Equating spatial summation in visual field testing reveals greater loss in optic nerve disease.
Kalloniatis, Michael; Khuu, Sieu K
2016-07-01
To test the hypothesis that visual field assessment in ocular disease measured with target stimuli within or close to complete spatial summation results in larger threshold elevation compared to when measured with the standard Goldmann III target size. The hypothesis predicts a greater loss will be identified in ocular disease. Additionally, we sought to develop a theoretical framework that would allow comparisons of thresholds with disease progression when using different Goldmann targets. The Humphrey Field Analyser (HFA) 30-2 grid was used in 13 patients with early/established optic nerve disease using the current Goldmann III target size or a combination of the three smallest stimuli (target size I, II and III). We used data from control subjects at each of the visual field locations for the different target sizes to establish the number of failed points (events) for the patients with optic nerve disease, as well as global indices for mean deviation (MD) and pattern standard deviation (PSD). The 30-2 visual field testing using alternate target size stimuli showed that all 13 patients displayed more defects (events) compared to the standard Goldmann III target size. The median increase for events was seven additional failed points: (range 1-26). The global indices also increased when the new testing approach was used (MD -3.47 to -6.25 dB and PSD 4.32 to 6.63 dB). Spatial summation mapping showed an increase in critical area (Ac) in disease and overall increase in thresholds when smaller target stimuli were used. When compared to the current Goldmann III paradigm, the use of alternate sized targets within the 30-2 testing protocol revealed a greater loss in patients with optic nerve disease for both event analysis and global indices (MD and PSD). We therefore provide evidence in a clinical setting that target size is important in visual field testing. © 2016 The Authors Ophthalmic & Physiological Optics © 2016 The College of Optometrists.
International Nuclear Information System (INIS)
Mackrodt, C.; Reeh, H.
1997-01-01
General summational invariants, i.e., conservation laws acting additively on asymptotic particle states, are investigated within a classical framework for point particles with nontrivial scattering. copyright 1997 American Institute of Physics
Ramanujan summation of divergent series
Candelpergher, Bernard
2017-01-01
The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory.
Generalization of a summation formula due to Fox
Directory of Open Access Journals (Sweden)
Medhat A. Rakha
2013-10-01
The aim of this research paper is to provide the generalization of Fox’s summation formula and to obtain 19 results of this type. The results are derived with the help of generalized Gauss’s second summation theorem recently obtained by Rakha, et al. and a general formula due to Fox. The results derived in this paper are simple, interesting, easily established and may be potentially useful.
Flatto, Leopold
2009-01-01
Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. The theorem is of great depth in that it relates to a large and diverse body of mathematics. There are several proofs of the theorem, none of which is elementary. A particularly attractive feature of the theorem, which is easily understood but difficult to prove, is that it serves as a prism through which one can learn and appreciate a lot of beautiful mathematics. This book stresses the modern appro
International Nuclear Information System (INIS)
Sprung, D.W.L.
1975-01-01
This paper is a brief review of those aspects of the effective interaction problem that can be grouped under the heading of infinite partial summations of the perturbation series. After a brief mention of the classic examples of infinite summations, the author turns to the effective interaction problem for two extra core particles. Their direct interaction is summed to produce the G matrix, while their indirect interaction through the core is summed in a variety of ways under the heading of core polarization. (orig./WL) [de
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Jensen, Tobias Lindstrøm; Jensen, Jesper Rindom
2017-01-01
-robust to noise, or very computationally inten- sive. In this paper, we propose a fast algorithm for the harmonic chirp summation method which has been demonstrated in the liter- ature to be accurate and robust to noise. The proposed algorithm is orders of magnitudes faster than previous algorithms which is also...
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
Debattista, Josephine
2000-01-01
Pythagoras 580 BC was a Greek mathematician who became famous for formulating Pythagoras Theorem but its principles were known earlier. The ancient Egyptians wanted to layout square (90°) corners to their fields. To solve this problem about 2000 BC they discovered the 'magic' of the 3-4-5 triangle.
International Nuclear Information System (INIS)
Palmer, R.
1994-06-01
Electromagnetic fields can be separated into near and far components. Near fields are extensions of static fields. They do not radiate, and they fall off more rapidly from a source than far fields. Near fields can accelerate particles, but the ratio of acceleration to source fields at a distance R, is always less than R/λ or 1, whichever is smaller. Far fields can be represented as sums of plane parallel, transversely polarized waves that travel at the velocity of light. A single such wave in a vacuum cannot give continuous acceleration, and it is shown that no sums of such waves can give net first order acceleration. This theorem is proven in three different ways; each method showing a different aspect of the situation
The quantitative Morse theorem
Loi, Ta Le; Phien, Phan
2013-01-01
In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \\cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse function theorem and the quantitative Morse lemma.
International Nuclear Information System (INIS)
Ma Zhongqi
2006-01-01
The Levinson theorem is a fundamental theorem in quantum scattering theory, which shows the relation between the number of bound states and the phase shift at zero momentum for the Schroedinger equation. The Levinson theorem was established and developed mainly with the Jost function, with the Green function and with the Sturm-Liouville theorem. In this review, we compare three methods of proof, study the conditions of the potential for the Levinson theorem and generalize it to the Dirac equation. The method with the Sturm-Liouville theorem is explained in some detail. References to development and application of the Levinson theorem are introduced. (topical review)
Analogues of Euler and Poisson Summation Formulae
Indian Academy of Sciences (India)
... f ( n ) have been obtained in a unified manner, where (()) is a periodic complex sequence; () is the divisor function and () is a sufficiently smooth function on [, ]. We also state a generalised Abel's summation formula, generalised Euler's summation formula and Euler's summation formula in several variables.
Fermat's Last Theorem A Theorem at Last!
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 1. Fermat's Last Theorem A Theorem at Last! C S Yogananda. General Article Volume 1 Issue 1 January 1996 pp 71-79. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/001/01/0071-0079 ...
Directory of Open Access Journals (Sweden)
William Graham
2010-03-01
Full Text Available My response to the conference focuses on five issues: (1 the importance of the reciprocity and interdependence of orality and writtenness; (2 the importance of socio-political-economic facets of textual uses; (3 the recitative, performative dimensions of the texts treated; (4 the largely Mediterranean provenance of the texts treated; and (5 the authority of texts, both written and oral. Finally, I make a tentative suggestion about the importance of the perceived authority rather than writtenness of major religious texts as the locus of sacrality, since the papers demonstrate how much both orality and writtenness are involved in the life of these texts.
Levinson, N
1940-01-01
A typical gap theorem of the type discussed in the book deals with a set of exponential functions { \\{e^{{{i\\lambda}_n} x}\\} } on an interval of the real line and explores the conditions under which this set generates the entire L_2 space on this interval. A typical gap theorem deals with functions f on the real line such that many Fourier coefficients of f vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various propertie
The Patchwork Divergence Theorem
Dray, Tevian; Hellaby, Charles
1994-01-01
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting "patchwork divergence theorem" which is independent of the metric signature in either region, and which is thus valid if the signature changes. (PA...
Race effects on temporal summation to heat pain in youth.
Morris, Matthew C; Walker, Lynn; Bruehl, Stephen; Hellman, Natalie; Sherman, Amanda L; Rao, Uma
2015-05-01
Racial differences in pain responsiveness have been demonstrated in adults. However, it is unclear whether racial differences are also present in youth and whether they extend to experimental pain indices assessing temporal summation of second pain (TSSP). Temporal summation of second pain provides an index of pain sensitivity and may be especially relevant in determining risk for chronic pain. This study assessed pain tolerance and TSSP to evoked thermal pain in 78 healthy youth (age range, 10-17), 51% of whom were African American and 49% were non-Hispanic white. Multilevel models revealed within-individual increases in pain ratings during the temporal summation task in non-Hispanic white youth that were consistent with TSSP. Pain ratings did not change significantly during the temporal summation task in African-American youth. Baseline evoked pain ratings were significantly higher in African-American compared with non-Hispanic white youth. These findings suggest that enhanced responsiveness to evoked thermal pain in African Americans is present in adolescence but is unlikely to be related to elevated TSSP. These results may have implications for understanding racial differences in chronic pain experience in adulthood.
Virtual continuity of the measurable functions of several variables, and Sobolev embedding theorems
Vershik, Anatoly; Zatitskiy, Pavel; Petrov, Fedor
2013-01-01
Classical Luzin's theorem states that the measurable function of one variable is "almost" continuous. This is not so anymore for functions of several variables. The search of right analogue of the Luzin theorem leads to a notion of virtually continuous functions of several variables. This probably new notion appears implicitly in the statements like embeddings theorems and traces theorems for Sobolev spaces. In fact, it reveals their nature as theorems about virtual continuity. This notion is...
The relativistic virial theorem
International Nuclear Information System (INIS)
Lucha, W.; Schoeberl, F.F.
1989-11-01
The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...
Nonextensive Pythagoras' Theorem
Dukkipati, Ambedkar
2006-01-01
Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And hence, this property is referred to as Pythagoras' theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches of statistical estimation theory like information geometry. Equvalent of Pythagoras' theo...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose K is a compact set in the complex plane and 0 belongs to the boundary ∂K. Let A(K) denote the space of all functions f on K such that f is holo- morphic in a neighborhood of K and f(0) = 0. Also for any given positive integer ...
Theorem on magnet fringe field
International Nuclear Information System (INIS)
Wei, Jie; Talman, R.
1995-01-01
Transverse particle motion in particle accelerators is governed almost totally by non-solenoidal magnets for which the body magnetic field can be expressed as a series expansion of the normal (b n ) and skew (a n ) multipoles, B y + iB x = summation(b n + ia n )(x + iy) n , where x, y, and z denote horizontal, vertical, and longitudinal (along the magnet) coordinates. Since the magnet length L is necessarily finite, deflections are actually proportional to ''field integrals'' such as bar BL ≡ ∫ B(x,y,z)dz where the integration range starts well before the magnet and ends well after it. For bar a n , bar b n , bar B x , and bar B y defined this way, the same expansion Eq. 1 is valid and the ''standard'' approximation is to neglect any deflections not described by this expansion, in spite of the fact that Maxwell's equations demand the presence of longitudinal field components at the magnet ends. The purpose of this note is to provide a semi-quantitative estimate of the importance of |Δp ∝ |, the transverse deflection produced by the ion-gitudinal component of the fringe field at one magnet end relative to |Δp 0 |, the total deflection produced by passage through the whole magnet. To emphasize the generality and simplicity of the result it is given in the form of a theorem. The essence of the proof is an evaluation of the contribution of the longitudinal field B x from the vicinity of one magnet end since, along a path parallel to the magnet axis such as path BC
Objective evaluation of binaural summation through acoustic reflex measures.
Rawool, Vishakha W; Parrill, Madaline
2018-02-12
A previous study [Rawool, V. W. (2016). Auditory processing deficits: Assessment and intervention. New York, NY: Thieme Medical Publishers, Inc., pp. 186-187] demonstrated objective assessment of binaural summation through right contralateral acoustic reflex thresholds (ARTs) in women. The current project examined if previous findings could be generalised to men and to the left ear. Cross-sectional. Sixty individuals participated in the study. Left and right contralateral ARTs were obtained in two conditions. In the alternated condition, the probe tone presentation was alternated with the presentation of the reflex activating clicks. In the simultaneous condition, the probe tone and the clicks were presented simultaneously. Binaural summation was calculated by subtracting the ARTs obtained in the simultaneous condition from the ARTs obtained in the alternated condition. MANOVA on ARTs revealed no significant gender or ear effects. The ARTs were significantly lower/better in the simultaneous condition compared to the alternated condition. Binaural summation was 4 dB or higher in 88% of the ears and 6 dB or higher in 76% of ears. Stimulation of six out of the total 120 (0.5%) ears resulted in worse thresholds in the simultaneous condition compared with the alternating condition, suggesting binaural interference.
Complex proofs of real theorems
Lax, Peter D
2011-01-01
Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, "The shortest and best way between two truths of the real domain often passes through the imaginary one." Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Müntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Żelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime ...
DEFF Research Database (Denmark)
Törnquist, Asger Dag; Weiss, W.
2009-01-01
We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible.......We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible....
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...
The Fluctuation Theorem and Dissipation Theorem for Poiseuille Flow
International Nuclear Information System (INIS)
Brookes, Sarah J; Reid, James C; Evans, Denis J; Searles, Debra J
2011-01-01
The fluctuation theorem and the dissipation theorem provide relationships to describe nonequilibrium systems arbitrarily far from, or close to equilibrium. They both rely on definition of a central property, the dissipation function. In this manuscript we apply these theorems to examine a boundary thermostatted system undergoing Poiseuille flow. The relationships are verified computationally and show that the dissipation theorem is potentially useful for study of boundary thermostatted systems consisting of complex molecules undergoing flow in the nonlinear regime.
Dalen, D. van
The following pages make form a new chapter for the book Logic and Structure. This chapter deals with the incompleteness theorem, and contains enough basic material for the treatment of the required notions of computability, representability and the like. This chapter will appear in the next
Indian Academy of Sciences (India)
eralizing the method of proof of the well known. Cantor's ... Godel's first incompleteness theorem is proved. ... that the number of elements in any finite set is a natural number. ..... proof also has a Godel number; of course, you have to fix.
Saikia, Manjil P.
2013-01-01
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \\cite{thales}, \\cite{wiki} and \\cite{wiki2} for the historical comments and sources.
Converse Barrier Certificate Theorems
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer
2016-01-01
This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither...
International Nuclear Information System (INIS)
Cahill, K.
1975-11-01
Local field theory is used to derive formulas that express certain boundary values of the N-point function as sums of products of scattering amplitudes. These formulas constitute a generalization of the optical theorem and facilitate the analysis of multiparticle scattering functions [fr
Khan, Asaduzzaman; Chien, Chi-Wen; Bagraith, Karl S
2015-04-01
To investigate whether using a parametric statistic in comparing groups leads to different conclusions when using summative scores from rating scales compared with using their corresponding Rasch-based measures. A Monte Carlo simulation study was designed to examine between-group differences in the change scores derived from summative scores from rating scales, and those derived from their corresponding Rasch-based measures, using 1-way analysis of variance. The degree of inconsistency between the 2 scoring approaches (i.e. summative and Rasch-based) was examined, using varying sample sizes, scale difficulties and person ability conditions. This simulation study revealed scaling artefacts that could arise from using summative scores rather than Rasch-based measures for determining the changes between groups. The group differences in the change scores were statistically significant for summative scores under all test conditions and sample size scenarios. However, none of the group differences in the change scores were significant when using the corresponding Rasch-based measures. This study raises questions about the validity of the inference on group differences of summative score changes in parametric analyses. Moreover, it provides a rationale for the use of Rasch-based measures, which can allow valid parametric analyses of rating scale data.
Virial theorem and hypervirial theorem in a spherical geometry
International Nuclear Information System (INIS)
Li Yan; Chen Jingling; Zhang Fulin
2011-01-01
The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)
Discovering the Theorem of Pythagoras
Lattanzio, Robert (Editor)
1988-01-01
In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.
Neural Summation in the Hawkmoth Visual System Extends the Limits of Vision in Dim Light.
Stöckl, Anna Lisa; O'Carroll, David Charles; Warrant, Eric James
2016-03-21
Most of the world's animals are active in dim light and depend on good vision for the tasks of daily life. Many have evolved visual adaptations that permit a performance superior to that of manmade imaging devices [1]. In insects, a major model visual system, nocturnal species show impressive visual abilities ranging from flight control [2, 3], to color discrimination [4, 5], to navigation using visual landmarks [6-8] or dim celestial compass cues [9, 10]. In addition to optical adaptations that improve their sensitivity in dim light [11], neural summation of light in space and time-which enhances the coarser and slower features of the scene at the expense of noisier finer and faster features-has been suggested to improve sensitivity in theoretical [12-14], anatomical [15-17], and behavioral [18-20] studies. How these summation strategies function neurally is, however, presently unknown. Here, we quantified spatial and temporal summation in the motion vision pathway of a nocturnal hawkmoth. We show that spatial and temporal summation combine supralinearly to substantially increase contrast sensitivity and visual information rate over four decades of light intensity, enabling hawkmoths to see at light levels 100 times dimmer than without summation. Our results reveal how visual motion is calculated neurally in dim light and how spatial and temporal summation improve sensitivity while simultaneously maximizing spatial and temporal resolution, thus extending models of insect motion vision derived predominantly from diurnal flies. Moreover, the summation strategies we have revealed may benefit manmade vision systems optimized for variable light levels [21]. Copyright © 2016 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Veltman, H.
1990-01-01
The equivalence theorem states that, at an energy E much larger than the vector-boson mass M, the leading order of the amplitude with longitudinally polarized vector bosons on mass shell is given by the amplitude in which these vector bosons are replaced by the corresponding Higgs ghosts. We prove the equivalence theorem and show its validity in every order in perturbation theory. We first derive the renormalized Ward identities by using the diagrammatic method. Only the Feynman-- 't Hooft gauge is discussed. The last step of the proof includes the power-counting method evaluated in the large-Higgs-boson-mass limit, needed to estimate the leading energy behavior of the amplitudes involved. We derive expressions for the amplitudes involving longitudinally polarized vector bosons for all orders in perturbation theory. The fermion mass has not been neglected and everything is evaluated in the region m f ∼M much-lt E much-lt m Higgs
Fully Quantum Fluctuation Theorems
Åberg, Johan
2018-02-01
Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.
Multivariable Chinese Remainder Theorem
Indian Academy of Sciences (India)
IAS Admin
to sleep. The 3rd thief wakes up and finds the rest of the coins make 7 equal piles excepting a coin which he pockets. If the total number of coins they stole is not more than 200, what is the exact number? With a bit of hit and miss, one can find that 157 is a possible number. The Chinese remainder theorem gives a systematic ...
Sukumar, Subash; Waugh, Sarah J
2007-03-01
We estimated spatial summation areas for the detection of luminance-modulated (LM) and contrast-modulated (CM) blobs at the fovea, 2.5, 5 and 10 deg eccentrically. Gaussian profiles were added or multiplied to binary white noise to create LM and CM blob stimuli and these were used to psychophysically estimate detection thresholds and spatial summation areas. The results reveal significantly larger summation areas for detecting CM than LM blobs across eccentricity. These differences are comparable to receptive field size estimates made in V1 and V2. They support the notion that separate spatial processing occurs for the detection of LM and CM stimuli.
Binaural loudness summation for directional sounds
DEFF Research Database (Denmark)
Sivonen, Ville Pekka; Ellermeier, Wolfgang
2006-01-01
the binaural loudness summation of the at-ear signals. Even though the effects of HRTFs were taken into account, considerable individual differences in the binaural summation of loudness remained. In order to create conditions in which the directional at-ear changes were identical for all participants......, the present experiment employed 'generic' HRTFs to create directional sounds via binaural synthesis. When inspecting the results of the listening tests, however, large individual differences were still evident, as in the earlier study. The generality of this finding was further corroborated by running...... an independent, inexperienced sample of ten participants exclusively being exposed to the present generic HRTFs. Despite the individual differences, the average results suggest a relatively simple rule for combining the binaural input when carrying out acoustical measurements using an artificial head...
Refined holonomic summation algorithms in particle physics
Energy Technology Data Exchange (ETDEWEB)
Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Round, Mark; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC)
2017-06-15
An improved multi-summation approach is introduced and discussed that enables one to simultaneously handle indefinite nested sums and products in the setting of difference rings and holonomic sequences. Relevant mathematics is reviewed and the underlying advanced difference ring machinery is elaborated upon. The flexibility of this new toolbox contributed substantially to evaluating complicated multi-sums coming from particle physics. Illustrative examples of the functionality of the new software package RhoSum are given.
Refined holonomic summation algorithms in particle physics
International Nuclear Information System (INIS)
Bluemlein, Johannes; Round, Mark; Schneider, Carsten
2017-06-01
An improved multi-summation approach is introduced and discussed that enables one to simultaneously handle indefinite nested sums and products in the setting of difference rings and holonomic sequences. Relevant mathematics is reviewed and the underlying advanced difference ring machinery is elaborated upon. The flexibility of this new toolbox contributed substantially to evaluating complicated multi-sums coming from particle physics. Illustrative examples of the functionality of the new software package RhoSum are given.
International Nuclear Information System (INIS)
Lloyd, Mark Anthony
1999-01-01
We in the nuclear power industry consider ourselves to be at the forefront of civilised progress. Yet, all too often, even we ourselves don't believe our public relations statements about nuclear power. Why is this? Let us approach the question by considering Godel's Theorem. Godel's Theorem is extremely complicated mathematically, but for our purposes can be simplified to the maxim that one cannot validate a system from within that system. Scientists, especially those in the fields of astronomy and nuclear physics, have long realised the implications of Godel's Theorem. The people to whom we must communicate look to us, who officially know everything about our industry, to comfort and reassure them. And we forget that we can only comfort them by addressing their emotional needs, not by demonstrating our chilling o bjectivity . Let us try something completely new in communication. Instead of looking for incremental rules which will help us marginally differentiate the way we communicate about minor or major incidents, let us leapfrog across 'objectivity' to meaning and relevance. If we truly believe that nuclear energy is a good thing, this leap should not be difficult. Finally, if we as communicators are not prepared to be meaningful and relevant - not prepared to leapfrog beyond weasel terms like 'minor incident' - what does that say about the kinds of people we believe the nuclear community to be? Are nuclear people a group apart, divisible from the rest of the human race by their evil? In fact the nuclear community is a living, laughing, normal part of a whole society; and is moreover a good contributor to the technological progress that society demands. When we ourselves recognise this, we will start to communicate nuclear issues in the same language as the rest of society. We will start to speak plainly and convincingly, and our conviction will leapfrog our audience into being able to believe us
Topological interpretation of Luttinger theorem
Seki, Kazuhiro; Yunoki, Seiji
2017-01-01
Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because i) the Luttinger volume is represented as the winding number of the single-particle Green's function and thus ii) the deviation of the theorem, expressed with a ratio between the interacting and n...
Bertrand's theorem and virial theorem in fractional classical mechanics
Yu, Rui-Yan; Wang, Towe
2017-09-01
Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.
The Non-Signalling theorem in generalizations of Bell's theorem
Walleczek, J.; Grössing, G.
2014-04-01
Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational
Directory of Open Access Journals (Sweden)
Coghetto Roland
2015-06-01
Full Text Available Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].
Geometry of the Adiabatic Theorem
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Thermodynamical and Green function many-body Wick theorems
International Nuclear Information System (INIS)
Westwanski, B.
1987-01-01
The thermodynamical and Green function many-body reduction theorems of Wick type are proved for the arbitrary mixtures of the fermion, boson and spin systems. ''Many-body'' means that the operators used are the products of the arbitrary number of one-body standard basis operators [of the fermion or (and) spin types] with different site (wave vector) indices, but having the same ''time'' (in the interaction representation). The method of proving is based on'' 1) the first-order differential equation of Schwinger type for: 1a) anti T-product of operators; 1b) its average value; 2) KMS boundary conditions for this average. It is shown that the fermion, boson and spin systems can be unified in the many-body formulation (bosonification of the fermion systems). It is impossible in the one-body approach. Both of the many-body versions of the Wick theorem have the recurrent feature: nth order moment diagrams for the free energy or Green functions can be expressed by the (n-1)th order ones. This property corresponds to the automatic realization of: (i) summations over Bose-Einstein or (and) Fermi-Dirac frequencies; (ii) elimination of Bose-Einstein or (and) Fermi-Dirac distributions. The procedures (i) and (ii), being the results of using the Green function one-body reduction theorem, have constituted the significant difficulty up to now in the treatment of quantum systems. (orig.)
A Decomposition Theorem for Finite Automata.
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
Simulation-based summative assessments in surgery.
Szasz, Peter; Grantcharov, Teodor P; Sweet, Robert M; Korndorffer, James R; Pedowitz, Robert A; Roberts, Patricia L; Sachdeva, Ajit K
2016-09-01
The American College of Surgeons-Accredited Education Institutes (ACS-AEI) Consortium aims to enhance patient safety and advance surgical education through the use of cutting-edge simulation-based training and assessment methods. The annual ACS-AEI Consortium meeting provides a forum to discuss the latest simulation-based training and assessment methods and includes special panel presentations on key topics. During the 8th annual Consortium, there was a panel presentation on simulation-based summative assessments, during which experiences from across surgical disciplines were presented. The formal presentations were followed by a robust discussion between the conference attendees and the panelists. This report summarizes the panelists' presentations and their ensuing discussion with attendees. The focus of this report is on the basis for and advances in simulation-based summative assessments, the current practices employed across various surgical disciplines, and future directions that may be pursued by the ACS-AEI Consortium. Copyright © 2016 Elsevier Inc. All rights reserved.
Smorynski, Craig
2017-01-01
This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mat...
Guney, Veli Ugur
In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible
Strong versions of Bell's theorem
International Nuclear Information System (INIS)
Stapp, H.P.
1994-01-01
Technical aspects of a recently constructed strong version of Bell's theorem are discussed. The theorem assumes neither hidden variables nor factorization, and neither determinism nor counterfactual definiteness. It deals directly with logical connections. Hence its relationship with modal logic needs to be described. It is shown that the proof can be embedded in an orthodox modal logic, and hence its compatibility with modal logic assured, but that this embedding weakens the theorem by introducing as added assumptions the conventionalities of the particular modal logic that is adopted. This weakening is avoided in the recent proof by using directly the set-theoretic conditions entailed by the locality assumption
Green's theorem and Gorenstein sequences
Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su
2016-01-01
We study consequences, for a standard graded algebra, of extremal behavior in Green's Hyperplane Restriction Theorem. First, we extend his Theorem 4 from the case of a plane curve to the case of a hypersurface in a linear space. Second, assuming a certain Lefschetz condition, we give a connection to extremal behavior in Macaulay's theorem. We apply these results to show that $(1,19,17,19,1)$ is not a Gorenstein sequence, and as a result we classify the sequences of the form $(1,a,a-2,a,1)$ th...
-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.
Complex integration and Cauchy's theorem
Watson, GN
2012-01-01
This brief monograph by one of the great mathematicians of the early twentieth century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.Author G. N. Watson begins by reviewing various propositions of Poincaré's Analysis Situs, upon which proof of the theorem's most general form depends. Subsequent chapters examine the calculus of residues, calculus optimization, the
The Levy sections theorem revisited
International Nuclear Information System (INIS)
Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Silva, Sergio Da
2007-01-01
This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets
Ortiz, Guillermo P.; Mochán, W. Luis
2018-02-01
Keller’s theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assumption that the response function relates an irrotational to a solenoidal field and that is valid for dispersive and dissipative anisotropic systems. We show that the usual statement of Keller’s theorem in terms of the conductivity is strictly valid only at zero frequency and we obtain a new generalization for finite frequencies. We develop applications of the theorem to the study of the optical properties of systems such as superlattices, 2D isotropic and anisotropic metamaterials and random media, to test the accuracy of theories and computational schemes, and to increase the accuracy of approximate calculations.
