large enough to be detected by a reasonably musical car. This, together with the fact that the effects cannot be controlled, gives a plausible explanation of why modern bellfounders use vertical lathes for tuning, even with small carillon bells, and do not anneal bells when trying to control warble.

  17. Bell's Inequality, Random Sequence, and Quantum Key Distribution

    CERN Document Server

    Hwang, W Y

    2005-01-01

    At first glance Ekert 91 quantum key distribution protocol can be secure even if legitimate users adopt whatever devices for the protocol as long as the devices give a result that violates Bell's inequality. However, it is not the case if they ignore non-detection events because Eve can make use of detection-loophole, as Larrson showed. What we show is that even when the legitimate users take into account non-detection events Eve can successfully eavesdrop if the manufacturer design the QKD system appropriately. A loophole utilized here is that of `free-choice' (or `real randomness'). We show how (local) quantum key distribution devices with pseudo-random sequence generator installed in them can apparently violate Bell's inequality. We briefly discuss a debate on Bell's inequality violation that is involved with a question on randomness.

  18. Violation of Bell inequality based on S4 symmetry

    Science.gov (United States)

    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.

  19. No-cloning theorem on quantum logics

    Science.gov (United States)

    Miyadera, Takayuki; Imai, Hideki

    2009-10-01

    This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.

  20. Godel's Incompleteness Theorems and Platonic Metaphysics

    CERN Document Server

    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.

  1. 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.

  2. On Clifford's theorem for singular curves

    CERN Document Server

    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.

  3. A Cauchy-Davenport theorem for semigroups

    OpenAIRE

    Tringali, Salvatore

    2012-01-01

    We generalize the Davenport transform and use it to prove that, for a (possibly non-commutative) cancellative semigroup $\\mathbb A = (A, +)$ and non-empty subsets $X,Y$ of $A$ such that the subsemigroup generated by $Y$ is commutative, we have $|X + Y| \\ge \\min(\\omega(Y), |X| + |Y| - 1)$, where $\\omega(Y) := \\sup_{y_0 \\in Y \\cap \\mathbb A^{\\times}} \\inf_{y \\in Y \\setminus \\{y_0\\}} ||$. This carries over the Cauchy-Davenport theorem to the broader setting of semigroups, and it implies, in part...

  4. 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.

  5. 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.

  6. An extension of Harrington's noncupping theorem

    Institute of Scientific and Technical Information of China (English)

    喻良; 丁德成

    2003-01-01

    (i) Call a c.e. degree b anti-cupping relative to x, if there is a c.e. a < b such that foranyc.e. w w ximpliesaUw bUx.(ii) Call a c.e. degree b everywhere anti-cupping (e.a.c.), if it is anti-cupping relative to x foreach c.e. degree x.By a tree method, we prove that every high c.e. degree has e.a.c. property by extendingHarrington's anti-cupping theorem.

  7. 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.

  8. 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.

  9. 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.

  10. Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

    Science.gov (United States)

    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.

  11. Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Woolgar, Eric, E-mail: ewoolgar@ualberta.ca [Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1 (Canada); Wylie, William, E-mail: wwylie@syr.edu [215 Carnegie Building, Department of Mathematics, Syracuse University, Syracuse, New York 13244 (United States)

    2016-02-15

    We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.

  12. Hadronic b {yields} c decays at Belle

    Energy Technology Data Exchange (ETDEWEB)

    Joshi, Nikhil Jayant [Tata Institute of Fundamental Research - TIFR, Homi Bhabha Road, Mumbai 400 005 (India)

    2010-07-01

    We present a measurement of the unitarity triangle angle {phi}{sub 3} using Dalitz plot analysis of three-body neutral D decays from the B{sup +} {yields} D{sup (*)}K{sup (*)+} process. The results are based on a large sample of B anti-B pairs recorded at the {Upsilon}(4S) resonance with the Belle detector at the KEKB e{sup +}e{sup -} collider. The decay B {yields} D{sup (*)} K{sup (*)} (D = D{sup 0} or anti-D{sup 0}) includes the b {yields} u transition and plays a crucial role in the measurement of the CP-violating angle {phi}{sub 3}. We present the result of a study of the decay B {yields} D{sup (*)} K{sup (*)} where the D meson is reconstructed from K{sup +} {pi}{sup -}. We also report improved measurements of the branching fractions for the decays B{sup 0} {yields} D{sub s}{sup (*)+} {pi}{sup -} and anti-B{sup 0} {yields} D{sub s}{sup (*)+} K{sup -}. Based on these results, we determine the ratio between the amplitudes of the doubly Cabibbo suppressed decay B{sup 0} {yields} D{sup (*)+} {pi}{sup -} and the Cabibbo favored decay B{sup 0} {yields} D{sup (*)-} {pi}{sup +}. We studied the three-body baryonic B{sup +} decays, B{sup +} {yields} p anti-{lambda} D{sup (*)0}. The branching fractions as well as the differential branching fractions as a function of the mass of the p anti-{lambda} system are presented. These results are compared with theoretical predictions based on the generalized factorization approach. We present a study of the exclusive decays B{sup 0} {yields} D{sub s}{sup -} K{sup 0}{sub S} {pi}{sup +} and B{sup -} to D{sub s}{sup +} K{sup -}K{sup -}. We use the D{sub s}{sup -} {yields} {phi} {pi}{sup -}, anti-K{sup *}(892)0 K{sup -} and K{sup 0}{sub S} K{sup -} decay modes for D{sub s} reconstruction. (author)

