International Nuclear Information System (INIS)
Li Chao; Lovelace, Geoffrey
2008-01-01
Extreme-mass-ratio inspirals (EMRIs) and intermediate-mass-ratio inspirals (IMRIs) - binaries in which a stellar-mass object spirals into a massive black hole or other massive, compact body - are important sources of gravitational waves for LISA and LIGO, respectively. Thorne has speculated that the waves from EMRIs and IMRIs encode, in principle, all the details of (i) the central body's spacetime geometry (metric), (ii) the tidal coupling (energy and angular momentum exchange) between the central body and orbiting object, and (iii) the evolving orbital elements. Fintan Ryan has given a first partial proof that this speculation is correct: Restricting himself to nearly circular, nearly equatorial orbits and ignoring tidal coupling, Ryan proved that the central body's metric is encoded in the waves. In this paper we generalize Ryan's theorem. Retaining Ryan's restriction to nearly circular and nearly equatorial orbits, and dropping the assumption of no tidal coupling, we prove that Thorne's conjecture is nearly fully correct: the waves encode not only the central body's metric but also the evolving orbital elements and (in a sense slightly different from Thorne's conjecture) the evolving tidal coupling.
Probing Quiescent Massive Black Holes: Insights from Tidal Disruption Events
Gezari, Suvi; Strubbe, Linda; Bloom, Joshua S.; Grindlay, J. E.; Soderberg, Alicia; Elvis, Martin; Coppi, Paolo; Lawrence, Andrew; Ivezic, Zeljko; Merritt, David; Komossa, Stefanie; Halpern, Jules; Eracleous, Michael
2009-01-01
Tidal disruption events provide a unique probe of quiescent black holes in the nuclei of distant galaxies. The next generation of synoptic surveys will yield a large sample of flares from the tidal disruption of stars by massive black holes that will give insights to four key science questions: 1) What is the assembly history of massive black holes in the universe? 2) Is there a population of intermediate mass black holes that are the primordial seeds of supermassive black holes? 3) How can w...
Schnepf, N. R.; Kuvshinov, A.; Sabaka, T.
2015-01-01
A few studies convincingly demonstrated that the magnetic fields induced by the lunar semidiurnal (M2) ocean flow can be identified in satellite observations. This result encourages using M2 satellite magnetic data to constrain subsurface electrical conductivity in oceanic regions. Traditional satellite-based induction studies using signals of magnetospheric origin are mostly sensitive to conducting structures because of the inductive coupling between primary and induced sources. In contrast, galvanic coupling from the oceanic tidal signal allows for studying less conductive, shallower structures. We perform global 3-D electromagnetic numerical simulations to investigate the sensitivity of M2 signals to conductivity distributions at different depths. The results of our sensitivity analysis suggest it will be promising to use M2 oceanic signals detected at satellite altitude for probing lithospheric and upper mantle conductivity. Our simulations also suggest that M2 seafloor electric and magnetic field data may provide complementary details to better constrain lithospheric conductivity.
New Probe of Early Phases of Jet Formation and Evolution using Stellar Tidal Disruption Flares
Ranga Reddy Pasham, Dheeraj; van Velzen, Sjoert
2018-01-01
The tidal disruption of a star by a supermassive black hole can result in transient radio emission. The electrons producing these synchrotron radio flares could either be accelerated inside a relativistic jet or externally by shocks resulting from an outflow interacting with the circumnuclear medium. Until now, evidence for the internal emission mechanism has been lacking; nearly all tidal disruption flare studies have adopted the external shock model to explain the observed properties of radio flares. I will talk about a result that presents a challenge to external emission models: we discovered a cross-correlation between the soft X-ray (0.3-1 keV) and 16 GHz radio flux of Rosetta Stone tidal disruption flare ASASSN-14li. Variability features in the X-ray light curve appear again in the radio light curve, but after a time lag of about 13 days. This demonstrates that soft X-ray emitting accretion disk regulates the radio emission. This coupling appears to be inconsistent with all previous external emission models for this source but is naturally explained if the radio emission originates from a freely expanding jet. I will show that emission internal to an adiabatically expanding jet can also reproduce the observed evolution of the radio spectral energy distribution. Furthermore, both the correlation between X-ray and radio luminosity as well as our radio spectral modeling imply an approximately linear coupling between the accretion rate and jet power. I will also discuss how future tidal disruption events can help us understand how jets form and evolve in general.
Using gaps in N-body tidal streams to probe missing satellites
International Nuclear Information System (INIS)
Ngan, W. H. W.; Carlberg, R. G.
2014-01-01
We use N-body simulations to model the tidal disruption of a star cluster in a Milky-Way-sized dark matter halo, which results in a narrow stream comparable to (but slightly wider than) Pal-5 or GD-1. The mean Galactic dark matter halo is modeled by a spherical Navarro-Frenk-White potential with subhalos predicted by the ΛCDM cosmological model. The distribution and mass function of the subhalos follow the results from the Aquarius simulation. We use a matched filter approach to look for 'gaps' in tidal streams at 12 length scales from 0.1 kpc to 5 kpc, which appear as characteristic dips in the linear densities along the streams. We find that, in addition to the subhalos' perturbations, the epicyclic overdensities (EOs) due to the coherent epicyclic motions of particles in a stream also produce gap-like signals near the progenitor. We measure the gap spectra—the gap formation rates as functions of gap length—due to both subhalo perturbations and EOs, which have not been accounted for together by previous studies. Finally, we project the simulated streams onto the sky to investigate issues when interpreting gap spectra in observations. In particular, we find that gap spectra from low signal-to-noise observations can be biased by the orbital phase of the stream. This indicates that the study of stream gaps will benefit greatly from high-quality data from future missions.
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
Duarte, B; Santos, D; Marques, J C; Caçador, I
2014-04-01
Submergence is one of the major constrains affecting wetland plants, with inevitable impacts on their physiology and productivity. Global warming as a driving force of sea level rise, tend to increase the submersion periods duration. Photosynthesis biophysical probing arise as an important tool to understand the energetics underlying plant feedback to these constrains. As in previous studies with Spartina maritima, there was no inhibition of photosynthetic activity in submerged individuals. Comparing both donor and acceptor sides of the PSII, the first was more severely affected during submersion, driven by the inactivation of the OEC with consequent impairment of the ETC. Although this apparent damage in the PSII donor side, the electron transport per active reaction centre was not substantially affected, indicating that this reduction in the electron flow is accompanied by a proportional increase in the number of active reaction centres. These conditions lead to the accumulation of excessive reducing power, source of damaging ROS, counteracted by efficient energy dissipation processes and anti-oxidant enzymatic defences. This way, S. maritima appears as a well-adapted species with an evident photochemical plasticity towards submersion, allowing it to maintain its photosynthetic activity even during prolonged submersion periods. Copyright © 2014 Elsevier Masson SAS. All rights reserved.
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
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.
Intersection theorems, inclusion theorems and related results
International Nuclear Information System (INIS)
Jiang Jiahe.
1986-07-01
In the present paper derived from the principle of KKM (Knaster, Kuratowski, and Mazurkiewicz) mappings are some intersection theorems, inclusion theorems and related results, generalizing a number of known results. (author)
Indian Academy of Sciences (India)
This article discusses two theorems of Georg Can- tor: Cantor's Little Theorem and Cantor's Diag- onal Theorem. The results are obtained by gen- eralizing the method of proof of the well known. Cantor's theorem about the cardinalities of a set and its power set. As an application of these,. Godel's first incompleteness ...
Indian Academy of Sciences (India)
Keywords. formalization of mathematics; Mizar; social choice theory; Arrow's theorem; Gibbard–Satterthwaite theorem; proof errors. ... Author Affiliations. Freek Wiedijk1. Institute for Computing and Information Sciences, Radboud University Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
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- .... Now by Hahn–Banach, we have Theorem 3. □. Proof of Theorem 1. Fix a z outside K and write the Taylor formula of order m for the. Cauchy kernel: 1 x − z.
International Nuclear Information System (INIS)
Baker, A.C.
1991-01-01
This book describes how large tides develop in particular places and how the energy could be extracted by building suitable barrages. The principal features of a barrage and possible methods of operation are described in detail. Although a tidal power barrage would be non-polluting, the resulting changes in the tidal regime would have important environmental effects. These are discussed together with the economics of tidal power. Methods of assessing the likely cost of electricity from any site are set out and applied to possible sites around the world. (author)
International Nuclear Information System (INIS)
Mashhoon, B.
1977-01-01
The general theory of tides is developed within the framework of Einstein's theory of gravitation. It is based on the concept of Fermi frame and the associated notion of tidal frame along an open curve in spacetime. Following the previous work of the author an approximate scheme for the evaluation of tidal gravitational radiation is presented which is valid for weak gravitational fields. The emission of gravitational radiation from a body in the field of a black hole is discussed, and for some cases of astrophysical interest estimates are given for the contributions of radiation due to center-of-mass motion, purely tidal deformation, and the interference between the center of mass and tidal motions
Impact of Science on Society, 1987
1987-01-01
States that tidal power projects are feasible in a relatively limited number of locations around the world. Claims that together they could theoretically produce the energy equivalent to more than one million barrels of oil per year. (TW)
Indian Academy of Sciences (India)
Institute, Calcutta. Apart from mathematics, he likes painting and reading. Unlike most others he dislikes computers. Ritabrata Munshi. Introduction. In this two-part article we will consider one of the classi- cal theorems of mathematics, the Jordan curve theorem. It states that a simple closed curve (i.e., a closed curve which.
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
IAS Admin
This article elucidates the important role the no- tion of symmetry has played in physics. It dis- cusses the proof of one of the important theorems of quantum mechanics, viz., Wigner's Symmetry. Representation Theorem. It also shows how the representations of various continuous and dis- crete symmetries follow from the ...
Dynamics and radiation from tidal disruption events
Bonnerot, C.A.
2017-01-01
When a star gets too close to a supermassive black hole, it is torn apart by strong tidal forces in a tidal disruption event (TDE). The stellar matter then fuels the compact object causing a bright flare that is a unique probe of the majority of galactic nuclei, otherwise quiescent. For
Trigonometry, Including Snell's Theorem.
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
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 ...
Roos, A.
1997-01-01
Basic phenomena, origin and generation of tides, analysis and prediction of tides, basic equation and types of long waves in one dimension, tidal propagation in one dimension, tidal propagation in two directions, analytical tidal computation, numerical tidal computation.
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...
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...... singular points nor closed orbits. In this paper, we redefine the standard notion of safety to comply with dynamical systems with multiple singular elements. Hereafter, we prove the converse barrier certificate theorems and highlight the differences between our results and previous work by a number...
Homar, Ambrož
2011-01-01
Solutions to NP-problems are deterministically verifiable in polynomial time. But the classic verification process has a drawback - typically we need to (at least) read the entire proof to decide whether the proof is correct or incorrect. In the thesis we present the PCP theorem which claims that solutions to NP- problems can be checked by only a small number of queries to bits in their corresponding proof strings. We describe the equivalent version of the theorem which is at the heart of man...
A game generalizing Hall's theorem
Rabern, Landon
2012-01-01
We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's edge coloring theorem follows from a special case.
Multivariable Chinese Remainder Theorem
Indian Academy of Sciences (India)
IAS Admin
number as sought since N could be negative. However, we may add a suitable multiple of m1m2 to N ... Further, we note that negative numbers are dealt on an equal footing; the statement that x leaves a remainder .... classical Chinese remainder theorem can be thou- ght of as the special case when the matrix {aij} has only.
DEFF Research Database (Denmark)
Thomassen, Carsten
2004-01-01
We present a short proof of the theorem of Tutte that every planar 3-connected graph has a drawing in the plane such that every vertex which is not on the outer cycle is the barycenter of its neighbors. Moreover, this holds for any prescribed representation of the outer cycle. (C) 2004 Wiley Peri...
Weyl's Equidistribution Theorem
Indian Academy of Sciences (India)
groups and matrix representations. It was during his re- search into representation theory that Weyl discovered his theorem on equidistribution. Subsequently a vast amount of literature was devoted to the review of his proof. However, there remain to this day, several unan- swered questions which arose in the aftermath of ...
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
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.
Probing gas and dust in the tidal tail of NGC 5221 with the type Ia supernova iPTF16abc
Ferretti, R.; Amanullah, R.; Goobar, A.; Petrushevska, T.; Borthakur, S.; Bulla, M.; Fox, O.; Freeland, E.; Fremling, C.; Hangard, L.; Hayes, M.
2017-10-01
Context. Type Ia supernovae (SNe Ia) can be used to address numerous questions in astrophysics and cosmology. Due to their well known spectral and photometric properties, SNe Ia are well suited to study gas and dust along the lines-of-sight to the explosions. For example, narrow Na I D and Ca II H&K absorption lines can be studied easily, because of the well-defined spectral continuum of SNe Ia around these features. Aims: We aim to study the gas and dust along the line-of-sight to iPTF16abc, which occurred in an unusual location, in a tidal arm, 80 kpc from centre of the galaxy NGC 5221. Methods: Using a time-series of high-resolution spectra, we have examined narrow Na I D and Ca II H&K absorption features for variations in time, which would be indicative for circumstellar (CS) matter. Furthermore, we have taken advantage of the well known photometric properties of SNe Ia to determine reddening due to dust along the line-of-sight. Results: From the lack of variations in Na I D and Ca II H&K, we determine that none of the detected absorption features originate from the CS medium of iPTF16abc. While the Na I D and Ca II H&K absorption is found to be optically thick, a negligible amount of reddening points to a small column of interstellar dust. Conclusions: We find that the gas along the line-of-sight to iPTF16abc is typical of what might be found in the interstellar medium (ISM) within a galaxy. It suggests that we are observing gas that has been tidally stripped during an interaction of NGC 5221 with one of its neighbouring galaxies in the past 109 yr. In the future, the gas clouds could become the locations of star formation. On a longer time scale, the clouds might diffuse, enriching the circum-galactic medium (CGM) with metals. The gas profile along the line-of-sight should be useful for future studies of the dynamics of the galaxy group containing NGC 5221. Based on observations collected at the European Organisation for Astronomical Research in the Southern
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.
Fully Quantum Fluctuation Theorems
Directory of Open Access Journals (Sweden)
Johan Åberg
2018-02-01
Full Text Available 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.
THE PARKER MAGNETOSTATIC THEOREM
International Nuclear Information System (INIS)
Low, B. C.
2010-01-01
We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly conducting fluid bounded by a pair of rigid plates where each field is anchored, taking the plates perpendicular to the uniform field. Those force-free fields obtainable from the uniform field by continuous magnetic footpoint displacements at the plates have field topologies that are shown to be a restricted subset of the field topologies similarly created without imposing the force-free equilibrium condition. The theorem then follows from the deduction that a continuous nonequilibrium field with a topology not in that subset must find a force-free state containing tangential discontinuities.
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 ...
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
Indian Academy of Sciences (India)
The last two inequalities imply δ(x) = [√. 8x + 1 + 1. 2. ] ,. 479. Page 2. 480. F Laytimi and W Nahm where the symbol [ ] denotes the integral part, i.e., δ(0) = 1, δ(1) = δ(2) = 2,δ(3) = δ(4) = δ(5) = 3, δ(6) = δ(7) = δ(8) = δ(9) = 4, .... Theorem 1.2. Let α, β ∈ N. If S α+β. E ⊗ L is ample, then. H p,q(X, Sα. E ⊗ ∧β. E ⊗ L) = 0 for q + p ...
DEFF Research Database (Denmark)
Krukow, Karl Kristian; Nielsen, Mogens
2006-01-01
Since the millennium, a quickly increasing number of research papers in the field of ``computational trust and reputation'' have appeared in the Computer Science literature. However, it remains hard to compare and evaluate the respective merits of proposed systems. We argue that rigorous use...... specified. We show how to compute (in this model) the so-called predictive probability: The probability that the next interaction with a specific principal will have a specific outcome. We sketch preliminary ideas and first theorems indicating how the use of probabilistic models could enable us...
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
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.
Interactive Theorem Proving and Verification
Indian Academy of Sciences (India)
The goal of Auto- mated Theorem Proving, as the name suggests, is to try to prove a wide range of mathematical theorems using a computer in an automatic fashion. On the other hand, Interactive Theo- rem Proving tries to achieve similar goals, but in the form of a collaborative effort between human beings and computers.
Legendre's and Kummer's Theorems Again
Indian Academy of Sciences (India)
mathematical education and mathematical contests. Dorel Mihet». Some results related to Legendre's Theorem and ... mentioned theorems in problem solving. We will see that many olympiad-type problems as: `If f(m) denotes the greatest k such that 2k divides m, prove that there are infinite many numbers m such that ...
Abelian theorems for Whittaker transforms
Directory of Open Access Journals (Sweden)
Richard D. Carmichael
1987-01-01
Full Text Available Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches 0 or ∞ in absolute value inside a wedge region in the right half plane.
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)
Stochastic separation theorems.
Gorban, A N; Tyukin, I Y
2017-10-01
The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real world. Its solution requires robust separation of samples with errors from samples where the system works properly. We demonstrate that in (moderately) high dimension this separation could be achieved with probability close to one by linear discriminants. Based on fundamental properties of measure concentration, we show that for M1-ϑ, where 1>ϑ>0 is a given small constant. Exact values of a,b>0 depend on the probability distribution that determines how the random M-element sets are drawn, and on the constant ϑ. These stochastic separation theorems provide a new instrument for the development, analysis, and assessment of machine learning methods and algorithms in high dimension. Theoretical statements are illustrated with numerical examples. Copyright © 2017 Elsevier Ltd. 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
Fluctuation theorem: A critical review
Malek Mansour, M.; Baras, F.
2017-10-01
Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.
-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.
Energy Technology Data Exchange (ETDEWEB)
O Rourke, Fergal; Boyle, Fergal; Reynolds, Anthony [Department of Mechanical Engineering, Dublin Institute of Technology, Bolton Street, Dublin 1 (Ireland)
2010-02-15
Tidal energy has the potential to play a valuable part in a sustainable energy future. It is an extremely predictable energy source, depending only on the gravitational pull of the moon and the sun and the centrifugal forces created by the rotation of the earth-moon system. Tidal energy has been exploited on a significant scale since the construction of the La Rance tidal barrage in France in 1967. A tidal barrage utilises the potential energy of the tide and has proven to be very successful, despite opposition from environmental groups. Kinetic energy can also be harnessed from tidal currents to generate electricity and involves the use of a tidal current turbine. This is the more desired method of capturing the energy in the tides. However, tidal current turbine technology is currently not economically viable on a large scale, as it is still in an early stage of development. This paper provides an up-to-date review of the status of tidal energy technology and identifies some of the key barriers challenging the development of tidal energy. The future development of tidal current devices and tidal barrage systems is discussed as well as examining the importance of a supportive policy to assist development. (author)
Nonrenormalization Theorems without Supersymmetry
Cheung, Clifford; Shen, Chia-Hsien
2015-08-01
We derive a new class of one-loop nonrenormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and antiholomorphic weights, (w ,w ¯)=(n -h ,n +h ), where n and h are the number and sum over helicities of the particles created by that operator. We argue that an operator Oi can only be renormalized by an operator Oj if wi≥wj and w¯i≥w¯j, absent nonholomorphic Yukawa couplings. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model. Since our claims rely on unitarity and helicity rather than an explicit symmetry, they apply quite generally.
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
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…
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.
A generalized saddle point theorem
International Nuclear Information System (INIS)
Liu, J.Q.
1988-11-01
The well-known saddle point theorem is extended to the case of functions defined on a product space X x V, where X is a Banach space and V is a compact manifold. Under some linking conditions, the existence of at least cuplength (V) + 1 critical points is proved. The abstract theorems are applied to the existence problems of periodic solutions of Hamiltonian systems with periodic nonlinearity and/or resonance. (author). 8 refs
Suarez, Antoine
2010-01-01
It is argued that the Strong Free Will Theorem (Conway-Kochen) does not prove nonlocal determinism wrong. This is done by the before-before (Suarez-Scarani) experiment, which is used here to prove the following General Free Will Theorem: If humans have a certain amount of free will, there are other free beings outside space-time producing nonlocal effects in our world, which are both random and lawful.
A fermionic de Finetti theorem
Krumnow, Christian; Zimborás, Zoltán; Eisert, Jens
2017-12-01
Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing one to bound the error made by mean-field approaches. Such theorems link the symmetry of a quantum state under the exchange of subsystems to negligible quantum correlations and are well understood and established in the context of distinguishable particles. In this work, we derive a de Finetti theorem for finite sized Majorana fermionic systems. It is shown, much reflecting the spirit of other quantum de Finetti theorems, that a state which is invariant under certain permutations of modes loses most of its anti-symmetric character and is locally well described by a mode separable state. We discuss the structure of the resulting mode separable states and establish in specific instances a quantitative link to the quality of the Hartree-Fock approximation of quantum systems. We hint at a link to generalized Pauli principles for one-body reduced density operators. Finally, building upon the obtained de Finetti theorem, we generalize and extend the applicability of Hudson's fermionic central limit theorem.
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.
O'Rourke, Fergal; Boyle, Fergal; Reynolds, Anthony
2010-01-01
Tidal energy has the potential to play a valuable part in a sustainable energy future. It is an extremely predictable energy source, depending only on the gravitational pull of the moon and the sun and the centrifugal forces created by the rotation of the earth-moon system. Tidal energy has been exploited on a significant scale since the construction of the La Rance tidal barrage in France in 1967. A tidal barrage utilises the potential energy of the tide and has proven to be very successful,...
Soft theorems from anomalous symmetries
Huang, Yu-tin; Wen, Congkao
2015-12-01
We discuss constraints imposed by soft limits for effective field theories arising from symmetry breaking. In particular, we consider those associated with anomalous conformal symmetry as well as duality symmetries in supergravity. We verify these soft theorems for the dilaton effective action relevant for the a-theorem, as well as the one-loop effective action for N=4 supergravity. Using the universality of leading transcendental coefficients in the α' expansion of string theory amplitudes, we study the matrix elements of operator R 4 with half maximal supersymmetry. We construct the non-linear completion of R 4 that satisfies both single and double soft theorems up to seven points. This supports the existence of duality invariant completion of R 4.