The Levy sections theorem revisited
Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Da Silva, Sergio
2007-06-01
This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.
Adiabatic theorem and spectral concentration
International Nuclear Information System (INIS)
Nenciu, G.
1981-01-01
The spectral concentration of arbitrary order, for the Stark effect is proved to exist for a large class of Hamiltonians appearing in nonrelativistic and relativistic quantum mechanics. The results are consequences of an abstract theorem about the spectral concentration for self-ad oint operators. A general form of the adiabatic theorem of quantum mechanics, generalizing an earlier result of the author as well as some results of Lenard, is also proved [ru
3D Imaging of Dead Sea Area Using Weighted Multipath Summation: A Case Study
Directory of Open Access Journals (Sweden)
Shemer Keydar
2013-01-01
Full Text Available The formation of sinkholes along the Dead Sea is caused by the rapid decline of the Dead Sea level, as a possible result of human extensive activity. According to one of the geological models, the sinkholes in several sites are clustered along a narrow coastal strip developing along lineaments representing faults in NNW direction. In order to understand the relationship between a developing sinkhole and its tectonic environment, a high-resolution (HR three-dimensional (3D seismic reflection survey was carried out at the western shoreline of the Dead Sea. A recently developed 3D imaging approach was applied to this 3D dataset. Imaging of subsurface is performed by a spatial summation of seismic waves along time surfaces using recently proposed multipath summation with proper weights. The multipath summation is performed by stacking the target waves along all possible time surfaces having a common apex at the given point. This approach does not require any explicit information on parameters since the involved multipath summation is performed for all possible parameters values within a wide specified range. The results from processed 3D time volume show subhorizontal coherent reflectors at approximate depth of 50–80 m which incline on closer location to the exposed sinkhole and suggest a possible linkage between revealed fault and the sinkholes.
Generalized Dandelin’s Theorem
Kheyfets, A. L.
2017-11-01
The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.
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.
Factor and Remainder Theorems: An Appreciation
Weiss, Michael
2016-01-01
The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…
From Einstein's theorem to Bell's theorem: a history of quantum non-locality
Wiseman, H. M.
2006-04-01
In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.
Suprathreshold contrast summation over area using drifting gratings.
McDougall, Thomas J; Dickinson, J Edwin; Badcock, David R
2018-04-01
This study investigated contrast summation over area for moving targets applied to a fixed-size contrast pedestal-a technique originally developed by Meese and Summers (2007) to demonstrate strong spatial summation of contrast for static patterns at suprathreshold contrast levels. Target contrast increments (drifting gratings) were applied to either the entire 20% contrast pedestal (a full fixed-size drifting grating), or in the configuration of a checkerboard pattern in which the target increment was applied to every alternate check region. These checked stimuli are known as "Battenberg patterns" and the sizes of the checks were varied (within a fixed overall area), across conditions, to measure summation behavior. Results showed that sensitivity to an increment covering the full pedestal was significantly higher than that for the Battenberg patterns (areal summation). Two observers showed strong summation across all check sizes (0.71°-3.33°), and for two other observers the summation ratio dropped to levels consistent with probability summation once check size reached 2.00°. Therefore, areal summation with moving targets does operate at high contrast, and is subserved by relatively large receptive fields covering a square area extending up to at least 3.33° × 3.33° for some observers. Previous studies in which the spatial structure of the pedestal and target covaried were unable to demonstrate spatial summation, potentially due to increasing amounts of suppression from gain-control mechanisms which increases as pedestal size increases. This study shows that when this is controlled, by keeping the pedestal the same across all conditions, extensive summation can be demonstrated.
Rejecting probability summation for radial frequency patterns, not so Quick!
Baldwin, Alex S; Schmidtmann, Gunnar; Kingdom, Frederick A A; Hess, Robert F
2016-05-01
Radial frequency (RF) patterns are used to assess how the visual system processes shape. They are thought to be detected globally. This is supported by studies that have found summation for RF patterns to be greater than what is possible if the parts were being independently detected and performance only then improved with an increasing number of cycles by probability summation between them. However, the model of probability summation employed in these previous studies was based on High Threshold Theory (HTT), rather than Signal Detection Theory (SDT). We conducted rating scale experiments to investigate the receiver operating characteristics. We find these are of the curved form predicted by SDT, rather than the straight lines predicted by HTT. This means that to test probability summation we must use a model based on SDT. We conducted a set of summation experiments finding that thresholds decrease as the number of modulated cycles increases at approximately the same rate as previously found. As this could be consistent with either additive or probability summation, we performed maximum-likelihood fitting of a set of summation models (Matlab code provided in our Supplementary material) and assessed the fits using cross validation. We find we are not able to distinguish whether the responses to the parts of an RF pattern are combined by additive or probability summation, because the predictions are too similar. We present similar results for summation between separate RF patterns, suggesting that the summation process there may be the same as that within a single RF. Copyright © 2016 Elsevier Ltd. All rights reserved.
Charbonneau, Jeremy
As the perceived quality of a product is becoming more important in the manufacturing industry, more emphasis is being placed on accurately predicting the sound quality of everyday objects. This study was undertaken to improve upon current prediction techniques with regard to the psychoacoustic descriptor of loudness and an improved binaural summation technique. The feasibility of this project was first investigated through a loudness matching experiment involving thirty-one subjects and pure tones of constant sound pressure level. A dependence of binaural summation on frequency was observed which had previously not been a subject of investigation in the reviewed literature. A follow-up investigation was carried out with forty-eight volunteers and pure tones of constant sensation level. Contrary to existing theories in literature the resulting loudness matches revealed an amplitude versus frequency relationship which confirmed the perceived increase in loudness when a signal was presented to both ears simultaneously as opposed to one ear alone. The resulting trend strongly indicated that the higher the frequency of the presented signal, the greater the increase in observed binaural summation. The results from each investigation were summarized into a single binaural summation algorithm and inserted into an improved time-varying loudness model. Using experimental techniques, it was demonstrated that the updated binaural summation algorithm was a considerable improvement over the state of the art approach for predicting the perceived binaural loudness. The improved function retained the ease of use from the original model while additionally providing accurate estimates of diotic listening conditions from monaural WAV files. It was clearly demonstrated using a validation jury test that the revised time-varying loudness model was a significant improvement over the previously standardized approach.
Summation by Asian Elephants (Elephas maximus
Directory of Open Access Journals (Sweden)
Naoko Irie
2012-03-01
Full Text Available Recent empirical evidence for complex cognition in elephants suggests that greater attention to comparative studies between non-human primates and other animals is warranted. We have previously shown that elephants possess the ability to judge the difference between two discrete quantities, and unlike other animals, their choice does not appear to be affected by distance or overall quantity. In this study, we investigated Asian elephants’ ability to perform summation, as exemplified by the ability to combine four quantities into two sums and subsequently compare them. We presented two discrete sums (3–7 to the elephants by baiting two buckets; they were loaded sequentially with two discrete quantities (1–5 pieces of food per bucket. All three elephants selected the larger grand sum significantly more often than the smaller grand sum. Moreover, their performance was not affected by either distance to the bait or the overall quantity evaluated. Studies report that the performance of other animal species on similar tasks declines as distance to the bait decreases and as the overall quantities evaluated increase. These results suggest that the numerical cognition of Asian elephants may be different from that of other animals, but further study is required to elucidate the differences precisely.
A software Event Summation System for MDSplus
International Nuclear Information System (INIS)
Davis, W.M.; Mastrovito, D.M.; Roney, P.G.; Sichta, P.
2008-01-01
The MDSplus data acquisition and management system uses software events for communication among interdependent processes anywhere on the network. Actions can then be triggered, such as a data-acquisition routine, or analysis or display programs waiting for data. A small amount of data, such as a shot number, can be passed with these events. Since programs sometimes need more than one data set, we developed a system on NSTX to declare composite events using logical AND and OR operations. The system is written in the IDL language, so it can be run on Linux, Macintosh or Windows platforms. Like MDSplus, the Experimental Physics and Industrial Control System (EPICS) is a core component of the NSTX software environment. The Event Summation System provides an IDL-based interface to EPICS. This permits EPICS-aware processes to be synchronized with MDSplus-aware processes, to provide, for example, engineering operators information about physics data acquisition and analysis. Reliability was a more important design consideration than performance for this system; the system's architecture includes features to support this. The system has run for weeks at a time without requiring manual intervention. Hundreds of incoming events per second can be handled reliably. All incoming and declared events are logged with a timestamp. The system can be configured easily through a single, easy-to-read text file
Secure Multiparty Quantum Computation for Summation and Multiplication.
Shi, Run-hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun
2016-01-21
As a fundamental primitive, Secure Multiparty Summation and Multiplication can be used to build complex secure protocols for other multiparty computations, specially, numerical computations. However, there is still lack of systematical and efficient quantum methods to compute Secure Multiparty Summation and Multiplication. In this paper, we present a novel and efficient quantum approach to securely compute the summation and multiplication of multiparty private inputs, respectively. Compared to classical solutions, our proposed approach can ensure the unconditional security and the perfect privacy protection based on the physical principle of quantum mechanics.
Preservation theorems on finite structures
International Nuclear Information System (INIS)
Hebert, M.
1994-09-01
This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ''homomorphism into'' case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs
Houston, Louis M.
2012-01-01
Sign data are the signs of signal added to noise. It is well known that a constant signal can be recovered from sign data. In this paper, we show that an integral over variant signal can be recovered from an integral over sign data based on the variant signal. We refer to this as a generalized sign data average. We use this result to derive a Green's theorem for sign data. Green's theorem is important to various seismic processing methods, including seismic migration. Results in this paper ge...
Scale symmetry and virial theorem
International Nuclear Information System (INIS)
Westenholz, C. von
1978-01-01
Scale symmetry (or dilatation invariance) is discussed in terms of Noether's Theorem expressed in terms of a symmetry group action on phase space endowed with a symplectic structure. The conventional conceptual approach expressing invariance of some Hamiltonian under scale transformations is re-expressed in alternate form by infinitesimal automorphisms of the given symplectic structure. That is, the vector field representing scale transformations leaves the symplectic structure invariant. In this model, the conserved quantity or constant of motion related to scale symmetry is the virial. It is shown that the conventional virial theorem can be derived within this framework
Nonperturbative Adler-Bardeen theorem
International Nuclear Information System (INIS)
Mastropietro, Vieri
2007-01-01
The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions
Kolmogorov-Arnold-Moser Theorem
Indian Academy of Sciences (India)
system (not necessarily the 2-body system). Kolmogorov was the first to provide a solution to the above general problem in a theorem formulated in 1954 (see Suggested. Reading). However, he provided only an outline of the proof. The actual proof (with all the details) turned to be quite difficult and was provided by Arnold ...
Dynamic Newton-Puiseux Theorem
DEFF Research Database (Denmark)
Mannaa, Bassel; Coquand, Thierry
2013-01-01
A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization...
Opechowski's theorem and commutator groups
International Nuclear Information System (INIS)
Caride, A.O.; Zanette, S.I.
1985-01-01
It is shown that the conditions of application of Opechowski's theorem for double groups of subgroups of O(3) are directly associated to the structure of their commutator groups. Some characteristics of the structure of classes are also discussed. (Author) [pt
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....
KLN theorem and infinite statistics
International Nuclear Information System (INIS)
Grandou, T.
1992-01-01
The possible extension of the Kinoshita-Lee-Nauenberg (KLN) theorem to the case of infinite statistics is examined. It is shown that it appears as a stable structure in a quantum field theory context. The extension is provided by working out the Fock space realization of a 'quantum algebra'. (author) 2 refs
The Geometric Mean Value Theorem
de Camargo, André Pierro
2018-01-01
In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…
Fermion fractionization and index theorem
International Nuclear Information System (INIS)
Hirayama, Minoru; Torii, Tatsuo
1982-01-01
The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)
The Completeness Theorem of Godel
Indian Academy of Sciences (India)
GENERAL I ARTICLE. The Completeness Theorem of Godel. 2. Henkin's Proof for First Order Logic. S M Srivastava is with the. Indian Statistical,. Institute, Calcutta. He received his PhD from the Indian Statistical. Institute in 1980. His research interests are in descriptive set theory. I Part 1. An Introduction to Math- ematical ...
Angle Defect and Descartes' Theorem
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
Optical theorem and its history
International Nuclear Information System (INIS)
Newton, R.G.
1978-01-01
A translation is presented of a paper submitted to the symposium ''Concepts and methods in microscopic physics'' held at Washington University in 1974. A detailed description is given of the history of the optical theorem, its various formulations and derivations and its use in the scattering theory. (Z.J.)
On the Fourier integral theorem
Koekoek, J.
1987-01-01
Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the
The Classical Version of Stokes' Theorem Revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2005-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we prove that the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...
Baker, Christa A.
2014-01-01
A variety of synaptic mechanisms can contribute to single-neuron selectivity for temporal intervals in sensory stimuli. However, it remains unknown how these mechanisms interact to establish single-neuron sensitivity to temporal patterns of sensory stimulation in vivo. Here we address this question in a circuit that allows us to control the precise temporal patterns of synaptic input to interval-tuned neurons in behaviorally relevant ways. We obtained in vivo intracellular recordings under multiple levels of current clamp from midbrain neurons in the mormyrid weakly electric fish Brienomyrus brachyistius during stimulation with electrosensory pulse trains. To reveal the excitatory and inhibitory inputs onto interval-tuned neurons, we then estimated the synaptic conductances underlying responses. We found short-term depression in excitatory and inhibitory pathways onto all interval-tuned neurons. Short-interval selectivity was associated with excitation that depressed less than inhibition at short intervals, as well as temporally summating excitation. Long-interval selectivity was associated with long-lasting onset inhibition. We investigated tuning after separately nullifying the contributions of temporal summation and depression, and found the greatest diversity of interval selectivity among neurons when both mechanisms were at play. Furthermore, eliminating the effects of depression decreased sensitivity to directional changes in interval. These findings demonstrate that variation in depression and summation of excitation and inhibition helps to establish tuning to behaviorally relevant intervals in communication signals, and that depression contributes to neural coding of interval sequences. This work reveals for the first time how the interplay between short-term plasticity and temporal summation mediates the decoding of temporal sequences in awake, behaving animals. PMID:25339741
An extended characterisation theorem for quantum logics
International Nuclear Information System (INIS)
Sharma, C.S.; Mukherjee, M.K.
1977-01-01
Two theorems are proved. In the first properties of an important mapping from an orthocomplemented lattice to itself are studied. In the second the characterisation theorem of Zierler (Pacific J. Math.; 11:1151 (1961)) is extended to obtain a very useful theorem characterising orthomodular lattices. Since quantum logics are merely sigma-complete orthomodular lattices, the principal result is, for application in quantum physics, a characterisation theorem for quantum logics. (author)
Instability of Nagaoka's Theorem within The Hubbard Model ...
African Journals Online (AJOL)
Hence the t – J model is a better model for studying magnetism than the t – U model. Investigation also revealed that the inclusion of the on-site Coulomb interaction term U, in the t – J model enhances ferromagnetic tendencies in the systems studied. In this work, Nagaoka's theorem on ferromagnetism has been extended ...
A note on generalized Weyl's theorem
Zguitti, H.
2006-04-01
We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.
A definability theorem for first order logic
Butz, C.; Moerdijk, I.
1997-01-01
In this paper we will present a definability theorem for first order logic This theorem is very easy to state and its proof only uses elementary tools To explain the theorem let us first observe that if M is a model of a theory T in a language L then clearly any definable subset S M ie a subset S
Hadronic interactions of the J/ψ and Adler's theorem
International Nuclear Information System (INIS)
Bourque, A.; Gale, C.; Haglin, K.L.
2004-01-01
Effective Lagrangian models of charmonium have recently been used to estimate dissociation cross sections with light hadrons. Detailed study of the symmetry properties reveals possible shortcomings relative to chiral symmetry. We therefore propose a new Lagrangian and point out distinguishing features amongst the different approaches. Moreover, we test the models against Adler's theorem, which requires, in the appropriate limit, the decoupling of pions from the theory for the normal parity sector. Using the newly proposed Lagrangian, which exhibits SU L (N f )xSU R (N f ) symmetry and complies with Adler's theorem, we find dissociation cross sections with pions that are reduced in an energy-dependent way, with respect to cases where the theorem is not fulfilled
Approximation Properties of Certain Summation Integral Type Operators
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Patel P.
2015-03-01
Full Text Available In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.
Tight closure and vanishing theorems
International Nuclear Information System (INIS)
Smith, K.E.
2001-01-01
Tight closure has become a thriving branch of commutative algebra since it was first introduced by Mel Hochster and Craig Huneke in 1986. Over the past few years, it has become increasingly clear that tight closure has deep connections with complex algebraic geometry as well, especially with those areas of algebraic geometry where vanishing theorems play a starring role. The purpose of these lectures is to introduce tight closure and to explain some of these connections with algebraic geometry. Tight closure is basically a technique for harnessing the power of the Frobenius map. The use of the Frobenius map to prove theorems about complex algebraic varieties is a familiar technique in algebraic geometry, so it should perhaps come as no surprise that tight closure is applicable to algebraic geometry. On the other hand, it seems that so far we are only seeing the tip of a large and very beautiful iceberg in terms of tight closure's interpretation and applications to algebraic geometry. Interestingly, although tight closure is a 'characteristic p' tool, many of the problems where tight closure has proved useful have also yielded to analytic (L2) techniques. Despite some striking parallels, there had been no specific result directly linking tight closure and L∼ techniques. Recently, however, the equivalence of an ideal central to the theory of tight closure was shown to be equivalent to a certain 'multiplier ideal' first defined using L2 methods. Presumably, deeper connections will continue to emerge. There are two main types of problems for which tight closure has been helpful: in identifying nice structure and in establishing uniform behavior. The original algebraic applications of tight closure include, for example, a quick proof of the Hochster-Roberts theorem on the Cohen-Macaulayness of rings of invariants, and also a refined version of the Brianqon-Skoda theorem on the uniform behaviour of integral closures of powers of ideals. More recent, geometric
The de Finetti theorem for test spaces
International Nuclear Information System (INIS)
Barrett, Jonathan; Leifer, Matthew
2009-01-01
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
A Randomized Central Limit Theorem
International Nuclear Information System (INIS)
Eliazar, Iddo; Klafter, Joseph
2010-01-01
The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√(n)), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √(n). This Letter considers scaling schemes which are stochastic and non-uniform, and presents a 'Randomized Central Limit Theorem' (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Levy laws.
Bell's theorem, accountability and nonlocality
International Nuclear Information System (INIS)
Vona, Nicola; Liang, Yeong-Cherng
2014-01-01
Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner (2011 Nature Commun. 2 411), we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)
Fluctuation theorems and atypical trajectories
International Nuclear Information System (INIS)
Sahoo, M; Lahiri, S; Jayannavar, A M
2011-01-01
In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work (W c ), thermodynamic work (W), total entropy (Δs tot ) and dissipated heat (Q), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at the macroscale. The distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit a peak in the regime of typical behaviour only.
Lectures on Fermat's last theorem
International Nuclear Information System (INIS)
Sury, B.
1993-09-01
The report presents the main ideas involved in the approach towards the so-called Fermat's last theorem (FLT). The discussion leads to the point where recent work of A. Wiles starts and his work is not discussed. After a short history of the FLT and of the present approach, are discussed the elliptic curves and the modular forms with their relations, the Taniyama-Shimura-Well conjecture and the FLT
Pythagoras Theorem and Relativistic Kinematics
Mulaj, Zenun; Dhoqina, Polikron
2010-01-01
In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.
Summation and subtraction using a modified autoshaping procedure in pigeons.
Ploog, Bertram O
2008-06-01
A modified autoshaping paradigm (significantly different from those previously reported in the summation literature) was employed to allow for the simultaneous assessment of stimulus summation and subtraction in pigeons. The response requirements and the probability of food delivery were adjusted such that towards the end of training 12 of 48 trials ended in food delivery, the same proportion as under testing. Stimuli (outlines of squares of three sizes and colors: A, B, and C) were used that could be presented separately or in any combination of two or three stimuli. Twelve of the pigeons (summation groups) were trained with either A, B, and C or with AB, BC, and CA, and tested with ABC. The remaining 12 pigeons (subtraction groups) received training with ABC but were tested with A, B, and C or with AB, BC, and CA. These groups were further subdivided according to whether stimulus elements were presented either in a concentric or dispersed manner. Summation did not occur; subtraction occurred in the two concentric groups. For interpretation of the results, configural theory, the Rescorla-Wagner model, and the composite-stimulus control model were considered. The results suggest different mechanisms responsible for summation and subtraction.
International Nuclear Information System (INIS)
Park, Mu-In
2008-01-01
Hawking's area theorem can be understood from a quasi-stationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual BTZ black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon 'can decrease', rather than increase, with the quasi-stationary process. However, I find that the area for the outer horizon 'never decreases' such that the usual area theorem still works in our examples, though this is quite non-trivial in general. There exists an instability problem of the inner horizons but it seems that the instability is not important in my analysis. I also find a generalized area theorem by combining those of the outer and inner horizons
Mental Summation of Temporal Duration within and across Senses.
Directory of Open Access Journals (Sweden)
Kohske Takahashi
Full Text Available Perceiving, memorizing, and estimating temporal durations are key cognitive functions in everyday life. In this study, a duration summation paradigm was used to examine whether summation of temporal durations introduces an underestimation or overestimation bias, and whether this bias is common to visual and auditory modalities. Two within- or across-modality stimuli were presented sequentially for variable durations. Participants were asked to reproduce the sum of the two durations (0.6-1.1 s. We found that the sum of two durations was overestimated regardless of stimulus modalities. A subsequent control experiment indicated that the overestimation bias arose from the summation process, not perceptual or memory processes. Furthermore, we observed strong positive correlations between the overestimation bias for different sensory modalities within participants. These results suggest that the sum of two durations is overestimated, and that supra-modal processes may be responsible for this overestimation bias.
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.
On Krasnoselskii's Cone Fixed Point Theorem
Directory of Open Access Journals (Sweden)
Man Kam Kwong
2008-04-01
Full Text Available In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.
Confinement, diquarks and goldstone's theorem
International Nuclear Information System (INIS)
Roberts, C.D.
1996-01-01
Determinations of the gluon propagator in the continuum and in lattice simulations are compared. A systematic truncation procedure for the quark Dyson-Schwinger and bound state Bethe-Salpeter equations is described. The procedure ensures the flavor-octet axial- vector Ward identity is satisfied order-by-order, thereby guaranteeing the preservation of Goldstone's theorem; and identifies a mechanism that simultaneously ensures the absence of diquarks in QCD and their presence in QCD N c =2 , where the color singlet diquark is the ''baryon'' of the theory
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
Bernstein Lethargy Theorem and Reflexivity
Aksoy, Asuman Güven; Peng, Qidi
2018-01-01
In this paper, we prove the equivalence of reflexive Banach spaces and those Banach spaces which satisfy the following form of Bernstein's Lethargy Theorem. Let $X$ be an arbitrary infinite-dimensional Banach space, and let the real-valued sequence $\\{d_n\\}_{n\\ge1}$ decrease to $0$. Suppose that $\\{Y_n\\}_{n\\ge1}$ is a system of strictly nested subspaces of $X$ such that $\\overline Y_n \\subset Y_{n+1}$ for all $n\\ge1$ and for each $n\\ge1$, there exists $y_n\\in Y_{n+1}\\backslash Y_n$ such that ...
Cyclic graphs and Apery's theorem
International Nuclear Information System (INIS)
Sorokin, V N
2002-01-01
This is a survey of results about the behaviour of Hermite-Pade approximants for graphs of Markov functions, and a survey of interpolation problems leading to Apery's result about the irrationality of the value ζ(3) of the Riemann zeta function. The first example is given of a cyclic graph for which the Hermite-Pade problem leads to Apery's theorem. Explicit formulae for solutions are obtained, namely, Rodrigues' formulae and integral representations. The asymptotic behaviour of the approximants is studied, and recurrence formulae are found
Abstract decomposition theorem and applications
Grossberg, R; Grossberg, Rami; Lessmann, Olivier
2005-01-01
Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies a main gap result for the class K. The setting is general enough to cover \\aleph_0-stable first-order theories (proved by Shelah in 1982), Excellent Classes of atomic models of a first order tehory (proved Grossberg and Hart 1987) and the class of submodels of a large sequentially homogenuus \\aleph_0-stable model (which is new).
Symbolic logic and mechanical theorem proving
Chang, Chin-Liang
1969-01-01
This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
Weissman-Fogel, Irit; Granovsky, Yelena; Crispel, Yonathan; Ben-Nun, Alon; Best, Lael Anson; Yarnitsky, David; Granot, Michal
2009-06-01
Recent evidence points to an association between experimental pain measures obtained preoperatively and acute postoperative pain (POP). We hypothesized that pain temporal summation (TS) might be an additional predictor for POP insofar as it represents the neuroplastic changes that occur in the central nervous system following surgery. Therefore, a wide range of psychophysical tests (TS to heat and mechanical repetitive stimuli, pain threshold, and suprathreshold pain estimation) and personality tests (pain catastrophizing and anxiety levels) were administered prior to thoracotomy in 84 patients. POP ratings were evaluated on the 2nd and 5th days after surgery at rest (spontaneous pain) and in response to activity (provoked pain). Linear regression models revealed that among all assessed variables, enhanced TS and higher pain scores for mechanical stimulation were significantly associated with greater provoked POP intensity (overall r2 = 0.225, P = .008). Patients who did not demonstrate TS to both modalities reported lower scores of provoked POP as compared with patients who demonstrated TS in response to at least 1 modality (F = 4.59 P = .013). Despite the moderate association between pain catastrophizing and rest POP, none of the variables predicted the spontaneous POP intensity. These findings suggest that individual susceptibility toward a greater summation response may characterize patients who are potentially vulnerable to augmented POP. This study proposed the role of pain temporal summation assessed preoperatively as a significant psychophysical predictor for acute postoperative pain intensity. The individual profile of enhanced pain summation is associated with the greater likelihood of higher postoperative pain scores.
High School Students' Perceptions of Narrative Evaluations as Summative Assessment
Bagley, Sylvia S.
2008-01-01
This study focuses on data collected at "Progressive Secondary School" in Southern California, a high school which uses narrative evaluations and other forms of alternative summative assessment on a school wide basis. Through a survey and personal interviews, students were asked to describe what they liked most and least about the use of…
Automating Formative and Summative Feedback for Individualised Assignments
Hamilton, Ian Robert
2009-01-01
Purpose: The purpose of this paper is to report on the rationale behind the use of a unique paper-based individualised accounting assignment, which automated the provision to students of immediate formative and timely summative feedback. Design/methodology/approach: As students worked towards completing their assignment, the package provided…
Equivalent conserved currents and generalized Noether's theorem
International Nuclear Information System (INIS)
Gordon, T.J.