  13. Bell's Nonlocality Can be Tested through Einstein-Podolsky-Rosen Steering

    OpenAIRE

    Chen, Jing-Ling; Ye, Xiang-Jun

    2015-01-01

    Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long...

  14. A paradigm of fragile Earth in Priestley's bell jar

    OpenAIRE

    Martin, Daniel; Thompson, Andrew; Stewart, Iain; Gilbert,Edward; Hope, Katrina; Kawai, Grace; Griffiths, Alistair

    2012-01-01

    Background Photosynthesis maintains aerobic life on Earth, and Joseph Priestly first demonstrated this in his eighteenth-century bell jar experiments using mice and mint plants. In order to demonstrate the fragility of life on Earth, Priestley's experiment was recreated using a human subject placed within a modern-day bell jar. Methods A single male subject was placed within a sealed, oxygen-depleted enclosure (12.4% oxygen), which contained 274 C3 and C4 plants for a total of 48 h. A combina...

  15. When is facial paralysis Bell palsy? Current diagnosis and treatment.

    Science.gov (United States)

    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.

  16. [Treatment of idiopathic peripheral facial nerve paralysis (Bell's palsy)].

    Science.gov (United States)

    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.

  17. Detection efficiency for loophole-free Bell experiments with postselection

    CERN Document Server

    Sciarrino, F; Cabello, A; Mataloni, P

    2010-01-01

    It is generally assumed that the violation of a Bell inequality by postselected events cannot be used for loophole-free tests of quantum nonlocality. We show that this is not the case if the postselection is performed locally and without communication between the observers. This permits the adoption of certain setups of locally selected entanglement, which are simpler and more efficient, for long-distance free-space Bell tests. For these setups, we investigate which is the minimum detection efficiency for loophole-free experiments.

  18. Constructing quantum games from a system of Bell's inequalities

    CERN Document Server

    Iqbal, Azhar

    2009-01-01

    We report constructing quantum games directly from a system of Bell's inequalities using Arthur Fine's analysis published in early 1980s. This analysis showed that such a system of inequalities forms a set of both necessary and sufficient conditions required to find a joint distribution function compatible with a given set of joint probabilities, in terms of which the system of Bell's inequalities is usually expressed. Using the setting of a quantum correlation experiment for playing a quantum game, and considering the examples of Prisoners' Dilemma and Matching Pennies, we argue that this approach towards constructing quantum games addresses well known criticism of quantum games.

  19. Structural Investigation on Bell Inequalities of High Dimensions

    CERN Document Server

    Lee, S W; Lee, J; Cheong, Yong Wook; Lee, Jinhyoung; Lee, Seung-Woo

    2005-01-01

    We present the generalized Bell inequality for high-dimensional systems and reformulate it in order to compare with Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality. It is shown that the maximal entanglement leads to the maximal violation of our Bell inequality, whereas a non-maximally entangled state maximally violates CGLMP inequality. In addition, it is shown that both types have the equivalent structure with respect to the joint probabilities, but they have the different correlation weights of measurement outcomes. We remark that the correlation weights plays a crucial role in determining the violation conditions and tightness conditions.

  20. Ground-state-energy theorem and the virial theorem of a many-particle system in d dimensions

    Science.gov (United States)

    Iwamoto, N.

    1984-01-01

    The equivalence of Pauli's ground-state-energy theorem and the virial theorem is demonstrated for a many-particle system interacting with an interparticle potential in d dimensions at zero and finite temperatures. Pauli's theorem has an integral form in which the variable is the coupling constant e-squared, while the virial theorem has a differential form in which the variable has the number density n. The essence of the equivalence proof consists in changing the variable from n to e-squared by noting the dependence of the excess free energy on dimensionless quantities for zero-temperature and classical cases.