Soft theorems from anomalous symmetries
Energy Technology Data Exchange (ETDEWEB)
Huang, Yu-tin [Department of Physics and Astronomy, National Taiwan University,Taipei 10617, Taiwan, ROC (China); Wen, Congkao [I.N.F.N. Sezione di Roma “Tor Vergata”,Via della Ricerca Scientifica, 00133 Roma (Italy)
2015-12-22
We discuss constraints imposed by soft limits for effective field theories arising from symmetry breaking. In particular, we consider those associated with anomalous conformal symmetry as well as duality symmetries in supergravity. We verify these soft theorems for the dilaton effective action relevant for the a-theorem, as well as the one-loop effective action for N=4 supergravity. Using the universality of leading transcendental coefficients in the α{sup ′} expansion of string theory amplitudes, we study the matrix elements of operator R{sup 4} with half maximal supersymmetry. We construct the non-linear completion of R{sup 4} that satisfies both single and double soft theorems up to seven points. This supports the existence of duality invariant completion of R{sup 4}.
Logical errors on proving theorem
Sari, C. K.; Waluyo, M.; Ainur, C. M.; Darmaningsih, E. N.
2018-01-01
In tertiary level, students of mathematics education department attend some abstract courses, such as Introduction to Real Analysis which needs an ability to prove mathematical statements almost all the time. In fact, many students have not mastered this ability appropriately. In their Introduction to Real Analysis tests, even though they completed their proof of theorems, they achieved an unsatisfactory score. They thought that they succeeded, but their proof was not valid. In this study, a qualitative research was conducted to describe logical errors that students made in proving the theorem of cluster point. The theorem was given to 54 students. Misconceptions on understanding the definitions seem to occur within cluster point, limit of function, and limit of sequences. The habit of using routine symbol might cause these misconceptions. Suggestions to deal with this condition are described as well.
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
Hoitink, A.J.F.; Jay, D.A.
2016-01-01
Tidal rivers are a vital and little studied nexus between physical oceanography and hydrology. It is only in the last few decades that substantial research efforts have been focused on the interactions of river discharge with tidal waves and storm surges into regions beyond the limit of salinity
Directory of Open Access Journals (Sweden)
Yin Chen
2004-01-01
Full Text Available We extend the Putnam-Fuglede theorem and the second-degree Putnam-Fuglede theorem to the nonnormal operators and to an elementary operator under perturbation by quasinilpotents. Some asymptotic results are also given.
The development of the princial genus theorem
Lemmermeyer, Franz
2002-01-01
In this article we sketch the development of the principal genus theorem from its conception by Gauss in the case of binary quadratic forms to the cohomological formulation of the principal genus theorem of class field theory by Emmy Noether.
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...
Lenstra theorem in number fields
Indian Academy of Sciences (India)
Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 4, November 2014, pp. 481– 485. c Indian Academy of Sciences. Lenstra theorem in number fields. S SUBBURAM. Department of Mathematics, SASTRA University, Thanjavur 613 401, India. Present Address: The Institute of Mathematics, CIT Campus, Taramani,. Chennai 600 113 ...
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
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 ...
Lenstra theorem in number fields
Indian Academy of Sciences (India)
2000 Mathematics Subject Classification. 11R04; 11R21. 1. Introduction. In 1984, Lenstra [1] proved the following theorem: Let r, s and n be integers satisfying. 0 ≤ r n1/3, (r, s) = 1. Then n has at most 11 positive divisors which are congruent to r modulo s. This result has been applied to solve many problems.
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 ...
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....
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.)
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
Generalizations of Ptolemy and Brahmagupta Theorems
Ayoub, Ayoub B.
2007-01-01
The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…
International Nuclear Information System (INIS)
2003-01-01
The world's first tidal power station is scheduled for stat-up in the spring of 2003. It is located in Kvalsundet, off Hammerfest, Norway. This is a pilot installation of a 300 kW tidal turbine at a depth of 50 metres. When fully developed in 2007, the tidal power plant will deliver 32 GWh per year. Hammerfest Stroem has patented the energy and the company hopes to be able to install similar power stations both in Norway and abroad. The potential worldwide is claimed to be more than 450 TWh per year
Efroimsky, Michael
2018-01-01
In the preceding paper (Efroimsky, 2017), we derived an expression for the tidal dissipation rate in a homogeneous near-spherical Maxwell body librating in longitude. Now, by equating this expression to the outgoing energy flux due to the vapour plumes, we estimate the mean tidal viscosity of Enceladus, under the assumption that the Enceladean mantle behaviour is Maxwell. This method yields a value of 0.24 × 1014 Pa s for the mean tidal viscosity, which is very close to the viscosity of ice near the melting point.
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.
Generalized Bloch theorem and chiral transport phenomena
Yamamoto, Naoki
2015-10-01
Bloch theorem states the impossibility of persistent electric currents in the ground state of nonrelativistic fermion systems. We extend this theorem to generic systems based on the gauged particle number symmetry and study its consequences on the example of chiral transport phenomena. We show that the chiral magnetic effect can be understood as a generalization of the Bloch theorem to a nonequilibrium steady state, similarly to the integer quantum Hall effect. On the other hand, persistent axial currents are not prohibited by the Bloch theorem and they can be regarded as Pauli paramagnetism of relativistic matter. An application of the generalized Bloch theorem to quantum time crystals is also discussed.
The Classical Version of Stokes' Theorem Revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2005-01-01
of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly that this latter fact usually does not get within reach for students in first year calculus courses and secondly that calculus textbooks in general only just hint at the correspondence alluded...... 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...
Navier Stokes Theorem in Hydrology
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
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.
Recursion relations from soft theorems
Energy Technology Data Exchange (ETDEWEB)
Luo, Hui [II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, Hamburg, D-22761 (Germany); Wen, Congkao [I.N.F.N. Sezione di Roma “Tor Vergata”,Via della Ricerca Scientifica, Roma, 00133 (Italy)
2016-03-14
We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large-z behaviour. This work is a generalization of the recursion relations recently obtained by Cheung et al. for amplitudes in scalar effective field theories with enhanced vanishing soft behaviours, which can be regarded as a special case of those with non-vanishing soft limits. We apply the recursion relations to tree-level amplitudes in various theories, including amplitudes in the Akulov-Volkov theory and amplitudes containing dilatons of spontaneously-broken conformal symmetry.
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)
Energy Technology Data Exchange (ETDEWEB)
Blazek, Jonathan; Vlah, Zvonimir; Seljak, Uroš
2015-08-01
We develop an analytic model for galaxy intrinsic alignments (IA) based on the theory of tidal alignment. We calculate all relevant nonlinear corrections at one-loop order, including effects from nonlinear density evolution, galaxy biasing, and source density weighting. Contributions from density weighting are found to be particularly important and lead to bias dependence of the IA amplitude, even on large scales. This effect may be responsible for much of the luminosity dependence in IA observations. The increase in IA amplitude for more highly biased galaxies reflects their locations in regions with large tidal fields. We also consider the impact of smoothing the tidal field on halo scales. We compare the performance of this consistent nonlinear model in describing the observed alignment of luminous red galaxies with the linear model as well as the frequently used "nonlinear alignment model," finding a significant improvement on small and intermediate scales. We also show that the cross-correlation between density and IA (the "GI" term) can be effectively separated into source alignment and source clustering, and we accurately model the observed alignment down to the one-halo regime using the tidal field from the fully nonlinear halo-matter cross correlation. Inside the one-halo regime, the average alignment of galaxies with density tracers no longer follows the tidal alignment prediction, likely reflecting nonlinear processes that must be considered when modeling IA on these scales. Finally, we discuss tidal alignment in the context of cosmic shear measurements.
Pythagoras Theorem and Relativistic Kinematics
Mulaj, Zenun; Dhoqina, Polikron
2010-01-01
In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.
Lectures on Fermat's last theorem
International Nuclear Information System (INIS)
Sury, B.
1993-09-01
The report presents the main ideas involved in the approach towards the so-called Fermat's last theorem (FLT). The discussion leads to the point where recent work of A. Wiles starts and his work is not discussed. After a short history of the FLT and of the present approach, are discussed the elliptic curves and the modular forms with their relations, the Taniyama-Shimura-Well conjecture and the FLT
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
No-hair theorem for black holes in astrophysical environments.
Gürlebeck, Norman
2015-04-17
According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.
On Krasnoselskii's Cone Fixed Point Theorem
Directory of Open Access Journals (Sweden)
Man Kam Kwong
2008-04-01
Full Text Available In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.
The classical version of Stokes' Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
of the vector field in a tubular shell around the given surface. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly...... that this latter fact usually does not get within reach for students in first year calculus courses and secondly that calculus textbooks in general only just hint at the correspondence alluded to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used...... 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....
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.
The Reciprocal of the Fundamental Theorem of Riemannian Geometry
Calderon, Hector
2008-05-01
The fundamental theorem of Riemannian geometry is inverted for analytic Christoffel symbols. The inversion formula, henceforth dubbed Ricardo's formula, is obtained without ancillary assumptions and it is well suited to compute the uncertainty in the metric that arises from the uncertainty in the measurement of positions. The solution is given up to a constant conformal factor, in part, because there are no experiments that can fix such factor without probing the whole universe. Ricardo's formula excludes some pathological examples and works for manifolds of any dimension and metrics of any signature.
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.
Adiabatic Theorem without a Gap Condition
International Nuclear Information System (INIS)
Avron, J.E.; Elgar, A.
1999-01-01
We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the adiabatic theorem holds for the ground state of atoms in quantized radiation field. She general result we prove gives no information on the rate at which the adiabatic limit is approached. With additional spectral information one can also estimate this rate
The Bell's theorem: GHZ states
International Nuclear Information System (INIS)
Cereceda Berdiel, J.L.
1997-01-01
In this paper we review a striking new version of Bell's theorem discovered some time ago for three spin-1/2 particles and derive explicitly the states leading to a direct (all or nothing) contradiction between the quantum-mechanical and locally realistic prediction. Due to the fact that perfect correlations exist between the spin measurements the resulting contradiction arises without using inequalities. The treatment that follows only presupposes some acquaintance with elementary quantum mechanics. In doing so, we attempt to outline some recent developments in the field of foundations at a level suitable for the early or intermediate part of introductory courses in quantum mechanics. (Author) 15 refs
International Nuclear Information System (INIS)
Abd El-Sattar, A. Dabbour.
1987-07-01
The K-Kolmogorov cohomology construction H k over a pair of discrete coefficient groups is given and discussed from the point of view of Eilenberg-Steenrod's axiom of the cohomology theory. This construction has many points of contiguity with other cohomology groups. The K-Kolmogorov cohomology groups on a pair of compact groups have been topologized by using their duality with the K-Kolmogorov homology groups. In the present work the Kolmogorov duality theorem is proved for H k . 11 refs
Confinement, diquarks and goldstone's theorem
International Nuclear Information System (INIS)
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
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).
Integral fluctuation theorems for stochastic resetting systems
Pal, Arnab; Rahav, Saar
2017-12-01
We study the stochastic thermodynamics of resetting systems. Violation of microreversibility means that the well-known derivations of fluctuations theorems break down for dynamics with resetting. Despite that we show that stochastic resetting systems satisfy two integral fluctuation theorems. The first is the Hatano-Sasa relation describing the transition between two steady states. The second integral fluctuation theorem involves a functional that includes both dynamical and thermodynamic contributions. We find that the second law-like inequality found by Fuchs et al. for resetting systems [Europhys. Lett. 113, 60009 (2016), 10.1209/0295-5075/113/60009] can be recovered from this integral fluctuation theorem with the help of Jensen's inequality.
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.
Coastal inlets and tidal basins
De Vriend, H.J.; Dronkers, J.; Stive, M.J.F.; Van Dongeren, A.; Wang, J.H.
2002-01-01
lecture note: Tidal inlets and their associated basins (lagoons) are a common feature of lowland coasts all around the world. A significant part ofthe world's coastlines is formed by barrier island coasts, and most other tidal coasts are interrupted by estuaries and lagoon inlets. These tidal
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
Integrating Testing and Interactive Theorem Proving
Directory of Open Access Journals (Sweden)
Harsh Raju Chamarthi
2011-10-01
Full Text Available Using an interactive theorem prover to reason about programs involves a sequence of interactions where the user challenges the theorem prover with conjectures. Invariably, many of the conjectures posed are in fact false, and users often spend considerable effort examining the theorem prover's output before realizing this. We present a synergistic integration of testing with theorem proving, implemented in the ACL2 Sedan (ACL2s, for automatically generating concrete counterexamples. Our method uses the full power of the theorem prover and associated libraries to simplify conjectures; this simplification can transform conjectures for which finding counterexamples is hard into conjectures where finding counterexamples is trivial. In fact, our approach even leads to better theorem proving, e.g. if testing shows that a generalization step leads to a false conjecture, we force the theorem prover to backtrack, allowing it to pursue more fruitful options that may yield a proof. The focus of the paper is on the engineering of a synergistic integration of testing with interactive theorem proving; this includes extending ACL2 with new functionality that we expect to be of general interest. We also discuss our experience in using ACL2s to teach freshman students how to reason about their programs.
SOME LIMIT-THEOREMS IN LOG DENSITY
BERKES, [No Value; DEHLING, H
Motivated by recent results on pathwise central limit theorems, we study in a systematic way log-average versions of classical limit theorems. For partial sums S(k) of independent r.v.'s we prove under mild technical conditions that (1/log N)SIGMA(k less-than-or-equal-to N)(1/k)I{S(k)/a(k)
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 Math ematics Impact factor: 0.618, year: 2015 http://cms. math .ca/10.4153/CJM-2014-030-6
Generalized Elitzur's theorem and dimensional reductions
Batista, C. D.; Nussinov, Zohar
2005-07-01
We extend Elitzur’s theorem to systems with symmetries intermediate between global and local. In general, our theorem formalizes the idea of dimensional reduction. We apply the results of this generalization to many systems that are of current interest. These include liquid crystalline phases of quantum Hall systems, orbital systems, geometrically frustrated spin lattices, Bose metals, and models of superconducting arrays.
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 ...
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.
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 way...
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
The Euler Line and Nine-Point-Circle Theorems.
Eccles, Frank M.
1999-01-01
Introduces the Euler line theorem and the nine-point-circle theorem which emphasize transformations and the power of functions in a geometric concept. Presents definitions and proofs of theorems. (ASK)
The Refined Lecture Hall Theorem via Abacus Diagrams
Bradford, Laura; Harris, Meredith; Jones, Brant; Komarinski, Alex; Matson, Carly; O'Shea, Edwin
2012-01-01
Bousquet-M\\'elou & Eriksson's lecture hall theorem generalizes Euler's celebrated distinct-odd partition theorem. We present an elementary and transparent proof of a refined version of the lecture hall theorem using a simple bijection involving abacus diagrams.
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.
A Comment on Holographic Luttinger Theorem
Hashimoto, Koji
2012-01-01
Robustness of the Luttinger theorem for fermionic liquids is examined in holography. The statement of the Luttinger theorem, the equality between the fermion charge density and the volume enclosed by the Fermi surface, can be mapped to a Gauss's law in the gravity dual, a la Sachdev. We show that various deformations in the gravity dual, such as inclusion of magnetic fields, a parity-violating theta-term, dilatonic deformations, and higher-derivative corrections, do not violate the holographic derivation of the Luttinger theorem, as long as the theory is in a confining phase. Therefore a robustness of the theorem is found for strongly correlated fermions coupled with strongly coupled sectors which admit gravity duals. On the other hand, in the deconfined phase, we also show that the deficit appearing in the Luttinger theorem is again universal. It measures a total deficit which measures the charge of the deconfined ("fractionalized") fermions, independent of the deformation parameters.
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...
Singlet and triplet instability theorems
Energy Technology Data Exchange (ETDEWEB)
Yamada, Tomonori; Hirata, So, E-mail: sohirata@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan)
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree–Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree–Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree–Fock-theory-based explanations of Hund’s rule, a singlet instability in Jahn–Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
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
The pointwise Hellmann-Feynman theorem
Directory of Open Access Journals (Sweden)
David Carfì
2010-02-01
Full Text Available In this paper we study from a topological point of view the Hellmann-Feynman theorem of Quantum Mechanics. The goal of the paper is twofold: On one hand we emphasize the role of the strong topology in the classic version of the theorem in Hilbert spaces, for what concerns the kind of convergence required on the space of continuous linear endomorphisms, which contains the space of (continuous observables.On the other hand we state and prove a new pointwise version of the classic Hellmann-Feynman theorem. This new version is not yet present in the literature and follows the idea of A. Bohm concerning the topology which is desiderable to use in Quantum Mechanics. It is indeed out of question that this non-trivial new version of the Hellmann-Feynman theorem is the ideal one - for what concerns the continuous observables on Hilbert spaces, both from a theoretical point of view, since it is the strongest version obtainable in this context - we recall that the pointwise topology is the coarsest one compatible with the linear structure of the space of continuous observables -, and from a practical point of view, because the pointwise topology is the easiest to use among topologies: it brings back the problems to the Hilbert space topology. Moreover, we desire to remark that this basic theorem of Quantum Mechanics, in his most desiderable form, is deeply interlaced with two cornerstones of Functional Analysis: the Banach-Steinhaus theorem and the Baire theorem.
Relativistic tidal disruption events
Directory of Open Access Journals (Sweden)
Levan A.
2012-12-01
Full Text Available In March 2011 Swift detected an extremely luminous and long-lived outburst from the nucleus of an otherwise quiescent, low luminosity (LMC-like galaxy. Named Swift J1644+57, its combination of high-energy luminosity (1048 ergs s−1 at peak, rapid X-ray variability (factors of >100 on timescales of 100 seconds and luminous, rising radio emission suggested that we were witnessing the birth of a moderately relativistic jet (Γ ∼ 2 − 5, created when a star is tidally disrupted by the supermassive black hole in the centre of the galaxy. A second event, Swift J2058+0516, detected two months later, with broadly similar properties lends further weight to this interpretation. Taken together this suggests that a fraction of tidal disruption events do indeed create relativistic outflows, demonstrates their detectability, and also implies that low mass galaxies can host massive black holes. Here, I briefly outline the observational properties of these relativistic tidal flares observed last year, and their evolution over the first year since their discovery.
Levinson's theorem for non-local interactions
International Nuclear Information System (INIS)
Ma Zhongqi; Dai Anying
1987-08-01
The Levinson theorem for a Schroedinger equation with both local and non-local symmetric potentials is studied in terms of the Sturm-Liouville theorem. A new convention for the phase shifts is applied instead of the usual one. It is proved that the usual Levinson theorem holds for the case with both local potential and non-local symmetric cutoff potential which is not necessary to be separable. The problems related with the positive energy bound states and the physical redundant states are also discussed in this paper. (author). 17 refs
The Nelson-Seiberg theorem revised
Kang, Zhaofeng; Li, Tianjun; Sun, Zheng
2013-12-01
The well-accepted Nelson-Seiberg theorem relates R-symmetries to supersymmetry (SUSY) breaking vacua, and provides a guideline for SUSY model building which is the most promising physics beyond the Standard Model. In the case of Wess-Zumino models with perturbative superpotentials, we revise the theorem to a combined necessary and sufficient condition for SUSY breaking which can be easily checked before solving the vacuum. The revised theorem provides a powerful tool to construct either SUSY breaking or SUSY vacua, and offers many practicable applications in low energy SUSY model building and string phenomenology.
Existence theorems for ordinary differential equations
Murray, Francis J
2007-01-01
Theorems stating the existence of an object-such as the solution to a problem or equation-are known as existence theorems. This text examines fundamental and general existence theorems, along with the Picard iterants, and applies them to properties of solutions and linear differential equations.The authors assume a basic knowledge of real function theory, and for certain specialized results, of elementary functions of a complex variable. They do not consider the elementary methods for solving certain special differential equations, nor advanced specialized topics; within these restrictions, th
Tidal Friction in the Earth and Ocean
Ray, R. D.
2006-12-01
"Tidal Friction" is a classic subject in geophysics, with ties to some of the great scientists of the Victorian era. The subject has been reinvigorated over the past decade by space geodesy, and particularly by the Topex/Poseidon satellite altimeter mission. In fact, the topic has now taken on some significance in oceanography, with potential implications for problems of mixing, thermocline maintenance, and the thermohaline circulation. Likewise, tidal measurements have become sufficiently precise to reveal new information about the solid earth. In this respect, the tidal force is an invaluable "probe" of the earth, at frequencies well outside the seismic band. This talk will "follow the energy" of tides while noting some important geophysical implications at each stage. In the present earth-moon-sun configuration, energy for tides is extracted from the earth's rotation. Ancient eclipses bear witness to this, and the discrepancy between Babylonian (and other) observations and tidal predictions yields unique information about the mantle and the overlying fluid envelope. Complementary information comes from tidal anelasticity estimates, which are now available at frequencies ranging from semidiurnal to fortnightly, monthly, and 18.6 years. These data, when combined with various kinds of gravity measurements, are relevant to the present-day sea-level problem. Solid-earth tidal dissipation represents less than 5% of the system total. As has long been realized, the largest energy sink is the ocean. About 70% of the oceanic dissipation occurs in shallow seas (the traditional sink) and 30% in the deep ocean, generally near rugged bottom topography. The latter represents a substantial amount of power, roughly 1 gigawatt, available for generation of internal tides and other baroclinic motions. Experiments like HOME are helping unravel the links between barotropic tides, internal tides, turbulence, and mixing. The latter opens possible linkages to climate, and recent work
Prehospital tidal volume influences hospital tidal volume: A cohort study.
Stoltze, Andrew J; Wong, Terrence S; Harland, Karisa K; Ahmed, Azeemuddin; Fuller, Brian M; Mohr, Nicholas M
2015-06-01
The purposes of the study are to describe current practice of ventilation in a modern air medical system and to measure the association of ventilation strategy with subsequent ventilator care and acute respiratory distress syndrome (ARDS). Retrospective observational cohort study of intubated adult patients (n = 235) transported by a university-affiliated air medical transport service to a 711-bed tertiary academic center between July 2011 and May 2013. Low tidal volume ventilation was defined as tidal volumes less than or equal to 8 mL/kg predicted body weight. Multivariable regression was used to measure the association between prehospital tidal volume, hospital ventilation strategy, and ARDS. Most patients (57%) were ventilated solely with bag valve ventilation during transport. Mean tidal volume of mechanically ventilated patients was 8.6 mL/kg predicted body weight (SD, 0.2 mL/kg). Low tidal volume ventilation was used in 13% of patients. Patients receiving low tidal volume ventilation during air medical transport were more likely to receive low tidal volume ventilation in the emergency department (P tidal volume (P = .840). Low tidal volume ventilation was rare during air medical transport. Air transport ventilation strategy influenced subsequent ventilation but was not associated with ARDS. Copyright © 2015 Elsevier Inc. All rights reserved.