1984-01-01
A generalized Noether theorem is presented, relating symmetries and equivalence classes of local) conservation laws in classical field theories; this is contrasted with the standard theorem. The concept of a ''Noether'' field theory is introduced, being a theory for which the generalized theorem applies; not only does this include the cases of Lagrangian and Hamiltonian field theories, these structures are ''derived'' from the Noether property in a natural way. The generalized theorem applies to currents and symmetries that contain derivatives of the fields up to an arbitrarily high order
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.
Stacked spheres and lower bound theorem
Indian Academy of Sciences (India)
BASUDEB DATTA
2011-11-20
Nov 20, 2011 ... Preliminaries. Lower bound theorem. On going work. Definitions. An n-simplex is a convex hull of n + 1 affinely independent points. (called vertices) in some Euclidean space R. N . Stacked spheres and lower bound theorem. Basudeb Datta. Indian Institute of Science. 2 / 27 ...
Howell, Russell W.; Schrohe, Elmar
2017-01-01
Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…
Other trigonometric proofs of Pythagoras theorem
Luzia, Nuno
2015-01-01
Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \\cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing, geometrically, the half-angle formula $\\cos\\theta=1-2\\sin^2 \\frac{\\theta}{2}$.
Borghi, Riccardo
2014-03-01
In the present letter, Newton’s theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton’s Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.
Theorems of low energy in Compton scattering
International Nuclear Information System (INIS)
Chahine, J.
1984-01-01
We have obtained the low energy theorems in Compton scattering to third and fouth order in the frequency of the incident photon. Next we calculated the polarized cross section to third order and the unpolarized to fourth order in terms of partial amplitudes not covered by the low energy theorems, what will permit the experimental determination of these partial amplitudes. (Author) [pt
A density Corradi-Hajnal theorem
Czech Academy of Sciences Publication Activity Database
Allen, P.; Böttcher, J.; Hladký, Jan; Piguet, D.
2015-01-01
Roč. 67, č. 4 (2015), s. 721-758 ISSN 0008-414X Institutional support: RVO:67985840 Keywords : extremal graph theory * Mantel's theorem * Corradi-Hajnal theorem Subject RIV: BA - General Mathematics Impact factor: 0.618, year: 2015 http://cms.math.ca/10.4153/CJM-2014-030-6
Visualizing the Central Limit Theorem through Simulation
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
The Classical Version of Stokes' Theorem Revisited
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
The divergence theorem for unbounded vector fields
De Pauw, Thierry; Pfeffer, Washek F.
2007-01-01
In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector. elds that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is. nite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions.
The Pomeranchuk theorem and its modifications
International Nuclear Information System (INIS)
Fischer, J.; Saly, R.
1980-01-01
A review of the various modifications and improvements of the Pomeranchuk theorem and also of related statements is given. The present status of the Pomeranchuk relation based on dispersion relation is discussed. Numerous problems related to the Pomeranchuk theorem and some answers to these problems are collected in a clear table
Coalgebraic Lindström Theorems
Kurz, A.; Venema, Y.
2010-01-01
We study modal Lindström theorems from a coalgebraic perspective. We provide three different Lindström theorems for coalgebraic logic, one of which is a direct generalisation of de Rijke's result for Kripke models. Both the other two results are based on the properties of bisimulation invariance,
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...
Viète's Formula and an Error Bound without Taylor's Theorem
Boucher, Chris
2018-01-01
This note presents a derivation of Viète's classic product approximation of pi that relies on only the Pythagorean Theorem. We also give a simple error bound for the approximation that, while not optimal, still reveals the exponential convergence of the approximation and whose derivation does not require Taylor's Theorem.
Uniqueness theorems in linear elasticity
Knops, Robin John
1971-01-01
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...
Riemannian and Lorentzian flow-cut theorems
Headrick, Matthew; Hubeny, Veronika E.
2018-05-01
We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.
OTTER, Resolution Style Theorem Prover
International Nuclear Information System (INIS)
McCune, W.W.
2001-01-01
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
Effects of gabapentin on experimental somatic pain and temporal summation
DEFF Research Database (Denmark)
Arendt-Nielsen, Lars; Frøkjaer, Jens Brøndum; Staahl, Camilla
2007-01-01
at 2 Hz); (2) stimulus-response function relating pain intensity scores (visual analog scale, VAS) to increasing current intensities for electrical skin and muscle stimuli (single and repeated, determined at baseline); and (3) the pain intensity (VAS) and pain areas after intramuscular injection......, was to examine the effect of a single dose of 1200 mg gabapentin on multi-modal experimental cutaneous and muscle pain models. METHODS: The following pain models were applied: (1) pain thresholds to single and repeated cutaneous and intramuscular electrical stimulation (temporal summation to 5 stimuli delivered...... reduced the area under the pain intensity curve to hypertonic saline injections in the muscle (P = .02); and (3) significantly reduced the area of pain evoked by hypertonic saline (P = .03). CONCLUSIONS: Gabapentin reduces temporal summation of skin stimuli at pain threshold intensities; this may have...
In vivo dissolution measurement with indium-111 summation peak ratios
International Nuclear Information System (INIS)
Jay, M.; Woodward, M.A.; Brouwer, K.R.
1985-01-01
Dissolution of [ 111 In]labeled tablets was measured in vivo in a totally noninvasive manner by using a modification of the perturbed angular correlation technique known as the summation peak ratio method. This method, which requires the incorporation of only 10-12 microCi into the dosage form, provided reliable dissolution data after oral administration of [ 111 In]lactose tablets. These results were supported by in vitro experiments which demonstrated that the dissolution rate as measured by the summation peak ratio method was in close agreement with the dissolution rate of salicylic acid in a [ 111 In]salicylic acid tablet. The method has the advantages of using only one detector, thereby avoiding the need for complex coincidence counting systems, requiring less radioactivity, and being potentially applicable to a gamma camera imaging system
Density of states, Poisson's formula of summation and Walfisz's formula
International Nuclear Information System (INIS)
Fucho, P.
1980-06-01
Using Poisson's formula for summation, we obtain an expression for density of states of d-dimensional scalar Helmoholtz's equation under various boundary conditions. Likewise, we also obtain formulas of Walfisz's type. It becomes evident that the formulas obtained by Pathria et al. in connection with ideal bosons in a finite system are exactly the same as those obtained by utilizing the formulas for density of states. (author)
Temporal summation of heat pain modulated by isometric exercise.
Koltyn, K F; Knauf, M T; Brellenthin, A G
2013-08-01
Little is known about the effects of isometric exercise on temporal summation of heat pain. Thus, the purposes of study 1 and study 2 were to examine the influence of exhaustive and non-exhaustive isometric exercise on temporal summation of heat pain in men and women. Forty-four men and 44 women (mean age = 20 years) completed an informed consent document and a packet of questionnaires. Ten heat pulses were applied to the thenar eminence of the dominant hand using a standardized temporal summation protocol. Participants rated the intensity of the heat pulses using a 0-100 pain rating scale before and following isometric exercise consisting of squeezing a hand dynamometer at 40% of maximal voluntary contraction (MVC) to exhaustion (exhaustive exercise, study 1) and at 25% MVC for 3 min (non-exhaustive exercise, study 2). Muscle pain and perceived exertion were rated every 30 s during exercise using validated rating scales. The data were analysed with repeated measures analysis of variance. The results indicated there were no sex differences (p > 0.05) in time to exhaustion (study 1), muscle pain or perceived exertion (studies 1 and 2). There was a significant reduction (p heat pain in men and women. © 2012 European Federation of International Association for the Study of Pain Chapters.
The classical version of Stokes' Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we show how the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together with a 'fattening' technique for surfaces and the inverse function theorem....
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.
Energy Technology Data Exchange (ETDEWEB)
Escane, J.M. [Ecole Superieure d' Electricite, 91 - Gif-sur-Yvette (France)
2005-04-01
The first part of this article defines the different elements of an electrical network and the models to represent them. Each model involves the current and the voltage as a function of time. Models involving time functions are simple but their use is not always easy. The Laplace transformation leads to a more convenient form where the variable is no more directly the time. This transformation leads also to the notion of transfer function which is the object of the second part. The third part aims at defining the fundamental operation rules of linear networks, commonly named 'general theorems': linearity principle and superimposition theorem, duality principle, Thevenin theorem, Norton theorem, Millman theorem, triangle-star and star-triangle transformations. These theorems allow to study complex power networks and to simplify the calculations. They are based on hypotheses, the first one is that all networks considered in this article are linear. (J.S.)
Dimensional analysis beyond the Pi theorem
Zohuri, Bahman
2017-01-01
Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First ...
Stable convergence and stable limit theorems
Häusler, Erich
2015-01-01
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level...
Theorem on axially symmetric gravitational vacuum configurations
Energy Technology Data Exchange (ETDEWEB)
Papadopoulos, A; Le Denmat, G [Paris-6 Univ., 75 (France). Inst. Henri Poincare
1977-01-24
A theorem is proved which asserts the non-existence of axially symmetric gravitational vacuum configurations with non-stationary rotation only. The eventual consequences in black-hole physics are suggested.
Non-renormalisation theorems in string theory
International Nuclear Information System (INIS)
Vanhove, P.
2007-10-01
In this thesis we describe various non renormalisation theorems for the string effective action. These results are derived in the context of the M theory conjecture allowing to connect the four gravitons string theory S matrix elements with that of eleven dimensional supergravity. These theorems imply that N = 8 supergravity theory has the same UV behaviour as the N = 4 supersymmetric Yang Mills theory at least up to three loops, and could be UV finite in four dimensions. (author)
There is No Quantum Regression Theorem
International Nuclear Information System (INIS)
Ford, G.W.; OConnell, R.F.
1996-01-01
The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem. copyright 1996 The American Physical Society
Singularity theorems from weakened energy conditions
International Nuclear Information System (INIS)
Fewster, Christopher J; Galloway, Gregory J
2011-01-01
We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.
The matrix Euler-Fermat theorem
International Nuclear Information System (INIS)
Arnol'd, Vladimir I
2004-01-01
We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem
Level comparison theorems and supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Baumgartner, B.; Grosse, H.
1986-01-01
The sign of the Laplacian of the spherical symmetric potential determines the order of energy levels with the same principal Coulomb quantum number. This recently derived theorem has been generalized, extended and applied to various situations in particle, nuclear and atomic physics. Besides a comparison theorem the essential step was the use of supersymmetric quantum mechanics. Recently worked out applications of supersymmetric quantum mechanics to index problems of Dirac operators are mentioned. (Author)
Liouville's theorem and phase-space cooling
International Nuclear Information System (INIS)
Mills, R.L.; Sessler, A.M.
1993-01-01
A discussion is presented of Liouville's theorem and its consequences for conservative dynamical systems. A formal proof of Liouville's theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur
The Osgood-Schoenflies theorem revisited
International Nuclear Information System (INIS)
Siebenmann, L C
2005-01-01
The very first unknotting theorem of a purely topological character established that every compact subset of the Euclidean plane homeomorphic to a circle can be moved onto a round circle by a globally defined self-homeomorphism of the plane. This difficult hundred-year-old theorem is here celebrated with a partly new elementary proof, and a first but tentative account of its history. Some quite fundamental corollaries of the proof are sketched, and some generalizations are mentioned
Double soft theorem for perturbative gravity
Saha, Arnab
2016-01-01
Following up on the recent work of Cachazo, He and Yuan \\cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.
A Converse of Fermat's Little Theorem
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
The large deviations theorem and ergodicity
International Nuclear Information System (INIS)
Gu Rongbao
2007-01-01
In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions
Pascal’s Theorem in Real Projective Plane
Coghetto Roland
2017-01-01
In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines.
Pascal’s Theorem in Real Projective Plane
Directory of Open Access Journals (Sweden)
Coghetto Roland
2017-07-01
Full Text Available In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem1. Pappus’ theorem is a special case of a degenerate conic of two lines.
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered...... we apply the key instrumental concepts and verify the various steps towards this alternative proof of the divergence theorem....
Commentaries on Hilbert's Basis Theorem | Apine | Science World ...
African Journals Online (AJOL)
The famous basis theorem of David Hilbert is an important theorem in commutative algebra. In particular the Hilbert's basis theorem is the most important source of Noetherian rings which are by far the most important class of rings in commutative algebra. In this paper we have used Hilbert's theorem to examine their unique ...
Illustrating the Central Limit Theorem through Microsoft Excel Simulations
Moen, David H.; Powell, John E.
2005-01-01
Using Microsoft Excel, several interactive, computerized learning modules are developed to demonstrate the Central Limit Theorem. These modules are used in the classroom to enhance the comprehension of this theorem. The Central Limit Theorem is a very important theorem in statistics, and yet because it is not intuitively obvious, statistics…
Towards a unifying basis of auditory thresholds: binaural summation.
Heil, Peter
2014-04-01
Absolute auditory threshold decreases with increasing sound duration, a phenomenon explainable by the assumptions that the sound evokes neural events whose probabilities of occurrence are proportional to the sound's amplitude raised to an exponent of about 3 and that a constant number of events are required for threshold (Heil and Neubauer, Proc Natl Acad Sci USA 100:6151-6156, 2003). Based on this probabilistic model and on the assumption of perfect binaural summation, an equation is derived here that provides an explicit expression of the binaural threshold as a function of the two monaural thresholds, irrespective of whether they are equal or unequal, and of the exponent in the model. For exponents >0, the predicted binaural advantage is largest when the two monaural thresholds are equal and decreases towards zero as the monaural threshold difference increases. This equation is tested and the exponent derived by comparing binaural thresholds with those predicted on the basis of the two monaural thresholds for different values of the exponent. The thresholds, measured in a large sample of human subjects with equal and unequal monaural thresholds and for stimuli with different temporal envelopes, are compatible only with an exponent close to 3. An exponent of 3 predicts a binaural advantage of 2 dB when the two ears are equally sensitive. Thus, listening with two (equally sensitive) ears rather than one has the same effect on absolute threshold as doubling duration. The data suggest that perfect binaural summation occurs at threshold and that peripheral neural signals are governed by an exponent close to 3. They might also shed new light on mechanisms underlying binaural summation of loudness.
The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation
Kowalenko, Victor
2009-01-01
The Stokes phenomenon refers to the emergence of jump discontinuities in asymptotic expansions at specific rays in the complex plane. This book presents a radical theory for the phenomenon by introducing the concept of regularization. Two methods of regularization, Borel summation and Mellin-Barnes regularization, are used to derive general expressions for the regularized values of asymptotic expansions throughout the complex plane. Though different, both yield identical values, which, where possible, agree with the original functions. Consequently, asymptotics has been elevated to a true disc
International Nuclear Information System (INIS)
Yu, Xiao-Dong; Tong, D M; Guo, Yan-Qing
2015-01-01
Quantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of the Kochen–Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been found that some proofs of the Kochen-Specker theorem, such as those based on rays, can be converted to a state-independent noncontextuality inequality, but it remains open whether this is true in general, i.e., whether any proof of the Kochen-Specker theorem can always be converted to a noncontextuality inequality. In this paper, we address this issue. We prove that all kinds of proofs of the Kochen-Specker theorem, based on rays or any other observables, can always be converted to state-independent noncontextuality inequalities. Besides, our constructive proof also provides a general approach for deriving a state-independent noncontextuality inequality from a proof of the KS theorem. (paper)
Dose fractionation theorem in 3-D reconstruction (tomography)
International Nuclear Information System (INIS)
Glaeser, R.M.
1997-01-01
It is commonly assumed that the large number of projections for single-axis tomography precludes its application to most beam-labile specimens. However, Hegerl and Hoppe have pointed out that the total dose required to achieve statistical significance for each voxel of a computed 3-D reconstruction is the same as that required to obtain a single 2-D image of that isolated voxel, at the same level of statistical significance. Thus a statistically significant 3-D image can be computed from statistically insignificant projections, as along as the total dosage that is distributed among these projections is high enough that it would have resulted in a statistically significant projection, if applied to only one image. We have tested this critical theorem by simulating the tomographic reconstruction of a realistic 3-D model created from an electron micrograph. The simulations verify the basic conclusions of high absorption, signal-dependent noise, varying specimen contrast and missing angular range. Furthermore, the simulations demonstrate that individual projections in the series of fractionated-dose images can be aligned by cross-correlation because they contain significant information derived from the summation of features from different depths in the structure. This latter information is generally not useful for structural interpretation prior to 3-D reconstruction, owing to the complexity of most specimens investigated by single-axis tomography. These results, in combination with dose estimates for imaging single voxels and measurements of radiation damage in the electron microscope, demonstrate that it is feasible to use single-axis tomography with soft X-ray microscopy of frozen-hydrated specimens
Dose fractionation theorem in 3-D reconstruction (tomography)
Energy Technology Data Exchange (ETDEWEB)
Glaeser, R.M. [Lawrence Berkeley National Lab., CA (United States)
1997-02-01
It is commonly assumed that the large number of projections for single-axis tomography precludes its application to most beam-labile specimens. However, Hegerl and Hoppe have pointed out that the total dose required to achieve statistical significance for each voxel of a computed 3-D reconstruction is the same as that required to obtain a single 2-D image of that isolated voxel, at the same level of statistical significance. Thus a statistically significant 3-D image can be computed from statistically insignificant projections, as along as the total dosage that is distributed among these projections is high enough that it would have resulted in a statistically significant projection, if applied to only one image. We have tested this critical theorem by simulating the tomographic reconstruction of a realistic 3-D model created from an electron micrograph. The simulations verify the basic conclusions of high absorption, signal-dependent noise, varying specimen contrast and missing angular range. Furthermore, the simulations demonstrate that individual projections in the series of fractionated-dose images can be aligned by cross-correlation because they contain significant information derived from the summation of features from different depths in the structure. This latter information is generally not useful for structural interpretation prior to 3-D reconstruction, owing to the complexity of most specimens investigated by single-axis tomography. These results, in combination with dose estimates for imaging single voxels and measurements of radiation damage in the electron microscope, demonstrate that it is feasible to use single-axis tomography with soft X-ray microscopy of frozen-hydrated specimens.
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.
Visual summation in night-flying sweat bees: a theoretical study.
Theobald, Jamie Carroll; Greiner, Birgit; Wcislo, William T; Warrant, Eric J
2006-07-01
Bees are predominantly diurnal; only a few groups fly at night. An evolutionary limitation that bees must overcome to inhabit dim environments is their eye type: bees possess apposition compound eyes, which are poorly suited to vision in dim light. Here, we theoretically examine how nocturnal bees Megalopta genalis fly at light levels usually reserved for insects bearing more sensitive superposition eyes. We find that neural summation should greatly increase M. genalis's visual reliability. Predicted spatial summation closely matches the morphology of laminal neurons believed to mediate such summation. Improved reliability costs acuity, but dark adapted bees already suffer optical blurring, and summation further degrades vision only slightly.
The Non-Signalling theorem in generalizations of Bell's theorem
International Nuclear Information System (INIS)
Walleczek, J; Grössing, G
2014-01-01
Does 'epistemic non-signalling' ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the
Gleason-Busch theorem for sequential measurements
Flatt, Kieran; Barnett, Stephen M.; Croke, Sarah
2017-12-01
Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957), 10.1512/iumj.1957.6.56050]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003), 10.1103/PhysRevLett.91.120403], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.
Adiabatic Theorem for Quantum Spin Systems
Bachmann, S.; De Roeck, W.; Fraas, M.
2017-08-01
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
A uniform Tauberian theorem in dynamic games
Khlopin, D. V.
2018-01-01
Antagonistic dynamic games including games represented in normal form are considered. The asymptotic behaviour of value in these games is investigated as the game horizon tends to infinity (Cesàro mean) and as the discounting parameter tends to zero (Abel mean). The corresponding Abelian-Tauberian theorem is established: it is demonstrated that in both families the game value uniformly converges to the same limit, provided that at least one of the limits exists. Analogues of one-sided Tauberian theorems are obtained. An example shows that the requirements are essential even for control problems. Bibliography: 31 titles.
The aftermath of the intermediate value theorem
Directory of Open Access Journals (Sweden)
Morales Claudio H
2004-01-01
Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (17811848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.
Pauli and the spin-statistics theorem
Duck, Ian M
1997-01-01
This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties. Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that
Elastic hadron scattering and optical theorem
Lokajicek, Milos V.; Prochazka, Jiri
2014-01-01
In principle all contemporary phenomenological models of elastic hadronic scattering have been based on the assumption of optical theorem validity that has been overtaken from optics. It will be shown that the given theorem which has not been actually proved cannot be applied to short-ranged strong interactions in any case. The actual progress in description of collision processes might then exist only if the initial states are specified on the basis of impact parameter values of colliding particles and probability dependence on this parameter is established.
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.
Closed-form summations of Dowker's and related trigonometric sums
International Nuclear Information System (INIS)
Cvijović, Djurdje; Srivastava, H M
2012-01-01
Through a unified and relatively simple approach which uses complex contour integrals, particularly convenient integration contours and calculus of residues, closed-form summation formulas for 12 very general families of trigonometric sums are deduced. One of them is a family of cosecant sums which was first summed in closed form in a series of papers by Dowker (1987 Phys. Rev. D 36 3095–101; 1989 J. Math. Phys. 30 770–3; 1992 J. Phys. A: Math. Gen. 25 2641–8), whose method has inspired our work in this area. All of the formulas derived here involve the higher-order Bernoulli polynomials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (paper)
A fast summation method for oscillatory lattice sums
Denlinger, Ryan; Gimbutas, Zydrunas; Greengard, Leslie; Rokhlin, Vladimir
2017-02-01
We present a fast summation method for lattice sums of the type which arise when solving wave scattering problems with periodic boundary conditions. While there are a variety of effective algorithms in the literature for such calculations, the approach presented here is new and leads to a rigorous analysis of Wood's anomalies. These arise when illuminating a grating at specific combinations of the angle of incidence and the frequency of the wave, for which the lattice sums diverge. They were discovered by Wood in 1902 as singularities in the spectral response. The primary tools in our approach are the Euler-Maclaurin formula and a steepest descent argument. The resulting algorithm has super-algebraic convergence and requires only milliseconds of CPU time.
Closed-form summations of Dowker's and related trigonometric sums
Cvijović, Djurdje; Srivastava, H. M.
2012-09-01
Through a unified and relatively simple approach which uses complex contour integrals, particularly convenient integration contours and calculus of residues, closed-form summation formulas for 12 very general families of trigonometric sums are deduced. One of them is a family of cosecant sums which was first summed in closed form in a series of papers by Dowker (1987 Phys. Rev. D 36 3095-101 1989 J. Math. Phys. 30 770-3 1992 J. Phys. A: Math. Gen. 25 2641-8), whose method has inspired our work in this area. All of the formulas derived here involve the higher-order Bernoulli polynomials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.
A symbolic summation approach to Feynman integral calculus
International Nuclear Information System (INIS)
Bluemlein, Johannes; Klein, Sebastian
2010-11-01
Given a Feynman parameter integral, depending on a single discrete variable N and a real parameter ε, we discuss a new algorithmic framework to compute the first coefficients of its Laurent series expansion in ε. In a first step, the integrals are expressed by hypergeometric multi sums by means of symbolic transformations. Given this sum format, we develop new summation tools to extract the first coefficients of its series expansion whenever they are expressible in terms of indefinite nested product-sum expressions. In particular, we enhance the known multi-sum algorithms to derive recurrences for sums with complicated boundary conditions, and we present new algorithms to find formal Laurent series solutions of a given recurrence relation. (orig.)
Summation of divergent series and Zel'dovich's regularization method
International Nuclear Information System (INIS)
Mur, V.D.; Pozdnyakov, S.G.; Popruzhenko, S.V.; Popov, V.S.
2005-01-01
The method of summation of divergent series, including series of a perturbation theory, which is an analog of the Zel'dovich regularization procedure in the theory of quasistationary states is considered. It is shown that this method is more powerful than the well-known Abel and Borel methods, but compatible with them (i. e., gives the same value for the sum of the series). The restrictions to the range of parameters which appear after removal of the regularization of integrals by this method are discussed. The dynamical Stark shifts and widths of weakly bound s states in a field of circularly polarized electromagnetic wave are calculated at different values of the Keldysh adiabaticity parameter and multiquantum parameter [ru
Summation on the basis of combinatorial representation of equal powers
Directory of Open Access Journals (Sweden)
Alexander I. Nikonov
2016-03-01
Full Text Available In the paper the conclusion of combinatorial expressions for the sums of members of several sequences is considered. Conclusion is made on the basis of combinatorial representation of the sum of the weighted equal powers. The weighted members of a geometrical progression, the simple arithmetic-geometrical and combined progressions are subject to summation. One of principal places in the given conclusion occupies representation of members of each of the specified progressions in the form of matrix elements. The row of this matrix is formed with use of a gang of equal powers with the set weight factor. Besides, in work formulas of combinatorial identities with participation of free components of the sums of equal powers, and also separate power-member of sequence of equal powers or a geometrical progression are presented. All presented formulas have the general basis-components of the sums of equal powers.
A symbolic summation approach to Feynman integral calculus
Energy Technology Data Exchange (ETDEWEB)
Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Klein, Sebastian [Technische Hochschule Aachen (Germany). Inst. fuer Theoretische Teilchenphysik und Kosmologie; Schneider, Carsten; Stan, Flavia [Johannes Kepler Univ. Linz (AT). Research Inst. for Symbolic Computation (RISC)
2010-11-15
Given a Feynman parameter integral, depending on a single discrete variable N and a real parameter {epsilon}, we discuss a new algorithmic framework to compute the first coefficients of its Laurent series expansion in {epsilon}. In a first step, the integrals are expressed by hypergeometric multi sums by means of symbolic transformations. Given this sum format, we develop new summation tools to extract the first coefficients of its series expansion whenever they are expressible in terms of indefinite nested product-sum expressions. In particular, we enhance the known multi-sum algorithms to derive recurrences for sums with complicated boundary conditions, and we present new algorithms to find formal Laurent series solutions of a given recurrence relation. (orig.)
Spectral and binaural loudness summation for hearing-impaired listeners.