2002-01-01
The moon's gravity imparts tremendous energy to the Earth, raising tides throughout the global oceans. What happens to all this energy? This question has been pondered by scientists for over 200 years, and has consequences ranging from the history of the moon to the mixing of the oceans. Richard Ray at NASA's Goddard Space Flight Center, Greenbelt, Md. and Gary Egbert of the College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Ore. studied six years of altimeter data from the TOPEX/Poseidon satellite to address this question. According to their report in the June 15 issue of Nature, about 1 terawatt, or 25 to 30 percent of the total tidal energy dissipation, occurs in the deep ocean. The remainder occurs in shallow seas, such as on the Patagonian Shelf. 'By measuring sea level with the TOPEX/Poseidon satellite altimeter, our knowledge of the tides in the global ocean has been remarkably improved,' said Richard Ray, a geophysicist at Goddard. The accuracies are now so high that this data can be used to map empirically the tidal energy dissipation. (Red areas, above) The deep-water tidal dissipation occurs generally near rugged bottom topography (seamounts and mid-ocean ridges). 'The observed pattern of deep-ocean dissipation is consistent with topographic scattering of tidal energy into internal motions within the water column, resulting in localized turbulence and mixing', said Gary Egbert an associate professor at OSU. One important implication of this finding concerns the possible energy sources needed to maintain the ocean's large-scale 'conveyor-belt' circulation and to mix upper ocean heat into the abyssal depths. It is thought that 2 terawatts are required for this process. The winds supply about 1 terawatt, and there has been speculation that the tides, by pumping energy into vertical water motions, supply the remainder. However, all current general circulation models of the oceans ignore the tides. 'It is possible that properly
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.)
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.
Tidal power: trends and developments
International Nuclear Information System (INIS)
1992-01-01
This volume covers works and studies on tidal power currently being undertaken, both nationally and internationally. The 20 papers included cover the proposed Mersey barrage, the Severn estuary and several papers on the Severn barrage. The Department of Energy's continued variety of generic work on tidal power and various overseas studies carried out by other experts are also detailed, giving the reader an up to date picture of developments in tidal power worldwide. Separate abstracts have been prepared for the individual papers. (author)
Fixed point theorems for paracompact convex sets
International Nuclear Information System (INIS)
Jiang Jiahe.
1986-08-01
In the present paper a few fixed point theorems are given for upper hemi-continuous mappings from a paracompact convex set to its embracing space, a real, locally convex, Hausdorff topological vector space. (author)
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...
Generalized characterization theorem for quantum logics
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, M.K. (Birkbeck Coll., London (UK). Dept. of Mathematics)
1984-08-11
In this paper the underlying methematical structure of a quantum logic is assumed to form a partially ordered set and not a lattice and a theorem which characterizes orthomodular partially ordered sets is proved.
Tidal Venuses: triggering a climate catastrophe via tidal heating.
Barnes, Rory; Mullins, Kristina; Goldblatt, Colin; Meadows, Victoria S; Kasting, James F; Heller, René
2013-03-01
Traditionally, stellar radiation has been the only heat source considered capable of determining global climate on long timescales. Here, we show that terrestrial exoplanets orbiting low-mass stars may be tidally heated at high-enough levels to induce a runaway greenhouse for a long-enough duration for all the hydrogen to escape. Without hydrogen, the planet no longer has water and cannot support life. We call these planets "Tidal Venuses" and the phenomenon a "tidal greenhouse." Tidal effects also circularize the orbit, which decreases tidal heating. Hence, some planets may form with large eccentricity, with its accompanying large tidal heating, and lose their water, but eventually settle into nearly circular orbits (i.e., with negligible tidal heating) in the habitable zone (HZ). However, these planets are not habitable, as past tidal heating desiccated them, and hence should not be ranked highly for detailed follow-up observations aimed at detecting biosignatures. We simulated the evolution of hypothetical planetary systems in a quasi-continuous parameter distribution and found that we could constrain the history of the system by statistical arguments. Planets orbiting stars with massesplanet orbiting a 0.3 MSun star at 0.12 AU. We found that it probably did not lose its water via tidal heating, as orbital stability is unlikely for the high eccentricities required for the tidal greenhouse. As the inner edge of the HZ is defined by the onset of a runaway or moist greenhouse powered by radiation, our results represent a fundamental revision to the HZ for noncircular orbits. In the appendices we review (a) the moist and runaway greenhouses, (b) hydrogen escape, (c) stellar mass-radius and mass-luminosity relations, (d) terrestrial planet mass-radius relations, and (e) linear tidal theories.
Generalized monotone convergence and Radon-Nikodym theorems
Gudder, S.; Zerbe, J.
1981-11-01
A measure and integration theory is presented in the quantum logic framework. A generalization of the monotone convergence theorem is proved. Counterexamples are used to show that the dominated convergence theorem, Fatou's lemma, Egoroff's theorem, and the additivity of the integral do not hold in this framework. Finally, a generalization of the Radon-Nikodym theorem is proved.
Sahoo- and Wayment-Type Integral Mean Value Theorems
Tiryaki, Aydin; Cakmak, Devrim
2010-01-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…
Convergence Theorems for Partial Sums of Arbitrary Stochastic Sequences
Directory of Open Access Journals (Sweden)
Wang Xiaosheng
2010-01-01
Full Text Available By using Doob's martingale convergence theorem, this paper presents a class of strong limit theorems for arbitrary stochastic sequence. Chow's two strong limit theorems for martingale-difference sequence and Loève's and Petrov's strong limit theorems for independent random variables are the particular cases of the main results.
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 ...
International Nuclear Information System (INIS)
Borghi, Riccardo
2014-01-01
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. (letters and comments)
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
Energy Technology Data Exchange (ETDEWEB)
Stelzenmuller, Nickolas [Univ of Washington; Aliseda, Alberto [Univ of Washington; Palodichuk, Michael [Univ of Washington; Polagye, Brian [Univ of Washington; Thomson, James [Univ of Washington; Chime, Arshiya [Univ of Washington; Malte, Philip [Univ of washington
2014-03-31
This technical report contains results on the following topics: 1) Testing and analysis of sub-scale hydro-kinetic turbines in a flume, including the design and fabrication of the instrumented turbines. 2) Field measurements and analysis of the tidal energy resource and at a site in northern Puget Sound, that is being examined for turbine installation. 3) Conceptual design and performance analysis of hydro-kinetic turbines operating at high blockage ratio, for use for power generation and flow control in open channel flows.
Sedimentary structures of tidal flats
Indian Academy of Sciences (India)
Sedimentary structures of some coastal tropical tidal ﬂats of the east coast of India, and inner estuarine tidal point bars located at 30 to 50 kilometers inland from the coast, have been extensively studied under varying seasonal conditions. The results reveal that physical features such as ﬂaser bedding, herringbone ...
Central limit theorem and almost sure central limit theorem for the ...
Indian Academy of Sciences (India)
where I denotes indicator function. Berkes and Csáki [2] extended this theory and showed that not only the central limit theorem, but every weak limit theorem for independent random variables, subject to minor technical conditions, has an analogous almost sure version. However under our model we only need the simplest ...
Real-time images of tidal recruitment using lung ultrasound.
Tusman, Gerardo; Acosta, Cecilia M; Nicola, Marco; Esperatti, Mariano; Bohm, Stephan H; Suarez-Sipmann, Fernando
2015-12-01
Ventilator-induced lung injury is a form of mechanical damage leading to a pulmonary inflammatory response related to the use of mechanical ventilation enhanced by the presence of atelectasis. One proposed mechanism of this injury is the repetitive opening and closing of collapsed alveoli and small airways within these atelectatic areas-a phenomenon called tidal recruitment. The presence of tidal recruitment is difficult to detect, even with high-resolution images of the lungs like CT scan. The purpose of this article is to give evidence of tidal recruitment by lung ultrasound. A standard lung ultrasound inspection detected lung zones of atelectasis in mechanically ventilated patients. With a linear probe placed in the intercostal oblique position. We observed tidal recruitment within atelectasis as an improvement in aeration at the end of inspiration followed by the re-collapse at the end of expiration. This mechanism disappeared after the performance of a lung recruitment maneuver. Lung ultrasound was helpful in detecting the presence of atelectasis and tidal recruitment and in confirming their resolution after a lung recruitment maneuver.
Ultraviolet and optical observations of tidal disruption events
Directory of Open Access Journals (Sweden)
Gezari S.
2012-12-01
Full Text Available Tidal disruption events are expected to produce a luminous flare of radiation from fallback accretion of tidally disrupted stellar debris onto the central supermassive black hole. The first convincing candidates for tidal disruption events were discovered in the soft X-rays: large-amplitude, luminous, extremely-soft X-ray flares from inactive galaxies in the ROSAT All-Sky survey. However, the sparsely sampled light curves and lack of multiwavelength observations for these candidates make it difficult to directly constrain the parameters of their events (e.g., Eddington ratio, mass of the black hole, type of star disrupted. Here I present a review of the recent progress made in studying tidal disruption events in detail from taking advantage of wide-field, multi-epoch observations of UV and optical surveys (GALEX, SDSS, PTF, Pan-STARRS1 to measure well-sampled light curves, trigger prompt multiwavelength follow-up observations, and measure rates. I conclude with the promising potential of the next generation of optical synoptic surveys, such as LSST, to probe black hole demographics with samples of thousands of tidal disruption events.
Anti-Bell - Refutation of Bell's theorem
Barukčić, Ilija
2012-12-01
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
DEFF Research Database (Denmark)
Duvaa, Uffe; Ørngreen, Rikke; Weinkouff, Anne-Gitte
2012-01-01
Mobile probing is a method, which has been developed for learning about digital work situations, as an approach to discover new grounds. The method can be used when there is a need to know more about users and their work with certain tasks, but where users at the same time are distributed (in time...... and space). Mobile probing was inspired by the cultural probe method, and was influenced by qualitative interview and inquiry approaches. The method has been used in two subsequent projects, involving school children (young adults at 15-17 years old) and employees (adults) in a consultancy company. Findings...... point to mobile probing being a flexible method for uncovering the unknowns, as a way of getting rich data to the analysis and design phases. On the other hand it is difficult to engage users to give in depth explanations, which seem easier in synchronous dialogs (whether online or face2face...
DEFF Research Database (Denmark)
Duvaa, Uffe; Ørngreen, Rikke; Weinkouff Mathiasen, Anne-Gitte
2013-01-01
Mobile probing is a method, developed for learning about digital work situations, as an approach to discover new grounds. The method can be used when there is a need to know more about users and their work with certain tasks, but where users at the same time are distributed (in time and space......). Mobile probing was inspired by the cultural probe method, and was influenced by qualitative interview and inquiry approaches. The method has been used in two subsequent projects, involving school children (young adults at 15-17 years old) and employees (adults) in a consultancy company. Findings point...... to mobile probing being a flexible method for uncovering the unknowns, as a way of getting rich data to the analysis and design phases. On the other hand it is difficult to engage users to give in depth explanations, which seem easier in synchronous dialogs (whether online or face2face). The development...
International Nuclear Information System (INIS)
Lemperiere, F.
2010-01-01
The author first discusses the potential theoretical production of tidal energy in the world and more particularly in France, and compares this potential production with that of hydroelectric energy. He discusses the existence of potentially interesting sites in France in terms of sizing and exploitation modes. He describes the main associated works for turbines and sea walls, impacts on the environment, on the economy and on employment. He discusses the production possibilities and their cost, and the issue of energy storage. He indicates sites which could be built before 2025: Saint-Brieuc, Portbail-Coutainville or Granville, Mers or Cayeux, Penly or Saint-Valery en Caux. For each of this site, the author describes the project implantation, gives an gross assessment of the construction cost, and therefore of the kWh cost
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.
Lindeberg theorem for Gibbs–Markov dynamics
Denker, Manfred; Senti, Samuel; Zhang, Xuan
2017-12-01
A dynamical array consists of a family of functions \\{ fn, i: 1≤slant i≤slant k_n, n≥slant 1\\} and a family of initial times \\{τn, i: 1≤slant i≤slant k_n, n≥slant 1\\} . For a dynamical system (X, T) we identify distributional limits for sums of the form for suitable (non-random) constants s_n>0 and an, i\\in { R} . We derive a Lindeberg-type central limit theorem for dynamical arrays. Applications include new central limit theorems for functions which are not locally Lipschitz continuous and central limit theorems for statistical functions of time series obtained from Gibbs–Markov systems. Our results, which hold for more general dynamics, are stated in the context of Gibbs–Markov dynamical systems for convenience.
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.
Tidal energy site - Tidal energy site mammal/bird survey
National Oceanic and Atmospheric Administration, Department of Commerce — A vessel-based line visual transect survey was conducted for birds and marine mammals near the proposed Snohomish County PUD Admiralty Inlet tidal energy site...
Tidal Venuses: Triggering a Climate Catastrophe via Tidal Heating
Mullins, Kristina; Goldblatt, Colin; Meadows, Victoria S.; Kasting, James F.; Heller, René
2013-01-01
Abstract Traditionally, stellar radiation has been the only heat source considered capable of determining global climate on long timescales. Here, we show that terrestrial exoplanets orbiting low-mass stars may be tidally heated at high-enough levels to induce a runaway greenhouse for a long-enough duration for all the hydrogen to escape. Without hydrogen, the planet no longer has water and cannot support life. We call these planets “Tidal Venuses” and the phenomenon a “tidal greenhouse.” Tidal effects also circularize the orbit, which decreases tidal heating. Hence, some planets may form with large eccentricity, with its accompanying large tidal heating, and lose their water, but eventually settle into nearly circular orbits (i.e., with negligible tidal heating) in the habitable zone (HZ). However, these planets are not habitable, as past tidal heating desiccated them, and hence should not be ranked highly for detailed follow-up observations aimed at detecting biosignatures. We simulated the evolution of hypothetical planetary systems in a quasi-continuous parameter distribution and found that we could constrain the history of the system by statistical arguments. Planets orbiting stars with massestidal heating. We have applied these concepts to Gl 667C c, a ∼4.5 MEarth planet orbiting a 0.3 MSun star at 0.12 AU. We found that it probably did not lose its water via tidal heating, as orbital stability is unlikely for the high eccentricities required for the tidal greenhouse. As the inner edge of the HZ is defined by the onset of a runaway or moist greenhouse powered by radiation, our results represent a fundamental revision to the HZ for noncircular orbits. In the appendices we review (a) the moist and runaway greenhouses, (b) hydrogen escape, (c) stellar mass-radius and mass-luminosity relations, (d) terrestrial planet mass-radius relations, and (e) linear tidal theories. Key Words: Extrasolar terrestrial planets—Habitability—Habitable zone
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
Spectral mapping theorems a bluffer's guide
Harte, Robin
2014-01-01
Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several and many variables. The basic algebraic systems – semigroups, rings and linear algebras – are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Spectral Mapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory.
On luminescence bleaching of tidal channel sediments
DEFF Research Database (Denmark)
Fruergaard, Mikkel; Pejrup, Morten; Murray, Andrew S.
2015-01-01
We investigate the processes responsible for bleaching of the quartz OSL signal from tidal channel sediment. Tidal dynamics are expected to play an important role for complete bleaching of tidal sediments. However, no studies have examined the amount of reworking occurring in tidal channels...... and on tidal flats due to the mixing caused by currents and waves. We apply bed level data to evaluate the amount of vertical sediment reworking in modern tidal channels and at a tidal flat. Cycles of deposition and erosion are measured with a bed level sensor, and the results show that gross sedimentation...... was several times higher than net sedimentation. We propose that tidal channel sediment is bleached either on the tidal flat before it is transported to the tidal channels and incorporated in channel-fill successions or, alternatively, on the shallow intertidal part of the channel banks. Based...
Tidal Creek Sentinel Habitat Database
National Oceanic and Atmospheric Administration, Department of Commerce — The Ecological Research, Assessment and Prediction's Tidal Creeks: Sentinel Habitat Database was developed to support the National Oceanic and Atmospheric...
Tidal locking of habitable exoplanets
Barnes, Rory
2017-12-01
Potentially habitable planets can orbit close enough to their host star that the differential gravity across their diameters can produce an elongated shape. Frictional forces inside the planet prevent the bulges from aligning perfectly with the host star and result in torques that alter the planet's rotational angular momentum. Eventually the tidal torques fix the rotation rate at a specific frequency, a process called tidal locking. Tidally locked planets on circular orbits will rotate synchronously, but those on eccentric orbits will either librate or rotate super-synchronously. Although these features of tidal theory are well known, a systematic survey of the rotational evolution of potentially habitable exoplanets using classic equilibrium tide theories has not been undertaken. I calculate how habitable planets evolve under two commonly used models and find, for example, that one model predicts that the Earth's rotation rate would have synchronized after 4.5 Gyr if its initial rotation period was 3 days, it had no satellites, and it always maintained the modern Earth's tidal properties. Lower mass stellar hosts will induce stronger tidal effects on potentially habitable planets, and tidal locking is possible for most planets in the habitable zones of GKM dwarf stars. For fast-rotating planets, both models predict eccentricity growth and that circularization can only occur once the rotational frequency is similar to the orbital frequency. The orbits of potentially habitable planets of very late M dwarfs ([InlineEquation not available: see fulltext.]) are very likely to be circularized within 1 Gyr, and hence, those planets will be synchronous rotators. Proxima b is almost assuredly tidally locked, but its orbit may not have circularized yet, so the planet could be rotating super-synchronously today. The evolution of the isolated and potentially habitable Kepler planet candidates is computed and about half could be tidally locked. Finally, projected TESS planets
A Dual of the Compression-Expansion Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Henderson Johnny
2007-01-01
Full Text Available This paper presents a dual of the fixed point theorems of compression and expansion of functional type as well as the original Leggett-Williams fixed point theorem. The multi-valued situation is also discussed.
Vector Valued Martingale-Ergodic and Ergodic-Martingale Theorems
Shahidi, Farruh; Ganiev, Inomjon
2012-01-01
We prove martingale-ergodic and ergodic-martingale theorems for vector valued Bochner integrable functions. We obtain dominant and maximal inequalities. We also prove weighted and multiparameter martingale-ergodic and ergodic martingale theorems.
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.…
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating Universes, expanding everywhere with a non-vanishing spatial average of the matter variables, show severe geodesic incompletness in the past. Another way of stating ...
Some Generalizations of Jungck's Fixed Point Theorem
Directory of Open Access Journals (Sweden)
J. R. Morales
2012-01-01
Full Text Available We are going to generalize the Jungck's fixed point theorem for commuting mappings by mean of the concepts of altering distance functions and compatible pair of mappings, as well as, by using contractive inequalities of integral type and contractive inequalities depending on another function.
The Story of Fermat's Last Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 3. The Story of Fermat's Last Theorem. Shailesh A Shirali. Book Review Volume 4 Issue 3 March 1999 pp 81-84. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/004/03/0081-0084. Author Affiliations.
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…
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.
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 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)
A Short Proof of Klee's Theorem
Zanazzi, John J.
2013-01-01
In 1959, Klee proved that a convex body $K$ is a polyhedron if and only if all of its projections are polygons. In this paper, a new proof of this theorem is given for convex bodies in $\\mathbb{R}^3$.
Czech Academy of Sciences Publication Activity Database
Narins, L.; Tran, Tuan
2017-01-01
Roč. 85, č. 2 (2017), s. 496-524 ISSN 0364-9024 Institutional support: RVO:67985807 Keywords : Turán’s theorem * stability method * multipartite version Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.601, year: 2016
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
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)
Kempe's Linkages and the Universality Theorem
Indian Academy of Sciences (India)
sriranga
. He is currently ... Theorem, has a distinctive standing in kinematics. He was the first to uniquely address the precise tracing of ... A simple transformation from Cartesian (i.e., x, y) to polar (i.e, r, µ) coordinates allows f(x; y) to be ex- pressed as a ...
A composition theorem for decision tree complexity
Montanaro, Ashley
2013-01-01
We completely characterise the complexity in the decision tree model of computing composite relations of the form h = g(f^1,...,f^n), where each relation f^i is boolean-valued. Immediate corollaries include a direct sum theorem for decision tree complexity and a tight characterisation of the decision tree complexity of iterated boolean functions.
An integrality theorem for spinc manifolds
International Nuclear Information System (INIS)
Seade, J.A.
1990-04-01
A spin c manifold M n is an oriented, Riemannian manifold with an associated hermitian live bundle det(M), together with a lifting to B(spin n c ) of the classifying map of the bundle TMxU(1). We prove here an integrality theorem for spin c manifolds. 11 refs
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
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…
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 2. Current Issue Volume 23 | Issue 2. February 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...
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.
On the exactness of soft theorems
Guerrieri, Andrea L.; Huang, Yu-tin; Li, Zhizhong; Wen, Congkao
2017-12-01
Soft behaviours of S-matrix for massless theories reflect the underlying symmetry principle that enforces its masslessness. As an expansion in soft momenta, sub-leading soft theorems can arise either due to (I) unique structure of the fundamental vertex or (II) presence of enhanced broken-symmetries. While the former is expected to be modified by infrared or ultraviolet divergences, the latter should remain exact to all orders in perturbation theory. Using current algebra, we clarify such distinction for spontaneously broken (super) Poincaré and (super) conformal symmetry. We compute the UV divergences of DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft theorems, while type (I) are shown to be broken and the soft-modifying higher-dimensional operators are identified. As further evidence for the exactness of type (II) soft theorems, we consider the α' expansion of both super and bosonic open strings amplitudes, and verify the validity of the translation symmetry breaking soft-theorems up to O({α}^' 6}) . Thus the massless S-matrix of string theory "knows" about the presence of D-branes.
Ptolemy's Theorem and Familiar Trigonometric Identities.
Bidwell, James K.
1993-01-01
Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)
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.
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...
Directory of Open Access Journals (Sweden)
SEVER ANGEL POPESCU
2015-03-01
Full Text Available In this note we make some remarks on the classical Laguerre’s theorem and extend it and some other old results of Walsh and Gauss-Lucas to the so called trace series associated with transcendental elements of the completion of the algebraic closure of Q in C, with respect to the spectral norm:
Lagrange’s Four-Square Theorem
Directory of Open Access Journals (Sweden)
Watase Yasushige
2015-02-01
Full Text Available This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23].
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
Explorations of the Gauss-Lucas Theorem
Brilleslyper, Michael A.; Schaubroeck, Beth
2017-01-01
The Gauss-Lucas Theorem is a classical complex analysis result that states the critical points of a single-variable complex polynomial lie inside the closed convex hull of the zeros of the polynomial. Although the result is well-known, it is not typically presented in a first course in complex analysis. The ease with which modern technology allows…
The Archimedes Principle and Gauss's Divergence Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 3; Issue 11. The Archimedes Principle and Gauss's Divergence Theorem. Subhashis Nag. General Article Volume 3 Issue 11 November 1998 pp 18-29. Fulltext. Click here to view fulltext PDF. Permanent link:
On the Schwartz space isomorphism theorem for rank one ...
Indian Academy of Sciences (India)
consists of analytic functions on the strip a. ∗. ϵ = {λ ∈ C||Im λ| ≤ ϵ}. Anticipating these and other ..... R>0 HR(a∗. C. ). We state the following topological Paley–. Wiener theorem for the K-types. The proof of this theorem follows from III, Theorem 5.11 of [9] and Lemma 2.1. Theorem 3.7. The δ-spherical transform defined in ...
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.
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.
Unitarity-Cuts, Stokes' Theorem and Berry's Phase
Mastrolia, Pierpaolo
2010-01-01
Two-particle unitarity-cuts of scattering amplitudes can be efficiently computed by applying Stokes' Theorem, in the fashion of the Generalised Cauchy Theorem. Consequently, the Optical Theorem can be related to the Berry Phase, showing how the imaginary part of arbitrary one-loop Feynman amplitudes can be interpreted as the flux of a complex 2-form.
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
A new proof of the theorem: Harmonic manifolds with minimal ...
Indian Academy of Sciences (India)
In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting theorem.
Fluctuation theorems and orbital magnetism in nonequilibrium state
Indian Academy of Sciences (India)
Fluctuation theorem; Jarzynski equality; orbital magnetism. PACS Nos 05.70.Ln; 05.40.Jc; 05.40.-a; 05.40.Ca. 1. Introduction. Recent developments in nonequilibrium statistical mechanics has led to the discov- ery of several rigorous theorems for systems far away from equilibrium [1–10]. The fluctuation theorems describe ...
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.
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
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered o...
Remnants of strong tidal interactions
International Nuclear Information System (INIS)
Mcglynn, T.A.
1990-01-01
This paper examines the properties of stellar systems that have recently undergone a strong tidal shock, i.e., a shock which removes a significant fraction of the particles in the system, and where the shocked system has a much smaller mass than the producer of the tidal field. N-body calculations of King models shocked in a variety of ways are performed, and the consequences of the shocks are investigated. The results confirm the prediction of Jaffe for shocked systems. Several models are also run where the tidal forces on the system are constant, simulating a circular orbit around a primary, and the development of tidal radii under these static conditions appears to be a mild process which does not dramatically affect material that is not stripped. The tidal radii are about twice as large as classical formulas would predict. Remnant density profiles are compared with a sample of elliptical galaxies, and the implications of the results for the development of stellar populations and galaxies are considered. 38 refs
International Nuclear Information System (INIS)
Denny, Eleanor
2009-01-01
Concern over global climate change has led policy makers to accept the importance of reducing greenhouse gas emissions. This in turn has led to a large growth in clean renewable generation for electricity production. Much emphasis has been on wind generation as it is among the most advanced forms of renewable generation, however, its variable and relatively unpredictable nature result in increased challenges for electricity system operators. Tidal generation on the other hand is almost perfectly forecastable and as such may be a viable alternative to wind generation. This paper calculates the break-even capital cost for tidal generation on a real electricity system. An electricity market model is used to determine the impact of tidal generation on the operating schedules of the conventional units on the system and on the resulting cycling costs, emissions and fuel savings. It is found that for tidal generation to produce positive net benefits for the case study, the capital costs would have to be less than Euro 510,000 per MW installed which is currently an unrealistically low capital cost. Thus, it is concluded that tidal generation is not a viable option for the case system at the present time.
Tidal effects on stellar activity
Poppenhaeger, K.
2017-10-01
The architecture of many exoplanetary systems is different from the solar system, with exoplanets being in close orbits around their host stars and having orbital periods of only a few days. We can expect interactions between the star and the exoplanet for such systems that are similar to the tidal interactions observed in close stellar binary systems. For the exoplanet, tidal interaction can lead to circularization of its orbit and the synchronization of its rotational and orbital period. For the host star, it has long been speculated if significant angular momentum transfer can take place between the planetary orbit and the stellar rotation. In the case of the Earth-Moon system, such tidal interaction has led to an increasing distance between Earth and Moon. For stars with Hot Jupiters, where the orbital period of the exoplanet is typically shorter than the stellar rotation period, one expects a decreasing semimajor axis for the planet and enhanced stellar rotation, leading to increased stellar activity. Also excess turbulence in the stellar convective zone due to rising and subsiding tidal bulges may change the magnetic activity we observe for the host star. I will review recent observational results on stellar activity and tidal interaction in the presence of close-in exoplanets, and discuss the effects of enhanced stellar activity on the exoplanets in such systems.
ENHANCED OFF-CENTER STELLAR TIDAL DISRUPTIONS BY SUPERMASSIVE BLACK HOLES IN MERGING GALAXIES
International Nuclear Information System (INIS)
Liu, F. K.; Chen, Xian
2013-01-01
Off-center stellar tidal disruption flares have been suggested to be a powerful probe of recoiling supermassive black holes (SMBHs) out of galactic centers due to anisotropic gravitational wave radiations. However, off-center tidal flares can also be produced by SMBHs in merging galaxies. In this paper, we computed the tidal flare rates by dual SMBHs in two merging galaxies before the SMBHs become self-gravitationally bounded. We employ an analytical model to calculate the tidal loss-cone feeding rates for both SMBHs, taking into account two-body relaxation of stars, tidal perturbations by the companion galaxy, and chaotic stellar orbits in triaxial gravitational potential. We show that for typical SMBHs with masses 10 7 M ☉ , the loss-cone feeding rates are enhanced by mergers up to Γ ∼ 10 –2 yr –1 , about two orders of magnitude higher than those by single SMBHs in isolated galaxies and about four orders of magnitude higher than those by recoiling SMBHs. The enhancements are mainly due to tidal perturbations by the companion galaxy. We suggest that off-center tidal flares are overwhelmed by those from merging galaxies, making the identification of recoiling SMBHs challenging. Based on the calculated rates, we estimate the relative contributions of tidal flare events by single, binary, and dual SMBH systems during cosmic time. Our calculations show that the off-center tidal disruption flares by un-bound SMBHs in merging galaxies contribute a fraction comparable to that by single SMBHs in isolated galaxies. We conclude that off-center tidal disruptions are powerful tracers of the merging history of galaxies and SMBHs.
Oseledec multiplicative ergodic theorem for laminations
Nguyên, Viêt-Anh
2017-01-01
Given a n-dimensional lamination endowed with a Riemannian metric, the author introduces the notion of a multiplicative cocycle of rank d, where n and d are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, the author defines the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. He also proves an Oseledec multiplicative ergodic theorem in this context. This theorem implies the existence of an Oseledec decomposition almost everywhere which is holonomy invariant. Moreover, in the case of differentiable cocycles the author establishes effective integral estimates for the Lyapunov exponents. These results find applications in the geometric and dynamical theory of laminations. They are also applicable to (not necessarily closed) laminations with singularities. Interesting holonomy properties of a generic leaf of a foliation are obtained...
Subleading soft graviton theorem for loop amplitudes
Sen, Ashoke
2017-11-01
Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.
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.
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.
An elementary approach to gap theorems
Indian Academy of Sciences (India)
In the second class, it is assumed that the sectional curvature has a definite sign and approaches zero at a certain rate. One of the early results in this direction was by Siu and Yau [5]. A by-product of this paper is a completely elementary and short proof of the main result in [5]. A host of theorems was also proved by Greene.
Remarks on some zero-sum theorems
Indian Academy of Sciences (India)
(1996) 100–103. [9] Griffiths Simon, The Erd˝os-Ginzburg-Ziv theorem with units, Discrete Math. 308(23). (2008) 5473–5484, doi:10.1016/j.disc.2007.09.060. [10] Luca Florian, A generalization of a classical zero-sum problem, Discrete Math. 307(13). (2007) 1672–1678. [11] Nathanson Melvyn B, Additive number theory.
Some generalizations of the virial theorem
International Nuclear Information System (INIS)
Teller, E.
1986-01-01
Generalizations of the virial theorem are derived: In atomic physics, in systems including electromagnetic radiation, in Newtonian gravitation, and in general relativity and also some types of nuclear forces. The cases discussed are limited to potentials which can be produced by the exchange of one particle, which include potentials of the form 1/r. The method used is to set equal a change in energy produced by an infinitesimal similarity transformation to a change of energy obtained by a first-order perturbation
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
A reduction theorem for supremum operators
Czech Academy of Sciences Publication Activity Database
Gogatishvili, Amiran; Pick, L.
2007-01-01
Roč. 208, č. 1 (2007), s. 270-279 ISSN 0377-0427 R&D Projects: GA ČR GA201/05/2033 Grant - others:GAČR(CZ) GA201/03/0935 Institutional research plan: CEZ:AV0Z10190503 Keywords : reduction theorems * Hardy operators * supremum operators Subject RIV: BA - General Mathematics Impact factor: 0.943, year: 2007
Indian Academy of Sciences (India)
The space C[0,1] is also not reflexive. One of the nice consequences of the Riesz representation theorem is that every Hilbert space is reflexive. 5. Vector Valued Integration. Let us consider the unit interval [0,1] endowed with the Lebesgue- measure. Let V be a normed linear space over R. Let ϕ : [0,1] →. V be a continuous ...
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
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)
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
Tidal variations of earth rotation
Yoder, C. F.; Williams, J. G.; Parke, M. E.
1981-01-01
The periodic variations of the earths' rotation resulting from the tidal deformation of the earth by the sun and moon were rederived including terms with amplitudes of 0.002 millisec and greater. The series applies to the mantle, crust, and oceans which rotate together for characteristic tidal periods; the scaling parameter is the ratio of the fraction of the Love number producing tidal variations in the moment of inertia of the coupled mantle and oceans (k) to the dimensionless polar moment of inertia of the coupled moments (C). The lunar laser ranging data shows that k/C at monthly and fortnightly frequencies equals 0.99 + or - 0.15 and 0.99 + or - 0.20 as compared to the theoretical value of 0.94 + or - 0.04.
Theorem Proving In Higher Order Logics
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
Soft theorems from conformal field theory
Energy Technology Data Exchange (ETDEWEB)
Lipstein, Arthur E. [II. Institute for Theoretical Physics, University of Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany)
2015-06-24
Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambtwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.
The 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)
Properties of active tidal bedforms
DEFF Research Database (Denmark)
Winter, Christian; Lefebvre, Alice; Becker, Marius
2016-01-01
Bedforms of various shapes and sizes are ubiquitous in tidal channels, inlets and estuaries. They constitute a form roughness which has a large scale effect on the hydrodynamics and sediment transport of coastal environments. It has been shown that this form roughness can be expressed in terms...... of the lee side slope of bedforms. This study compiles data on the topography and hydraulics of compound dunes from different settings in the German Bight to discuss implications of a critical lee slope in tidal environments with reversing flow. Data from the Weser estuary is used to exemplify and quantify...
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
The distribution and tapping tidal energy
Directory of Open Access Journals (Sweden)
Zygmunt Kowalik
2004-09-01
Full Text Available Tidal power along tidal shores has been used for centuries to run small tidal mills. Generating electricity by tapping tidal power proved to be very successful only in the last century through the tidal power plant constructed in 1967 in La Rance, France. This used a large barrier to generate the sea level head necessary for driving turbines. Construction of such plants evolved very slowly because of prohibitive costs and concerns about the environmental impact. Developments in the construction of small, efficient and inexpensive underwater turbines admit the possibility of small scale operations that will use local tidal currents to bring electricity to remote locations. Since the generation of such electricity is concerned with the tidal energy in local water bodies, it is important to understand the site-specific energy balance, i.e., the energy flowing in through open boundaries, and the energy generated and dissipated within the local domain. The question is how to tap the tidal energy while keeping possible changes in the present tidal regimes to a minimum. The older approach of constructing barrages may still be quite useful in some locations. The basics of such tidal power plants constructed in a small bay are analyzed in order to understand the principal parameter for tidal plant evaluation, i.e., the power produced. The new approach is to place turbines - devices similar to windmills - in the pathway of tidal currents. Theoretically, the amount of power available by such turbines for electricity generation is proportional to the water density and velocity cubed of the tidal flow. The naturally dissipated tidal power due to bottom friction forces is also proportional to the cube of the velocity. Because of this similarity, the exploitation of tidal energy can be directed to reinvesting the naturally dissipated power into tidal power for the generation of electricity. This approach to tidal power exploitation is better tuned
Turning the tide : tidal power in the UK
Sustainable Development Commission
2007-01-01
Contents: Turning the tide : tidal power in the UK -- Executive summary -- Tidal power in the UK : research report 1 : UK tidal resource assessment -- Tidal power in the UK : research report 2 : tidal technologies overview -- Tidal power in the UK : research report 3 : Severn barrage proposals -- Tidal power in the UK : research report 4 : Severn non-barrage options -- Tidal power in the UK : research report 5 : UK case studies. Summarised in the Welsh language version of the executive ...
Facies architecture of heterolithic tidal deposits : The Holocene Holland Tidal Basin
Donselaar, M.E.; Geel, C.R.
2007-01-01
The size, shape and spatial position of lithofacies types (or facies architecture) in a tidal estuarine basin are complex and therefore difficult to model. The tidal currents in the basin concentrate sand-sized sediment in a branching pattern of tidal channels and fringing tidal flats. Away from the
Relativistic theory of tidal Love numbers
Binnington, Taylor; Poisson, Eric
2009-01-01
In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neut...
Morphodynamics of ebb-tidal deltas
Ridderinkhof, W.
2016-01-01
Ebb-tidal deltas are bodies of sand that are located seaward of tidal inlets. The latter connect the open sea with a back-barrier basin and separate barrier islands. The morphology (e.g., sand volume, geometry, shoal formation) of ebb-tidal deltas evolves continuously, both due to natural processes
Tidal energy - a technology review
International Nuclear Information System (INIS)
Price, R.
1991-01-01
The tides are caused by gravitational attraction of the sun and the moon acting upon the world's oceans. This creates a clean renewable form of energy which can in principle be tapped for the benefit of mankind. This paper reviews the status of tidal energy, including the magnitude of the resource, the technology which is available for its extraction, the economics, possible environmental effects and non-technical barriers to its implementation. Although the total energy flux of the tides is large, at about 2 TW, in practice only a very small fraction of this total potential can be utilised in the foreseeable future. This is because the energy is spread diffusely over a wide area, requiring large and expensive plant for its collection, and is often available remote from centres of consumption. The best mechanism for exploiting tidal energy is to employ estuarine barrages at suitable sites with high tidal ranges. The technology is relatively mature and components are commercially available now. Also, many of the best sites for implementation have been identified. However, the pace and extent of commercial exploitation of tidal energy is likely to be significantly influenced, both by the treatment of environmental costs of competing fossil fuels, and by the availability of construction capital at modest real interest rates. The largest projects could require the involvement of national governments if they are to succeed. (author) 8 figs., 2 tabs., 19 refs
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.
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
Fatou type theorems for series in Mittag-Leffler functions
Paneva-Konovska, Jordanka
2012-11-01
In studying the behaviour of series, defined by means of the Mittag-Leffler functions, on the boundary of its domain of convergence in the complex plane, we give analogues of the classical theorems for the power series like Cauchy-Hadamard, Abel, as well as Fatou theorems. The asymptotic formulae for the Mittag-Leffler functions in the cases of "large" values of indices that are used in the proofs of the convergence theorems for the considered series are also provided.
On Upper Bounds on the Church-Rosser Theorem
Directory of Open Access Journals (Sweden)
Ken-etsu Fujita
2017-01-01
Full Text Available The Church-Rosser theorem in the type-free lambda-calculus is well investigated both for beta-equality and beta-reduction. We provide a new proof of the theorem for beta-equality with no use of parallel reductions, but simply with Takahashi's translation (Gross-Knuth strategy. Based on this, upper bounds for reduction sequences on the theorem are obtained as the fourth level of the Grzegorczyk hierarchy.
Borsuk-Ulam theorem in infinite-dimensional Banach spaces
International Nuclear Information System (INIS)
Gel'man, B D
2002-01-01
The well-known classical Borsuk-Ulam theorem has a broad range of applications to various problems. Its generalization to infinite-dimensional spaces runs across substantial difficulties because its statement is essentially finite-dimensional. A result established in the paper is a natural generalization of the Borsuk-Ulam theorem to infinite-dimensional Banach spaces. Applications of this theorem to various problems are discussed
Fixed point theorems for generalized weakly contractive mappings
Directory of Open Access Journals (Sweden)
Ramendra Krishna Bose
2009-12-01
Full Text Available In this paper several fixed point theorems for generalized weakly contractive mappings in a metric space setting are proved. The set of generalized weakly contractive mappings considered in this paper contains the family of weakly contractive mappings as a proper subset. Fixed point theorems for single and multi-valued mappings, approximating scheme for common fixed point for some mappings, and fixed point theorems for fuzzy mappings are presented. It extends the work of several authors including Bose and Roychowdhury.
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.
Lampart, Jonas; Lewin, Mathieu
2015-12-01
We prove a generalized version of the RAGE theorem for N-body quantum systems. The result states that only bound states of systems with {0 ≤slant n ≤slant N} particles persist in the long time average. The limit is formulated by means of an appropriate weak topology for many-body systems, which was introduced by the second author in a previous work, and is based on reduced density matrices. This topology is connected to the weak-* topology of states on the algebras of canonical commutation or anti-commutation relations, and we give a formulation of our main result in this setting.
Interval logic. Proof theory and theorem proving
DEFF Research Database (Denmark)
Rasmussen, Thomas Marthedal
2002-01-01
of a direction of an interval, and present a sound and complete Hilbert proof system for it. Because of its generality, SIL can conveniently act as a general formalism in which other interval logics can be encoded. We develop proof theory for SIL including both a sequent calculus system and a labelled natural...... deduction system. We conduct theoretical investigations of the systems with respect to subformula properties, proof search, etc. The generic theorem proving system Isabelle is used as a framework for encoding both proof theoretical systems. We consider a number of examples/small case-studies and discuss...
A Levinson-Sjoeberg type theorem. Applications
International Nuclear Information System (INIS)
Gaisin, A M; Kinzyabulatov, I G
2008-01-01
A generalization of the well-known Levinson-Sjoeberg theorem is obtained for a family of analytic functions f that have estimates of the form |f(z)|≤M(dist(z,γ)) outside an arc γ, where M is a decreasing function on (0,∞) that is unbounded in a neighbourhood of the origin. Applications to questions of quasianalyticity for Carleman classes are indicated as well as to the completeness of a system of exponentials on arcs, to analytic continuation and to representation by Dirichlet series. Bibliography: 24 titles.
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.
Applicability constraints of the equivalence theorem
Energy Technology Data Exchange (ETDEWEB)
Dobado, A.; Pelaez, J.R. [Departamento de Fisica Teorica, Universidad Complutense, 28040 Madrid (Spain); Urdiales, M.T. [Departamento de Fisica Teorica, Universidad Autonoma, 28049 Madrid (Spain)
1997-12-01
In this work we study the applicability of the equivalence theorem, either for unitary models or within an effective Lagrangian approach. There are two types of limitations: the existence of a validity energy window and the use of the lowest order in the electroweak constants. For the first kind, we consider some methods, based on dispersion theory or the large N limit, that allow us to extend the applicability. For the second, we obtain numerical estimates of the effect of neglecting higher orders in the perturbative expansion. {copyright} {ital 1997} {ital The American Physical Society}
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.
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.
Maine Tidal Power Initiative: Environmental Impact Protocols For Tidal Power
Energy Technology Data Exchange (ETDEWEB)
Peterson, Michael Leroy [Univ. of Maine, Orono, ME; Zydlewski, Gayle Barbin [Univ. of Maine, Orono, ME; Xue, Huijie [Univ. of Maine, Orono, ME; Johnson, Teresa R. [Univ. of Maine, Orono, ME
2014-02-02
The Maine Tidal Power Initiative (MTPI), an interdisciplinary group of engineers, biologists, oceanographers, and social scientists, has been conducting research to evaluate tidal energy resources and better understand the potential effects and impacts of marine hydro-kinetic (MHK) development on the environment and local community. Project efforts include: 1) resource assessment, 2) development of initial device design parameters using scale model tests, 3) baseline environmental studies and monitoring, and 4) human and community responses. This work included in-situ measurement of the environmental and social response to the pre-commercial Turbine Generator Unit (TGU®) developed by Ocean Renewable Power Company (ORPC) as well as considering the path forward for smaller community scale projects.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
Energy Technology Data Exchange (ETDEWEB)
Woolgar, Eric, E-mail: ewoolgar@ualberta.ca [Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1 (Canada); Wylie, William, E-mail: wwylie@syr.edu [215 Carnegie Building, Department of Mathematics, Syracuse University, Syracuse, New York 13244 (United States)
2016-02-15
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
Central limit theorem and almost sure central limit theorem for the ...
Indian Academy of Sciences (India)
College of Mathematics and Information Science, Henan Normal University,. 453007 Henan, China ... theorem for products of some partial sums of independent identically distributed random variables. Keywords. ... Let (Xn)n≥1 be a sequence of independent identically distributed (i.i.d.) positive random variables (r.v.).
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.
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...
Microscopic Irreversibility and the H Theorem
Magpantay, Jose A.
2013-02-01
Time-reversal had always been assumed to be a symmetry of physics at the fundamental level. In this paper we will explore the violations of time-reversal symmetry at the fundamental level and the consequence on thermodynamic systems. First, we will argue from current physics that the universe dynamics is not time-reversal invariant. Second, we will argue that any thermodynamic system cannot be isolated completely from the universe. We then discuss how these two make the dynamics of thermodynamics systems very weakly irreversible at the classical and quantum level. Since time-reversal is no longer a symmetry of realistic systems, the problem of how macroscopic irreversibility arises from microscopic reversibility becomes irrelevant because there is no longer microscopic reversibility. At the classical level of a thermodynamic system, we show that the H theorem of Boltzmann is still valid even without microscopic reversibility. We do this by deriving a modified H theorem, which still shows entropy monotonically increasing. At the quantum level, we explicitly show the effect of CP violation, small irreversible changes on the internal states of the nuclear and atomic energy levels of thermodynamic systems. Thus, we remove Loschmidt's objection to Boltzmann's ideas.