Oetting, Dirk; Hohmann, Volker; Appell, Jens-E; Kollmeier, Birger; Ewert, Stephan D
2016-05-01
Sensorineural hearing loss typically results in a steepened loudness function and a reduced dynamic range from elevated thresholds to uncomfortably loud levels for narrowband and broadband signals. Restoring narrowband loudness perception for hearing-impaired (HI) listeners can lead to overly loud perception of broadband signals and it is unclear how binaural presentation affects loudness perception in this case. Here, loudness perception quantified by categorical loudness scaling for nine normal-hearing (NH) and ten HI listeners was compared for signals with different bandwidth and different spectral shape in monaural and in binaural conditions. For the HI listeners, frequency- and level-dependent amplification was used to match the narrowband monaural loudness functions of the NH listeners. The average loudness functions for NH and HI listeners showed good agreement for monaural broadband signals. However, HI listeners showed substantially greater loudness for binaural broadband signals than NH listeners: on average a 14.1 dB lower level was required to reach "very loud" (range 30.8 to -3.7 dB). Overall, with narrowband loudness compensation, a given binaural loudness for broadband signals above "medium loud" was reached at systematically lower levels for HI than for NH listeners. Such increased binaural loudness summation was not found for loudness categories below "medium loud" or for narrowband signals. Large individual variations in the increased loudness summation were observed and could not be explained by the audiogram or the narrowband loudness functions. Copyright © 2016 Elsevier B.V. All rights reserved.
Group Peer Assessment for Summative Evaluation in a Graduate-Level Statistics Course for Ecologists
ArchMiller, Althea; Fieberg, John; Walker, J.D.; Holm, Noah
2017-01-01
Peer assessment is often used for formative learning, but few studies have examined the validity of group-based peer assessment for the summative evaluation of course assignments. The present study contributes to the literature by using online technology (the course management system Moodle™) to implement structured, summative peer review based on…
Summative Evaluation on the Hospital Wards. What Do Faculty Say to Learners?
Hasley, Peggy B.; Arnold, Robert M.
2009-01-01
No previous studies have described how faculty give summative evaluations to learners on the medical wards. The aim of this study was to describe summative evaluations on the medical wards. Participants were students, house staff and faculty at the University of Pittsburgh. Ward rotation evaluative sessions were tape recorded. Feedback was…
Summation in Autoshaping with Compounds Formed by the Rapid Alternation of Elements
Gomez-Sancho, Luis E.; Fernandez-Serra, Francisco; Arias, M. Francisca
2013-01-01
Summation is the usual result in composition procedures with excitatory stimuli. However, summation is difficult to obtain in autoshaping with pigeons. The problems with this preparation have been related to the stimuli used: combinations of intramodal conditioned stimuli (CSs). During the perceptual processing of this type of stimuli, some mutual…
Two-phase summation imaging using transvenous DSA in subclavian steal syndrome
International Nuclear Information System (INIS)
Arlart, I.P.
1984-01-01
A simple method is reported to obtain a two-phase summation image in subclavian steal syndrome using digital subtraction angiography (DSA) via selection of a mask during the early arterial phase and the contrast image during delayed retrograde filling of the ipsilateral vertebral artery and the postocclusive subclavian artery. The summation image results by employing replay of the stored image information. (orig.) [de
A note on the Pfaffian integration theorem
International Nuclear Information System (INIS)
Borodin, Alexei; Kanzieper, Eugene
2007-01-01
Two alternative, fairly compact proofs are presented of the Pfaffian integration theorem that surfaced in the recent studies of spectral properties of Ginibre's Orthogonal Ensemble. The first proof is based on a concept of the Fredholm Pfaffian; the second proof is purely linear algebraic. (fast track communication)
Mean value theorem in topological vector spaces
International Nuclear Information System (INIS)
Khan, L.A.
1994-08-01
The aim of this note is to give shorter proofs of the mean value theorem, the mean value inequality, and the mean value inclusion for the class of Gateaux differentiable functions having values in a topological vector space. (author). 6 refs
1/4-pinched contact sphere theorem
DEFF Research Database (Denmark)
Ge, Jian; Huang, Yang
2016-01-01
Given a closed contact 3-manifold with a compatible Riemannian metric, we show that if the sectional curvature is 1/4-pinched, then the contact structure is universally tight. This result improves the Contact Sphere Theorem in [EKM12], where a 4/9-pinching constant was imposed. Some tightness...
Generalized Friedland's theorem for C0-semigroups
Cichon, Dariusz; Jung, Il Bong; Stochel, Jan
2008-07-01
Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.
Automated theorem proving theory and practice
Newborn, Monty
2001-01-01
As the 21st century begins, the power of our magical new tool and partner, the computer, is increasing at an astonishing rate. Computers that perform billions of operations per second are now commonplace. Multiprocessors with thousands of little computers - relatively little! -can now carry out parallel computations and solve problems in seconds that only a few years ago took days or months. Chess-playing programs are on an even footing with the world's best players. IBM's Deep Blue defeated world champion Garry Kasparov in a match several years ago. Increasingly computers are expected to be more intelligent, to reason, to be able to draw conclusions from given facts, or abstractly, to prove theorems-the subject of this book. Specifically, this book is about two theorem-proving programs, THEO and HERBY. The first four chapters contain introductory material about automated theorem proving and the two programs. This includes material on the language used to express theorems, predicate calculus, and the rules of...
Answering Junior Ant's "Why" for Pythagoras' Theorem
Pask, Colin
2002-01-01
A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…
On Callan's proof of the BPHZ theorem
International Nuclear Information System (INIS)
Lesniewski, A.
1984-01-01
The author gives an elementary proof of the BPHZ theorem in the case of the Euclidean lambdaphi 4 theory. The method of proof relies on a detailed analysis of the skeleton structure of graphs and estimates based on the Callan-Symanzik equations. (Auth.)
A Short Proof of Klee's Theorem
Zanazzi, John J.
2013-01-01
In 1959, Klee proved that a convex body $K$ is a polyhedron if and only if all of its projections are polygons. In this paper, a new proof of this theorem is given for convex bodies in $\\mathbb{R}^3$.
On Noethers theorem in quantum field theory
International Nuclear Information System (INIS)
Buchholz, D.; Doplicher, S.; Longo, R.
1985-03-01
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)
Green-Tao theorem in function fields
Le, Thai Hoang
2009-01-01
We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every $k$, the irreducible polynomials in $\\mathbf{F}_q[t]$ contain configurations of the form $\\{f+ Pg : \\d(P)
Pauli and The Spin-Statistics Theorem
International Nuclear Information System (INIS)
Duck, Ian; Sudarshan, E.C.G.
1998-03-01
This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties.Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that 'everyone knows the spin-statistics theorem, but no one understands it'. This book simplifies and clarifies the formal statements of the theorem, and also corrects the invariably flawed intuitive explanations which are frequently put forward. The book will be of interest to many practising physicists in all fields who have long been frustrated by the impenetrable discussions on the subject which have been available until now.It will also be accessible to students at an advanced undergraduate level as an introduction to modern physics based directly on the classical writings of the founders, including Pauli, Dirac, Heisenberg, Einstein and many others
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.
Reciprocity theorem in high-temperature superconductors
Czech Academy of Sciences Publication Activity Database
Janeček, I.; Vašek, Petr
2003-01-01
Roč. 390, - (2003), s. 330-340 ISSN 0921-4534 R&D Projects: GA ČR GA202/00/1602; GA AV ČR IAA1010919 Institutional research plan: CEZ:AV0Z1010914 Keywords : transport properties * reciprocity theorem Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.192, year: 2003
Some Generalizations of Jungck's Fixed Point Theorem
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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.
Limit theorems for functionals of Gaussian vectors
Institute of Scientific and Technical Information of China (English)
Hongshuai DAI; Guangjun SHEN; Lingtao KONG
2017-01-01
Operator self-similar processes,as an extension of self-similar processes,have been studied extensively.In this work,we study limit theorems for functionals of Gaussian vectors.Under some conditions,we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process.
Bell's theorem and the nature of reality
International Nuclear Information System (INIS)
Bertlmann, R.A.
1988-01-01
We rediscuss the Einstein-Podolsky-Rosen paradox in Bohm's spin version and oppose to it Bohr's controversial point of view. Then we explain Bell's theorem, Bell inequalities and its consequences. We describe the experiment of Aspect, Dalibard and Roger in detail. Finally we draw attention to the nonlocal structure of the underlying theory. 61 refs., 8 tabs. (Author)
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
journal of. July 2007 physics pp. 31–47. A singularity theorem based on spatial ... In this paper I would like to present a result which confirms – at least partially – ... A detailed analysis of how the model fits in with the .... Further, the statement that the spatial average ...... Financial support under grants FIS2004-01626 and no.
Czech Academy of Sciences Publication Activity Database
Narins, L.; Tran, Tuan
2017-01-01
Roč. 85, č. 2 (2017), s. 496-524 ISSN 0364-9024 Institutional support: RVO:67985807 Keywords : Turán’s theorem * stability method * multipartite version Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.601, year: 2016
H-theorems from macroscopic autonomous equations
Czech Academy of Sciences Publication Activity Database
De Roeck, W.; Maes, C.; Netočný, Karel
2006-01-01
Roč. 123, č. 3 (2006), s. 571-583 ISSN 0022-4715 Institutional research plan: CEZ:AV0Z10100520 Keywords : H-theorem, entropy * irreversible equations Subject RIV: BE - Theoretical Physics Impact factor: 1.437, year: 2006
Student Research Project: Goursat's Other Theorem
Petrillo, Joseph
2009-01-01
In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…
On Viviani's Theorem and Its Extensions
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
The Embedding Theorems of Whitney and Nash
Indian Academy of Sciences (India)
We begin by briefly motivating the idea of amanifold and then discuss the embedding theorems of Whitney and Nash that allow us toview these objects inside appropriately large Euclidean spaces. Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 4. Current Issue Volume 23 | Issue 4. April 2018.
Nash-Williams’ cycle-decomposition theorem
DEFF Research Database (Denmark)
Thomassen, Carsten
2016-01-01
We give an elementary proof of the theorem of Nash-Williams that a graph has an edge-decomposition into cycles if and only if it does not contain an odd cut. We also prove that every bridgeless graph has a collection of cycles covering each edge at least once and at most 7 times. The two results...
General Correlation Theorem for Trinion Fourier Transform
Bahri, Mawardi
2017-01-01
- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.
Directory of Open Access Journals (Sweden)
SEVER ANGEL POPESCU
2015-03-01
Full Text Available In this note we make some remarks on the classical Laguerre’s theorem and extend it and some other old results of Walsh and Gauss-Lucas to the so called trace series associated with transcendental elements of the completion of the algebraic closure of Q in C, with respect to the spectral norm:
Lagrange’s Four-Square Theorem
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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].
Anomalous Levinson theorem and supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Boya, L.J.; Casahorran, J.; Esteve, J.G.
1993-01-01
We analyse the symmetry breaking associated to anomalous realization of supersymmetry in the context of SUSY QM. In this case one of the SUSY partners is singular; that leads to peculiar forms of the Levinson theorem relating phase shifts and bound states. Some examples are exhibited; peculiarities include negative energies, incomplete pairing of states and extra phases in scattering. (Author) 8 refs
Another look at the second incompleteness theorem
Visser, A.
2017-01-01
In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is xed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the interpretation
Another look at the second incompleteness theorem
Visser, Albert
2017-01-01
In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is fixed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the
On the Leray-Hirsch Theorem for the Lichnerowicz cohomology
International Nuclear Information System (INIS)
Ait Haddoul, Hassan
2004-03-01
The purpose of this paper is to prove the Leray-Hirsch theorem for the Lichnerowicz; cohomology with respect to basic and vertical closed 1-forms. This is a generalization of the Kfirmeth theorem to fiber bundles. (author)
A Note on a Broken-Cycle Theorem for Hypergraphs
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Trinks Martin
2014-08-01
Full Text Available Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there
A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
程立新; 腾岩梅
2003-01-01
This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.
Institute of Scientific and Technical Information of China (English)
YIN Ya-jun; WU Ji-ye; HUANG Ke-zhi; FAN Qin-shan
2008-01-01
By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian (or spherical) mapping, a series of invariants or geometric conservation quantities under Gaussian (or spherical) mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed.
Applications of square-related theorems
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
DISCRETE FIXED POINT THEOREMS AND THEIR APPLICATION TO NASH EQUILIBRIUM
Sato, Junichi; Kawasaki, Hidefumi
2007-01-01
Fixed point theorems are powerful tools in not only mathematics but also economic. In some economic problems, we need not real-valued but integer-valued equilibriums. However, classical fixed point theorems guarantee only real-valued equilibria. So we need discrete fixed point theorems in order to get discrete equilibria. In this paper, we first provide discrete fixed point theorems, next apply them to a non-cooperative game and prove the existence of a Nash equilibrium of pure strategies.
A general comparison theorem for backward stochastic differential equations
Cohen, Samuel N.; Elliott, Robert J.; Pearce, Charles E. M.
2010-01-01
A useful result when dealing with backward stochastic differential equations is the comparison theorem of Peng (1992). When the equations are not based on Brownian motion, the comparison theorem no longer holds in general. In this paper we present a condition for a comparison theorem to hold for backward stochastic differential equations based on arbitrary martingales. This theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectat...
Theorems of Tarski's Undefinability and Godel's Second Incompleteness - Computationally
Salehi, Saeed
2015-01-01
We present a version of Godel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions (first discussed by M. Detlefsen 2001). We also argue that Tarski's theorem on the Undefinability of Truth is Godel's First Incompleteness Theorem relativized to definable oracles; here a unification of these two theorems is given.
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
2014-01-01
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
On Comparison Theorems for Conformable Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Mehmet Zeki Sarikaya
2016-10-01
Full Text Available In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm's separation and Sturm's comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented to verify the proposed theorem.
COMPARISON THEOREMS AND APPLICATIONS OF OSCILLATION OF NEUTRAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
燕居让
1991-01-01
We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equation is reduced to that of nonneutral delay differential equa-tion, from which we give a series of oscillation theorems for neutral delay differentialequation.
A generalization of the virial theorem for strongly singular potentials
International Nuclear Information System (INIS)
Gesztesy, F.; Pittner, L.
1978-09-01
Using scale transformations the authors prove a generalization of the virial theorem for the eigenfunctions of non-relativistic Schroedinger Hamiltonians which are defined as the Friedrichs extension of strongly singular differential operators. The theorem also applies to situations where the ground state has divergent kinetic and potential energy and thus the usual version of the virial theorem becomes meaningless. (Auth.)
No-go theorems for the minimization of potentials
International Nuclear Information System (INIS)
Chang, D.; Kumar, A.
1985-01-01
Using a theorem in linear algebra, we prove some no-go theorems in the minimization of potentials related to the problem of symmetry breaking. Some applications in the grand unified model building are mentioned. Another application of the algebraic theorem is also included to demonstrate its usefulness
Search strategy for theorem proving in artificial systems. I
Energy Technology Data Exchange (ETDEWEB)
Lovitskii, V A; Barenboim, M S
1981-01-01
A strategy is contrived, employing the language of finite-order predicate calculus, for finding proofs of theorems. A theorem is formulated, based on 2 known theorems on purity and absorption, and used to determine 5 properties of a set of propositions. 3 references.
Goedel incompleteness theorems and the limits of their applicability. I
International Nuclear Information System (INIS)
Beklemishev, Lev D
2011-01-01
This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.
Kochen-Specker theorem as a precondition for secure quantum key distribution
International Nuclear Information System (INIS)
Nagata, Koji
2005-01-01
We show that (1) the violation of the Ekert 1991 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 1992 (BBM92) inequality is, also, a sufficient condition for certification of the KS theorem. Therefore the success in each quantum key distribution protocol reveals the nonclassical feature of quantum theory, in the sense that the KS realism is violated. Further, it turned out that the Ekert inequality and the BBM inequality are depictured by distillable entanglement witness inequalities. Here, we connect the success in these two key distribution processes into the no-hidden-variables theorem and into witness on distillable entanglement. We also discuss the explicit difference between the KS realism and Bell's local realism in the Hilbert space formalism of quantum theory
Generalised summation-by-parts operators and variable coefficients
Ranocha, Hendrik
2018-06-01
High-order methods for conservation laws can be highly efficient if their stability is ensured. A suitable means mimicking estimates of the continuous level is provided by summation-by-parts (SBP) operators and the weak enforcement of boundary conditions. Recently, there has been an increasing interest in generalised SBP operators both in the finite difference and the discontinuous Galerkin spectral element framework. However, if generalised SBP operators are used, the treatment of the boundaries becomes more difficult since some properties of the continuous level are no longer mimicked discretely - interpolating the product of two functions will in general result in a value different from the product of the interpolations. Thus, desired properties such as conservation and stability are more difficult to obtain. Here, new formulations are proposed, allowing the creation of discretisations using general SBP operators that are both conservative and stable. Thus, several shortcomings that might be attributed to generalised SBP operators are overcome (cf. Nordström and Ruggiu (2017) [38] and Manzanero et al. (2017) [39]).
Parameter tuning for the NFFT based fast Ewald summation
Directory of Open Access Journals (Sweden)
Franziska Nestler
2016-07-01
Full Text Available The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditionsis possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT. In this paper we consider the particle-particle NFFT (P$^2$NFFT approach, which is based on the fast Fourier transform for nonequispaced data (NFFT and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. Typically B-splines are applied in the scope of particle mesh methods, as for instance within the well known particle-particle particle-mesh (P$^3$M algorithm. The publicly available P$^2$NFFT algorithm allows the application of an oversampled FFT as well as the usage of different window functions. We consider for the first time also an approximation by Bessel functions and show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that, if the parameters are tuned appropriately, the Bessel window function is in many cases even the better choice in terms of computational costs. Moreover, the results indicate that it is often advantageous in terms of efficiency to spend some oversampling within the NFFT while using a window function with a smaller support.
Parameter tuning for the NFFT based fast Ewald summation
Nestler, Franziska
2016-07-01
The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P^2NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. Typically B-splines are applied in the scope of particle mesh methods, as for instance within the well known particle-particle particle-mesh (P^3M) algorithm. The publicly available P^2NFFT algorithm allows the application of an oversampled FFT as well as the usage of different window functions. We consider for the first time also an approximation by Bessel functions and show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that, if the parameters are tuned appropriately, the Bessel window function is in many cases even the better choice in terms of computational costs. Moreover, the results indicate that it is often advantageous in terms of efficiency to spend some oversampling within the NFFT while using a window function with a smaller support.
Application of summative content analysis to a postal questionnaire.
Griffiths, Thomas Howard
2016-01-01
Content analysis of replies to closed questions in questionnaires can be undertaken to understand remarks that may explain the responses, provide illustrative examples of issues raised in the questionnaire, define new issues or issues of importance that were not covered in the questionnaire and inform the design of new questions in future surveys. To discuss the usefulness of summative content analysis to free text in postal questionnaires. Content analysis provides useful comparative insights between two respondent groups in the case example provided. Five themes emerged: poor understanding of the concept of 'patient lateral transfer work technique' and the direct instrument nursing observation (DINO) instrument's key directions; outcomes of patient transfer; positive responses; manual handling risk; and poor translation into English of DINO. Respondents need an opportunity to clarify their responses to questionnaires using free text, to provide insight into their understanding of the question being asked, understanding of the concept or construct being discussed, and data triangulation through the confirmation of item responses and free-text comments. Responses to questions in a postal questionnaire and the opportunity for free-text commentary by respondents enable the identification of hidden meanings behind tickbox responses to questions.
Summations over equilaterally triangulated surfaces and the critical string measure
International Nuclear Information System (INIS)
Smit, D.J.; Lawrence Berkeley Lab., CA
1992-01-01
We propose a new approach to the summation over dynamically triangulated Riemann surfaces which does not rely on properties of the potential in a matrix model. Instead, we formulate a purely algebraic discretization of critical string path integral. This is combined with a technique which assigns to each equilateral triangulation of a two-dimensional surface a Riemann surface defined over a certain finite extension of the field of rational numbers, i.e. an arithmetic surface. Thus we establish a new formulated in which the sum over randomly triangulated surfaces defines an invariant measure on the moduli space of arithmetic surfaces. It is shown that because of this it is far from obvious that this measure for large genera approximates the measure defined by the continuum theory, i.e. Liouville theory or critical string theory. In low genus this subtlety does not exist. In the case of critical string theory we explicitly compute the volume of the moduli space of arithmetic surfaces in terms of the modular height function and show that for low genus it approximates correctly the continuum measure. We also discuss a continuum limit which bears some resemblance with a double scaling limit in matrix models. (orig.)
Application of particle-mesh Ewald summation to ONIOM theory
International Nuclear Information System (INIS)
Kobayashi, Osamu; Nanbu, Shinkoh
2015-01-01
Highlights: • Particle-mesh Ewald sum is extended to ONIOM scheme. • Non-adiabatic MD simulation in solution is performed. • The behavior of excited (Z)-penta-2,4-dieniminium cation in methanol is simulated. • The difference between gas phase and solution is predicted. - Abstract: We extended a particle mesh Ewald (PME) summation method to the ONIOM (our Own N-layered Integrated molecular Orbitals and molecular Mechanics) scheme (PME-ONIOM) to validate the simulation in solution. This took the form of a nonadiabatic ab initio molecular dynamics (MD) simulation in which the Zhu-Nakamura trajectory surface hopping (ZN-TSH) method was performed for the photoisomerization of a (Z)-penta-2,4-dieniminium cation (protonated Schiff base, PSB3) electronically excited to the S 1 state in a methanol solution. We also calculated a nonadiabatic ab initio MD simulation with only minimum image convention (MI-ONIOM). The lifetime determined by PME-ONIOM-MD was 3.483 ps. The MI-ONIOM-MD lifetime of 0.4642 ps was much shorter than those of PME-ONIOM-MD and the experimentally determined excited state lifetime. The difference eminently illustrated the accurate treatment of the long-range solvation effect, which destines the electronically excited PSB3 for staying in S 1 at the pico-second or the femto-second time scale.
A Meinardus Theorem with Multiple Singularities
Granovsky, Boris L.; Stark, Dudley
2012-09-01
Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
A Geometrical Approach to Bell's Theorem
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
A THEOREM ON CENTRAL VELOCITY DISPERSIONS
International Nuclear Information System (INIS)
An, Jin H.; Evans, N. Wyn
2009-01-01
It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere (SIS), the logarithmic cusp slope γ of the tracers must be given exactly by γ = 2β, where β is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster than that of the SIS, the velocity dispersion of the tracers must diverge at the center too. In particular, if the logarithmic halo cusp slope is larger than two, the diverging velocity dispersion also traces the behavior of the potential. The implication of our theorem on projected quantities is also discussed. We argue that our theorem should be understood as a warning against interpreting results based on simplifying assumptions such as isotropy and spherical symmetry.
Asymptotic twistor theory and the Kerr theorem
International Nuclear Information System (INIS)
Newman, Ezra T
2006-01-01
We first review asymptotic twistor theory with its real subspace of null asymptotic twistors: a five-dimensional CR manifold. This is followed by a description of the Kerr theorem (the identification of shear-free null congruences, in Minkowski space, with the zeros of holomorphic functions of three variables) and an asymptotic version of the Kerr theorem that produces regular asymptotically shear-free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes. A surprising aspect of this work is the role played by analytic curves in H-space, each curve generating an asymptotically flat null geodesic congruence. Also there is a discussion of the physical space realizations of the two associated five- and three-dimensional CR manifolds
Theorem of comparative sensitivity of fibre sensors
Belovolov, M. I.; Paramonov, V. M.; Belovolov, M. M.
2017-12-01
We report an analysis of sensitivity of fibre sensors of physical quantities based on different types of interferometers. We formulate and prove the following theorem: under the time-dependent external physical perturbations at nonzero frequencies (i.e., except the static and low-frequency ones) on the sensitive arms of an interferometer in the form of multiturn elements (coils), there exist such lengths L of the measuring arms of the fibre interferometers at which the sensitivity of sensors based on the Sagnac fibre interferometers can be comparable with the sensitivity of sensors based on Michelson, Mach - Zehnder, or Fabry - Perot fibre interferometers, as well as exceed it under similar other conditions (similar-type perturbations, similar arm lengths and single-mode fibre types). The consequences that follow from the theorem, important for practical implementation of arrays of fibre sensors for measurement purposes and the devices with stable metrological properties, are discussed.
Proofs and generalizations of the pythagorean theorem
Directory of Open Access Journals (Sweden)
Lialda B. Cavalcanti
2011-01-01
Full Text Available This article explores a topic developed by a group of researchers of the Science and Technology Teaching School of Instituto Federal de Pernambuco, Brazil (IFPE, in assistance to the development of the Mathematics Practical and Teaching Laboratory of the distance learning Teaching Licensure, financed by the Universidad Abierta de Brasil. In this article, we describe the peculiarities present in the proofs of the Pythagorean theorem with the purpose of illustrating some of these methods. The selection of these peculiarities was founded and based on the comparison of areas by means of the superimposition of geometrical shapes and used several different class resources. Some generalizations of this important theorem in mathematical problem-solving are also shown.
The self-normalized Donsker theorem revisited
Parczewski, Peter
2016-01-01
We extend the Poincar\\'{e}--Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the self-normalized Donsker theorem in Cs\\"{o}rg\\H{o} et al. (2003). Some notes on spheres with respect to $\\ell_p$-norms are given.
The untyped stack calculus and Bohm's theorem
Directory of Open Access Journals (Sweden)
Alberto Carraro
2013-03-01
Full Text Available 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.
Gauge Invariance and the Goldstone Theorem
Guralnik, Gerald S.
This paper was originally created for and printed in the "Proceedings of seminar on unified theories of elementary particles" held in Feldafing, Germany from July 5 to 16, 1965 under the auspices of the Max-Planck-Institute for Physics and Astrophysics in Munich. It details and expands upon the 1964 Guralnik, Hagen, and Kibble paper demonstrating that the Goldstone theorem does not require physical zero mass particles in gauge theories.
A remark on three-surface theorem
International Nuclear Information System (INIS)
Lu Zhujia
1991-01-01
The three-surface theorem for uniformly elliptic differential inequalities with nonpositive coefficient of zero-order term in some domain D is included in R n becomes trivial if the maximum of u on two separate boundary surface of D is nonpositive. We give a method in this paper for obtaining a nontrivial estimate of the maximum of u on a family of closed surfaces. (author). 2 refs
Asynchronous networks: modularization of dynamics theorem
Bick, Christian; Field, Michael
2017-02-01
Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or dynamical modules. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network: the modularization of dynamics theorem. We give examples to illustrate the main results.
Fractional and integer charges from Levinson's theorem
International Nuclear Information System (INIS)
Farhi, E.; Graham, N.; Jaffe, R.L.; Weigel, H.
2001-01-01
We compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson's theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional regularization in a (1+1)-dimensional gauge theory. We demonstrate that this regularization procedure automatically eliminates the anomaly in the vector current that a naive regulator would produce. We also apply these techniques to bag models in one and three dimensions
Theorems for asymptotic safety of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Bond, Andrew D.; Litim, Daniel F. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)
2017-06-15
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 emphasised. 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. (orig.)
Optical theorem, depolarization and vector tomography
International Nuclear Information System (INIS)
Toperverg, B.P.