Dynamical modeling of tidal streams
International Nuclear Information System (INIS)
Bovy, Jo
2014-01-01
I present a new framework for modeling the dynamics of tidal streams. The framework consists of simple models for the initial action-angle distribution of tidal debris, which can be straightforwardly evolved forward in time. Taking advantage of the essentially one-dimensional nature of tidal streams, the transformation to position-velocity coordinates can be linearized and interpolated near a small number of points along the stream, thus allowing for efficient computations of a stream's properties in observable quantities. I illustrate how to calculate the stream's average location (its 'track') in different coordinate systems, how to quickly estimate the dispersion around its track, and how to draw mock stream data. As a generative model, this framework allows one to compute the full probability distribution function and marginalize over or condition it on certain phase-space dimensions as well as convolve it with observational uncertainties. This will be instrumental in proper data analysis of stream data. In addition to providing a computationally efficient practical tool for modeling the dynamics of tidal streams, the action-angle nature of the framework helps elucidate how the observed width of the stream relates to the velocity dispersion or mass of the progenitor, and how the progenitors of 'orphan' streams could be located. The practical usefulness of the proposed framework crucially depends on the ability to calculate action-angle variables for any orbit in any gravitational potential. A novel method for calculating actions, frequencies, and angles in any static potential using a single orbit integration is described in the Appendix.
Prospects for Fundy tidal power
International Nuclear Information System (INIS)
Clark, R.H.
1997-01-01
The Bay of Fundy in Canada probably possesses the most favourable conditions in the world for the exploitation of tidal energy. The results of the comprehensive investigations carried out during the past quarter-century are reviewed together with operating and environmental aspects of the modest (20 MW) Annapolis Tidal Power Station, commissioned in 1984, the primary purpose of which was to evaluate the operation of a large (7.6 m) diameter Straflo turbine unit under low heads. The results of the operating and maintenance experience for the Annapolis Station are reviewed as well as the results of the environmental/ecological studies that have been on-going in the Annapolis Basin. The tidal power investigations have shown that a 1400 MW development at the mouth of the Cumberland Basin, at the head of the bay of Fundy, is technically and economically feasible and that its output would probably be competitive with fossil-fired plants, particularly if a 'green' accounting technique were applied to such energy sources. The importance of timing, if the exploitation of this non-polluting, renewable and completely predicable source is to be used to meet the future electrical energy needs of the maritime provinces, is discussed. (author)
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
Generalizations of Karp's theorem to elastic scattering theory
Tuong, Ha-Duong
Karp's theorem states that if the far field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle in R2 is invariant under the group of rotations, then the scatterer is a circle. The theorem is generalized to the elastic scattering problems and the axisymmetric scatterers in R3.
On Euler's Theorem for Homogeneous Functions and Proofs Thereof.
Tykodi, R. J.
1982-01-01
Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)
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…
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.
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.
On the Weighted Mean Value Theorem for Integrals
Polezzi, M.
2006-01-01
The Mean Value Theorem for Integrals is a powerful tool, which can be used to prove the Fundamental Theorem of Calculus, and to obtain the average value of a function on an interval. On the other hand, its weighted version is very useful for evaluating inequalities for definite integrals. This article shows the solutions on applying the weighted…
Caristi Fixed Point Theorem in Metric Spaces with a Graph
Directory of Open Access Journals (Sweden)
M. R. Alfuraidan
2014-01-01
Full Text Available We discuss Caristi’s fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi’s fixed point theorem. It extends some recent works on the extension of Banach contraction principle to metric spaces with graph.
An integral Riemann-Roch theorem for surface bundles
DEFF Research Database (Denmark)
Madsen, Ib Henning
2010-01-01
This paper is a response to a conjecture by T. Akita about an integral Riemann–Roch theorem for surface bundles.......This paper is a response to a conjecture by T. Akita about an integral Riemann–Roch theorem for surface bundles....
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.)
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 ...
Szemerédi's theorem and problems on arithmetic progressions
Shkredov, I. D.
2006-12-01
Szemerédi's famous theorem on arithmetic progressions asserts that every subset of integers of positive asymptotic density contains arithmetic progressions of arbitrary length. His remarkable theorem has been developed into a major new area of combinatorial number theory. This is the topic of the present survey.
Fluctuation theorems and orbital magnetism in nonequilibrium state
Indian Academy of Sciences (India)
There has been an explosion in the number of fluctuation theorems relating var- ious physical quantities ... well-known Bohr–van-Leeuwen theorem states that a classical thermodynamic equi- librium system does not ... Thermodynamic work done on the system for case (i) (or the input energy injected into the system) for an ...
Rank theorem in infinite dimension and lagrange multipliers
Blot, Joël
2018-01-01
We use an extension to the infinite dimension of the rank theorem of the differential calculus to establish a Karush-Huhn-Tucker theorem for optimization problems in Banach spaces. We provide an application to variational problems on bounded processus under equality constraints.
Computer Algebra Systems and Theorems on Real Roots of Polynomials
Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.
2010-01-01
A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)
A note on the Fuglede–Putnam theorem
Indian Academy of Sciences (India)
Introduction and preliminaries. In this note, we use the notion of a bounding sequence for an unbounded normal opera- tor to prove the unbounded version and a generalization of the Fuglede–Putnam theorem. [6]. This paper gives a new and much simpler proof of the rather complicated proof of Theorem 5 of [3] due to ...
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 ...
Level reduction and the quantum threshold theorem
Aliferis, Panagiotis (Panos)
Computers have led society to the information age revolutionizing central aspects of our lives from production and communication to education and entertainment. There exist, however, important problems which are intractable with the computers available today and, experience teaches us, will remain so even with the more advanced computers we can envision for tomorrow.Quantum computers promise speedups to some of these important but classically intractable problems. Simulating physical systems, a problem of interest in a diverse range of areas from testing physical theories to understanding chemical reactions, and solving number factoring, a problem at the basis of cryptographic protocols that are used widely today on the internet, are examples of applications for which quantum computers, when built, will offer a great advantage over what is possible with classical computer technology.The construction of a quantum computer of sufficient scale to solve interesting problems is, however, especially challenging. The reason for this is that, by its very nature, operating a quantum computer will require the coherent control of the quantum state of a very large number of particles. Fortunately, the theory of quantum error correction and fault-tolerant quantum computation gives us confidence that such quantum states can be created, can be stored in memory and can also be manipulated provided the quantum computer can be isolated to a sufficient degree from sources of noise.One of the central results in the theory of fault-tolerant quantum computation, the quantum threshold theorem shows that a noisy quantum computer can accurately and efficiently simulate any ideal quantum computation provided that noise is weakly correlated and its strength is below a critical value known as the quantum accuracy threshold. This thesis provides a simpler and more transparent non-inductive proof of this theorem based on the concept of level reduction. This concept is also used in proving the
International Nuclear Information System (INIS)
Efroimsky, Michael; Makarov, Valeri V.
2013-01-01
Tidal torques play a key role in rotational dynamics of celestial bodies. They govern these bodies' tidal despinning and also participate in the subtle process of entrapment of these bodies into spin-orbit resonances. This makes tidal torques directly relevant to the studies of habitability of planets and their moons. Our work begins with an explanation of how friction and lagging should be built into the theory of bodily tides. Although much of this material can be found in various publications, a short but self-consistent summary on the topic has been lacking in the hitherto literature, and we are filling the gap. After these preparations, we address a popular concise formula for the tidal torque, which is often used in the literature, for planets or stars. We explain why the derivation of this expression, offered in the paper by Goldreich and in the books by Kaula (Equation (4.5.29)) and Murray and Dermott (Equation (4.159)), implicitly sets the time lag to be frequency independent. Accordingly, the ensuing expression for the torque can be applied only to bodies having a very special (and very hypothetical) rheology which makes the time lag frequency independent, i.e., the same for all Fourier modes in the spectrum of tide. This expression for the torque should not be used for bodies of other rheologies. Specifically, the expression cannot be combined with an extra assertion of the geometric lag being constant, because at finite eccentricities the said assumption is incompatible with the constant-time-lag condition.
Energy Technology Data Exchange (ETDEWEB)
Efroimsky, Michael; Makarov, Valeri V., E-mail: michael.efroimsky@usno.navy.mil, E-mail: vvm@usno.navy.mil [US Naval Observatory, Washington, DC 20392 (United States)
2013-02-10
Tidal torques play a key role in rotational dynamics of celestial bodies. They govern these bodies' tidal despinning and also participate in the subtle process of entrapment of these bodies into spin-orbit resonances. This makes tidal torques directly relevant to the studies of habitability of planets and their moons. Our work begins with an explanation of how friction and lagging should be built into the theory of bodily tides. Although much of this material can be found in various publications, a short but self-consistent summary on the topic has been lacking in the hitherto literature, and we are filling the gap. After these preparations, we address a popular concise formula for the tidal torque, which is often used in the literature, for planets or stars. We explain why the derivation of this expression, offered in the paper by Goldreich and in the books by Kaula (Equation (4.5.29)) and Murray and Dermott (Equation (4.159)), implicitly sets the time lag to be frequency independent. Accordingly, the ensuing expression for the torque can be applied only to bodies having a very special (and very hypothetical) rheology which makes the time lag frequency independent, i.e., the same for all Fourier modes in the spectrum of tide. This expression for the torque should not be used for bodies of other rheologies. Specifically, the expression cannot be combined with an extra assertion of the geometric lag being constant, because at finite eccentricities the said assumption is incompatible with the constant-time-lag condition.
TIDAL NOVAE IN COMPACT BINARY WHITE DWARFS
International Nuclear Information System (INIS)
Fuller, Jim; Lai Dong
2012-01-01
Compact binary white dwarfs (WDs) undergoing orbital decay due to gravitational radiation can experience significant tidal heating prior to merger. In these WDs, the dominant tidal effect involves the excitation of outgoing gravity waves in the inner stellar envelope and the dissipation of these waves in the outer envelope. As the binary orbit decays, the WDs are synchronized from outside in (with the envelope synchronized first, followed by the core). We examine the deposition of tidal heat in the envelope of a carbon-oxygen WD and study how such tidal heating affects the structure and evolution of the WD. We show that significant tidal heating can occur in the star's degenerate hydrogen layer. This layer heats up faster than it cools, triggering runaway nuclear fusion. Such 'tidal novae' may occur in all WD binaries containing a CO WD, at orbital periods between 5 minutes and 20 minutes, and precede the final merger by 10 5 -10 6 years.
Tidal acceleration of black holes and superradiance
International Nuclear Information System (INIS)
Cardoso, Vitor; Pani, Paolo
2013-01-01
Tidal effects have long ago locked the Moon in a synchronous rotation with the Earth and progressively increase the Earth–Moon distance. This ‘tidal acceleration’ hinges on dissipation. Binaries containing black holes may also be tidally accelerated, dissipation being caused by the event horizon—a flexible, viscous one-way membrane. In fact, this process is known for many years under a different guise: superradiance. Here, we provide compelling evidence for a strong connection between tidal acceleration and superradiant scattering around spinning black holes. In general relativity, tidal acceleration is obscured by the gravitational-wave emission. However, when coupling to light scalar degrees of freedom is allowed, an induced dipole moment produces a ‘polarization acceleration’, which might be orders of magnitude stronger than tidal quadrupolar effects. Consequences for optical and gravitational-wave observations are intriguing and it is not impossible that imprints of such a mechanism have already been observed. (paper)
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
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.
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.
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)
Dynamics of tidal and non-tidal currents along the southwest continental shelf of India
Digital Repository Service at National Institute of Oceanography (India)
Aruna, C.; Ravichandran, C.; Srinivas, K.; Rasheed, P.A.A.; Lekshmi, S.
The tidal regimes over the continental shelves are often less documented due to lack of coastal water level data. This is of concern since continental shelves rule the global dissipation of tidal energy. The tides along the Southwest Indian shelf...
RED CLUMP STARS IN THE SAGITTARIUS TIDAL STREAMS
International Nuclear Information System (INIS)
Carrell, Kenneth; Chen Yuqin; Wilhelm, Ronald
2012-01-01
We have probed a section (l ∼ 150, b ∼ –60) of the trailing tidal arm of the Sagittarius dwarf spheroidal galaxy by identifying a sample of Red Clump (RC) stream stars. RC stars are not generally found in the halo field, but are found in significant numbers in both the Sagittarius galaxy and its tidal streams, making them excellent probes of stream characteristics. Our target sample was selected using photometric data from the Sloan Digital Sky Survey, Data Release 6, which was constrained in color to match the Sagittarius RC stars. Spectroscopic observations of the target stars were conducted at Kitt Peak National Observatory using the WIYN telescope. The resulting spectroscopic sample is magnitude limited and contains both main-sequence disk stars and evolved RC stars. We have developed a method to systematically separate these two stellar classes using kinematic information and a Bayesian approach for surface gravity determination. The resulting RC sample allows us to determine an absolute stellar density of ρ = 2.7 ± 0.5 RC stars kpc –3 at this location in the stream. Future measurements of stellar densities for a variety of populations and at various locations along the streams will lead to a much improved understanding of the original nature of the Sagittarius galaxy and the physical processes controlling its disruption and subsequent stream generation.
DEFF Research Database (Denmark)
Madsen, Jacob Østergaard
The aim of this study was thus to explore cultural probes (Gaver, Boucher et al. 2004), as a possible methodical approach, supporting knowledge production on situated and contextual aspects of occupation.......The aim of this study was thus to explore cultural probes (Gaver, Boucher et al. 2004), as a possible methodical approach, supporting knowledge production on situated and contextual aspects of occupation....
Support theorems for the Radon transform and Cram\\'er-Wold theorems
Boman, Jan; Lindskog, Filip
2008-01-01
This article presents extensions of the Cram{\\'e}r-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a few tools from distribution theory and Fourier analysis we show that the presented injectivity results for the Radon ...
Array Optimization for Tidal Energy Extraction in a Tidal Channel – A Numerical Modeling Analysis
Yang, Zhaoqing; Wang, Taiping; Copping, Andrea
2014-01-01
This paper presents an application of a hydrodynamic model to simulate tidal energy extraction in a tidal dominated estuary in the Pacific Northwest coast. A series of numerical experiments were carried out to simulate tidal energy extraction with different turbine array configurations, including location, spacing and array size. Preliminary model results suggest that array optimization for tidal energy extraction in a real-world site is a very complex process that requires consideration of m...
Formation of double galaxies by tidal capture
International Nuclear Information System (INIS)
Alladin, S.M.; Potdar, A.; Sastry, K.S.
1975-01-01
The conditions under which double galaxies may be formed by tidal capture are considered. Estimates for the increase in the internal energy of colliding galaxies due to tidal effects are used to determine the magnitudes Vsub(cap) and Vsub(dis) of the maximum relative velocities at infinite separation required for tidal capture and tidal disruption respectively. A double galaxy will be formed by tidal capture without tidal disruption of a component if Vsub(cap)>Vsub(i) and Vsub(cap)>Vsub(dis) where Vsub(i) is the initial relative speed of the two galaxies at infinite separation. If the two galaxies are of the same dimension, formulation of double galaxies by tidal capture is possible in a close collision either if the two galaxies do not differ much in mass and density distribution or if the more massive galaxy is less centrally concentrated than the other. If it is assumed as statistics suggest, that the mass of a galaxy is proportional to the square of its radius, it follows that the probability of the formation of double galaxies by tidal capture increases with the increase in mass of the galaxies and tidal distribution does not occur in a single collision for any distance of closest approach of the two galaxies. (Auth.)
Interactions Between Wetlands and Tidal Inlets
National Research Council Canada - National Science Library
Sanchez, Alejandro
2008-01-01
This Coastal and Hydraulics Engineering Technical Note (CHETN) presents numerical simulations investigating how the loss of wetlands in estuaries modifies tidal processes in inlet navigation channels...
Tidal evolution of globular clusters. I - Method
Oh, K. S.; Lin, D. N. C.; Aarseth, S. J.
1992-01-01
Tidal evolution of globular clusters is regulated by both Galactic tidal effects and internal relaxation processes. In order to investigate the tidal evolution of globular clusters, a numerical scheme which utilizes a Fokker-Planck approach as well as direct numerical integration of the restricted three-body problem is developed. In the inner regions of the cluster, stellar orbits are mapped with the cluster's gravitational potential and orbit-averaged diffusion coefficients. In the outer regions, the Galactic tidal field is explicitly included in the direct orbital integration. This method is presented here with some tests on King-Michie models.
International Nuclear Information System (INIS)
Matthews, M.E.; Young, R.M.
1992-01-01
Amongst the estuaries around the United Kingdom, the Wyre has been found to be prominent in possessing the main requirements for a small scale tidal energy scheme. This paper describes the results of a Preliminary Feasibility Study undertaken to assess the viability of the construction of a barrage at the mouth of the Wyre estuary by establishing the form, cost, energy output and the nature and broad scale effect that the project may have on the environment and surrounding region. The study also investigated the potential benefits of utilising the barrage as a road crossing between the town of Fleetwood and Over Wyre. (author)
Looijenga, Paul J.; Dieleman, Jan C.
1980-01-01
The activity of G. zaddachi from a non-tidal environment (the brackish lake “De Putten”, prov. North Holland, The Netherlands), has been studied in a current chamber in which tidal cycles can be simulated, in order to make a comparison with estuarine populations. The animals show a clear nocturnal
Kozai Cycles and Tidal Friction
Energy Technology Data Exchange (ETDEWEB)
L, K; P.P., E
2009-07-17
Several studies in the last three years indicate that close binaries, i.e. those with periods of {approx}< 3 d, are very commonly found to have a third body in attendance. We argue that this proves that the third body is necessary in order to make the inner period so short, and further argue that the only reasonable explanation is that the third body causes shrinkage of the inner period, from perhaps a week or more to the current short period, by means of the combination of Kozai cycles and tidal friction (KCTF). In addition, once KCTF has produced a rather close binary, magnetic braking also combined with tidal friction (MBTF) can decrease the inner orbit further, to the formation of a contact binary or even a merged single star. Some of the products of KCTF that have been suggested, either by others or by us, are W UMa binaries, Blue Stragglers, X-ray active BY Dra stars, and short-period Algols. We also argue that some components of wide binaries are actually merged remnants of former close inner pairs. This may include such objects as rapidly rotating dwarfs (AB Dor, BO Mic) and some (but not all) Be stars.
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.
Theorems on Positive Data: On the Uniqueness of NMF
Directory of Open Access Journals (Sweden)
Hans Laurberg
2008-01-01
Full Text Available We investigate the conditions for which nonnegative matrix factorization (NMF is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.
Theorems on positive data: on the uniqueness of NMF.
Laurberg, Hans; Christensen, Mads Graesbøll; Plumbley, Mark D; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.
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
The CAP Theorem Versus Databases with Relaxed ACID properties
DEFF Research Database (Denmark)
Frank, Lars; Ulslev Pedersen, Rasmus; Frank, Christian Havnø
2014-01-01
The CAP theorem combines the three desirable properties C (data consistency), A (data availability), and P (partition-tolerance: tolerance of inconsistencies between data stored in a distributed database where partitions are allowed). The CAP theorem asserts that any distributed system that uses ...... 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 traditional ACID (atomicity, consistency, isolation, and durability) databases, which prioritize consistency and partition...
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.
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.
Soft pion theorem, asymptotic symmetry and new memory effect
Hamada, Yuta; Sugishita, Sotaro
2017-11-01
It is known that soft photon and graviton theorems can be regarded as the Ward-Takahashi identities of asymptotic symmetries. In this paper, we consider soft theorem for pions, i.e., Nambu-Goldstone bosons associated with a spontaneously broken axial symmetry. The soft pion theorem is written as the Ward-Takahashi identities of the S-matrix under asymptotic transformations. We investigate the asymptotic dynamics, and find that the conservation of charges generating the asymptotic transformations can be interpreted as a pion memory effect.
Davis-type theorems for martingale difference sequences
Directory of Open Access Journals (Sweden)
George Stoica
2005-01-01
Full Text Available We study Davis-type theorems on the optimal rate of convergence of moderate deviation probabilities. In the case of martingale difference sequences, under the finite pth moments hypothesis (1≤p<∞, and depending on the normalization factor, our results show that Davis' theorems either hold if and only if p>2 or fail for all p≥1. This is in sharp contrast with the classical case of i.i.d. centered sequences, where both Davis' theorems hold under the finite second moment hypothesis (or less.
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
DEFF Research Database (Denmark)
Ørngreen, Rikke; Jørgensen, Anna Neustrup; Noesgaard, Signe Schack
2016-01-01
to in an interview. This method provided valuable insight into the contextual use, i.e. how did the online resource transfer to the work practice. However, the research team also found that mobile probes may provide the scaffolding necessary for individual and peer learning at a very local (intra-school) community...... level. This paper is an initial investigation of how the mobile probes process proved to engage teachers in their efforts to improve teaching. It also highlights some of the barriers emerging when applying mobile probes as a scaffold for learning.......A project investigating the effectiveness of a collection of online resources for teachers' professional development used mobile probes as a data collection method. Teachers received questions and tasks on their mobile in a dialogic manner while in their everyday context as opposed...
Morphodynamics of Hue tidal inlets, Vietnam
Lam, N.T.; Stive, M.J.F.; Verhagen, H.J.; Wang, Z.B.
2007-01-01
Morphodynamics of a tidal inlet system on a micro-tidal coast in a tropical monsoon influenced region is modelled and discussed. Effects of tides, waves, river flows and system configuration on the inlet morphologies are investigated with the aid of process-based state-of-the-art numerical models.
Tidal Freshwater Wetlands: Variation and Changes
Barendregt, A.; Swarth, C.W.