2003-01-01
A law of the total flux conservation is formulated in the form of the optical theorem. It is employed to explicitly derive equations for the description of the neutron polarization within the range of the direct beam defined by its angular divergence. General considerations are illustrated by calculations using the Born and Eikonal approximations. Results are briefly discussed as applied to Larmor-Fourier tomography
Central limit theorem and deformed exponentials
International Nuclear Information System (INIS)
Vignat, C; Plastino, A
2007-01-01
The central limit theorem (CLT) can be ranked among the most important ones in probability theory and statistics and plays an essential role in several basic and applied disciplines, notably in statistical thermodynamics. We show that there exists a natural extension of the CLT from exponentials to so-called deformed exponentials (also denoted as q-Gaussians). Our proposal applies exactly in the usual conditions in which the classical CLT is used. (fast track communication)
Convergence theorems for quasi-contractive mappings
International Nuclear Information System (INIS)
Chidume, C.E.
1992-01-01
It is proved that each of two well known fixed point iteration methods (the Mann and Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of a quasi-contractive map in real Banach spacers with property (U, α, m+1, m). These Banach spaces include the L p (or l p ) spaces, p ≥ 2. Our theorems generalize important known results. (author). 29 refs
Optical theorem for heavy-ion scattering
International Nuclear Information System (INIS)
Schwarzschild, A.Z.; Auerbach, E.H.; Fuller, R.C.; Kahana, S.
1976-01-01
An heuristic derivation is given of an equivalent of the optical theorem stated in the charged situation with the remainder or nuclear elastic scattering amplitude defined as a difference of elastic and Coulomb amplitudes. To test the detailed behavior of this elastic scattering amplitude and the cross section, calculations were performed for elastic scattering of 18 O + 58 Ni, 136 Xe + 209 Bi, 84 Kr + 208 Pb, and 11 B + 26 Mg at 63.42 to 114 MeV
Applications of Wck's theorem, ch. 17
International Nuclear Information System (INIS)
Brussaard, P.J.; Glaudemans, P.W.M.
1977-01-01
Wick's theorem is introduced and used to write the many-body Hamiltonian in a selfconsistent basis. The terms of a perturbation expansion are evaluated with the use of the second-quantization formalism.The correspondence with Feyman diagrams is demonstrated. For some nuclei a description in terms of particle-hole configurations is quite convenient. The simplest case, i.e. one-particle, one-hole states, is treated
Theorem Proving In Higher Order Logics
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
The universality of the Carnot theorem
International Nuclear Information System (INIS)
Gonzalez-Ayala, Julian; Angulo-Brown, F
2013-01-01
It is common in many thermodynamics textbooks to illustrate the Carnot theorem through the use of diverse state equations for gases, paramagnets, and other simple thermodynamic systems. As is well known, the universality of the Carnot efficiency is easily demonstrated in a temperature–entropy diagram, which means that η C is independent of the working substance. In this paper we remark that the universality of the Carnot theorem goes beyond conventional state equations, and is fulfilled by gas state equations that do not correspond to an ideal gas in the dilution limit, namely V → ∞. Some of these unconventional state equations have certain thermodynamic ‘anomalies’ that nonetheless do not forbid them from obeying the Carnot theorem. We discuss how this very general behaviour arises from Maxwell relations, which are connected with a geometrical property expressed through preserving area transformations. A rule is proposed to calculate the Maxwell relations associated with a thermodynamic system by using the preserving area relationships. In this way it is possible to calculate the number of possible preserving area mappings by giving the number of possible Jacobian identities between all pairs of thermodynamic variables included in the corresponding Gibbs equation. This paper is intended for undergraduates and specialists in thermodynamics and related areas. (paper)
Soft theorems from conformal field theory
International Nuclear Information System (INIS)
Lipstein, Arthur E.
2015-01-01
Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambtwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.
Joint probability distributions and fluctuation theorems
International Nuclear Information System (INIS)
García-García, Reinaldo; Kolton, Alejandro B; Domínguez, Daniel; Lecomte, Vivien
2012-01-01
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation–dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators
Four theorems on the psychometric function.
May, Keith A; Solomon, Joshua A
2013-01-01
In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus
Four theorems on the psychometric function.
Directory of Open Access Journals (Sweden)
Keith A May
Full Text Available In a 2-alternative forced-choice (2AFC discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise x β(Transducer, where β(Noise is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer depends on the transducer. We derive general expressions for β(Noise and β(Transducer, from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx(b, β ≈ β(Noise x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is
Source reconstruction using phase space beam summation technique
International Nuclear Information System (INIS)
Graubart, Gideon.
1990-10-01
In this work, the phase-space beam summation technique (PSBS), is applied to back propagation and inverse source problems. The PSBS expresses the field as a superposition of shifted and tilted beams. This phase space spectrum of beams is matched to the source distribution via an amplitude function which expresses the local spectrum of the source function in terms of a local Fourier transform. In this work, the emphasis is on the phase space processing of the data, on the information content of this data and on the back propagation scheme. More work is still required to combine this back propagation approach in a full, multi experiment inverse scattering scheme. It is shown that the phase space distribution of the data, computed via the local spectrum transform, is localized along lines that define the local arrival direction of the wave data. We explore how the choice of the beam width affects the compactification of this distribution, and derive criteria for choosing a window that optimizes this distribution. It should be emphasized that compact distribution implies fewer beams in the back propagation scheme and therefore higher numerical efficiency and better physical insight. Furthermore it is shown how the local information property of the phase space representation can be used to improve the performance of this simple back propagation problem, in particular with regard to axial resolution; the distance to the source can be determined by back propagating only the large angle phase space beams that focus on the source. The information concerning transverse distribution of the source, on the other hand, is contained in the axial phase space region and can therefore be determined by the corresponding back propagating beams. Because of the global nature of the plane waves propagators the conventional plane wave back propagation scheme does not have the same 'focusing' property, and therefore suffers from lack of information localization and axial resolution. The
General proof of the Greenberger-Horne-Zeilinger theorem
International Nuclear Information System (INIS)
Chen Zeqian
2004-01-01
It is proved that all states of three spin-(1/2) particles exhibiting an 'all versus nothing' contradiction between quantum mechanics and the local realism of Einstein, Podolsky, and Rosen are exactly the Greenberger-Horne-Zeilinger (GHZ) states and the states obtained from them by local unitary transformations. The proof is obtained by showing that there are at most four elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the three-qubit system and using the certain algebraic properties that Pauli's matrices satisfy. We show that only does such a set of four nonlocal spin observables present a Greenberger-Horne-Zeilinger-Mermin-like argument. This also reveals the equivalence between the GHZ theorem and maximal violation of the Bell inequality
Mismatched summation mechanisms in older adults for the perception of small moving stimuli.
McDougall, Thomas J; Nguyen, Bao N; McKendrick, Allison M; Badcock, David R
2018-01-01
Previous studies have found evidence for reduced cortical inhibition in aging visual cortex. Reduced inhibition could plausibly increase the spatial area of excitation in receptive fields of older observers, as weaker inhibitory processes would allow the excitatory receptive field to dominate and be psychophysically measureable over larger areas. Here, we investigated aging effects on spatial summation of motion direction using the Battenberg summation method, which aims to control the influence of locally generated internal noise changes by holding overall display size constant. This method produces more accurate estimates of summation area than conventional methods that simply increase overall stimulus dimensions. Battenberg stimuli have a checkerboard arrangement, where check size (luminance-modulated drifting gratings alternating with mean luminance areas), but not display size, is varied and compared with performance for a full field stimulus to provide a measure of summation. Motion direction discrimination thresholds, where contrast was the dependent variable, were measured in 14 younger (24-34 years) and 14 older (62-76 years) adults. Older observers were less sensitive for all check sizes, but the relative sensitivity across sizes, also differed between groups. In the older adults, the full field stimulus offered smaller performance improvements compared to that for younger adults, specifically for the small checked Battenberg stimuli. This suggests aging impacts on short-range summation mechanisms, potentially underpinned by larger summation areas for the perception of small moving stimuli. Copyright © 2017 Elsevier Ltd. All rights reserved.
Activity-related summation of pain and functional disability in patients with whiplash injuries.
Sullivan, Michael J L; Larivière, Christian; Simmonds, Maureen
2010-11-01
This study investigated the relation between repetition-induced summation of activity-related pain (RISP) and indicators of functional disability in a sample of 62 individuals who had sustained whiplash injuries. Participants completed measures of pain severity, pain catastrophizing, fear of movement and depression prior to lifting a series of 36 weighted canisters. An index of RISP was computed as the increase in pain reported by participants over successive lifts of the weighted canisters. Measures of functional disability included physical lifting tolerance, self-reported disability and perceived work demands. Regression analyses revealed that the index of RISP accounted for significant variance in measures of lifting tolerance and perceived work demands, even when controlling for age, sex and pain severity. The index of RISP was also significantly correlated with pain catastrophizing and pain duration. The discussion addresses the mechanisms by which physiological and psychological factors might contribute to increases in pain during repeated physical activity. Discussion also addresses whether RISP might represent a risk factor for problematic recovery outcomes following whiplash injury. Copyright © 2010 International Association for the Study of Pain. Published by Elsevier B.V. All rights reserved.
Performance evaluation of the zero-multipole summation method in modern molecular dynamics software.
Sakuraba, Shun; Fukuda, Ikuo
2018-05-04
The zero-multiple summation method (ZMM) is a cutoff-based method for calculating electrostatic interactions in molecular dynamics simulations, utilizing an electrostatic neutralization principle as a physical basis. Since the accuracies of the ZMM have been revealed to be sufficient in previous studies, it is highly desirable to clarify its practical performance. In this paper, the performance of the ZMM is compared with that of the smooth particle mesh Ewald method (SPME), where the both methods are implemented in molecular dynamics software package GROMACS. Extensive performance comparisons against a highly optimized, parameter-tuned SPME implementation are performed for various-sized water systems and two protein-water systems. We analyze in detail the dependence of the performance on the potential parameters and the number of CPU cores. Even though the ZMM uses a larger cutoff distance than the SPME does, the performance of the ZMM is comparable to or better than that of the SPME. This is because the ZMM does not require a time-consuming electrostatic convolution and because the ZMM gains short neighbor-list distances due to the smooth damping feature of the pairwise potential function near the cutoff length. We found, in particular, that the ZMM with quadrupole or octupole cancellation and no damping factor is an excellent candidate for the fast calculation of electrostatic interactions. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.
Stochastic thermodynamics, fluctuation theorems and molecular machines
International Nuclear Information System (INIS)
Seifert, Udo
2012-01-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (review article)
The implicit function theorem history, theory, and applications
Krantz, Steven G
2003-01-01
The implicit function theorem is part of the bedrock of mathematics analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth function, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash-Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex store, and intimately bound up with the development of fundamental ideas in a...
Some fixed point theorems in fuzzy reflexive Banach spaces
International Nuclear Information System (INIS)
Sadeqi, I.; Solaty kia, F.
2009-01-01
In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.
On the inverse of the Pomeranchuk theorem
International Nuclear Information System (INIS)
Nagy, E.
1977-04-01
The Pomeranchuk theorem is valid only for bounded total cross sections at infinite energies, and for arbitrarily rising cross sections one cannot prove the zero asymptotic limit of the difference of the particle and antiparticle total cross sections. In the paper the problem is considered from the inverse point of view. It is proved using dispersion relations that if the total cross sections rise with some power of logarithm and the difference of the particle and antiparticle total cross sections remain finite, then the real to imaginary ratios of both the particle and antiparticle forward scattering amplitudes are bounded. (Sz.N.Z.)
Noncommutative gauge theories and Kontsevich's formality theorem
International Nuclear Information System (INIS)
Jurco, B.; Schupp, P.; Wess, J.
2001-01-01
The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a 'Mini Seiberg-Witten map' that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor
The Invariance and the General CCT Theorems
Stancu, Alin
2010-01-01
The \\begin{it} Invariance Theorem \\end{it} of M. Gerstenhaber and S. D. Schack states that if $\\mathbb{A}$ is a diagram of algebras then the subdivision functor induces a natural isomorphism between the Yoneda cohomologies of the category $\\mathbb{A}$-$\\mathbf{mod}$ and its subdivided category $\\mathbb{A}'$-$\\mathbf{mod}$. In this paper we generalize this result and show that the subdivision functor is a full and faithful functor between two suitable derived categories of $\\mathbb{A}$-$\\mathb...
No-cloning theorem on quantum logics
International Nuclear Information System (INIS)
Miyadera, Takayuki; Imai, Hideki
2009-01-01
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.
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.
Stone's representation theorem in fuzzy topology
Institute of Scientific and Technical Information of China (English)
刘应明; 张德学
2003-01-01
In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0 ∈ L is a prime or 1 ∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L-locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L-topological spaces.
Soft theorems for shift-symmetric cosmologies
Finelli, Bernardo; Goon, Garrett; Pajer, Enrico; Santoni, Luca
2018-03-01
We derive soft theorems for single-clock cosmologies that enjoy a shift symmetry. These so-called consistency conditions arise from a combination of a large diffeomorphism and the internal shift symmetry and fix the squeezed limit of all correlators with a soft scalar mode. As an application, we show that our results reproduce the squeezed bispectrum for ultra-slow-roll inflation, a particular shift-symmetric, nonattractor model which is known to violate Maldacena's consistency relation. Similar results have been previously obtained by Mooij and Palma using background-wave methods. Our results shed new light on the infrared structure of single-clock cosmological spacetimes.
Central limit theorems under special relativity.
McKeague, Ian W
2015-04-01
Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.
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.
Logic for computer science foundations of automatic theorem proving
Gallier, Jean H
2015-01-01
This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in fir
On Pythagoras Theorem for Products of Spectral Triples
D'Andrea, Francesco; Martinetti, Pierre
2013-01-01
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some un...
A remark on the energy conditions for Hawking's area theorem
Lesourd, Martin
2018-06-01
Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
Markvorsen, Steen
2006-01-01
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered only much later in more advanced math courses - is comprehensible with only a little extension of the first year curriculum. Moreover, it is more intuitive than the static proof. We support this intuit...
A Converse to the Cayley-Hamilton Theorem
Indian Academy of Sciences (India)
follows that qj = api, where a is a unit. Thus, we must have that the expansion of I into irreducibles is unique. Hence, K[x] is a UFD. A famous theorem of Gauss implies that K[XI' X2,. ,xn] is also an UFD. Gauss's Theorem: R[x] is a UFD, if and only if R is a UFD. For a proof of Gauss's theorem and a detailed proof of the fact that ...
The Surprise Examination Paradox and the Second Incompleteness Theorem
Kritchman, Shira; Raz, Ran
2010-01-01
We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest that the second incompleteness theorem gives a possible resolution of the surprise examination paradox. Roughly speaking, we argue that the flaw in the derivation of the paradox is that it contains a hidden assumption that one can prove the consistency of the...
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.
Generalizations of the Nash Equilibrium Theorem in the KKM Theory
Directory of Open Access Journals (Sweden)
Sehie Park
2010-01-01
Full Text Available The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minimax theorem, the von Neumann-Fan intersection theorem, the Fan-type analytic alternative, and the Nash equilibrium theorem for abstract convex spaces satisfying the partial KKM principle. These results are compared with previously known cases for G-convex spaces. Consequently, our results unify and generalize most of previously known particular cases of the same nature. Finally, we add some detailed historical remarks on related topics.
Randomized central limit theorems: A unified theory.
Eliazar, Iddo; Klafter, Joseph
2010-08-01
The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.
Birth of a theorem a mathematical adventure
Villani, Cédric
2015-01-01
This man could plainly do for mathematics what Brian Cox has done for physics" (Sunday Times). What goes on inside the mind of a rock-star mathematician? Where does inspiration come from? With a storyteller's gift, Cedric Villani takes us on a mesmerising journey as he wrestles with a new theorem that will win him the most coveted prize in mathematics. Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, doubt and anxiety, elation and despair. We discover how it feels to be obsessed by a theorem during your child's cello practise and throughout your dreams, why appreciating maths is a bit like watching an episode of Columbo, and how sometimes inspiration only comes from locking yourself away in a dark room to think. Blending science with history, biography with myth, Villani conjures up an inimitable cast of characters including the omnipresent Einstein, mad genius Kurt Godel, and Villani's personal hero, John Nash. Bir...
Does the central limit theorem always apply to phase noise? Some implications for radar problems
Gray, John E.; Addison, Stephen R.
2017-05-01
The phase noise problem or Rayleigh problem occurs in all aspects of radar. It is an effect that a radar engineer or physicist always has to take into account as part of a design or in attempt to characterize the physics of a problem such as reverberation. Normally, the mathematical difficulties of phase noise characterization are avoided by assuming the phase noise probability distribution function (PDF) is uniformly distributed, and the Central Limit Theorem (CLT) is invoked to argue that the superposition of relatively few random components obey the CLT and hence the superposition can be treated as a normal distribution. By formalizing the characterization of phase noise (see Gray and Alouani) for an individual random variable, the summation of identically distributed random variables is the product of multiple characteristic functions (CF). The product of the CFs for phase noise has a CF that can be analyzed to understand the limitations CLT when applied to phase noise. We mirror Kolmogorov's original proof as discussed in Papoulis to show the CLT can break down for receivers that gather limited amounts of data as well as the circumstances under which it can fail for certain phase noise distributions. We then discuss the consequences of this for matched filter design as well the implications for some physics problems.
A perceptron network theorem prover for the propositional calculus
Drossaers, M.F.J.
In this paper a short introduction to neural networks and a design for a perceptron network theorem prover for the propositional calculus are presented. The theorem prover is a representation of a variant of the semantic tableau method, called the parallel tableau method, by a network of
Leaning on Socrates to Derive the Pythagorean Theorem
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…
A new proof of the positive energy theorem
International Nuclear Information System (INIS)
Witten, E.
1981-01-01
A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by Schoen and Yau). The relevance of these results to the stability of Minkowski space is discussed. (orig.)
COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It-Kunita integral. By the application of this theorem, we give an existence result of the solutions to these equations with continuous coefficients.
The Boundary Crossing Theorem and the Maximal Stability Interval
Directory of Open Access Journals (Sweden)
Jorge-Antonio López-Renteria
2011-01-01
useful tools in the study of the stability of family of polynomials. Although both of these theorem seem intuitively obvious, they can be used for proving important results. In this paper, we give generalizations of these two theorems and we apply such generalizations for finding the maximal stability interval.
K S Krishnan's 1948 Perception of the Sampling Theorem
Indian Academy of Sciences (India)
K S Krishnan's 1948 Perception of the. Sampling Theorem. Raiiah Simon is a. Professor at the Institute of Mathematical. Sciences, Chennai. His primary interests are in classical and quantum optics, geometric phases, group theoretical techniques and quantum information science. Keywords. Sompling theorem, K S ...
On Frobenius, Mazur, and Gelfand-Mazur theorems on division ...
African Journals Online (AJOL)
... R of real numbers, the field C of complex numbers, or the non-commutative algebra Q of quaternions. Gelfand [15] proved that every normed division algebra over the field C is isomorphic to C. He named this theorem, which is fundamental for the development of the theory of Banach Algebras, the Gelfand-Mazur theorem.
An extension of Brosowski-Meinardus theorem on invariant approximation
International Nuclear Information System (INIS)
Liaqat Ali Khan; Abdul Rahim Khan.
1991-07-01
We obtain a generalization of a fixed point theorem of Dotson for non-expansive mappings on star-shaped sets and then use it to prove a unified Brosowski-Meinardus theorem on invariant approximation in the setting of p-normed linear spaces. (author). 13 refs
A general conservative extension theorem in process algebras with inequalities
d' Argenio, P.R.; Verhoef, Chris
1997-01-01
We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to
A power counting theorem for Feynman integrals on the lattice
International Nuclear Information System (INIS)
Reisz, T.
1988-01-01
A convergence theorem is proved, which states sufficient conditions for the existence of the continuum limit for a wide class of Feynman integrals on a space-time lattice. A new kind of a UV-divergence degree is introduced, which allows the formulation of the theorem in terms of power counting conditions. (orig.)
A Hohenberg-Kohn theorem for non-local potentials
International Nuclear Information System (INIS)
Meron, E.; Katriel, J.
1977-01-01
It is shown that within any class of commuting one-body potentials a Hohenberg-Kohn type theorem is satisfied with respect to an appropriately defined density. The Hohenberg-Kohn theorem for local potentials follows as a special case. (Auth.)
A note on the homomorphism theorem for hemirings
Directory of Open Access Journals (Sweden)
D. M. Olson
1978-01-01
Full Text Available The fundamental homomorphism theorem for rings is not generally applicable in hemiring theory. In this paper, we show that for the class of N-homomorphism of hemirings the fundamental theorem is valid. In addition, the concept of N-homomorphism is used to prove that every hereditarily semisubtractive hemiring is of type (K.
On the Riesz representation theorem and integral operators ...
African Journals Online (AJOL)
We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions. Keywords: Vector integral, integral operators, operator ...
Bell's "Theorem": loopholes vs. conceptual flaws
Kracklauer, A. F.
2017-12-01
An historical overview and detailed explication of a critical analysis of what has become known as Bell's Theorem to the effect that, it should be impossible to extend Quantum Theory with the addition of local, real variables so as to obtain a version free of the ambiguous and preternatural features of the currently accepted interpretations is presented. The central point on which this critical analysis, due originally to Edwin Jaynes, is that Bell incorrectly applied probabilistic formulas involving conditional probabilities. In addition, mathematical technicalities that have complicated the understanding of the logical or mathematical setting in which current theory and experimentation are embedded, are discussed. Finally, some historical speculations on the sociological environment, in particular misleading aspects, in which recent generations of physicists lived and worked are mentioned.
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.
Theorem Proving in Intel Hardware Design
O'Leary, John
2009-01-01
For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.
Virial Theorem in Nonlocal Newtonian Gravity
Directory of Open Access Journals (Sweden)
Bahram Mashhoon
2016-05-01
Full Text Available Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for “isolated” astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy’s baryonic diameter D 0 —namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time—is predicted to be larger than the effective dark matter fraction f D M times a universal length that is the basic nonlocality length scale λ 0 ≈ 3 ± 2 kpc.
On a curvature-statistics theorem
International Nuclear Information System (INIS)
Calixto, M; Aldaya, V
2008-01-01
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature (κ = ±1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.
On a curvature-statistics theorem
Energy Technology Data Exchange (ETDEWEB)
Calixto, M [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de Astrofisica de Andalucia, Apartado Postal 3004, 18080 Granada (Spain)], E-mail: Manuel.Calixto@upct.es
2008-08-15
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature ({kappa} = {+-}1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.
An interlacing theorem for reversible Markov chains
International Nuclear Information System (INIS)
Grone, Robert; Salamon, Peter; Hoffmann, Karl Heinz
2008-01-01
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
An interlacing theorem for reversible Markov chains
Energy Technology Data Exchange (ETDEWEB)
Grone, Robert; Salamon, Peter [Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720 (United States); Hoffmann, Karl Heinz [Institut fuer Physik, Technische Universitaet Chemnitz, D-09107 Chemnitz (Germany)
2008-05-30
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
Asset management using an extended Markowitz theorem
Directory of Open Access Journals (Sweden)
Paria Karimi
2014-06-01
Full Text Available Markowitz theorem is one of the most popular techniques for asset management. The method has been widely used to solve many applications, successfully. In this paper, we present a multi objective Markowitz model to determine asset allocation by considering cardinality constraints. The resulted model is an NP-Hard problem and the proposed study uses two metaheuristics, namely genetic algorithm (GA and particle swarm optimization (PSO to find efficient solutions. The proposed study has been applied on some data collected from Tehran Stock Exchange over the period 2009-2011. The study considers four objectives including cash return, 12-month return, 36-month return and Lower Partial Moment (LPM. The results indicate that there was no statistical difference between the implementation of PSO and GA methods.
Experimental knee pain evoke spreading hyperalgesia and facilitated temporal summation of pain
DEFF Research Database (Denmark)
Jørgensen, Tanja Schjødt; Henriksen, Marius; Danneskiold-Samsøe, Bente
2013-01-01
OBJECTIVES: This study evaluated the deep-tissue pressure pain sensitivity and temporal summation of pain within and around healthy knees exposed to experimental pain. DESIGN: The study was designed as a randomized crossover trial, with each subject tested on 1 day. SETTING: All tests were carried...... occasions: baseline, immediately after the injection, and when pain had vanished. Assessments sites were located in the peripatellar region, vastus lateralis, and tibialis anterior muscles. RESULTS: The experimental knee pain model demonstrated 1) hyperalgesia to pressure stimulation on the infrapatellar...... fat pad during experimental pain, and 2) facilitated temporal summation of pressure pain at the infrapatellar fat pad and knee-related muscles. CONCLUSION: The increased sensitivity and temporal summation found in this study were exclusive to deep -tissue with no contralateral decreased pain...
McNulty, John A; Espiritu, Baltazar R; Hoyt, Amy E; Ensminger, David C; Chandrasekhar, Arcot J
2015-01-01
Formative practice quizzes have become common resources for self-evaluation and focused reviews of course content in the medical curriculum. We conducted two separate studies to (1) compare the effects of a single or multiple voluntary practice quizzes on subsequent summative examinations and (2) examine when students are most likely to use practice quizzes relative to the summative examinations. In the first study, providing a single on-line practice quiz followed by instructor feedback had no effect on examination average grades compared to the previous year or student performances on similar questions. However, there were significant correlations between student performance on each practice quiz and each summative examination (r = 0.42 and r = 0.24). When students were provided multiple practice quizzes with feedback (second study), there were weak correlations between the frequency of use and performance on each summative examination (r = 0.17 and r = 0.07). The frequency with which students accessed the practice quizzes was greatest the day before each examination. In both studies, there was a decline in the level of student utilization of practice quizzes over time. We conclude that practice quizzes provide some predictive value for performances on summative examinations. Second, making practice quizzes available for longer periods prior to summative examinations does not promote the use of the quizzes as a study strategy because students appear to use them mostly to assess knowledge one to two days prior to examinations. © 2014 American Association of Anatomists.
Measuring temporal summation in visual detection with a single-photon source.