2013-01-01
Tidal freshwater wetlands (TFW) are situated in the upper estuary in a zone bordered upstream by the nontidal river and downstream by the oligohaline region. Here, discharge of freshwater from the river and the daily tidal pulse from the sea combine to create conditions where TFW develop. TFW
International Nuclear Information System (INIS)
Matsumoto, Haruya; Kaya, Nobuyuki; Yuasa, Kazuhiro; Hayashi, Tomoaki
1976-01-01
Electron counting method has been devised and experimented for the purpose of measuring electron temperature and density, the most fundamental quantities to represent plasma conditions. Electron counting is a method to count the electrons in plasma directly by equipping a probe with the secondary electron multiplier. It has three advantages of adjustable sensitivity, high sensitivity of the secondary electron multiplier, and directional property. Sensitivity adjustment is performed by changing the size of collecting hole (pin hole) on the incident front of the multiplier. The probe is usable as a direct reading thermometer of electron temperature because it requires to collect very small amount of electrons, thus it doesn't disturb the surrounding plasma, and the narrow sweep width of the probe voltage is enough. Therefore it can measure anisotropy more sensitively than a Langmuir probe, and it can be used for very low density plasma. Though many problems remain on anisotropy, computer simulation has been carried out. Also it is planned to provide a Helmholtz coil in the vacuum chamber to eliminate the effect of earth magnetic field. In practical experiments, the measurement with a Langmuir probe and an emission probe mounted to the movable structure, the comparison with the results obtained in reverse magnetic field by using a Helmholtz coil, and the measurement of ionic sound wave are scheduled. (Wakatsuki, Y.)
A preliminary study of tidal current ridges
Liu, Zhenxia; Xia, Dongxing
1985-06-01
Tidal current ridges, widely distributed geomorphological phenomena over the continental shelf of the world, are studied. They are formed by tidal current and the trend of their sand bodies runs parallel to the direction of tidal current. There are two types of the plane shapes: the parallel and the fingered. Conditions of forming tidal current ridges are the velocities of tidal current ranging from 1 to 3.5 knots and the supply of abundant sediments. Tidal current ridges often develop in following morphological locations: the bays, estuaries, the mouths of channels, as well as the offshore area with strong tidal current. Tidal current ridges occur generally at a water depth of less than 35 metres. The sediments of tidal current ridges are mainly composed of sand. The grain size of the sediments is uniform and well sorted. The characteristics of grain size of the sand imply that their formation mechanism is similar to that of river sand, that is, both of them are the result of flow movements in a trongth channel controlled by boundary. There is however difference between them that the river sand is formed by one-way flow movement while the tidal current sand by two-way movement. There are two saltation populations in the log-probability curves of tidal current sand, the sorting of first saltation population is better than the second one, and having positive skewness, which differs from beach sand. In the C-M grain size pattern tidal current sand is most found in graded suspension segment. The continental shelves of the Yellow Sea, the East China Sea and the South China Sea have favourable conditions for developing tidal current ridges in massive scale and special shape, such as the tidal current ridges in the offshore of Jiangsu, the Gulf of Korea, the shoal of Liaodong, the east and west mouths of the channel of Qiongzhou, Jiaozhou Bay, the shoal of Taiwan, Lingdingyang, the north branch of Changjiang estuary. The studies of them are of vital significance in
Relativistic theory of tidal Love numbers
International Nuclear Information System (INIS)
Binnington, Taylor; Poisson, Eric
2009-01-01
In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.
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)
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.
Luttinger's theorem, superfluid vortices and holography
Iqbal, Nabil; Liu, Hong
2012-10-01
Strongly coupled field theories with gravity duals can be placed at finite density in two ways: electric field flux emanating from behind a horizon, or bulk charged fields outside of the horizon that explicitly source the density. We discuss field-theoretical observables that are sensitive to this distinction. If the charged fields are fermionic, we discuss a modified Luttinger's theorem that holds for holographic systems, in which the sum of boundary theory Fermi surfaces counts only the charge outside of the horizon. If the charged fields are bosonic, we show that the resulting superfluid phase may be characterized by the coefficient of the transverse Magnus force on a moving superfluid vortex, which again is sensitive only to the charge outside of the horizon. For holographic systems, these observables provide a field-theoretical way to distinguish how much charge is held by a dual horizon, but they may be useful in more general contexts as measures of deconfined (i.e. ‘fractionalized’) charge degrees of freedom.
Flat deformation theorem and symmetries in spacetime
Energy Technology Data Exchange (ETDEWEB)
Llosa, Josep [Departament de Fisica Fonamental, Universitat de Barcelona (Spain); Carot, Jaume [Departament de Fisica, Universitat de les Illes Balears (Spain)
2009-03-07
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 PSI(c, F, x) = 0, such that the deformed metric eta = cg - epsilonF{sup 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 eta{sub ab} := ag{sub ab} - 2bk{sub (al{sub b})} where eta is flat and k{sub a}, l{sub a} are two null covectors such that k{sub a}l{sup a} = -1; next we show how the symmetries of g are connected to those of eta, 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 eta 'inherits' that symmetry.
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.
Browder-Krasnoselskii-Type Fixed Point Theorems in Banach Spaces
Directory of Open Access Journals (Sweden)
Taoudi Mohamed-Aziz
2010-01-01
Full Text Available Abstract We present some fixed point theorems for the sum of a weakly-strongly continuous map and a nonexpansive map on a Banach space . Our results cover several earlier works by Edmunds, Reinermann, Singh, and others.
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 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...
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.
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.
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.
Tauberian theorems for generalized functions with values in Banach spaces
International Nuclear Information System (INIS)
Drozhzhinov, Yu N; Zav'yalov, B I
2002-01-01
We state and prove Tauberian theorems of a new type. In these theorems we give sufficient conditions under which the values of a generalized function (distribution) that are assumed to lie in a locally convex topological space actually belong to some narrower (Banach) space. These conditions are stated in terms of 'general class estimates' for the standard average of this generalized function with a fixed kernel belonging to a space of test functions. The applications of these theorems are based, in particular, on the fact that asymptotical (and some other) properties of the generalized functions under investigation can be described in terms of membership of certain Banach spaces. We apply these theorems to the study of asymptotic properties of solutions of the Cauchy problem for the heat equation in the class of generalized functions of small growth (tempered distributions), and to the study of Banach spaces of Besov-Nikol'skii type
Limit theorems for solutions of stochastic differential equation problems
Directory of Open Access Journals (Sweden)
J. Vom Scheidt
1980-01-01
Full Text Available In this paper linear differential equations with random processes as coefficients and as inhomogeneous term are regarded. Limit theorems are proved for the solutions of these equations if the random processes are weakly correlated processes.
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
On a fixed point theorem Krasnoselskii-Shafer type
Directory of Open Access Journals (Sweden)
Bapurao Dhage
2002-01-01
Full Text Available In this paper a variant of a fixed point theorem to Krasnoselskii-Schaefer type is proved and it is further applied to certain nonlinear integral equation of mixed type for proving the existence of the solution.
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.
A Computer Science Version of Goedel’s Theorem.
1983-08-01
The author presents a simplified proof of Godel’s theorem by appealing to well-known programming concepts. The significance of Goedel’s result to computer science , mathematics and logic is discussed. (Author)
Two time physics and Hamiltonian Noether theorem for gauge systems
International Nuclear Information System (INIS)
Nieto, J. A.; Ruiz, L.; Silvas, J.; Villanueva, V. M.
2006-01-01
Motivated by two time physics theory we revisited the Noether theorem for Hamiltonian constrained systems. Our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints
Thermodynamic proof of Rosseland's theorem
Energy Technology Data Exchange (ETDEWEB)
Sobolev, A.M.; Strel' nitskii, V.S. Chugai, N.N.
1985-11-01
A proof of Rosseland's theorem for all regions of the spectrum is given on the basis of the use of the brightness temperature to describe a nonequilibrium radiation field. Such a method of proof reveals the simple thermodynamic significance of the theorem. The classical explanation of the fluorescence of gas nebulas in the optical lines of atoms is provided by Rosseland's theorem, that in a three-level quantum system in a field of dilute Planck radiation the direct cycles proceed more rapidly than the reverse cycles. The method presented was used to prove Rosseland's theorem for the Wien part of the spectrum, to which a restriction can be made when the optical fluorescence of gas nebulas is being analyzed. Also considered is the opposite limiting case, which is the Rayleigh-Jeans region, as well as the spectrum as a whole.
Dai, Peng; Zhang, Jisheng; Zheng, Jinhai
2017-12-01
The Taiwan Strait has recently been proposed as a promising site for dynamic tidal power systems because of its shallow depth and strong tides. Dynamic tidal power is a new concept for extracting tidal potential energy in which a coast-perpendicular dike is used to create water head and generate electricity via turbines inserted in the dike. Before starting such a project, the potential power output and hydrodynamic impacts of the dike must be assessed. In this study, a two-dimensional numerical model based on the Delft3D-FLOW module is established to simulate tides in China. A dike module is developed to account for turbine processes and estimate power output by integrating a special algorithm into the model. The domain decomposition technique is used to divide the computational zone into two subdomains with grid refinement near the dike. The hydrodynamic processes predicted by the model, both with and without the proposed construction, are examined in detail, including tidal currents and tidal energy flux. The predicted time-averaged power yields with various opening ratios are presented. The results show that time-averaged power yield peaks at an 8% opening ratio. For semidiurnal tides, the flow velocity increases in front of the head of the dike and decreases on either side. For diurnal tides, these changes are complicated by the oblique incidence of tidal currents with respect to the dike as well as by bathymetric features. The dike itself blocks the propagation of tidal energy flux.
Fatou's Lemma and Lebesgue's convergence theorem for measures
Directory of Open Access Journals (Sweden)
Onésimo Hernández-Lerma
2000-01-01
Full Text Available Analogues of Fatou's Lemma and Lebesgue's convergence theorems are established for ∫fdμn when {μn} is a sequence of measures. A generalized Dominated Convergence Theorem is also proved for the asymptotic behavior of ∫fndμn and the latter is shown to be a special case of a more general result established in vector lattices and related to the Dunford-Pettis property in Banach spaces.
Existence Theorems for Generalized Distance on Complete Metric Spaces
Directory of Open Access Journals (Sweden)
Ume JeongSheok
2010-01-01
Full Text Available We first introduce the new concept of a distance called -distance, which generalizes -distance, Tataru's distance, and -distance. Then we prove a new minimization theorem and a new fixed point theorem by using a -distance on a complete metric space. Our results extend and unify many known results due to Caristi, Ćirić, Ekeland, Kada-Suzuki-Takahashi, Kannan, Ume, and others.
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....
An Abstract Existence Theorem at Resonance and Its Applications
Ma, Shiwang; Wang, Zhicheng; Yu, Jianshe
1998-05-01
By using Brouwer degree theory and a continuation theorem based on Mawhin's coincidence degree, an abstract existence theorem at resonance for operator equations is developed. As applications of this result, some sufficient conditions are given for the existence of periodic solutions of semilinear equations at resonance where the kernel of the linear part has dimensionN(N⩾2). The results due to Nagle and Sinkala are generalized, improved, and unified.
Experimental studies of the transient fluctuation theorem using liquid ...
Indian Academy of Sciences (India)
(kχ) of the harmonic potential associated with χ for a given applied voltage can be determined by measuring the thermal fluctuation of χ and by the application of the equipartition theorem kχ = kBT/σ2 χ where σ2 χ is the variance of χ. Equipartition theorem has been used extensively for the study of thermal fluctuations of the.
Fardal, Mark A.
2014-06-01
The Pandas survey of stars in M31's disk and halo is crisscrossed by numerous tidal features from both M31 and the Milky Way. Here I focus on two narrow stellar streams visible in the survey. They have comparable angular extent in the survey (10-13 degrees long versus only 0.3 degree wide), but one is a local Milky Way stream at about 30 kpc and one is in M31, roughly 25 times more distant. I estimate the stellar mass and metallicity in the streams and the distance gradient along them. The kinematics of the M31 stream is sparsely sampled by red giant stars and globular clusters. Bayesian modeling of the stream data yields accurate constraints on the orbital parameters of the streams.
International Nuclear Information System (INIS)
Castelino, J.
1992-01-01
The creation of DNA probes for detection of specific nucleotide segments differs from ligand detection in that it is a chemical rather than an immunological reaction. Complementary DNA or RNA is used in place of the antibody and is labelled with 32 P. So far, DNA probes have been successfully employed in the diagnosis of inherited disorders, infectious diseases, and for identification of human oncogenes. The latest approach to the diagnosis of communicable and parasitic infections is based on the use of deoxyribonucleic acid (DNA) probes. The genetic information of all cells is encoded by DNA and DNA probe approach to identification of pathogens is unique because the focus of the method is the nucleic acid content of the organism rather than the products that the nucleic acid encodes. Since every properly classified species has some unique nucleotide sequences that distinguish it from every other species, each organism's genetic composition is in essence a finger print that can be used for its identification. In addition to this specificity, DNA probes offer other advantages in that pathogens may be identified directly in clinical specimens
The influence of waves on the tidal kinetic energy resource at a tidal stream energy site
International Nuclear Information System (INIS)
Guillou, Nicolas; Chapalain, Georges; Neill, Simon P.
2016-01-01
Highlights: • We model the influence of waves on tidal kinetic energy in the Fromveur Strait. • Numerical results are compared with field data of waves and currents. • The introduction of waves improve predictions of tidal stream power during storm. • Mean spring tidal stream potential is reduced by 12% during extreme wave conditions. • Potential is reduced by 7.8% with waves forces and 5.3% with enhanced friction. - Abstract: Successful deployment of tidal energy converters relies on access to accurate and high resolution numerical assessments of available tidal stream power. However, since suitable tidal stream sites are located in relatively shallow waters of the continental shelf where tidal currents are enhanced, tidal energy converters may experience effects of wind-generated surface-gravity waves. Waves may thus influence tidal currents, and associated kinetic energy, through two non-linear processes: the interaction of wave and current bottom boundary layers, and the generation of wave-induced currents. Here, we develop a three-dimensional tidal circulation model coupled with a phase-averaged wave model to quantify the impact of the waves on the tidal kinetic energy resource of the Fromveur Strait (western Brittany) - a region that has been identified with strong potential for tidal array development. Numerical results are compared with in situ observations of wave parameters (significant wave height, peak period and mean wave direction) and current amplitude and direction 10 m above the seabed (the assumed technology hub height for this region). The introduction of waves is found to improve predictions of tidal stream power at 10 m above the seabed at the measurement site in the Strait, reducing kinetic energy by up to 9% during storm conditions. Synoptic effects of wave radiation stresses and enhanced bottom friction are more specifically identified at the scale of the Strait. Waves contribute to a slight increase in the spatial gradient of
More on soft theorems: Trees, loops, and strings
Bianchi, Massimo; He, Song; Huang, Yu-tin; Wen, Congkao
2015-09-01
We study soft theorems in a broader context, their universality in effective field theories and string theory, as well as continue the analysis of their fate at loop level. In effective field theories with F3 and R3 interactions, the soft theorems are not modified. However, for gravity theories with R2ϕ interactions, the sub-subleading order soft graviton theorem, which is beyond what is implied by the extended Bondi, van der Burg, Metzner, and Sachs symmetry, requires modifications at tree level for nonsupersymmetric theories and at loop level for N ≤4 supergravity due to anomalies. For open and closed superstrings at finite α', via explicit calculation for lower-point examples as well as world sheet operator product expansion analysis for arbitrary multiplicity, we show that scattering amplitudes satisfy the same soft theorem as their field-theory counterpart. This is no longer true for closed bosonic or heterotic strings due to the presence of R2ϕ interactions. We also consider loop corrections to gauge theories in the planar limit, where we show that tree-level soft gluon theorems are respected at the integrand level for 1 ≤N ≤4 SYM. Finally, we discuss the fate of soft theorems for finite loop amplitudes in pure Yang-Mills theory and gravity.
Atmospheric noise of a breaking tidal bore.
Chanson, Hubert
2016-01-01
A tidal bore is a surge of waters propagating upstream in an estuary as the tidal flow turns to rising and the flood tide propagates into a funnel-shaped system. Large tidal bores have a marked breaking roller. The sounds generated by breaking tidal bores were herein investigated in the field (Qiantang River) and in laboratory. The sound pressure record showed two dominant periods, with some similarity with an earlier study [Chanson (2009). J. Acoust. Soc. Am. 125(6), 3561-3568]. The two distinct phases were the incoming tidal bore when the sound amplitude increased with the approaching bore, and the passage of the tidal bore in front of the microphone when loud and powerful noises were heard. The dominant frequency ranged from 57 to 131 Hz in the Qiantang River bore. A comparison between laboratory and prototype tidal bores illustrated both common features and differences. The low pitch sound of the breaking bore had a dominant frequency close to the collective oscillations of bubble clouds, which could be modeled with a bubble cloud model using a transverse dimension of the bore roller. The findings suggest that this model might be over simplistic in the case of a powerful breaking bore, like that of the Qiantang River.
No Snowball on Habitable Tidally Locked Planets
Energy Technology Data Exchange (ETDEWEB)
Checlair, Jade; Abbot, Dorian S. [Department of the Geophysical Sciences, University of Chicago, 5734 South Ellis Avenue, Chicago, IL 60637 (United States); Menou, Kristen, E-mail: jadecheclair@uchicago.edu [Centre for Planetary Sciences, Department of Physical and Environmental Sciences, University of Toronto at Scarborough, Toronto, ON M1C 1A4 (Canada)
2017-08-20
The TRAPPIST-1, Proxima Centauri, and LHS 1140 systems are the most exciting prospects for future follow-up observations of potentially inhabited planets. All of the planets orbit nearby M-stars and are likely tidally locked in 1:1 spin–orbit states, which motivates the consideration of the effects that tidal locking might have on planetary habitability. On Earth, periods of global glaciation (snowballs) may have been essential for habitability and remote signs of life (biosignatures) because they are correlated with increases in the complexity of life and in the atmospheric oxygen concentration. In this paper, we investigate the snowball bifurcation (sudden onset of global glaciation) on tidally locked planets using both an energy balance model and an intermediate-complexity global climate model. We show that tidally locked planets are unlikely to exhibit a snowball bifurcation as a direct result of the spatial pattern of insolation they receive. Instead, they will smoothly transition from partial to complete ice coverage and back. A major implication of this work is that tidally locked planets with an active carbon cycle should not be found in a snowball state. Moreover, this work implies that tidally locked planets near the outer edge of the habitable zone with low CO{sub 2} outgassing fluxes will equilibrate with a small unglaciated substellar region rather than cycling between warm and snowball states. More work is needed to determine how the lack of a snowball bifurcation might affect the development of life on a tidally locked planet.
No Snowball on Habitable Tidally Locked Planets
Checlair, Jade; Menou, Kristen; Abbot, Dorian S.
2017-08-01
The TRAPPIST-1, Proxima Centauri, and LHS 1140 systems are the most exciting prospects for future follow-up observations of potentially inhabited planets. All of the planets orbit nearby M-stars and are likely tidally locked in 1:1 spin–orbit states, which motivates the consideration of the effects that tidal locking might have on planetary habitability. On Earth, periods of global glaciation (snowballs) may have been essential for habitability and remote signs of life (biosignatures) because they are correlated with increases in the complexity of life and in the atmospheric oxygen concentration. In this paper, we investigate the snowball bifurcation (sudden onset of global glaciation) on tidally locked planets using both an energy balance model and an intermediate-complexity global climate model. We show that tidally locked planets are unlikely to exhibit a snowball bifurcation as a direct result of the spatial pattern of insolation they receive. Instead, they will smoothly transition from partial to complete ice coverage and back. A major implication of this work is that tidally locked planets with an active carbon cycle should not be found in a snowball state. Moreover, this work implies that tidally locked planets near the outer edge of the habitable zone with low CO2 outgassing fluxes will equilibrate with a small unglaciated substellar region rather than cycling between warm and snowball states. More work is needed to determine how the lack of a snowball bifurcation might affect the development of life on a tidally locked planet.
No Snowball on Habitable Tidally Locked Planets
International Nuclear Information System (INIS)
Checlair, Jade; Abbot, Dorian S.; Menou, Kristen
2017-01-01
The TRAPPIST-1, Proxima Centauri, and LHS 1140 systems are the most exciting prospects for future follow-up observations of potentially inhabited planets. All of the planets orbit nearby M-stars and are likely tidally locked in 1:1 spin–orbit states, which motivates the consideration of the effects that tidal locking might have on planetary habitability. On Earth, periods of global glaciation (snowballs) may have been essential for habitability and remote signs of life (biosignatures) because they are correlated with increases in the complexity of life and in the atmospheric oxygen concentration. In this paper, we investigate the snowball bifurcation (sudden onset of global glaciation) on tidally locked planets using both an energy balance model and an intermediate-complexity global climate model. We show that tidally locked planets are unlikely to exhibit a snowball bifurcation as a direct result of the spatial pattern of insolation they receive. Instead, they will smoothly transition from partial to complete ice coverage and back. A major implication of this work is that tidally locked planets with an active carbon cycle should not be found in a snowball state. Moreover, this work implies that tidally locked planets near the outer edge of the habitable zone with low CO 2 outgassing fluxes will equilibrate with a small unglaciated substellar region rather than cycling between warm and snowball states. More work is needed to determine how the lack of a snowball bifurcation might affect the development of life on a tidally locked planet.
Spin Dependence in Tidal Disruption Events
Kesden, Michael; Stone, Nicholas; van Velzen, Sjoert
2018-01-01
A supermassive black hole (SBH) can tidally disrupt stars when its tidal field overwhelms the stars’ self-gravity. The stellar debris produced in such tidal disruption events (TDEs) evolves into tidal streams that can self-intersect. These inelastic stream collisions dissipate orbital energy, both circularizing the tidal stream and contributing to the emission observed during the TDE. Once circularized into a disk, the stellar debris can be viscously accreted by the SBH powering additional luminous emission. We explore how SBH spin can affect the tidal disruption process. Tidal forces are spin dependent, as is the minimum orbital angular momentum below which stars are directly captured by the SBH. This implies that the TDE rate will be spin dependent, particularly for more massive SBHs for which relativistic effects are more significant. SBH spin also affects TDE light curves through the initial debris orbits, the nature of the stream collisions, the viscous evolution of the accretion disk, and the possibility of launching jets. We explore the spin dependence of these phenomena to identify promising signatures for upcoming surveys expected to discover hundreds of TDE candidates in the next decade.