Holmes, Rebecca; Victora, Michelle; Wang, Ranxiao Frances; Kwiat, Paul G
2017-11-01
Temporal summation is an important feature of the visual system which combines visual signals that arrive at different times. Previous research estimated complete summation to last for 100ms for stimuli judged "just detectable." We measured the full range of temporal summation for much weaker stimuli using a new paradigm and a novel light source, developed in the field of quantum optics for generating small numbers of photons with precise timing characteristics and reduced variance in photon number. Dark-adapted participants judged whether a light was presented to the left or right of their fixation in each trial. In Experiment 1, stimuli contained a stream of photons delivered at a constant rate while the duration was systematically varied. Accuracy should increase with duration as long as the later photons can be integrated with the proceeding ones into a single signal. The temporal integration window was estimated as the point that performance no longer improved, and was found to be 650ms on average. In Experiment 2, the duration of the visual stimuli was kept short (100ms or photons was varied to explore the efficiency of summation over the integration window compared to Experiment 1. There was some indication that temporal summation remains efficient over the integration window, although there is variation between individuals. The relatively long integration window measured in this study may be relevant to studies of the absolute visual threshold, i.e., tests of single-photon vision, where "single" photons should be separated by greater than the integration window to avoid summation. Copyright © 2017 Elsevier Ltd. All rights reserved.
Investigating the neural processing of spatial summation of pain: the role of A-delta nociceptors.
Raz, Netta; Granovsky, Yelena; Defrin, Ruth
2015-02-01
The underlying mechanism of spatial summation (SS) of pain, an essential component in pain perception and detection, is unknown. Because of the possible differential innervations by A-delta nociceptors and pain sensitivity of hairy and glabrous skin, a comparison of the SS characteristics between the two skin types could contribute to the elucidation of its subserving system and processing. The effect of sex on SS of pain was also evaluated due to the scarcity of information on the subject. Twenty-nine healthy subjects (13 males, 16 females) received four series of heat stimuli of various intensities, in hairy and glabrous skin of the hand using large (27 mm diameter) and small (12 mm) stimulation areas, and the perceived pain intensity (PPI) was rated. A fast temperature increase rate (70°/s) was used in order to selectively activate A-delta nociceptors. The effect of skin type, stimulation intensity and sex on SS and PPI was calculated. Skin type significantly affected PPI and SS of pain; values of both variables were significantly greater in hairy compared with glabrous skin. SS of pain gradually increased concomitantly with stimulation intensity magnitude, to a point when it became saturated in both skin types. Females exhibited greater SS in glabrous skin. It would appear that AMH-II nociceptive fibers in particular subserve SS of pain. Furthermore, SS is increased under stronger stimulation intensities, probably as defense mechanism against tissue damage. Sex differences in dynamic sensory processes such as SS are revealed only under conditions where the phenomenon is subtle (as in glabrous skin).
Don't Tell It Like It Is: Preserving Collegiality in the Summative Peer Review of Teaching
Iqbal, Isabeau A.
2014-01-01
While much literature has considered feedback and professional growth in formative peer reviews of teaching, there has been little empirical research conducted on these issues in the context of summative peer reviews. This article explores faculty members' perceptions of feedback practices in the summative peer review of teaching and reports on…
On Pythagoras Theorem for Products of Spectral Triples
D'Andrea, Francesco; Martinetti, Pierre
2013-05-01
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.
Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle
Evans, Denis J.; Searles, Debra J.; Mittag, Emil
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
International Nuclear Information System (INIS)
Stenlund, Mikko
2016-01-01
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
A note on the weighted Khintchine-Groshev Theorem
DEFF Research Database (Denmark)
Hussain, Mumtaz; Yusupova, Tatiana
Let W(m,n;ψ−−) denote the set of ψ1,…,ψn-approximable points in Rmn. The classical Khintchine-Groshev theorem assumes a monotonicity condition on the approximating functions ψ−−. Removing monotonicity from the Khintchine-Groshev theorem is attributed to different authors for different cases of m...... and n. It can not be removed for m=n=1 as Duffin-Shcaeffer provided the counter example. We deal with the only remaining case m=2 and thereby remove all unnecessary conditions from the Khintchine-Groshev theorem....
Quantum voting and violation of Arrow's impossibility theorem
Bao, Ning; Yunger Halpern, Nicole
2017-06-01
We propose a quantum voting system in the spirit of quantum games such as the quantum prisoner's dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's impossibility theorem. Arrow's theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's theorem. A quantum version of majority rule, we show, violates this quantum Arrow conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.
Convergence theorems for certain classes of nonlinear mappings
International Nuclear Information System (INIS)
Chidume, C.E.
1992-01-01
Recently, Xinlong Weng announced a convergence theorem for the iterative approximation of fixed points of local strictly pseudo-contractive mappings in uniformly smooth Banach spaces, (Proc. Amer. Math. Soc. Vol.113, No.3 (1991) 727-731). An example is presented which shows that this theorem of Weng is false. Then, a convergence theorem is proved, in certain real Banach spaces, for approximation a solution of the inclusion f is an element of x + Tx, where T is a set-valued monotone operator. An explicit error estimate is also presented. (author). 26 refs
Direct and converse theorems the elements of symbolic logic
Gradshtein, I S; Stark, M; Ulam, S
1963-01-01
Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chap
A primer on Higgs boson low-energy theorems
International Nuclear Information System (INIS)
Dawson, S.; Haber, H.E.; California Univ., Santa Cruz, CA
1989-05-01
We give a pedagogical review of Higgs boson low-energy theorems and their applications in the study of light Higgs boson interactions with mesons and baryons. In particular, it is shown how to combine the chiral Lagrangian method with the Higgs low-energy theorems to obtain predictions for the interaction of Higgs bosons and pseudoscalar mesons. Finally, we discuss the relation between the low-energy theorems and a technique which makes use of the trace of the QCD energy-momentum tensor. 35 refs
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
Energy Technology Data Exchange (ETDEWEB)
Stenlund, Mikko, E-mail: mikko.stenlund@helsinki.fi [University of Helsinki, Department of Mathematics and Statistics (Finland)
2016-09-15
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
Markov's theorem and algorithmically non-recognizable combinatorial manifolds
International Nuclear Information System (INIS)
Shtan'ko, M A
2004-01-01
We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem
Summation integrals for a Green function in a 3-D inhomogeneous anisotropic medium
Czech Academy of Sciences Publication Activity Database
Červený, V.; Pšenčík, Ivan
2014-01-01
Roč. 24, č. 1 (2014), s. 131-158 ISSN 2336-3827 R&D Projects: GA ČR(CZ) GAP210/11/0117 Institutional support: RVO:67985530 Keywords : Gaussian beam summation integrals * Maslov-Chapman integrals * target surface * dynamic ray tracing Subject RIV: DC - Siesmology, Volcanology, Earth Structure
Science Museum Exhibits' Summative Evaluation with Knowledge Hierarchy Method
Yasar, Erkan; Gurel, Cem
2016-01-01
It is aimed in this research to measure via knowledge hierarchy the things regarding exhibit themes learned by the visitors of the exhibits and compare them with the purpose that the exhibits are designed for, thereby realizing a summative evaluation of the exhibits by knowledge hierarchy method. The research has been conducted in a children's…
10 CFR 20.1202 - Compliance with requirements for summation of external and internal doses.
2010-01-01
... external and internal doses. (a) If the licensee is required to monitor under both §§ 20.1502 (a) and (b), the licensee shall demonstrate compliance with the dose limits by summing external and internal doses... compliance with the requirements for summation of external and internal doses by meeting one of the...
Modern summation methods and the computation of 2- and 3-loop Feynman diagrams
International Nuclear Information System (INIS)
Ablinger, Jakob; Schneider, Carsten; Bluemlein, Johannes; Klein, Sebastian
2010-06-01
By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in this task with all our concrete calculations of 2-loop and 3-loop massive single scale Feynman diagrams with local operator insertion. (orig.)
Walker, Marquita
2013-01-01
This summative evaluation is the result of two years' of data reflecting the impact of an ethics class in terms of students' ethical decision-making. The research compares aggregate responses from scenario-based pre- and post-survey open-ended survey questions designed to measure changes in ethical decision-making by comparing students' cognitive…
International Nuclear Information System (INIS)
Hardy, David J.; Schulten, Klaus; Wolff, Matthew A.; Skeel, Robert D.; Xia, Jianlin
2016-01-01
The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle–mesh Ewald method falls short.
Bijsterbosch, Erik; van der Schee, Joop; Kuiper, Wilmad; Beneker, T.
2016-01-01
To start a teacher professional development programme on the relationship between classroom summative assessment and learning, the current practices and dispositions of geography teachers towards internal school-based examinations in pre-vocational education in the Netherlands were investigated. A
Spatial summation in macaque parietal area 7a follows a winner-take-all rule
Oleksiak, Anna; Klink, P. Christiaan; Postma, Albert; van der Ham, Ineke J.M.; Lankheet, Martin J.M.; van Wezel, Richard Jack Anton
2011-01-01
While neurons in posterior parietal cortex have been found to signal the presence of a salient stimulus among multiple items in a display, spatial summation within their receptive field in the absence of an attentional bias has never been investigated. This information, however, is indispensable
Should Global Items on Student Rating Scales Be Used for Summative Decisions?
Berk, Ronald A.
2013-01-01
One of the simplest indicators of teaching or course effectiveness is student ratings on one or more global items from the entire rating scale. That approach seems intuitively sound and easy to use. Global items have even been recommended by a few researchers to get a quick-read, at-a-glance summary for summative decisions about faculty. The…
Web-based feedback after summative assessment: how do students engage?
Harrison, C.J.; Konings, K.D.; Molyneux, A.; Schuwirth, L.W.; Wass, V.; Vleuten, C.P.M. van der
2013-01-01
CONTEXT: There is little research into how to deliver summative assessment student feedback effectively. The main aims of this study were to clarify how students engage with feedback in this context and to explore the roles of learning-related characteristics and previous and current performance.
Including Students with Disabilities in Common Non-Summative Assessments. NCEO Brief. Number 6
National Center on Educational Outcomes, 2012
2012-01-01
Inclusive large-scale assessments have become the norm in states across the U.S. Participation rates of students with disabilities in these assessments have increased dramatically since the mid-1990s. As consortia of states move toward the development and implementation of assessment systems that include both non-summative assessments and…
Summative Self-Assessment in Higher Education: Implications of Its Counting towards the Final Mark
Tejeiro, Ricardo A.; Gomez-Vallecillo, Jorge L.; Romero, Antonio F.; Pelegrina, Manuel; Wallace, Agustin; Emberley, Enrique
2012-01-01
Introduction: Our study aims at assessing the validity of summative criteria-referenced self-assessment in higher education, and in particular, if that validity varies when the professor counts self-assessment toward the final mark. Method: One hundred and twenty-two first year students from two groups in Teacher Education at the Universidad de…
Viger, Steven Guy
2014-01-01
The current study investigates the phenomenon of measurement invariance by examining the construct stability of a summative mathematics achievement instrument over time gleaned from an existing data set. In doing so, not only is the general question of measurement invariance of the particular instrument addressed, but also in the context of growth…
Evaluating Written, Audio and Video Feedback in Higher Education Summative Assessment Tasks
McCarthy, Josh
2015-01-01
This paper evaluates various feedback models utilised for summative assessment tasks for tertiary digital media students at the University of South Australia in Australia. The aim of this research project was to establish the advantages and disadvantages of each technique, and to determine which model provided students with more insight into their…
Energy Technology Data Exchange (ETDEWEB)
Bulatov, M.G.; Telegin, A.N.
1984-01-01
The effect of the dimensions of a processing base on the results of diffraction transformation of seismic recordings is examined. A formula is cited for rating the optimal summation base on the basis of a proposed range of slant angles of the reflecting boundaries. The recommendations for selecting a processing base are confirmed by factual material.
Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams
International Nuclear Information System (INIS)
Ablinger, Jakob; Bluemlein, Johannes; Klein, Sebastian; Schneider, Carsten
2010-01-01
By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in this task with all our concrete calculations of 2-loop and 3-loop massive single scale Feynman diagrams with local operator insertion.
Modern summation methods and the computation of 2- and 3-loop Feynman diagrams
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob; Schneider, Carsten [Linz Univ. (AT). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Klein, Sebastian [RWTH Aachen (Germany). Inst. fuer Theoretische Teilchenphysik und Kosmologie
2010-06-15
By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in this task with all our concrete calculations of 2-loop and 3-loop massive single scale Feynman diagrams with local operator insertion. (orig.)
Affordances and Constraints of Using the Socio-Political Debate for Authentic Summative Assessment
Anker-Hansen, Jens; Andrée, Maria
2015-01-01
This article reports from an empirical study on the affordances and constraints for using staged socio-political debates for authentic summative assessment of scientific literacy. The article focuses on conditions for student participation and what purposes emerge in student interaction in a socio-political debate. As part of the research project,…
Flat deformation theorem and symmetries in spacetime
International Nuclear Information System (INIS)
Llosa, Josep; Carot, Jaume
2009-01-01
The flat deformation theorem states that given a semi-Riemannian analytic metric g on a manifold, locally there always exists a two-form F, a scalar function c, and an arbitrarily prescribed scalar constraint depending on the point x of the manifold and on F and c, say Ψ(c, F, x) = 0, such that the deformed metric η = cg - εF 2 is semi-Riemannian and flat. In this paper we first show that the above result implies that every (Lorentzian analytic) metric g may be written in the extended Kerr-Schild form, namely η ab := ag ab - 2bk (a l b) where η is flat and k a , l a are two null covectors such that k a l a = -1; next we show how the symmetries of g are connected to those of η, more precisely; we show that if the original metric g admits a conformal Killing vector (including Killing vectors and homotheties), then the deformation may be carried out in a way such that the flat deformed metric η 'inherits' that symmetry.
The Michaelis-Menten-Stueckelberg Theorem
Directory of Open Access Journals (Sweden)
Alexander N. Gorban
2011-05-01
Full Text Available We study chemical reactions with complex mechanisms under two assumptions: (i intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS and (ii they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE. Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events. This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.
Low energy theorems of hidden local symmetries
International Nuclear Information System (INIS)
Harada, Masayasu; Kugo, Taichiro; Yamawaki, Koichi.
1994-01-01
We prove to all orders of the loop expansion the low energy theorems of hidden local symmetries in four-dimensional nonlinear sigma models based on the coset space G/H, with G and H being arbitrary compact groups. Although the models are non-renormalizable, the proof is done in an analogous manner to the renormalization proof of gauge theories and two-dimensional nonlinear sigma models by restricting ourselves to the operators with two derivatives (counting a hidden gauge boson field as one derivative), i.e., with dimension 2, which are the only operators relevant to the low energy limit. Through loop-wise mathematical induction based on the Ward-Takahashi identity for the BRS symmetry, we solve renormalization equation for the effective action up to dimension-2 terms plus terms with the relevant BRS sources. We then show that all the quantum corrections to the dimension-2 operators, including the finite parts as well as the divergent ones, can be entirely absorbed into a re-definition (renormalization) of the parameters and the fields in the dimension-2 part of the tree-level Lagrangian. (author)
Quantum fluctuation theorems and power measurements
International Nuclear Information System (INIS)
Prasanna Venkatesh, B; Watanabe, Gentaro; Talkner, Peter
2015-01-01
Work in the paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system’s dynamics is frozen in the power measurement basis due to the quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics. (paper)
Subexponential estimates in Shirshov's theorem on height
International Nuclear Information System (INIS)
Belov, Aleksei Ya; Kharitonov, Mikhail I
2012-01-01
Suppose that F 2,m is a free 2-generated associative ring with the identity x m =0. In 1993 Zelmanov put the following question: is it true that the nilpotency degree of F 2,m has exponential growth? We give the definitive answer to Zelmanov's question by showing that the nilpotency class of an l-generated associative algebra with the identity x d =0 is smaller than Ψ(d,d,l), where Ψ(n,d,l)=2 18 l(nd) 3log 3 (nd)+13 d 2 . This result is a consequence of the following fact based on combinatorics of words. Let l, n and d≥n be positive integers. Then all words over an alphabet of cardinality l whose length is not less than Ψ(n,d,l) are either n-divisible or contain x d ; a word W is n-divisible if it can be represented in the form W=W 0 W 1 …W n so that W 1 ,...,W n are placed in lexicographically decreasing order. Our proof uses Dilworth's theorem (according to V.N. Latyshev's idea). We show that the set of not n-divisible words over an alphabet of cardinality l has height h 87 l·n 12log 3 n+48 . Bibliography: 40 titles.
Three-Dimensional Ankle Moments and Nonlinear Summation of Rat Triceps Surae Muscles
Tijs, Chris; van Dieën, Jaap H.; Baan, Guus C.; Maas, Huub
2014-01-01
The Achilles tendon and epimuscular connective tissues mechanically link the triceps surae muscles. These pathways may cause joint moments exerted by each muscle individually not to sum linearly, both in magnitude and direction. The aims were (i) to assess effects of sagittal plane ankle angle (varied between 150° and 70°) on isometric ankle moments, in both magnitude and direction, exerted by active rat triceps surae muscles, (ii) to assess ankle moment summation between those muscles for a range of ankle angles and (iii) to assess effects of sagittal plane ankle angle and muscle activation on Achilles tendon length. At each ankle angle, soleus (SO) and gastrocnemius (GA) muscles were first excited separately to assess ankle-angle moment characteristics and subsequently both muscles were excited simultaneously to investigate moment summation. The magnitude of ankle moment exerted by SO and GA, the SO direction in the transverse and sagittal planes, and the GA direction in the transverse plane were significantly affected by ankle angle. SO moment direction in the frontal and sagittal planes were significantly different from that of GA. Nonlinear magnitude summation varied between 0.6±2.9% and −3.6±2.9%, while the nonlinear direction summation varied between 0.3±0.4° and −0.4±0.7° in the transverse plane, between 0.5±0.4° and 0.1±0.4° in the frontal plane, and between 3.0±7.9° and 0.3±2.3° in the sagittal plane. Changes in tendon length caused by SO contraction were significantly lower than those during contraction of GA and GA+SO simultaneously. Thus, moments exerted by GA and SO sum nonlinearly both in the magnitude and direction. The limited degree of nonlinear summation may be explained by different mechanisms acting in opposite directions. PMID:25360524
A non linear ergodic theorem and application to a theorem of A. Pazy
International Nuclear Information System (INIS)
Djafari Rouhani, B.
1989-07-01
We prove that if (y n )n≥1 is a sequence in a real Hilbert space H such that for every non negative integer m the sequence (parallelΣ l =0 m y i +l parallel) i≥1 is non increasing, then: s n = 1/n Σ i=1 n y i converges strongly in H to the element of minimum norm in the closed convex hull of the sequence (y n ) n≥1 . We deduce a direct proof of a result containing a theorem of A. Pazy. (author). 27 refs
International Nuclear Information System (INIS)
Halliwell, J.J.
2014-01-01
Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH inequalities are well-known to be necessary conditions, but Fine's theorem is the striking result that they are also sufficient conditions. Here two transparent and self-contained proofs of Fine's theorem are presented. The first is a physically motivated proof using an explicit local hidden variables model. The second is an algebraic proof which uses a representation of the probabilities in terms of correlation functions. - Highlights: • A discussion of the various approaches to proving Fine's theorem. • A new physically-motivated proof using a local hidden variables model. • A new algebraic proof. • A new form of the CHSH inequalities
A Coordinate-Based Proof of the Scallop Theorem
Ishimoto, Kenta; Yamada, Michio
2012-01-01
We reconsider fluid dynamics for a self-propulsive swimmer in Stokes flow. With an exact definition of deformation of a swimmer, a coordinate-based proof is first given to Purcell's scallop theorem including the body rotation.
Forest Carbon Uptake and the Fundamental Theorem of Calculus
Zobitz, John
2013-01-01
Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.
The power counting theorem for Feynman integrals with massless propagators
International Nuclear Information System (INIS)
Lowenstein, J.H.
2000-01-01
Dyson's power counting theorem is extended to the case where some of the mass parameters vanish. Weinberg's ultraviolet convergence conditions are supplemented by infrared convergence conditions which combined are sufficient for the convergence of Feynman integrals. (orig.)
The power counting theorem for Feynman integrals with massless propagators
International Nuclear Information System (INIS)
Lowenstein, J.H.
1975-01-01
Dyson's power counting theorem is extended to the case where some of the mass parameters vanish. Weinberg's ultraviolet convergence conditions are supplemented by infrared convergence conditions which combined are sufficient for the convergence of Feynman integrals. (orig.) [de
A divergence theorem for pseudo-Finsler spaces
Minguzzi, E.
2015-01-01
We study the divergence theorem on pseudo-Finsler spaces and obtain a completely Finslerian version for spaces having a vanishing mean Cartan torsion. This result helps to clarify the problem of energy-momentum conservation in Finsler gravity theories.
The Weinberg-Witten theorem on massless particles: an essay
International Nuclear Information System (INIS)
Loebbert, F.
2008-01-01
In this essay we deal with the Weinberg-Witten theorem which imposes limitations on massless particles. First we motivate a classification of massless particles given by the Poincare group as the symmetry group of Minkowski spacetime. We then use the fundamental structure of the background in the form of Poincare covariance to derive restrictions on charged massless particles known as the Weinberg-Witten theorem. We address possible misunderstandings in the proof of this theorem motivated by several papers on this topic. In the last section the consequences of the theorem are discussed. We treat it in the context of known particles and as a constraint for emergent theories. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
Integrable equations, addition theorems, and the Riemann-Schottky problem
International Nuclear Information System (INIS)
Buchstaber, Viktor M; Krichever, I M
2006-01-01
The classical Weierstrass theorem claims that, among the analytic functions, the only functions admitting an algebraic addition theorem are the elliptic functions and their degenerations. This survey is devoted to far-reaching generalizations of this result that are motivated by the theory of integrable systems. The authors discovered a strong form of the addition theorem for theta functions of Jacobian varieties, and this form led to new approaches to known problems in the geometry of Abelian varieties. It is shown that strong forms of addition theorems arise naturally in the theory of the so-called trilinear functional equations. Diverse aspects of the approaches suggested here are discussed, and some important open problems are formulated.
Generalized Optical Theorem Detection in Random and Complex Media
Tu, Jing
The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar
A priori knowledge and the Kochen-Specker theorem
International Nuclear Information System (INIS)
Brunet, Olivier
2007-01-01
We introduce and formalize a notion of 'a priori knowledge' about a quantum system, and show some properties about this form of knowledge. Finally, we show that the Kochen-Specker theorem follows directly from this study
Supersymmetric extension of the Adler-Bardeen theorem
International Nuclear Information System (INIS)
Novikov, V.A.; Zakharov, V.I.; Shifman, M.A.; Vainshtein, A.I.
1985-01-01
A supersymmetric generalization of the Adler-Bardeen theorem in SUSY gauge theories is given. We show that within the Adler-Bardeen procedure, both the conformal and axial anomalies are exhausted by one loop. (orig.)
An Elementary Proof of the Polynomial Matrix Spectral Factorization Theorem
Ephremidze, Lasha
2010-01-01
A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.
Perron–Frobenius theorem for nonnegative multilinear forms and extensions
Friedland, S.; Gaubert, S.; Han, L.
2013-01-01
We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector.
Analogy to Derive an Extended Pythagorean Theorem to ''N'' Dimensions
Directory of Open Access Journals (Sweden)
Acosta-Robledo J.U.
2012-01-01
Full Text Available This article demonstrates that it is possible to extend the Pythagorean Theorem to ''N'' dimensions. This demonstration is mainly done based on linear algebra, especially in the vector product of ''N'' dimensions.
Quantum nonlocality and reality 50 years of Bell's theorem
Gao, Shan
2016-01-01
Description Contents Resources Courses About the Authors Combining twenty-six original essays written by an impressive line-up of distinguished physicists and philosophers of physics, this anthology reflects some of the latest thoughts by leading experts on the influence of Bell's theorem on quantum physics. Essays progress from John Bell's character and background, through studies of his main work, and on to more speculative ideas, addressing the controversies surrounding the theorem, and investigating the theorem's meaning and its deep implications for the nature of physical reality. Combined, they present a powerful comment on the undeniable significance of Bell's theorem for the development of ideas in quantum physics over the past 50 years. Questions surrounding the assumptions and significance of Bell's work still inspire discussion in the field of quantum physics. Adding to this with a theoretical and philosophical perspective, this balanced anthology is an indispensable volume for students and researc...
An imbedding theorem and its applications in degenerate elliptic equations
International Nuclear Information System (INIS)
Duong Minh Duc.
1988-06-01
We improve the Rellich-Kondrachov theorem and apply it to study strongly degenerate and singular elliptic equations. We obtain the maximum principle, Harnacks's inequality and global regularity for solutions of those equations. (author). 11 refs
Quantum work fluctuation theorem: Nonergodic Brownian motion case
International Nuclear Information System (INIS)
Bai, Zhan-Wu
2014-01-01
The work fluctuations of a quantum Brownian particle driven by an external force in a general nonergodic heat bath are studied under a general initial state. The exact analytical expression of the work probability distribution function is derived. Results show the existence of a quantum asymptotic fluctuation theorem, which is in general not a direct generalization of its classical counterpart. The form of this theorem is dependent on the structure of the heat bath and the specified initial condition.
Probability densities and the radon variable transformation theorem
International Nuclear Information System (INIS)
Ramshaw, J.D.
1985-01-01
D. T. Gillespie recently derived a random variable transformation theorem relating to the joint probability densities of functionally dependent sets of random variables. The present author points out that the theorem can be derived as an immediate corollary of a simpler and more fundamental relation. In this relation the probability density is represented as a delta function averaged over an unspecified distribution of unspecified internal random variables. The random variable transformation is derived from this relation
A short list color proof of Grotzsch's theorem
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable.......We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable....
Locally Hamiltonian systems with symmetry and a generalized Noether's theorem
International Nuclear Information System (INIS)
Carinena, J.F.; Ibort, L.A.
1985-01-01
An analysis of global aspects of the theory of symmetry groups G of locally Hamiltonian dynamical systems is carried out for particular cases either of the symmetry group, or the differentiable manifold M supporting the symplectic structure, or the action of G on M. In every case it is obtained a generalization of Noether's theorem. It has been looked at the classical Noether's theorem for Lagrangian systems from a modern perspective
Metrical theorems on systems of small inhomogeneous linear forms
DEFF Research Database (Denmark)
Hussain, Mumtaz; Kristensen, Simon
In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed.......In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed....
Extension and reconstruction theorems for the Urysohn universal metric space
Czech Academy of Sciences Publication Activity Database
Kubiś, Wieslaw; Rubin, M.
2010-01-01
Roč. 60, č. 1 (2010), s. 1-29 ISSN 0011-4642 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Urysohn space * bilipschitz homeomorphism * modulus of continuity * reconstruction theorem * extension theorem Subject RIV: BA - General Mathematics Impact factor: 0.265, year: 2010 http://dml.cz/handle/10338.dmlcz/140544
A New Simple Approach for Entropy and Carnot Theorem
International Nuclear Information System (INIS)
Veliev, E. V.
2004-01-01
Entropy and Carnot theorem occupy central place in the typical Thermodynamics courses at the university level. In this work, we suggest a new simple approach for introducing the concept of entropy. Using simple procedure in TV plane, we proved that for reversible processes ∫dQ/T=0 and it is sufficient to define entropy. And also, using reversible processes in TS plane, we give an alternative simple proof for Carnot theorem
On the c-theorem in higher genus
International Nuclear Information System (INIS)
Espriu, D.; Mavromatos, N.E.