Relevance of tidal heating on large TNOs
Saxena, Prabal; Renaud, Joe P.; Henning, Wade G.; Jutzi, Martin; Hurford, Terry
2018-03-01
We examine the relevance of tidal heating for large Trans-Neptunian Objects, with a focus on its potential to melt and maintain layers of subsurface liquid water. Depending on their past orbital evolution, tidal heating may be an important part of the heat budget for a number of discovered and hypothetical TNO systems and may enable formation of, and increased access to, subsurface liquid water. Tidal heating induced by the process of despinning is found to be particularly able to compete with heating due to radionuclide decay in a number of different scenarios. In cases where radiogenic heating alone may establish subsurface conditions for liquid water, we focus on the extent by which tidal activity lifts the depth of such conditions closer to the surface. While it is common for strong tidal heating and long lived tides to be mutually exclusive, we find this is not always the case, and highlight when these two traits occur together. We find cases where TNO systems experience tidal heating that is a significant proportion of, or greater than radiogenic heating for periods ranging from100‧s of millions to a billion years. For subsurface oceans that contain a small antifreeze component, tidal heating due to very high initial spin states may enable liquid water to be preserved right up to the present day. Of particular interest is the Eris-Dysnomia system, which in those cases may exhibit extant cryovolcanism.
2008-01-01
The Thermal and Electrical Conductivity Probe (TECP) for NASA's Phoenix Mars Lander took measurements in Martian soil and in the air. The needles on the end of the instrument were inserted into the Martian soil, allowing TECP to measure the propagation of both thermal and electrical energy. TECP also measured the humidity in the surrounding air. The needles on the probe are 15 millimeters (0.6 inch) long. The Phoenix Mission is led by the University of Arizona, Tucson, on behalf of NASA. Project management of the mission is by NASA's Jet Propulsion Laboratory, Pasadena, Calif. Spacecraft development is by Lockheed Martin Space Systems, Denver.
Tidal interactions with Kerr black holes
International Nuclear Information System (INIS)
Hiscock, W.A.
1977-01-01
The tidal deformation of an extended test body falling with zero angular momentum into a Kerr black hole is calculated. Numerical results for infall along the symmetry axis and in the equatorial plane of the black hole are presented for a range of values of a, the specific angular momentum of the black hole. Estimates of the tidal contribution to the gravitational radiation are also given. The tidal contribution in equatorial infall into a maximally rotating Kerr black hole may be of the same order as the center-of-mass contribution to the gravitational radiation
Exploitation of tidal power in the Bay of Cadiz: ancient tidal mills
Directory of Open Access Journals (Sweden)
José J. Alonso del Rosario
2006-03-01
Full Text Available Tidal mills were the main industrial activity in the Bay of Cadiz for centuries. They were the last step in the production of salt and flour made by grinding grains. They were installed along the shallow channels, called “caños”, around the Bay, where the frictional and geometrical effects are very strong. The authors have analyzed the propagation of the semidiurnal tidal waves along the Caño de Sancti Petri and the available tidal power in the area. The ancient tidal mills were located where the available tidal potential energy is highest, which ensured productivity for grinding salt and wheat in ancient times. Some considerations about the possibility of installing tidal power plants in the Bay of Cadiz now are given, which show that it could be a real and renewal alternative source of energy for the area.
Development of tidal watersheds in the Wadden Sea
Wang, Z.B.; Vroom, J.; van Prooijen, B.C.; Labeur, R.J.; Stive, M.J.F.; Hansen, M.H.P.
2011-01-01
The Wadden Sea consists of a series of tidal lagoons which are connected to the North Sea by tidal inlets. Boundaries to each lagoon are the mainland coast, the barrier islands on both sides of the tidal inlet, and the tidal watersheds behind the two barrier islands. Behind each Wadden Island there
Downstream hydraulic geometry of a tidally influenced river delta
Sassi, M.G.; Hoitink, A.J.F.; Brye, de B.; Deleersnijder, E.
2012-01-01
Channel geometry in tidally influenced river deltas can show a mixed scaling behavior between that of river and tidal channel networks, as the channel forming discharge is both of river and tidal origin. We present a method of analysis to quantify the tidal signature on delta morphology, by
Relationship between regional ventilation and aerosol deposition in tidal breathing
International Nuclear Information System (INIS)
Trajan, M.; Logus, J.W.; Enns, E.G.; Man, S.F.
1984-01-01
The regional distribution of the deposition of 1.2 micron particles of 99mTc sulfur colloid inhaled by tidal breathing was compared with the distribution of ventilation as measured by a 133Xe washout technique. Twelve subjects were studied, 6 with normal pulmonary function tests, 5 with air-flow limitation, and 1 with unilateral phrenic nerve paralysis. Both xenon and aerosol were inhaled at tidal volume by the subjects while seated upright. A large field gamma camera acquired posterior scans. Thirteen experiments were also done on 7 dogs: 1 with extrathoracic obstruction of the airway to 1 lung, and 12 with bronchoconstriction from the instillation of methacholine chloride into the airways of a lower lobe. Two of these dogs were studied with a gamma camera system, and the others were studied with a Picker multi-probe system. Both in humans and in dogs, an increase in time constant, which indicated a decrease in ventilation, was associated with an increase in peripheral aerosol deposition when normalized for ventilation. It is suggested that the increased residence time is responsible for the increased deposition in regions that received lesser ventilation
Chant, Donald A.
This book is written as a statement of concern about pollution by members of Pollution Probe, a citizens' anti-pollution group in Canada. Its purpose is to create public awareness and pressure for the eventual solution to pollution problems. The need for effective government policies to control the population explosion, conserve natural resources,…
International Nuclear Information System (INIS)
Laget, J.M.
1986-11-01
Specificity and complementarity of hadron and electron probes must be systematically developed to answer three questions currently asked in intermediate energy nuclear physics: what is nucleus structure at short distances, what is nature of short range correlations, what is three body force nature [fr
Camp, Jordan; Transient Astrophysics Probe Team
2018-01-01
The Transient Astrophysics Probe (TAP) is a wide-field multi-wavelength transient mission proposed for flight starting in the late 2020s. The mission instruments include unique “Lobster-eye” imaging soft X-ray optics that allow a ~1600 deg2 FoV; a high sensitivity, 1 deg2 FoV soft X-ray telescope; a 1 deg2 FoV Infrared telescope with bandpass 0.6-3 micron; and a set of 8 NaI gamma-ray detectors. TAP’s most exciting capability will be the observation of tens per year of X-ray and IR counterparts of GWs involving stellar mass black holes and neutron stars detected by LIGO/Virgo/KAGRA/LIGO-India, and possibly several per year X-ray counterparts of GWs from supermassive black holes, detected by LISA and Pulsar Timing Arrays. TAP will also discover hundreds of X-ray transients related to compact objects, including tidal disruption events, supernova shock breakouts, and Gamma-Ray Bursts from the epoch of reionization.
Tidal Mixing at the Shelf Break
National Research Council Canada - National Science Library
Hogg, Nelson; Legg, Sonya
2005-01-01
The aim of this project was to study mixing forced by tidal flow over sudden changes in topographic slope such as near the shelf-break, using high-resolution nonhydrostatic numerical simulations employing the MIT gem...
Tides and tidal harmonics at Umbharat, Gujarat
Digital Repository Service at National Institute of Oceanography (India)
Suryanarayana, A.; Swamy, G.N.
A part of the data on tides recorded at Machiwada near Umbharat, Gulf of Cambay during April 1978 was subjected to harmonic analysis following the Admiralty procedure. The general tidal characteristics and the value of four major harmonic...
Tidal mixing in Dahej creek waters
Digital Repository Service at National Institute of Oceanography (India)
Swamy, G.N.; Sarma, R.V.
of effluent discharge has been worked out. The allowable duration of discharge of the hypothetical effluent over a tidal cycle ensuring a specified minimum dilution has also been indicated to help optimise the degree of inplant treatment. The results suggested...
Microbial quality of a marine tidal pool
CSIR Research Space (South Africa)
Genthe, Bettina
1995-01-01
Full Text Available In this study the source of microbial pollution to a tidal pool was investigated. Both adjacent seawater which could contribute to possible faecal pollution and potential direct bather pollution were studied. The microbial quality of the marine...
Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases
International Nuclear Information System (INIS)
Brandino, G. P.; Caux, J.-S.; Konik, R. M.
2015-01-01
Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess non-trivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasi-conserved quantities, so providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasi-conserved quantities can be probed experimentally.
Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases
Directory of Open Access Journals (Sweden)
G. P. Brandino
2015-12-01
Full Text Available Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess nontrivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low-dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasiconserved quantities, thus providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasiconserved quantities can be probed experimentally.
On the ambiguity in relativistic tidal deformability
Gralla, Samuel E.
2018-04-01
The LIGO collaboration recently reported the first gravitational-wave constraints on the tidal deformability of neutron stars. I discuss an inherent ambiguity in the notion of relativistic tidal deformability that, while too small to affect the present measurement, may become important in the future. I propose a new way to understand the ambiguity and discuss future prospects for reliably linking observed gravitational waveforms to compact object microphysics.
The environmental effects of tidal energy
International Nuclear Information System (INIS)
Muirhead, H.J.
1992-01-01
The aim of this paper is to outline the environmental effects of tidal energy in relation to the estuarine ecosystem, and therefore will not deal with the regional environmental and socioeconomic implications of tidal power. The topics covered are: hydrodynamics of sediments; turbidity; water quality; fish; birds and wildlife conservation. The nature of the estuarine environment and how, as a system, it works, is briefly described by way of introduction. (author)
Cael, B. B.; Bisson, Kelsey; Lambert, Bennett Spencer
2015-01-01
Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of p...
WIYN Open Cluster Study: Tidal Interactions in Solar type Binaries
Meibom, S.; Mathieu, R. D.
2003-01-01
We present an ongoing study on tidal interactions in late-type close binary stars. New results on tidal circularization are combined with existing data to test and constrain theoretical predictions of tidal circularization in the pre-main-sequence (PMS) phase and throughout the main-sequence phase of stellar evolution. Current data suggest that tidal circularization during the PMS phase sets the tidal cutoff period for binary populations younger than ~1 Gyr. Binary populations older than ~1 G...
Ocean renewable energy : Tidal power in the Yellow Sea
Lee, Han Soo
2011-01-01
Ocean renewable energy sources are briefly introduced in this review article. Special focus on tidal energy from ocean renewable energy in the Yellow Sea and its practical utilization in South Korea are illustrated with several examples. Among them, the Sihwa Lake tidal power plant, the Garolim Bay tidal power project, the Incheon tidal power project, and the Uldolmok tidal current power station were introduced with more details. A numerical modelling system, Regional Ocean Tide Simulator, is...
TIDAL INTERACTIONS IN MERGING WHITE DWARF BINARIES
International Nuclear Information System (INIS)
Piro, Anthony L.
2011-01-01
The recently discovered system J0651 is the tightest known detached white dwarf (WD) binary. Since it has not yet initiated Roche-lobe overflow, it provides a relatively clean environment for testing our understanding of tidal interactions. I investigate the tidal heating of each WD, parameterized in terms of its tidal Q parameter. Assuming that the heating can be radiated efficiently, the current luminosities are consistent with Q 1 ∼ 7 x 10 10 and Q 2 ∼ 2 x 10 7 , for the He and C/O WDs, respectively. Conversely, if the observed luminosities are merely from the cooling of the WDs, these estimated values of Q represent the upper limits. A large Q 1 for the He WD means its spin velocity will be slower than that expected if it was tidally locked, which, since the binary is eclipsing, may be measurable via the Rossiter-McLaughlin effect. After one year, gravitational wave emission shifts the time of eclipses by 5.5 s, but tidal interactions cause the orbit to shrink more rapidly, changing the time by up to an additional 0.3 s after a year. Future eclipse timing measurements may therefore infer the degree of tidal locking.
VISCOELASTIC MODELS OF TIDALLY HEATED EXOMOONS
International Nuclear Information System (INIS)
Dobos, Vera; Turner, Edwin L.
2015-01-01
Tidal heating of exomoons may play a key role in their habitability, since the elevated temperature can melt the ice on the body even without significant solar radiation. The possibility of life has been intensely studied on solar system moons such as Europa or Enceladus where the surface ice layer covers a tidally heated water ocean. Tidal forces may be even stronger in extrasolar systems, depending on the properties of the moon and its orbit. To study the tidally heated surface temperature of exomoons, we used a viscoelastic model for the first time. This model is more realistic than the widely used, so-called fixed Q models because it takes into account the temperature dependence of the tidal heat flux and the melting of the inner material. Using this model, we introduced the circumplanetary Tidal Temperate Zone (TTZ), which strongly depends on the orbital period of the moon and less on its radius. We compared the results with the fixed Q model and investigated the statistical volume of the TTZ using both models. We have found that the viscoelastic model predicts 2.8 times more exomoons in the TTZ with orbital periods between 0.1 and 3.5 days than the fixed Q model for plausible distributions of physical and orbital parameters. The viscoelastic model provides more promising results in terms of habitability because the inner melting of the body moderates the surface temperature, acting like a thermostat
Half Moon Cove Tidal Project. Feasibility report
Energy Technology Data Exchange (ETDEWEB)
1980-11-01
The proposed Half Moon Cove Tidal Power Project would be located in a small cove in the northern part of Cobscook Bay in the vicinity of Eastport, Maine. The project would be the first tidal electric power generating plant in the United States of America. The basin impounded by the barrier when full will approximate 1.2 square miles. The average tidal range at Eastport is 18.2 feet. The maximum spring tidal range will be 26.2 feet and the neap tidal range 12.8 feet. The project will be of the single pool-type single effect in which generation takes place on the ebb tide only. Utilizing an average mean tidal range of 18.2 feet the mode of operation enables generation for approximately ten and one-half (10-1/2) hours per day or slightly in excess of five (5) hours per tide. The installed capacity will be 12 MW utilizing 2 to 6 MW units. An axial flow, or Bulb type of turbine was selected for this study.
VISCOELASTIC MODELS OF TIDALLY HEATED EXOMOONS
Energy Technology Data Exchange (ETDEWEB)
Dobos, Vera [Konkoly Thege Miklos Astronomical Institute, Research Centre of Astronomy and Earth Sciences, Hungarian Academy of Sciences, H-1121 Konkoly Thege Miklós út 15-17, Budapest (Hungary); Turner, Edwin L., E-mail: dobos@konkoly.hu [Department of Astrophysical Sciences, Princeton University, 08544, 4 Ivy Lane, Peyton Hall, Princeton, NJ (United States)
2015-05-01
Tidal heating of exomoons may play a key role in their habitability, since the elevated temperature can melt the ice on the body even without significant solar radiation. The possibility of life has been intensely studied on solar system moons such as Europa or Enceladus where the surface ice layer covers a tidally heated water ocean. Tidal forces may be even stronger in extrasolar systems, depending on the properties of the moon and its orbit. To study the tidally heated surface temperature of exomoons, we used a viscoelastic model for the first time. This model is more realistic than the widely used, so-called fixed Q models because it takes into account the temperature dependence of the tidal heat flux and the melting of the inner material. Using this model, we introduced the circumplanetary Tidal Temperate Zone (TTZ), which strongly depends on the orbital period of the moon and less on its radius. We compared the results with the fixed Q model and investigated the statistical volume of the TTZ using both models. We have found that the viscoelastic model predicts 2.8 times more exomoons in the TTZ with orbital periods between 0.1 and 3.5 days than the fixed Q model for plausible distributions of physical and orbital parameters. The viscoelastic model provides more promising results in terms of habitability because the inner melting of the body moderates the surface temperature, acting like a thermostat.
Central limit theorem: the cornerstone of modern statistics.
Kwak, Sang Gyu; Kim, Jong Hae
2017-04-01
According to the central limit theorem, the means of a random sample of size, n , from a population with mean, µ, and variance, σ 2 , distribute normally with mean, µ, and variance, [Formula: see text]. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-parametric tests, which do not require any assumptions about the population probability distribution, parametric tests produce more accurate and precise estimates with higher statistical powers. However, many medical researchers use parametric tests to present their data without knowledge of the contribution of the central limit theorem to the development of such tests. Thus, this review presents the basic concepts of the central limit theorem and its role in binomial distributions and the Student's t-test, and provides an example of the sampling distributions of small populations. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding.
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).
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.
Stirring up a storm: convective climate variability on tidally locked exoplanets
Koll, D. D. B.; Cronin, T.
2017-12-01
Earth-sized exoplanets are extremely common in the galaxy and many of them are likely tidally locked, such that they have permanent day- and nightsides. Astronomers have started to probe the atmospheres of such planets, which raises the question: can tidally locked planets support habitable climates and life?Several studies have explored this question using global circulation models (GCMs). Not only did these studies find that tidally locked Earth analogs can indeed sustain habitable climates, their large day-night contrast should also create a distinct cloud structure that could help astronomers identify such planets. These studies, however, relied on GCMs which do not explicitly resolve convection, raising the question of how robust their results are.Here we consider the dynamics of clouds and convection on a tidally locked planet using the System for Atmospheric Modeling (SAM) cloud-resolving model. We simulate a 3d `channel', representing an equatorial strip that covers both day- and nightside of a tidally locked planet. We use interactive radiation and an interactive slab ocean surface and investigate the response to changes in the stellar constant. We find mean climates that are broadly comparable to those produced by a GCM. However, when the slab ocean is shallow, we also find internal variability that is far bigger than in a GCM. Convection in a tidally locked domain can self-organize in a dramatic fashion, with large outbursts of convection followed by periods of relative calm. We show that one of the timescales for this behavior is set by the time it takes for a dry gravity wave to travel between day- and nightside. The quasi-periodic self-organization of clouds can vary the planetary albedo by up to 50%. Changes this large are potentially detectable with future space telescopes, which raises the prospect of using convectively driven variability to identify high priority targets in the search for life around other stars.
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
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.
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 ...
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.
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.
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).
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...... thus obtained can be extended to a large class of distributions containing the rapidly decreasing smooth functions and the compactly supported distributions. For these transforms we derive support theorems in which the support of ϕ is (partially) characterized in terms of the support of RPϕ. The proof...... 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....
A Macro for Reusing Abstract Functions and Theorems
Directory of Open Access Journals (Sweden)
Sebastiaan J. C. Joosten
2013-04-01
Full Text Available Even though the ACL2 logic is first order, the ACL2 system offers several mechanisms providing users with some operations akin to higher order logic ones. In this paper, we propose a macro, named instance-of-defspec, to ease the reuse of abstract functions and facts proven about them. Defspec is an ACL2 book allowing users to define constrained functions and their associated properties. It contains macros facilitating the definition of such abstract specifications and instances thereof. Currently, lemmas and theorems derived from these abstract functions are not automatically instantiated. This is exactly the purpose of our new macro. instance-of-defspec will not only instantiate functions and theorems within a specification but also many more functions and theorems built on top of the specification. As a working example, we describe various fold functions over monoids, which we gradually built from arbitrary functions.
Three-dimensional semi-idealized model for tidal motion in tidal estuaries
Kumar, M.; Schuttelaars, H.M.; Roos, P.C.; Möller, M.
2015-01-01
In this paper, a three-dimensional semi-idealized model for tidal motion in a tidal estuary of arbitrary shape and bathymetry is presented. This model aims at bridging the gap between idealized and complex models. The vertical profiles of the velocities are obtained analytically in terms of the
van Damme, S.; Dehairs, F.; Tackx, M.; Beauchard, O.; Struyf, E.; Gribsholt, B.; van Cleemput, O.; Meire, P.
2009-01-01
Tidal marsh exchange studies are relatively simple tools to investigate the interaction between tidal marshes and estuaries. They have mostly been confined to only a few elements and to saltwater or brackish systems. This study presents mass-balance results of an integrated one year campaign in a
A comparative study of nitrogen and phosphorus cycling in tidal and non-tidal riverine wetlands
Verhoeven, J. T.A.; Whigham, D.F.; van Logtestijn, R.; O'Neill, J.K.
2001-01-01
This paper describes a study of nutrient dynamics in 12 tidal and non-tidal freshwater riverine wetlands in The Netherlands, Belgium, and Maryland (USA). The purpose of the study was to investigate the relationships between nutrient cycling processes in riverine wetlands that were geographically
Vandenbruwaene, W.; Meire, P.; Temmerman, S.; Bouma, T.J.
2013-01-01
The long-term (10–100 years) evolution of tidal channels is generally considered to interact with the bio-geomorphic evolution of the surrounding intertidal platform. Here we studied how the geometric properties of tidal channels (channel drainage density and channel width) change as (1) vegetation
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.
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)
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
A *-mixing convergence theorem for convex set valued processes
Directory of Open Access Journals (Sweden)
A. de Korvin
1987-01-01
Full Text Available In this paper the concept of a *-mixing process is extended to multivalued maps from a probability space into closed, bounded convex sets of a Banach space. The main result, which requires that the Banach space be separable and reflexive, is a convergence theorem for *-mixing sequences which is analogous to the strong law of large numbers. The impetus for studying this problem is provided by a model from information science involving the utilization of feedback data by a decision maker who is uncertain of his goals. The main result is somewhat similar to a theorem for real valued processes and is of interest in its own right.
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
Towards a Reverse Newman's Theorem in Interactive Information Complexity
DEFF Research Database (Denmark)
Brody, Joshua Eric; Buhrman, Harry; Koucký, Michal
2016-01-01
that uses private randomness and convert it into one that only uses public randomness while preserving the information revealed to each player? We prove that the answer is yes, at least for protocols that use a bounded number of rounds. As an application, we prove new direct sum theorems through......Newman’s theorem states that we can take any public-coin communication protocol and convert it into one that uses only private randomness with only a little increase in communication complexity. We consider a reversed scenario in the context of information complexity: can we take a protocol...
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.
On Fixed Point Theorems in Probabilistic Metric Spaces and Applications
GoleÅ£, Ioan; GoleÅ£, IonuÅ£
2008-09-01
In [4] S. Gähler formulated an appropriate system of axioms for a distance between three points and developed a theory of 2-metric spaces. A slight enlargement of the concept of 2-metric space was given in [3], where B. C. Dhage studied so called generalized metric spaces. In the present paper we have studied contraction conditions for mappings defined on a class of probabilistic metric space and fixed point theorems for such mappings. As a particular cases we have obtain fixed point theorems for random operator and for mappings defined on deterministic metric spaces.
Weyl type theorems for algebraically Quasi-$\\mathcal{HNP}$ operators
Rashid, M. H. M.; Prasad, T.
2015-01-01
In this paper, by introducing the class of quasi hereditarily normaloid polaroid operators, we obtain a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators. This framework also entails Weyl type theorems for perturbations $f(T + A)$, where $A$ is algebraic and commutes with $T,$ and $f$ is an analytic function, defined on an open neighborhood of the spectrum of $T +A$, such that $f$ is non constant on each of the c...
A vizing-type theorem for matching forests
Keijsper, J.C.M.