1990-01-01
We study the extension of the c-therorem to arbitrary genus Riemann surfaces. We analyze the breakdown of conformal invariance caused by the need of cutting off regions of moduli space to regulate divergences and argue how these can be absorbed in the bare couplings on the sphere. An extension of the c-theorem then follows. We also discuss the relationship between the c-theorem and the effective action when corrections from higher genera are accounted for. (orig.)
Some functional limit theorems for compound Cox processes
Energy Technology Data Exchange (ETDEWEB)
Korolev, Victor Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Institute of Informatics Problems FRC CSC RAS (Russian Federation); Chertok, A. V. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Euphoria Group LLC (Russian Federation); Korchagin, A. Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Kossova, E. V. [Higher School of Economics National Research University, Moscow (Russian Federation); Zeifman, Alexander I. [Vologda State University, S.Orlova, 6, Vologda (Russian Federation); Institute of Informatics Problems FRC CSC RAS, ISEDT RAS (Russian Federation)
2016-06-08
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
Some functional limit theorems for compound Cox processes
International Nuclear Information System (INIS)
Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.
2016-01-01
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
Cosmological constant, inflation and no-cloning theorem
Energy Technology Data Exchange (ETDEWEB)
Huang Qingguo, E-mail: huangqg@itp.ac.cn [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Science, Beijing 100190 (China); Lin Fengli, E-mail: linfengli@phy.ntnu.edu.tw [Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Department of Physics, National Taiwan Normal University, Taipei, 116, Taiwan (China)
2012-05-30
From the viewpoint of no-cloning theorem we postulate a relation between the current accelerated expansion of our universe and the inflationary expansion in the very early universe. It implies that the fate of our universe should be in a state with accelerated expansion. Quantitatively we find that the no-cloning theorem leads to a lower bound on the cosmological constant which is compatible with observations.
The Hellman-Feynman theorem at finite temperature
International Nuclear Information System (INIS)
Cabrera, A.; Calles, A.
1990-01-01
The possibility of a kind of Hellman-Feynman theorem at finite temperature is discussed. Using the cannonical ensembles, the derivative of the internal energy is obtained when it depends explicitly on a parameter. It is found that under the low temperature regime the derivative of the energy can be obtained as the statistical average of the derivative of the hamiltonian operator. The result allows to speak of the existence of the Hellman-Feynman theorem at finite temperatures (Author)
Generalized Perron--Frobenius Theorem for Nonsquare Matrices
Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David
2013-01-01
The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the...
Generalized Panofsky-Wenzel theorem and hybrid coupling
Smirnov, A V
2001-01-01
The Panofsky-Wenzel theorem is reformulated for the case in which phase slippage between the wave and beam is not negligible. The extended theorem can be applied in analysis of detuned waveguides, RF injectors, bunchers, some tapered waveguides or high-power sources and multi-cell cavities for dipole and higher order modes. As an example, the relative contribution of the Lorentz' component of the deflecting force is calculated for a conventional circular disk-loaded waveguide.
On the first case of Fermat's theorem for cyclotomic fields
International Nuclear Information System (INIS)
Kolyvagin, V A
1999-01-01
The classical criteria of Kummer, Mirimanov and Vandiver for the validity of the first case of Fermat's theorem for the field Q of rationals and prime exponent l are generalized to the field Q( l √1) and exponent l. As a consequence, some simpler criteria are established. For example, the validity of the first case of Fermat's theorem is proved for the field Q( l √1) and exponent l on condition that l 2 does not divide 2 l -2
Factorization theorems in perturbative quantum field theory
International Nuclear Information System (INIS)
Date, G.D.
1982-01-01
This dissertation deals with factorization properties of Green functions and cross-sections in perturbation theory. It consists of two parts. Part I deals with the factorization theorem for the Drell-Yan cross-section. The new approach developed for this purpose is based upon a renormalization group equation with a generalized anomalous dimension. Using an alternate form of factorization for the Drell-Yan cross-section, derived in perturbation theory, a corresponding generalized anomalous dimension is defined, and explicit Feynman rules for its calculation are given. The resultant renormalization group equation is solved by a formal solution which is exhibited explicitly. Simple, explicit calculations are performed which verify Mueller's conjecture for the recovery of the usual parton model results for the Drell-Yan cross-section. The approach developed in this work offers a general framework to analyze the role played by the group factors in the cancellation of the soft divergences, and study their influence on the asymptotic behavior. Part II deals with factorization properties of the Green functions in position space. In this part, a Landau equation analysis is carried out for the singularities of the position space Green fucntions, in perturbation theory with the theta 4 interaction Lagrangian. A physical picture interpretation is given for the corresponding Landau equations. It is used to suggest a light-cone expansion. Using a power counting method, a formal derivation of the light-cone expansion for the two point function, the three point function and a product of two currents, is given without assuming a short distance expansion. Possible extensions to other theories is also considered
Experimental Results and Numerical Simulation of the Target RCS using Gaussian Beam Summation Method
Directory of Open Access Journals (Sweden)
Ghanmi Helmi
2018-05-01
Full Text Available This paper presents a numerical and experimental study of Radar Cross Section (RCS of radar targets using Gaussian Beam Summation (GBS method. The purpose GBS method has several advantages over ray method, mainly on the caustic problem. To evaluate the performance of the chosen method, we started the analysis of the RCS using Gaussian Beam Summation (GBS and Gaussian Beam Launching (GBL, the asymptotic models Physical Optic (PO, Geometrical Theory of Diffraction (GTD and the rigorous Method of Moment (MoM. Then, we showed the experimental validation of the numerical results using experimental measurements which have been executed in the anechoic chamber of Lab-STICC at ENSTA Bretagne. The numerical and experimental results of the RCS are studied and given as a function of various parameters: polarization type, target size, Gaussian beams number and Gaussian beams width.
Arthur, Winfred; Cho, Inchul; Muñoz, Gonzalo J
2016-10-01
We examined the so-called "red effect" in the context of higher education summative exams under the premise that unlike the conditions or situations where this effect typically has been obtained, the totality of factors, such as higher motivation, familiarity with exam material, and more reliance on domain knowledge that characterize high-stakes testing such as those in operational educational settings, are likely to mitigate any color effects. Using three naturally occurring archival data sets in which students took exams on either red or green exam booklets, the results indicated that booklet color (red vs. green) did not affect exam performance. From a scientific perspective, the results suggest that color effects may be attenuated by factors that characterize high-stakes assessments, and from an applied perspective, they suggest that the choice of red vs. green exam booklets in higher education summative evaluations is likely not a concern.
Renormalization group summation of Laplace QCD sum rules for scalar gluon currents
Directory of Open Access Journals (Sweden)
Farrukh Chishtie
2016-03-01
Full Text Available We employ renormalization group (RG summation techniques to obtain portions of Laplace QCD sum rules for scalar gluon currents beyond the order to which they have been explicitly calculated. The first two of these sum rules are considered in some detail, and it is shown that they have significantly less dependence on the renormalization scale parameter μ2 once the RG summation is used to extend the perturbative results. Using the sum rules, we then compute the bound on the scalar glueball mass and demonstrate that the 3 and 4-Loop perturbative results form lower and upper bounds to their RG summed counterparts. We further demonstrate improved convergence of the RG summed expressions with respect to perturbative results.
Hyperalgesia and temporal summation of pain after heat injury in man
DEFF Research Database (Denmark)
Pedersen, J L; Andersen, O K; Arendt-Nielsen, L
1998-01-01
of pain in normal skin with summation of pain in skin with primary and secondary hyperalgesia evoked by a heat injury. A heat injury was produced on the crus of 12 volunteers with a 50 x 25 mm thermode (47 degrees C, 7 min). Measurements were made before, and 0, 1, 2, and 4 h after the heat injury......, in three areas: primary and secondary mechanical hyperalgesia induced by the heat injury, and in a mirror image of the injury on the opposite leg. Temporal summation of pain was induced by repeated electrical stimuli (five stimuli at 2 Hz) and assessed by visual analog scale (VAS). Primary hyperalgesia...... was evaluated by von Frey hairs and electrical stimuli, and the areas of secondary hyperalgesia with a rigid von Frey hair (314 mN). Significant primary (P heat injury. The pain threshold to single electrical stimuli was reduced...
Solution of systems of linear algebraic equations by the method of summation of divergent series
International Nuclear Information System (INIS)
Kirichenko, G.A.; Korovin, Ya.S.; Khisamutdinov, M.V.; Shmojlov, V.I.
2015-01-01
A method for solving systems of linear algebraic equations has been proposed on the basis on the summation of the corresponding continued fractions. The proposed algorithm for solving systems of linear algebraic equations is classified as direct algorithms providing an exact solution in a finite number of operations. Examples of solving systems of linear algebraic equations have been presented and the effectiveness of the algorithm has been estimated [ru
Theta frequency background tunes transmission but not summation of spiking responses.
Directory of Open Access Journals (Sweden)
Dhanya Parameshwaran
Full Text Available Hippocampal neurons are known to fire as a function of frequency and phase of spontaneous network rhythms, associated with the animal's behaviour. This dependence is believed to give rise to precise rate and temporal codes. However, it is not well understood how these periodic membrane potential fluctuations affect the integration of synaptic inputs. Here we used sinusoidal current injection to the soma of CA1 pyramidal neurons in the rat brain slice to simulate background oscillations in the physiologically relevant theta and gamma frequency range. We used a detailed compartmental model to show that somatic current injection gave comparable results to more physiological synaptically driven theta rhythms incorporating excitatory input in the dendrites, and inhibitory input near the soma. We systematically varied the phase of synaptic inputs with respect to this background, and recorded changes in response and summation properties of CA1 neurons using whole-cell patch recordings. The response of the cell was dependent on both the phase of synaptic inputs and frequency of the background input. The probability of the cell spiking for a given synaptic input was up to 40% greater during the depolarized phases between 30-135 degrees of theta frequency current injection. Summation gain on the other hand, was not affected either by the background frequency or the phasic afferent inputs. This flat summation gain, coupled with the enhanced spiking probability during depolarized phases of the theta cycle, resulted in enhanced transmission of summed inputs during the same phase window of 30-135 degrees. Overall, our study suggests that although oscillations provide windows of opportunity to selectively boost transmission and EPSP size, summation of synaptic inputs remains unaffected during membrane oscillations.
Effective Summation and Interpolation of Series by Self-Similar Root Approximants
Directory of Open Access Journals (Sweden)
Simon Gluzman
2015-06-01
Full Text Available We describe a simple analytical method for effective summation of series, including divergent series. The method is based on self-similar approximation theory resulting in self-similar root approximants. The method is shown to be general and applicable to different problems, as is illustrated by a number of examples. The accuracy of the method is not worse, and in many cases better, than that of Padé approximants, when the latter can be defined.
Hadronic total cross-sections through soft gluon summation in impact parameter space
International Nuclear Information System (INIS)
Grau, A.
1999-01-01
IThe Bloch-Nordsieck model for the parton distribution of hadrons in impact parameter space, constructed using soft gluon summation, is investigated in detail. Its dependence upon the infrared structure of the strong coupling constant α s is discussed, both for finite as well as singular, but integrable, α s . The formalism is applied to the prediction of total proton-proton and proton-antiproton cross-sections, where screening, due to soft gluon emission from the initial valence quarks, becomes evident
Changing the culture of assessment: the dominance of the summative assessment paradigm
Harrison, Christopher J.; Konings, Karen D.; Schuwirth, Lambert W. T.; Wass, Valerie; van der Vleuten, Cees P. M.
2017-01-01
BACKGROUND: Despite growing evidence of the benefits of including assessment for learning strategies within programmes of assessment, practical implementation of these approaches is often problematical. Organisational culture change is often hindered by personal and collective beliefs which encourage adherence to the existing organisational paradigm. We aimed to explore how these beliefs influenced proposals to redesign a summative assessment culture in order to improve students' use of asses...
Changing the culture of assessment: the dominance of the summative assessment paradigm.
Harrison, Christopher J; Könings, Karen D; Schuwirth, Lambert W T; Wass, Valerie; van der Vleuten, Cees P M
2017-04-28
Despite growing evidence of the benefits of including assessment for learning strategies within programmes of assessment, practical implementation of these approaches is often problematical. Organisational culture change is often hindered by personal and collective beliefs which encourage adherence to the existing organisational paradigm. We aimed to explore how these beliefs influenced proposals to redesign a summative assessment culture in order to improve students' use of assessment-related feedback. Using the principles of participatory design, a mixed group comprising medical students, clinical teachers and senior faculty members was challenged to develop radical solutions to improve the use of post-assessment feedback. Follow-up interviews were conducted with individual members of the group to explore their personal beliefs about the proposed redesign. Data were analysed using a socio-cultural lens. Proposed changes were dominated by a shared belief in the primacy of the summative assessment paradigm, which prevented radical redesign solutions from being accepted by group members. Participants' prior assessment experiences strongly influenced proposals for change. As participants had largely only experienced a summative assessment culture, they found it difficult to conceptualise radical change in the assessment culture. Although all group members participated, students were less successful at persuading the group to adopt their ideas. Faculty members and clinical teachers often used indirect techniques to close down discussions. The strength of individual beliefs became more apparent in the follow-up interviews. Naïve epistemologies and prior personal experiences were influential in the assessment redesign but were usually not expressed explicitly in a group setting, perhaps because of cultural conventions of politeness. In order to successfully implement a change in assessment culture, firmly-held intuitive beliefs about summative assessment will need to
International Nuclear Information System (INIS)
Wolf, D.; Keblinski, P.; Phillpot, S.R.; Eggebrecht, J.
1999-01-01
Based on a recent result showing that the net Coulomb potential in condensed ionic systems is rather short ranged, an exact and physically transparent method permitting the evaluation of the Coulomb potential by direct summation over the r -1 Coulomb pair potential is presented. The key observation is that the problems encountered in determining the Coulomb energy by pairwise, spherically truncated r -1 summation are a direct consequence of the fact that the system summed over is practically never neutral. A simple method is developed that achieves charge neutralization wherever the r -1 pair potential is truncated. This enables the extraction of the Coulomb energy, forces, and stresses from a spherically truncated, usually charged environment in a manner that is independent of the grouping of the pair terms. The close connection of our approach with the Ewald method is demonstrated and exploited, providing an efficient method for the simulation of even highly disordered ionic systems by direct, pairwise r -1 summation with spherical truncation at rather short range, i.e., a method which fully exploits the short-ranged nature of the interactions in ionic systems. The method is validated by simulations of crystals, liquids, and interfacial systems, such as free surfaces and grain boundaries. copyright 1999 American Institute of Physics
Subiaul, Francys; Krajkowski, Edward; Price, Elizabeth E; Etz, Alexander
2015-01-01
Children are exceptional, even 'super,' imitators but comparatively poor independent problem-solvers or innovators. Yet, imitation and innovation are both necessary components of cumulative cultural evolution. Here, we explored the relationship between imitation and innovation by assessing children's ability to generate a solution to a novel problem by imitating two different action sequences demonstrated by two different models, an example of imitation by combination, which we refer to as "summative imitation." Children (N = 181) from 3 to 5 years of age and across three experiments were tested in a baseline condition or in one of six demonstration conditions, varying in the number of models and opening techniques demonstrated. Across experiments, more than 75% of children evidenced summative imitation, opening both compartments of the problem box and retrieving the reward hidden in each. Generally, learning different actions from two different models was as good (and in some cases, better) than learning from 1 model, but the underlying representations appear to be the same in both demonstration conditions. These results show that summative imitation not only facilitates imitation learning but can also result in new solutions to problems, an essential feature of innovation and cumulative culture.
Massey, Scott; Stallman, John; Lee, Louise; Klingaman, Kathy; Holmerud, David
2011-01-01
This paper describes how a systematic analysis of students at risk for failing the Physician Assistant National Certifying Examination (PANCE) may be used to identify which students may benefit from intervention prior to taking the PANCE and thus increase the likelihood of successful completion of the PANCE. The intervention developed and implemented uses various formative and summative examinations to predict students' PANCE scores with a high degree of accuracy. Eight end-of-rotation exams (EOREs) based upon discipline-specific diseases and averaging 100 questions each, a 360-question PANCE simulation (SUMM I), the PACKRAT, and a 700-question summative cognitive examination based upon the NCCPA blueprint (SUMM II) were administered to all students enrolled in the program during the clinical year starting in January 2010 and concluding in December 2010. When the PACKRAT, SUMM I, SUMM II, and the surgery, women's health, and pediatrics EOREs were combined in a regression model, an Rvalue of 0.87 and an R2 of 0.75 were obtained. A predicted score was generated for the class of 2009. The predicted PANCE score based upon this model had a final correlation of 0.790 with the actual PANCE score. This pilot study demonstrated that valid predicted scores could be generated from formative and summative examinations to provide valuable feedback and to identify students at risk of failing the PANCE.
Formalization of the Integral Calculus in the PVS Theorem Prover
Directory of Open Access Journals (Sweden)
Ricky Wayne Butler
2009-04-01
Full Text Available The PVS Theorem prover is a widely used formal verification tool used for the analysis of safetycritical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht’s classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
Formalization of the Integral Calculus in the PVS Theorem Prover
Butler, Ricky W.
2004-01-01
The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
The Goldstone equivalence theorem and AdS/CFT
Energy Technology Data Exchange (ETDEWEB)
Anand, Nikhil; Cantrell, Sean [Department of Physics & Astronomy, Johns Hopkins University,Baltimore, MD 21218 (United States)
2015-08-03
The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the non-conserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields. We then go on to generalize the theorem using conformal blocks in two and four-dimensional CFTs. We show that when the scaling dimensions of the exchanged operators are large compared to both their spins and the dimension of the current, the conformal blocks satisfy an equivalence theorem.
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).
Isna Nur Hikmah; Usep Kustiawan
2016-01-01
The reseach’s purpose was to analyze the effect of picture numeric card media toward improvement of the summation computation ability for student with intellectual disability of grade IV in SDLB. Data collected was analyzed with experiment technique and single subject research A-B design. Research result showed that: after being analyzed between condition overlap persentase was 0%. Thus, it could be concluded that there was effect of pictorial numeric card media toward summation computation a...
Quantum de Finetti theorem in phase-space representation
International Nuclear Information System (INIS)
Leverrier, Anthony; Cerf, Nicolas J.
2009-01-01
The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
Fourier diffraction theorem for diffusion-based thermal tomography
International Nuclear Information System (INIS)
Baddour, Natalie
2006-01-01
There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging
More on Weinberg's no-go theorem in quantum gravity
Nagahama, Munehiro; Oda, Ichiro
2018-05-01
We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.
Noncommutative gauge field theories: A no-go theorem
International Nuclear Information System (INIS)
Chaichian, M.; Tureanu, A.; Presnajder, P.; Sheikh-Jabbari, M.M.
2001-06-01
Studying the mathematical structure of the noncommutative groups in more detail, we prove a no-go theorem for the noncommutative gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local noncommutative u(n) algebra only admits the irreducible nxn matrix-representation. Hence the gauge fields, as elements of the algebra, are in nxn matrix form, while the matter fields can only be either in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple group factors, the matter fields can transform nontrivially under at most two noncommutative group factors. In other words, the matter fields cannot carry more than two simple noncommutative gauge group charges. This no-go theorem imposes strong restrictions on the construction of the noncommutative version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED. (author)
Deviations from Wick's theorem in the canonical ensemble
Schönhammer, K.
2017-07-01
Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.
An improved version of the Mar otto Theorem
International Nuclear Information System (INIS)
Li Changpin; Chen Guanrong
2003-01-01
In 1975, Li and Yorke introduced the first precise definition of discrete chaos and established a very simple criterion for chaos in one-dimensional difference equations, 'period three implies chaos' for brevity. After three years. Marotto generalized this result to n-dimensional difference equations, showing that the existence of a snap-back repeller implies chaos in the sense of Li-Yorke. This theorem is up to now the best one in predicting and analyzing discrete chaos in multidimensional difference equations. Yet, it is well known that there exists an error in the condition of the original Marotto Theorem, and several authors had tried to correct it in different ways. In this paper, we further clarify the issue, with an improved version of the Marotto Theorem derived
Out-of-time-order fluctuation-dissipation theorem
Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito
2018-01-01
We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.
Kochen-Specker theorem studied with neutron interferometer.
Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut
2011-04-01
The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
Kochen-Specker theorem studied with neutron interferometer
Energy Technology Data Exchange (ETDEWEB)
Hasegawa, Yuji, E-mail: Hasegawa@ati.ac.a [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria); Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria)
2011-04-01
The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291{+-}0.008 not {<=} 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
Limit theorems for multi-indexed sums of random variables
Klesov, Oleg
2014-01-01
Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who ...
Some commutativity theorems for a certain class of rings
International Nuclear Information System (INIS)
Khan, M.A.
1994-08-01
In the present paper we first establish the commutativity theorem for semiprime ring satisfying the polynomial identity [x n ,y]x r = ±y s [x,y m ]y t for all x,y in R, where m,n,r,s and t are fixed nonnegative integers, and further, we investigate commutativity of rings with unity under some additional hypothesis. Moreover, it is also shown that the above result is true for s-unital. Also, we provide some counter examples which show that the hypothesis of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital. (author). 21 refs
A general product measurability theorem with applications to variational inequalities
Directory of Open Access Journals (Sweden)
Kenneth L. Kuttler
2016-03-01
Full Text Available This work establishes the existence of measurable weak solutions to evolution problems with randomness by proving and applying a novel theorem on product measurability of limits of sequences of functions. The measurability theorem is used to show that many important existence theorems within the abstract theory of evolution inclusions or equations have straightforward generalizations to settings that include random processes or coefficients. Moreover, the convex set where the solutions are sought is not fixed but may depend on the random variables. The importance of adding randomness lies in the fact that real world processes invariably involve randomness and variability. Thus, this work expands substantially the range of applications of models with variational inequalities and differential set-inclusions.
Kochen-Specker theorem studied with neutron interferometer
International Nuclear Information System (INIS)
Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut
2011-01-01
The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008 not ≤ 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
Zamolodchikov's c-theorem and string effective actions
International Nuclear Information System (INIS)
Mavromatos, N.E.; Miramontes, J.L.
1988-01-01
Zamolodchikov's c-theorem for 2D renormalisable field theories is presented in a way which allows for a straightforward application to the case of bosonic σ-models. As a consistency check in the latter case, the Curci-Paffuti relation is rederived. It is also shown that the 'metric' in coupling constant space in this case is a c-number function of the backgrounds. Attempts to derive off-shell functional relations between the Weyl anomaly coefficients and field variations of string effective actions, compatible with the c-theorem, are discussed by emphasising the necessity of performing explicit perturbative calculations in order to arrive at definite conclusions. Comments concerning the extension of the c-theorem to the case of supersymmetric and heterotic σ-models are also made. (orig.)
Towards a Novel no-hair Theorem for Black Holes
Hertog, T
2006-01-01
We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.
Non-renormalization theorems andN=2 supersymmetric backgrounds
International Nuclear Information System (INIS)
Butter, Daniel; Wit, Bernard de; Lodato, Ivano
2014-01-01
The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed
Radon transformation on reductive symmetric spaces:Support theorems
DEFF Research Database (Denmark)
Kuit, Job Jacob
2013-01-01
We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and derive support theorems for these transforms. A reductive symmetric space is a homogeneous space G/H for a reductive Lie group G of the Harish-Chandra class, where H is an open sub...... is based on the relation between the Radon transform and the Fourier transform on G/H, and a Paley–Wiener-shift type argument. Our results generalize the support theorem of Helgason for the Radon transform on a Riemannian symmetric space....
Reasoning by analogy as an aid to heuristic theorem proving.
Kling, R. E.
1972-01-01
When heuristic problem-solving programs are faced with large data bases that contain numbers of facts far in excess of those needed to solve any particular problem, their performance rapidly deteriorates. In this paper, the correspondence between a new unsolved problem and a previously solved analogous problem is computed and invoked to tailor large data bases to manageable sizes. This paper outlines the design of an algorithm for generating and exploiting analogies between theorems posed to a resolution-logic system. These algorithms are believed to be the first computationally feasible development of reasoning by analogy to be applied to heuristic theorem proving.
Refinement of Representation Theorems for Context-Free Languages
Fujioka, Kaoru
In this paper, we obtain some refinement of representation theorems for context-free languages by using Dyck languages, insertion systems, strictly locally testable languages, and morphisms. For instance, we improved the Chomsky-Schützenberger representation theorem and show that each context-free language L can be represented in the form L = h (D ∩ R), where D is a Dyck language, R is a strictly 3-testable language, and h is a morphism. A similar representation for context-free languages can be obtained, using insertion systems of weight (3, 0) and strictly 4-testable languages.
On the proof of the first Carnot theorem in thermodynamics
International Nuclear Information System (INIS)
Morad, M R; Momeni, F
2013-01-01
The proof of the first Carnot theorem in classical thermodynamics is revisited in this study. The underlying conditions of a general proof of this principle presented by Senft (1978 Phys. Educ. 13 35–37) are explored and discussed. These conditions are analysed in more detail using a physical description of heat and work to present a simpler proof of the first principle prior to using the violation of the second law of thermodynamics. Finally, a new simple proof is also presented based on Gibbs relation. This discussion will benefit the teaching of classical thermodynamics and promote better understanding of the proof of the first Carnot theorem in general form. (paper)
Strong limit theorems in noncommutative L2-spaces
Jajte, Ryszard
1991-01-01
The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.
Vanishing theorems and effective results in algebraic geometry
International Nuclear Information System (INIS)
Demailly, J.P.; Goettsche, L.; Lazarsfeld, R.
2001-01-01
The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks
Bell's theorem based on a generalized EPR criterion of reality
International Nuclear Information System (INIS)
Eberhard, P.H.; Rosselet, P.
1995-01-01
First, the demonstration of Bell's theorem, i.e., of the nonlocal character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedanken experiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almost with certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future
Poisson's theorem and integrals of KdV equation
International Nuclear Information System (INIS)
Tasso, H.
1978-01-01
Using Poisson's theorem it is proved that if F = integral sub(-infinity)sup(+infinity) T(u,usub(x),...usub(n,t))dx is an invariant functional of KdV equation, then integral sub(-infinity)sup(+infinity) delta F/delta u dx integral sub(-infinity)sup(+infinity) delta T/delta u dx is also an invariant functional. In the case of a polynomial T, one finds in a simple way the known recursion ΔTr/Δu = Tsub(r-1). This note gives an example of the usefulness of Poisson's theorem. (author)
Testing subleading multiple soft graviton theorem for CHY prescription
Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay
2018-01-01
In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.
A variational proof of Thomson's theorem
Energy Technology Data Exchange (ETDEWEB)
Fiolhais, Miguel C.N., E-mail: miguel.fiolhais@cern.ch [Department of Physics, City College of the City University of New York, 160 Convent Avenue, New York, NY 10031 (United States); Department of Physics, New York City College of Technology, 300 Jay Street, Brooklyn, NY 11201 (United States); LIP, Department of Physics, University of Coimbra, 3004-516 Coimbra (Portugal); Essén, Hanno [Department of Mechanics, Royal Institute of Technology (KTH), Stockholm SE-10044 (Sweden); Gouveia, Tomé M. [Cavendish Laboratory, 19 JJ Thomson Avenue, Cambridge CB3 0HE (United Kingdom)
2016-08-12
Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.
Dispersive approach to the axial anomaly and nonrenormalization theorem
International Nuclear Information System (INIS)
Pasechnik, R.S.; Teryaev, O.V.
2006-01-01
Anomalous triangle graphs for the divergence of the axial-vector current are studied using the dispersive approach generalized for the case of higher orders of perturbation theory. The validity of this procedure is proved up to the two-loop level. By direct calculation in the framework of dispersive approach we have obtained that the two-loop axial-vector-vector (AVV) amplitude is equal to zero. According to the Vainshtein's theorem, the transversal part of the anomalous triangle is not renormalized in the chiral limit. We generalize this theorem for the case of finite fermion mass in the triangle loop
Convergence theorems for Banach space valued integrable multifunctions
Directory of Open Access Journals (Sweden)
Nikolaos S. Papageorgiou
1987-01-01
Full Text Available In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω (1≤p≤∞. Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.
A generalized integral fluctuation theorem for general jump processes
International Nuclear Information System (INIS)
Liu Fei; Ouyang Zhongcan; Luo Yupin; Huang Mingchang
2009-01-01
Using the Feynman-Kac and Cameron-Martin-Girsanov formulae, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Unlike the latter approach that has been extensively employed in the existing literature, our approach can naturally bring out the definition of a time reversal of a Markovian stochastic system. Additionally, we find that the robust GIFT usually does not result in a detailed fluctuation theorem. (fast track communication)
Twelve years before the quantum no-cloning theorem
Ortigoso, Juan
2018-03-01
The celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Found. Phys. 1, 23-33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park's demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning.
Two theorems on flat space-time gravitational theories
International Nuclear Information System (INIS)
Castagnino, M.; Chimento, L.
1980-01-01
The first theorem states that all flat space-time gravitational theories must have a Lagrangian with a first term that is an homogeneous (degree-1) function of the 4-velocity usup(i), plus a functional of nsub(ij)usup(i)usup(j). The second theorem states that all gravitational theories that satisfy the strong equivalence principle have a Lagrangian with a first term gsub(ij)(x)usup(i)usup(j) plus an irrelevant term. In both cases the theories must issue from a unique variational principle. Therefore, under this condition it is impossible to find a flat space-time theory that satisfies the strong equivalence principle. (author)
Bell's theorem based on a generalized EPR criterion of reality
International Nuclear Information System (INIS)
Eberhard, P.H.; Rosselet, P.
1993-04-01
First, the demonstration of Bell's theorem, i.e. of the non-local character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedanken experiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almost with certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future. (author) 1 fig., 11 refs
Vanishing theorems and effective results in algebraic geometry
Energy Technology Data Exchange (ETDEWEB)
Demailly, J P [Universite de Grenoble (France); Goettsche, L [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Lazarsfeld, R [University of Michigan (United States)
2001-12-15
The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks.
Restriction Theorem for Principal bundles in Arbitrary Characteristic
DEFF Research Database (Denmark)
Gurjar, Sudarshan
2015-01-01
The aim of this paper is to prove two basic restriction theorem for principal bundles on smooth projective varieties in arbitrary characteristic generalizing the analogues theorems of Mehta-Ramanathan for vector bundles. More precisely, let G be a reductive algebraic group over an algebraically...... closed field k and let X be a smooth, projective variety over k together with a very ample line bundle O(1). The main result of the paper is that if E is a semistable (resp. stable) principal G-bundle on X w.r.t O(1), then the restriction of E to a general, high multi-degree, complete-intersection curve...
Bar-Shalita, T; Vatine, J-J; Yarnitsky, D; Parush, S; Weissman-Fogel, I
2014-02-01
Sensory over-responsivity (SOR), a subtype of the proposed sensory modulation disorder (SMD), is characterized by over-responsiveness to stimuli in several sensory modalities. SMD individuals demonstrate abnormal responses to naturally occurring stimuli in a manner that interferes with daily life participation. Previous psychophysical testing of the somatosensory system revealed that SOR individuals rated pain sensations higher than controls, demonstrating hyperalgesia that can be centrally mediated. Temporal summation (TS) of second pain and after-sensation are manifestations of central sensitization; therefore, this study explored these measures for better characterization of central pain processing in SOR. Twelve SOR adults and 12 healthy controls participated. TS was produced by a train of fifteen repetitive heat pulses, 0.7 s duration each, and 2 s of inter-stimulus interval, applied to the thenar-eminence, while four pain ratings were obtained. An after-sensation was then measured for 5 min, obtaining six pain ratings. No TS of pain was indicated in the SOR group (SOR: p = 0.36; control: p sensation, individuals with SOR continued to report pain for the duration of the 5 min measured (p = 0.002). These results demonstrate an atypical response pattern, suggesting alteration in pain processing and/or modulation at a central level in individuals with SOR. These possible neural changes may manifest themselves as interference with daily functioning as well as shed light on some of the between-subject variability seen in psychophysical testing in non-painful subjects.
Effectiveness of MnemoPow (Mnemonics Power Device in Teaching Limit Theorems of Calculus
Directory of Open Access Journals (Sweden)
Aldrin John J. Estonanto
2017-11-01
Full Text Available Calculus is oftentimes avoided by most students due to the common notion of its difficulty as a subject. Likewise, some studies revealed that most students find the topics in this subject very abstract to understand. To address these problems, a mnemonic device called MnemoPow (Mnemonics Power was developed. A quasi- experimental study was conducted in the laboratory high school of one state college in Sorsogon City to evaluate the effectiveness of the proposed mnemonic device. Two classes composed of forty- five (n= 45 students each were involved in this study as controlled and experimental group. The controlled group was introduced to Limit Theorems of Calculus using traditional lecture method while the experimental group was exposed to MnemoPow Device. Results of Pretest and Posttest were tested using t- test at 0. 05 level. Findings revealed that there is a significant difference between the performance of both groups. MnemoPow Device was found to be an effective approach in teaching Limit Theorems in Calculus.
Natural relations and Appelquist-Carazzone decoupling theorem
International Nuclear Information System (INIS)
Grzadkowski, B.; Krawczyk, P.; Pokorski, S.
1984-01-01
It is pointed out that in some cases violation of the Appelquist-Carazzone decoupling theorem in spontaneously broken gauge theories is related to the presence in such theories of the so-called natural zeroth-order relations. In this context heavy-fermion effects in the Glashow-Salam-Weinberg model are discussed
The Completeness Theorem of Gödel - An Introduction to ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 7. The Completeness Theorem of Gödel - An Introduction to Mathematical Logic. S M Srivastava. General Article Volume 6 Issue 7 July 2001 pp 29-41. Fulltext. Click here to view fulltext PDF. Permanent link:
Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos
Boozer, A. D.
2011-01-01
We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…
Quantum golden field theory - Ten theorems and various conjectures
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
Ten theorems and few conjectures related to quantum field theory as applied to high energy physics are presented. The work connects classical quantum field theory with the golden mean renormalization groups of non-linear dynamics and E-Infinity theory
The CAP Theorem Versus Databases with Relaxed ACID properties
DEFF Research Database (Denmark)
Frank, Lars; Pedersen, Rasmus Ulslev; Havnø Frank, Christian
2014-01-01
data from different locations can have at most two of the three desirable CAP properties [5]. The NoSQL movement has applied the CAP theorem as an argument against tradi- tional ACID (atomicity, consistency, isolation, and durabil- ity) databases, which prioritize consistency and partition- tolerance...
An Extension of the Mean Value Theorem for Integrals
Khalili, Parviz; Vasiliu, Daniel
2010-01-01
In this note we present an extension of the mean value theorem for integrals. The extension we consider is motivated by an older result (here referred as Corollary 2), which is quite classical for the literature of Mathematical Analysis or Calculus. We also show an interesting application for computing the sum of a harmonic series.
An Elementary Proof of a Converse Mean-Value Theorem
Almeida, Ricardo
2008-01-01
We present a new converse mean value theorem, with a rather elementary proof. [The work was supported by Centre for Research on Optimization and Control (CEOC) from the "Fundacaopara a Ciencia e a Tecnologia" FCT, co-financed by the European Community Fund FEDER/POCTI.
Multiphonon theory: generalized Wick's theorem and recursion formulas
International Nuclear Information System (INIS)
Silvestre-Brac, B.; Piepenbring, R.
1982-04-01
Overlaps and matrix elements of one and two-body operators are calculated in a space spanned by multiphonons of different types taking properly the Pauli principle into account. Two methods are developped: a generalized Wick's theorem dealing with new contractions and recursion formulas well suited for numerical applications
Farmer Brown v. Rancher Wyatt: Teaching the Coase Theorem
Gourley, Patrick
2018-01-01
The Coase Theorem is a fundamental tenet of environmental economics and is taught to thousands of principles of microeconomics students each year. Its counterintuitive conclusion, that a Pareto optimal solution can result between private parties regardless of the initial allocation of property rights over a scarce resource, is difficult for…
A Bayesian perspective on Markovian dynamics and the fluctuation theorem
Virgo, Nathaniel
2013-08-01
One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.
Modified intuitionistic fuzzy metric spaces and some fixed point theorems
International Nuclear Information System (INIS)
Saadati, R.; Sedghi, S.; Shobe, N.
2008-01-01
Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Veereamani P. A note on intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2006;28:902-5]). In this paper, we consider modified intuitionistic fuzzy metric spaces and prove some fixed point theorems in these spaces. All the results presented in this paper are new
The Unforgettable Experience of a Workshop on Pythagoras Theorem
Arwani, Salima Shahzad
2011-01-01
The author conducted a workshop with colleagues in which awareness of Pythagoras' theorem was raised. This workshop was an unforgettable event in the author's life because it was the first time that she had interacted with teachers from a different school system, and it allowed her to develop presentation skills and confidence in her own…
Another proof of Gell-Mann and Low's theorem
Molinari, Luca Guido
2006-01-01
The theorem by Gell-Mann and Low is a cornerstone in QFT and zero-temperature many-body theory. The standard proof is based on Dyson's time-ordered expansion of the propagator; a proof based on exact identities for the time-propagator is here given.
Another proof of Gell-Mann and Low's theorem
International Nuclear Information System (INIS)
Molinari, Luca Guido
2007-01-01
The theorem by Gell-Mann and Low is a cornerstone in quantum field theory and zero-temperature many-body theory. The standard proof is based on Dyson's time-ordered expansion of the propagator; a proof based on exact identities for the time propagator is here given
Virial theorem and Gibbs thermodynamic potential for Coulomb systems
International Nuclear Information System (INIS)
Bobrov, V. B.; Trigger, S. A.
2014-01-01
Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei. This result is valid beyond the perturbation theory with respect to the interparticle interaction
Virial theorem and Gibbs thermodynamic potential for Coulomb systems
Bobrov, V. B.; Trigger, S. A.
2013-01-01
Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei. This result is valid beyond the perturbation theory with respect to the interparticle interaction.
Quantum Many-Body Virial Theorem And Matsubara Green's Function
International Nuclear Information System (INIS)
Anma, D.; Fukuda, T.; Fujita, M.; Toyoda, T.; Takiuchi, K.
2004-01-01
We discuss the quantum field theoretical formulation of the virial theorem on the basis of the canonical field theory of the generalized coordinate transformation and show the equation of motion of a charged Fermion system coupled to an electromagnetic field. Possible application to Fermion-Boson mixtures is also discussed
A General Representation Theorem for Integrated Vector Autoregressive Processes
DEFF Research Database (Denmark)
Franchi, Massimo
We study the algebraic structure of an I(d) vector autoregressive process, where d is restricted to be an integer. This is useful to characterize its polynomial cointegrating relations and its moving average representation, that is to prove a version of the Granger representation theorem valid...
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we ...
The Second Fundamental Theorem of Welfare Economics: A Pedagogical Note
Parrinello Sergio
1998-01-01
The author extends the criticism that W. Bryant (1994) levelled against the usual treatment given to the Second Fundamental Theorem of Welfare Economics in many microeconomics textbooks and economic journal literature. He argues that the omission of basic caveats makes the usual interpretation misleading and an obstacle to better economic education.
Fermat's last theorem and Catalan's conjecture in weak exponential arithmetics
Czech Academy of Sciences Publication Activity Database
Glivický, Petr; Kala, V.
2017-01-01
Roč. 63, 3-4 (2017), s. 162-174 ISSN 0942-5616 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : Fermat's last theorem * Catalan's conjecture Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.250, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/malq.201500069/full
Limits theorems for tail processes with applications tointermediate quantile estimation
Einmahl, J.H.J.
1992-01-01
A description of the weak and strong limiting behaviour of weighted uniform tail empirical and tail quantile processes is given. The results for the tail quantile process are applied to obtain weak and strong functional limit theorems for a weighted non-uniform tail-quantile-type process based on a
Local central limit theorem for a Gibbs random field
Energy Technology Data Exchange (ETDEWEB)
Campanino, M; Capocaccia, D; Tirozzi, B [L' Aquila Univ. (Italy). Istituto di Matematica; Rome Univ. (Italy). Istituto di Matematica)
1979-12-01
The validity of the implication of a local limit theorem is extended from an integral one. The extension eliminates the finite range assumption present in the previous works by using the cluster expansion to analyze the contribution from the tail of the potential.
Hamiltonian Noether theorem for gauge systems and two time physics
International Nuclear Information System (INIS)
Villanueva, V M; Nieto, J A; Ruiz, L; Silvas, J
2005-01-01
The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al model and, with special emphasis, to two time physics
Rigidity theorem for Willmore surfaces in a sphere
Indian Academy of Sciences (India)
(Math. Sci.) Vol. 126, No. 2, May 2016, pp. 253–260. c Indian Academy of Sciences. Rigidity theorem for Willmore surfaces in a sphere. HONGWEI XU1 and DENGYUN YANG2,∗. 1Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027,. People's Republic of China. 2College of Mathematics and ...
Externalities and the Coase Theorem: A Diagrammatic Presentation
Halteman, James
2005-01-01
In intermediate microeconomic textbooks the reciprocal nature of externalities is presented using numerical examples of costs and benefits. This treatment of the Coase theorem obscures the fact that externality costs and benefits are best understood as being on a continuum where costs vary with the degree of intensity of the externality. When…
Liouville's theorem and the method of the inverse problem
International Nuclear Information System (INIS)
Its, A.R.
1985-01-01
An approach to the investigation of the Zakharov-Shabat equations is developed. This approach is based on a classical theorem of Liouville and is the synthesis of ''finite-zone'' integration, the matrix Riemann problem method and the theory of isomonodromy deformations of differential equations. The effectiveness of the proposed scheme is demonstrated by developing ''dressing procedures'' for the Bullough-Dodd equation
Matching factorization theorems with an inverse-error weighting
Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; Pisano, Cristian; Signori, Andrea
2018-06-01
We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.
Negating Four Color Theorem with Neutrosophy and Quadstage Method
Directory of Open Access Journals (Sweden)
Fu Yuhua
2015-03-01
Full Text Available With the help of Neutrosophy and Quad-stage Method, the proof for negation of “the four color theorem” is given. In which the key issue is to consider the color of the boundary, thus “the two color theorem” and “the five color theorem” are derived to replace "the four color theorem".
Generalization of boson-fermion equivalence and Fay's addition theorem
International Nuclear Information System (INIS)
Kato, Hideyuki; Saito, Satoru
1989-01-01
Generalizations of Fay's addition theorem for Abel functions are obtained by using generalized boson-fermion equivalence of off-shell string amplitudes. A simple example of such generalizations is presented explicitly which relates derivatives of a Riemann θ-function to its determinant. (orig.)
The generalized Mayer theorem in the approximating hamiltonian method
International Nuclear Information System (INIS)
Bakulev, A.P.; Bogoliubov, N.N. Jr.; Kurbatov, A.M.
1982-07-01
With the help of the generalized Mayer theorem we obtain the improved inequality for free energies of model and approximating systems, where only ''connected parts'' over the approximating hamiltonian are taken into account. For the concrete system we discuss the problem of convergency of appropriate series of ''connected parts''. (author)
Szegö's theorem on Parreau-Widom sets
DEFF Research Database (Denmark)
Christiansen, Jacob Stordal
2012-01-01
In this paper, we generalize Szego's theorem for orthogonal polynomials on the real line to infinite gap sets of Parreau–Widom type. This notion includes Cantor sets of positive measure. The Szego condition involves the equilibrium measure which in turn is absolutely continuous. Our approach builds...
Testing the No-Hair Theorem with Sgr A*
Directory of Open Access Journals (Sweden)
Tim Johannsen
2012-01-01
Full Text Available The no-hair theorem characterizes the fundamental nature of black holes in general relativity. This theorem can be tested observationally by measuring the mass and spin of a black hole as well as its quadrupole moment, which may deviate from the expected Kerr value. Sgr A*, the supermassive black hole at the center of the Milky Way, is a prime candidate for such tests thanks to its large angular size, high brightness, and rich population of nearby stars. In this paper, I discuss a new theoretical framework for a test of the no-hair theorem that is ideal for imaging observations of Sgr A* with very long baseline interferometry (VLBI. The approach is formulated in terms of a Kerr-like spacetime that depends on a free parameter and is regular everywhere outside of the event horizon. Together with the results from astrometric and timing observations, VLBI imaging of Sgr A* may lead to a secure test of the no-hair theorem.
The confining string from the soft dilaton theorem
International Nuclear Information System (INIS)
Alvarez, Enrique; Gomez, Cesar
2000-01-01
A candidate for the confining string of gauge theories is constructed via a representation of the ultraviolet divergences of quantum field theory by a closed string dilaton insertion, computed through the soft dilaton theorem. The resulting (critical) confining string is conformally invariant, singles out naturally d=4 dimensions, and can not be used to represent theories with Landau poles
Modulus of smoothness and theorems concerning approximation on compact groups
Directory of Open Access Journals (Sweden)
H. Vaezi
2003-01-01
Full Text Available We consider the generalized shift operator defined by (Shuf(g=∫Gf(tut−1gdt on a compact group G, and by using this operator, we define spherical modulus of smoothness. So, we prove Stechkin and Jackson-type theorems.
Radon transformation on reductive symmetric spaces: support theorems
Kuit, J.J.|info:eu-repo/dai/nl/313872589
2011-01-01
In this thesis we introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and study some of their properties. In particular we obtain a generalization of Helgason's support theorem for the horospherical transform on a Riemannian symmetric space.
Fluctuation theorem for the effusion of an ideal gas.
Cleuren, B; Van den Broeck, C; Kawai, R
2006-08-01
The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.
An Experiment on a Physical Pendulum and Steiner's Theorem
Russeva, G. B.; Tsutsumanova, G. G.; Russev, S. C.
2010-01-01
Introductory physics laboratory curricula usually include experiments on the moment of inertia, the centre of gravity, the harmonic motion of a physical pendulum, and Steiner's theorem. We present a simple experiment using very low cost equipment for investigating these subjects in the general case of an asymmetrical test body. (Contains 3 figures…
On the Robinson theorem and shearfree geodesic null congruences
International Nuclear Information System (INIS)
Tafel, J.
1985-01-01
Null electromagnetic fields and shearfree geodesic null congruences in curved and flat spacetimes are studied. We point out some mathematical problems connected with the validity of the Robinson theorem. The problem of finding nonanalytic twisting congruences in the Minkowski space is reduced to the construction of holomorphic functions with specific boundary conditions. (orig.)
Axial anomaly and index theorem for Dirac-Kaehler fermions
International Nuclear Information System (INIS)
Linhares, C.A.; Mignaco, J.A.; Monteiro, M.A.R.
1985-01-01
We present the calculation of the axial anomaly for Dirac-Kaehler fermions in two and four dimensions applying the procedure developed by Seeley to the signature operator in the twisted complex. The result is equal to the one for the twisted spin complex times 2 n/2 (n:number of dimensions) and agrees with the expressions from the index theorem. (author) [pt
Axial anomaly and index theorem for Dirac-Kaehler fermions
International Nuclear Information System (INIS)
Linhares, C.A.; Mignaco, J.A.; Rego Monteiro, M.A.
1985-01-01
We present a calculation of the axial anomaly for Dirac-Kaehler fermions in two and four dimensions applying the procedure developed by Seeley to the signature operator in the twisted complex. The result is equal to the one for the twisted spin complex times 2sup(π/2) (n: number of dimensions) and agrees with the expressions from the index theorem. (orig.)
Birkhoff-Kellogg theorems on invariant directions for multimaps
Directory of Open Access Journals (Sweden)
Donal O'Regan
2003-04-01
Full Text Available We establish Birkhoff-Kellogg type theorems on invariant directions for a general class of maps. Our results, in particular, apply to Kakutani, acyclic, O'Neill, approximable, admissible, and Ã°ÂÂ’Â°cÃŽÂº maps.
Strong ergodic theorem for commutative semigroup of non ...
Indian Academy of Sciences (India)
M Azhini
2017-08-14
Aug 14, 2017 ... of non-Lipschitzian mappings in multi-Banach space ... to studying nonlinear ergodic theory for (asymptotically) non-expansive ... As we know, Bruck's lemmas are essential tools in the proof of almost all mean ergodic theorem ...
Improving Conceptions in Analytical Chemistry: The Central Limit Theorem
Rodriguez-Lopez, Margarita; Carrasquillo, Arnaldo, Jr.
2006-01-01
This article describes the central limit theorem (CLT) and its relation to analytical chemistry. The pedagogic rational, which argues for teaching the CLT in the analytical chemistry classroom, is discussed. Some analytical chemistry concepts that could be improved through an understanding of the CLT are also described. (Contains 2 figures.)
Regularity theorem for functions that are extremal to Paley inequality ...
African Journals Online (AJOL)
Regularity theorem for functions that are extremal to Paley inequality. Seid Mohammed. Abstract. In this paper we study the asymptotic behavior of functions that are extremal to the inequality introduced by Paley (1932) via a normal family of subharmonic functions. SINET: Ethiopian Journal of Science Volume 24, No.
Quasi-gedanken experiment challenging the no-signalling theorem
Indian Academy of Sciences (India)
Keywords. Quantum information; quantum entanglement; no-signalling theorem ... the construction of empirically testable schemes wherein superluminal exchange of information can occur. In light of this thesis,we present a potentially feasible quantum-optical scheme that purports to enable superluminal signalling.
Bayes' theorem: A paradigm research tool in biomedical sciences
African Journals Online (AJOL)
STORAGESEVER
2008-12-29
Dec 29, 2008 ... It is on this premise that this article presents Bayes' theorem as a vital tool. A brief intuitive ... diseased individual will be selected or that a disease-free individual will be selected? ...... Ultrasound physics and. Instruction 3rd ed ...
Asymptotic representation theorems for poverty indices | Lo | Afrika ...
African Journals Online (AJOL)
Abstract. 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 asymptotic of the bulk of poverty indices and issues in poverty ...
Fluctuation Theorems of Work and Entropy in Hamiltonian Systems
Indian Academy of Sciences (India)
These theorems lead to the fact that the second law holds for aver-. RESONANCE | May 2018 ... thermodynamic quantities like work, heat or entropy change are also stochastic and follow .... In the third line, we have used the fact that W[z(t)] ...
Beurling Algebra Analogues of the Classical Theorems of Wiener ...
Indian Academy of Sciences (India)
absolutely convergent for some weight on the set of integers Z . If is nowhere vanishing on , then there exists a weight on Z such that 1/ had -absolutely convergent Fourier series. This includes Wiener's classical theorem. As a corollary ...
A stochastic Ergodic Theorem in Von-Neumann algebras | Tijani ...
African Journals Online (AJOL)
In this paper we introduce the notion of stochastic convergence of τ- measurable operators and prove a noncommutative extension of pointwise ergodic theorem of G. D. Birkhoff by means of it by using the techniques developed by Petz in [12] Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp.
The Semantic Isomorphism Theorem in Abstract Algebraic Logic
Czech Academy of Sciences Publication Activity Database
Moraschini, Tommaso
2016-01-01
Roč. 167, č. 12 (2016), s. 1298-1331 ISSN 0168-0072 R&D Projects: GA ČR GA13-14654S Institutional support: RVO:67985807 Keywords : algebra izable logics * abstract algebra ic logic * structural closure operators * semantic isomorphism theorem * evaluational frames * compositional lattice Subject RIV: BA - General Mathematics Impact factor: 0.647, year: 2016
A Neutrosophic Binomial Factorial Theorem with their Refrains
Directory of Open Access Journals (Sweden)
Huda E. Khalid
2016-12-01
Full Text Available The Neutrosophic Precalculus and the Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the method used to deal with such indeterminacy. This article is innovative since the form of neutrosophic binomial factorial theorem was constructed in addition to its refrains.
Fluctuation theorems and orbital magnetism in nonequilibrium state
Indian Academy of Sciences (India)
We study Langevin dynamics of a driven charged particle in the presence as well as in the absence of magnetic field. We discuss the validity of various work fluctuation theorems using different model potentials and external drives. We also show that one can generate an orbital magnetic moment in a nonequilibrium state ...
Thermodynamic laws and equipartition theorem in relativistic Brownian motion.
Koide, T; Kodama, T
2011-06-01
We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.
Can we make the second incompleteness theorem coordinate free?
Visser, A.
2008-01-01
Is it possible to give a coordinate free formulation of the Second Incompleteness Theorem? We pursue one possible approach to this question. We show that (i) cutfree consistency for finitely axiomatized theories can be uniquely characterized modulo EA-provable equivalence, (ii) consistency
Fermat's Last Theorem for Factional and Irrational Exponents
Morgan, Frank
2010-01-01
Fermat's Last Theorem says that for integers n greater than 2, there are no solutions to x[superscript n] + y[superscript n] = z[superscript n] among positive integers. What about rational exponents? Irrational n? Negative n? See what an undergraduate senior seminar discovered.
Understanding the Sampling Distribution and the Central Limit Theorem.
Lewis, Charla P.
The sampling distribution is a common source of misuse and misunderstanding in the study of statistics. The sampling distribution, underlying distribution, and the Central Limit Theorem are all interconnected in defining and explaining the proper use of the sampling distribution of various statistics. The sampling distribution of a statistic is…