2000-01-01
A well known Theorem of Vizing states that one can colour the edges of a graph by $\\Delta +\\alpha$ colours, such that edges of the same colour form a matching. Here, $\\Delta$ denotes the maximum degree of a vertex, and $\\alpha$ the maximum multiplicity of an edge in the graph. An analogue of this Theorem for directed graphs was proved by Frank. It states that one can colour the arcs of a digraph by $\\Delta +\\alpha$ colours, such that arcs of the same colour form a branching. For a digraph, $\\...
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.
Decomposing Borel functions using the Shore-Slaman join theorem
Kihara, Takayuki
2013-01-01
Jayne and Rogers proved that every function from an analytic space into a separable metric space is decomposable into countably many continuous functions with closed domains if and only if the preimage of each $F_\\sigma$ set under it is again $F_\\sigma$. Many researchers conjectured that the Jayne-Rogers theorem can be generalized to all finite levels of Borel functions. In this paper, by using the Shore-Slaman join theorem on the Turing degrees, we show the following variant of the Jayne-Rog...
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.
Abelian theorems for the stieltjes transform of functions, II
Directory of Open Access Journals (Sweden)
Richard D. Carmichael
1981-01-01
is a result in which known behavior of the function as its domain variable approaches zero (approaches ∞ is used to infer the behavior of the transform as its domain variable approaches zero (approaches ∞. We obtain such theorems in this paper concerning the Stieltjes transform. In our results all parameters are complex; the variable s of the transform is complex in the right half plane; and the initial (final value Abelian theorems are obtained as |s|→0(|s|→∞ within an arbitrary wedge in the right half plane.
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
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.
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...
On the migration rate of tidal meanders
D'Alpaos, A.; Finotello, A.; Ghinassi, M.; Lanzoni, S.; Marani, M.; Rinaldo, A.
2016-12-01
Sinuous channels shaped by periodically reversing tidal flows are a ubiquitous feature of tidal landscapes. Despite their fundamental role on the morphology and sedimentary patterns of these landscapes, tidal meanders have received less attention than their fluvial counterparts, particularly as far as migration processes are concerned. We have analyzed the migration of about 300 meander bends in the Northern Venice Lagoon (Italy), from 1968 to nowadays, through observations and modeling interpretation. Similarities with fluvial meanders occur, although important difference also emerge. Meanders cutting through salt-marshes in the Venice Lagoon follow the relationship between Cartesian length and channel width, typical of meanders developed within different settings. We find a mean migration rate of about 0.20 m/year. However, the potential migration rate can reach values of about 0.20 channel widths per year thus suggesting similarities with fluvial meanders. In addition, tidal channel migration dynamics displays features which qualitatively agree with theories developed for the fluvial setting. We deem our results are valuable for the understanding of the morphological evolution and architecture of tidal landscapes, with implications for restoration strategies, also in the face of changes in environmental conditions.
Carbon sequestration by Australian tidal marshes
Macreadie, Peter I.
2017-03-10
Australia\\'s tidal marshes have suffered significant losses but their recently recognised importance in CO2 sequestration is creating opportunities for their protection and restoration. We compiled all available data on soil organic carbon (OC) storage in Australia\\'s tidal marshes (323 cores). OC stocks in the surface 1 m averaged 165.41 (SE 6.96) Mg OC ha-1 (range 14-963 Mg OC ha-1). The mean OC accumulation rate was 0.55 ± 0.02 Mg OC ha-1 yr-1. Geomorphology was the most important predictor of OC stocks, with fluvial sites having twice the stock of OC as seaward sites. Australia\\'s 1.4 million hectares of tidal marshes contain an estimated 212 million tonnes of OC in the surface 1 m, with a potential CO2-equivalent value of $USD7.19 billion. Annual sequestration is 0.75 Tg OC yr-1, with a CO2-equivalent value of $USD28.02 million per annum. This study provides the most comprehensive estimates of tidal marsh blue carbon in Australia, and illustrates their importance in climate change mitigation and adaptation, acting as CO2 sinks and buffering the impacts of rising sea level. We outline potential further development of carbon offset schemes to restore the sequestration capacity and other ecosystem services provided by Australia tidal marshes.
Bart, G.D.; Turtle, E.P.; Jaeger, W.L.; Keszthelyi, L.P.; Greenberg, R.
2004-01-01
Sets of ridges of uncertain origin are seen in twenty-nine high-resolution Galileo images, which sample seven locales on Io. These ridges are on the order of a few kilometers in length with a spacing of about a kilometer. Within each locale, the ridges have a consistent orientation, but the orientations vary from place to place. We investigate whether these ridges could be a result of tidal flexing of Io by comparing their orientations with the peak tidal stress orientations at the same locations. We find that ridges grouped near the equator are aligned either north-south or east-west, as are the predicted principal stress orientations there. It is not clear why particular groups run north-south and others east-west. The one set of ridges observed far from the equator (52?? S) has an oblique azimuth, as do the tidal stresses at those latitudes. Therefore, all observed ridges have similar orientations to the tidal stress in their region. This correlation is consistent with the hypothesis that tidal flexing of Io plays an important role in ridge formation. ?? 2004 Elsevier Inc. All rights reserved.
Probing electroweak symmetry braking mechanism at the LHC: A guideline from power counting analysis
International Nuclear Information System (INIS)
He Hongjian; Virginia Polytechnic Inst. and State Univ., Blacksburg, VA; Virginia Polytechnic Inst. and State Univ., Blacksburg, VA; Kuang, Y.P.; Tsinghua Univ., Beijing, BJ; Yuan, C.P.
1996-01-01
We formulate the equivalence theorem as a criterion for sensitively probing the electroweak symmetry breaking mechanism, and develop a precise power counting rule for chiral Lagrangian formulated electroweak theories (CLEWT). With these we give a systematic analysis on the sensitivities of the scattering processes W ± W ± →W ± W ± and q anti q'→W ± Z to probing all possible effective bosonic operators in the CLEWT at the CERN Large Hadron Collider (LHC). (orig.)
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.
A Basic Elementary Extension of the Duchet-Meyniel Theorem
DEFF Research Database (Denmark)
Pedersen, Anders Sune; Toft, Bjarne
2010-01-01
$ by $2\\alpha - 2$ when $\\alpha$ is at least 3. In this paper a basic elementary extension of the Theorem of Duchet and Meyniel is presented. This may be of help to avoid dealing with basic cases when looking for more substantial improvements. The main unsolved problem (due to Seymour) is to improve, even...
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
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.
A general theorem characterizing some absolute summability methods
Indian Academy of Sciences (India)
... theorem is given which gives the necessary and sufficient conditions satisfied by a sequence ( n ) in order to have the series ∑ a n n summable to || whenever ∑ a n is summable to || for some summability method . Author Affiliations. W T Sulaiman1. Ajman University, P.O. Box 346, Ajman, United Arab Emirates ...
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…
The Great Theorems of Mathematics -8-6 ...
Indian Academy of Sciences (India)
cal culture by reading books that reveal the exciting, inspirational, and human aspects of mathematics. This is ... theorem using modern terminology. He faithfully follows that scheme throughout the Journey. The author ... turer can use it as a source book for lectures. - either in the classroom or on more popu- lar occasions.
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.
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.
A Novel Passive Tracking Scheme Exploiting Geometric and Intercept Theorems.
Zhou, Biao; Sun, Chao; Ahn, Deockhyeon; Kim, Youngok
2018-03-17
Passive tracking aims to track targets without assistant devices, that is, device-free targets. Passive tracking based on Radio Frequency (RF) Tomography in wireless sensor networks has recently been addressed as an emerging field. The passive tracking scheme using geometric theorems (GTs) is one of the most popular RF Tomography schemes, because the GT-based method can effectively mitigate the demand for a high density of wireless nodes. In the GT-based tracking scheme, the tracking scenario is considered as a two-dimensional geometric topology and then geometric theorems are applied to estimate crossing points (CPs) of the device-free target on line-of-sight links (LOSLs), which reveal the target's trajectory information in a discrete form. In this paper, we review existing GT-based tracking schemes, and then propose a novel passive tracking scheme by exploiting the Intercept Theorem (IT). To create an IT-based CP estimation scheme available in the noisy non-parallel LOSL situation, we develop the equal-ratio traverse (ERT) method. Finally, we analyze properties of three GT-based tracking algorithms and the performance of these schemes is evaluated experimentally under various trajectories, node densities, and noisy topologies. Analysis of experimental results shows that tracking schemes exploiting geometric theorems can achieve remarkable positioning accuracy even under rather a low density of wireless nodes. Moreover, the proposed IT scheme can provide generally finer tracking accuracy under even lower node density and noisier topologies, in comparison to other schemes.
A Classroom Simulation of the Central Limit Theorem.
McLean, James E.
This simple method for simulating the Central Limit Theorem with students in a beginning nonmajor statistics class requires students to use dice to simulate drawing samples from a discrete uniform distribution. On a chalkboard, the distribution of sample means is superimposed on a graph of the discrete uniform distribution to provide visual…
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…
The Jordan curve theorem in the Khalimsky plane
Directory of Open Access Journals (Sweden)
Ezzeddine Bouassida
2008-10-01
Full Text Available The connectivity in Alexandroff topological spaces is equivalent to the path connectivity. This fact gets some specific properties to Z2, equipped with the Khalimsky topology. This allows a sufficiently precise description of the curves in Z2 and permit to prove a digital Jordan curve theorem in Z2.
Fixed point theorems for densifying mappings and compact mappings
Directory of Open Access Journals (Sweden)
Zeqing Liu
2002-01-01
Full Text Available The purpose of this note is to establish fixed point theorems for densifying mappings and compact mappings which are contractive in metric spaces and to investigate the existence of fixed points for a family of mappings in bounded metric spaces. The results of this note generalize the results of Bailey (1966 and Liu (1994.
Babylonian Pythagoras' Theorem, the Early History of Zero and a ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 1. Babylonian Pythagoras' Theorem, the Early History of Zero and a Polemic on the Study of the History of Science. Rahul Roy. General Article Volume 8 Issue 1 January 2003 pp 30-40 ...
A Converse to the Cayley-Hamilton Theorem
Indian Academy of Sciences (India)
Polynomials Satisfied by Square Matrices: A. Converse to the Cayley-Hamilton Theorem. Anandam Banerjee. Some Linear Algebra. Given a matrix A E Mn( R), the polynomial XA(X) = det(A - xl) is called the characteristic polynomial of. A. We can also define it for matrices over C or more generally for any arbitrary field K, ...
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.
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 Math ematics OBOR OECD: Pure math ematics Impact factor: 0.250, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/malq.201500069/full
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
Abstract. 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.
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.
Reflections on the PBR Theorem: Reality Criteria & Preparation Independence
Directory of Open Access Journals (Sweden)
Shane Mansfield
2014-12-01
Full Text Available This paper contains initial work on attempting to bring recent developments in the foundations of quantum mechanics concerning the nature of the wavefunction within the scope of more logical and structural methods. A first step involves dualising a criterion for the reality of the wavefunction proposed by Harrigan & Spekkens, which was central to the Pusey-Barrett-Rudolph theorem. The resulting criterion has several advantages, including the avoidance of certain technical difficulties relating to sets of measure zero. By considering the 'reality' not of the wavefunction but of the observable properties of any ontological physical theory a new characterisation of non-locality and contextuality is found. Secondly, a careful analysis of preparation independence, one of the key assumptions of the PBR theorem, leads to a precise analogy with the kind of locality prohibited by Bell's theorem. Motivated by this, we propose a weakening of the assumption to something analogous to no-signalling. This amounts to allowing global or non-local correlations in the joint ontic state, which nevertheless do not allow for superluminal signalling. This is, at least, consistent with the Bell and Kochen-Specker theorems. We find a counter-example to the PBR argument, which violates preparation independence, but does satisfy this physically motivated assumption. The question of whether the PBR result can be strengthened to hold under the relaxed assumption is therefore posed.
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
Lyapunov convexity type theorems for non-atomic vector measures ...
African Journals Online (AJOL)
atomic, and σ-additive X-valued measure has a convex closure. We give a survey of Lyapunov convexity type theorems pertaining to this problem. We also give a necessary and sufficient condition that will insure the convexity of the closure of the ...
Critical types of Krasnoselskii fixed point theorems in weak topologies
African Journals Online (AJOL)
In this note, by means of the technique of measures of weak noncompactness, we establish a generalized form of fixed point theorem for the sum of T + S in weak topology setups of a metrizable locally convex space, where S is not weakly compact, I − T allows to be noninvertible, and T is not necessarily continuous.
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
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 do not assume anything about the spectral nature of the harmonic bath the ...
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 ...
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)
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.
Bounding the number of remarkable values via Jouanolou's theorem
Chèze , Guillaume
2015-01-01
In this article we bound the number of remarkable values of a polynomial vector field. The proof is short and based on Jouanolou's theorem about rational first integrals of planar polynomial derivations. Our bound is given in term of the size of a Newton polygon associated to the vector field. We prove that this bound is almost reached.
An analogous of Jouanolou's Theorem in positive characteristic
Pereira, Jorge Vitorio
2000-01-01
We show that a generic vector field on an affine space of positive characteristic admits an invariant algebraic hypersurface. This contrast with Jouanolou's Theorem that shows that in characteristic zero the situation is completely opposite. That is a generic vector field in the complex plane does not admit any invariant algebraic curve.
Bounding the number of remarkable values via Jouanolou's theorem
Chèze, Guillaume
2015-05-01
In this article we bound the number of remarkable values of a polynomial vector field. The proof is short and based on Jouanolou's theorem about rational first integrals of planar polynomial derivations. Our bound is given in term of the size of a Newton polygon associated to the vector field. We prove that this bound is almost reached.
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...
The Wiener-Khinchin theorem and recurrence quantification
Energy Technology Data Exchange (ETDEWEB)
Zbilut, Joseph P. [Department of Molecular Biophysics and Physiology, Rush University Medical Center, 1653 W. Congress, Chicago, IL 60612 (United States)], E-mail: jzbilut@rush.edu; Marwan, Norbert [Potsdam Institute for Climate Impact Research (PIK), 14412 Potsdam (Germany)
2008-10-27
The Wiener-Khinchin theorem states that the power spectrum is the Fourier transform of the autocovariance function. One form of the autocovariance function can be obtained through recurrence quantification. We show that the advantage of defining the autocorrelation function with recurrences can demonstrate higher dimensional dynamics.
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 ...
Sturm-Picone type theorems for nonlinear differential systems
Directory of Open Access Journals (Sweden)
Aydin Tiryaki
2015-06-01
Full Text Available In this article, we establish a Picone-type inequality for a pair of first-order nonlinear differential systems. By using this inequality, we give Sturm-Picone type comparison theorems for these systems and a special class of second-order half-linear equations with damping term.
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
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".
A note on the Fuglede–Putnam theorem
Indian Academy of Sciences (India)
Annual Meetings · Mid Year Meetings · Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 123; Issue 2. A Note on the Fuglede-Putnam Theorem. Fotios C Paliogiannis. Volume 123 Issue 2 May 2013 ...
On the Applicability of the Surface Equivalence Theorem Inside Enclosures
DEFF Research Database (Denmark)
Franek, Ondrej; Sørensen, Morten; Ebert, Hans
2012-01-01
A scenario of a generic printed circuit board (PCB) representing an electronic module inside a metallic enclosure is studied numerically. Following the surface equivalence theorem, the PCB is replaced with surface currents running on a Huygens box (HB) inside the enclosure and near-field errors w...
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...
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.
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.
Pólya's One Theorem with 100 Pages of Applications
Indian Academy of Sciences (India)
IAS Admin
before proceeding to some other applications of Pólya's theorem. As mentioned earlier, one could assign a value for each shape/colour in R and enumerate the number of configurations with a given value. It is convenient to constrain values of shapes to be non-negative integers. One forms the generating function c(x) = c0 ...
A vizing-type theorem for matching forests
Keijsper, J.C.M.
2000-01-01
A well known Theorem of Vizing states that one can colour the edges of a graph by $\\Delta +\\alpha$ colours, such that edges of the same colour form a matching. Here, $\\Delta$ denotes the maximum degree of a vertex, and $\\alpha$ the maximum multiplicity of an edge in the graph. An analogue of this
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 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 : algebraizable logic s * abstract algebraic logic * structural closure operators * semantic isomorphism theorem * evaluational frames * compositional lattice Subject RIV: BA - General Mathematics Impact factor: 0.647, year: 2016
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…
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…
No-go theorem for static boson stars
Directory of Open Access Journals (Sweden)
Shahar Hod
2018-03-01
Full Text Available It is proved that self-gravitating static scalar fields whose self-interaction potential V(ψ2 is a monotonically increasing function of its argument cannot form spherically symmetric asymptotically flat bound matter configurations. Our compact theorem rules out, in particular, the existence of spatially regular static boson stars made of nonlinear massive scalar fields.
Cowling–Price Theorem and Characterization of Heat Kernel on ...
Indian Academy of Sciences (India)
We extend the uncertainty principle, the Cowling–Price theorem, on non-compact Riemannian symmetric spaces . We establish a characterization of the heat kernel of the Laplace–Beltrami operator on from integral estimates of the Cowling–Price type.
Experimental studies of the transient fluctuation theorem using liquid ...
Indian Academy of Sciences (India)
Boltzmann constant and T being the absolute temperature of the system, thermal noise is expected to play an important role. In particular, the validity of the second law of thermodynamics for small systems is under considerable debate since the time of Boltzmann. Recently, a nonequilibrium fluctuation theorem (FT) known.
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 ...
Cowling–Price theorem and characterization of heat kernel on ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Keywords. Hardy's theorem; spherical harmonics; symmetric space; Jacobi function; heat kernel. 1. Introduction. Our starting point in this paper is the classical Hardy's ... solutions of the heat equation of the Laplace–Beltrami operator. .... similar argument with the role of ˜z and zn reversed and the induction hypothesis for d =.
A general theorem characterizing some absolute summability methods
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Ajman University, P.O. Box 346, Ajman, United Arab Emirates. MS received 29 October 2001; revised 26 March 2002. Abstract. A general theorem is given which gives the necessary and sufficient con- ditions satisfied by a sequence (εn) in order to have the series. ∑ anεn summable to |A| whenever. ∑ an is summable to ...
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
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 ...
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 very simple proof of Pascal's hexagon theorem and some ...
Indian Academy of Sciences (India)
In this article we present a simple and elegant algebraic proof of Pascal's hexagon theorem which requires only knowledge of basics on conic sections without theory of projective transformations. Also, we provide an efficient algorithm for finding an equation of the conic containing five given points and a criterion for ...
The Nielsen-Ninomiya theorem, \\renewcommand{\\P}{{{ P}}} \
Chernodub, M. N.
2017-09-01
The Nielsen-Ninomiya theorem implies that any local, Hermitian and translationally invariant lattice action in even-dimensional spacetime possesses an equal number of left- and right-handed chiral fermions. We argue that if one sacrifices the property of Hermiticity while keeping the locality and translation invariance, and imposing invariance of the action under the space-time ( \\renewcommand{\\P}{{{ P}}} \
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…
Limit Theorems For the Grover Walk Without Memory
Ampadu, Clement
2011-01-01
We consider the Grover walk as a 4-state quantum walk without memory in one dimension. The walker in our 4-state quantum walk moves to the left or right. We compute the stationary distribution of the walk, in addition, we obtain the weak limit theorem
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:
No-go theorem for static boson stars
Hod, Shahar
2018-03-01
It is proved that self-gravitating static scalar fields whose self-interaction potential V (ψ2) is a monotonically increasing function of its argument cannot form spherically symmetric asymptotically flat bound matter configurations. Our compact theorem rules out, in particular, the existence of spatially regular static boson stars made of nonlinear massive scalar fields.
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.
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.
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.)
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
Gauss-Bonnet's Theorem and Closed Frenet Frames
DEFF Research Database (Denmark)
Røgen, Peter
1997-01-01
curves are found using Gauss-Bonnet's Theorem after cutting the curve into simple closed sub-curves. At this point an error in the litterature is corrected. If the spherecal curve is the tangent indicatrix of a space-curve we obtain a new short proof of a formula for integrated torsion presented...
Quantum optical ABCD theorem in two-mode case
International Nuclear Information System (INIS)
Fan Hongyi; Hu Liyun
2008-01-01
By introducing the entangled Fresnel operator (EFO) this paper demonstrates that there exists ABCD theorem for two-mode entangled case in quantum optics. The canonical operator method as mapping of ray-transfer ABCD matrix is explicitly shown by EFO's normally ordered expansion through the coherent state representation and the technique of integration within an ordered product of operators
Tidal analysis of Met rocket wind data
Bedinger, J. F.; Constantinides, E.
1976-01-01
A method of analyzing Met Rocket wind data is described. Modern tidal theory and specialized analytical techniques were used to resolve specific tidal modes and prevailing components in observed wind data. A representation of the wind which is continuous in both space and time was formulated. Such a representation allows direct comparison with theory, allows the derivation of other quantities such as temperature and pressure which in turn may be compared with observed values, and allows the formation of a wind model which extends over a broader range of space and time. Significant diurnal tidal modes with wavelengths of 10 and 7 km were present in the data and were resolved by the analytical technique.
TIDAL TURBULENCE SPECTRA FROM A COMPLIANT MOORING
Energy Technology Data Exchange (ETDEWEB)
Thomson, Jim; Kilcher, Levi; Richmond, Marshall C.; Talbert, Joe; deKlerk, Alex; Polagye, Brian; Guerra, Maricarmen; Cienfuegos, Rodrigo
2013-06-13
A compliant mooring to collect high frequency turbulence data at a tidal energy site is evaluated in a series of short demon- stration deployments. The Tidal Turbulence Mooring (TTM) improves upon recent bottom-mounted approaches by suspend- ing Acoustic Doppler Velocimeters (ADVs) at mid-water depths (which are more relevant to tidal turbines). The ADV turbulence data are superior to Acoustic Doppler Current Profiler (ADCP) data, but are subject to motion contamination when suspended on a mooring in strong currents. In this demonstration, passive stabilization is shown to be sufficient for acquiring bulk statistics of the turbulence, without motion correction. With motion cor- rection (post-processing), data quality is further improved; the relative merits of direct and spectral motion correction are dis- cussed.
Yang, Chuan-Fu
Inverse spectral problems are considered for differential pencils with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions. We give formulations of the associated inverse problems such as Titchmarsh-Weyl theorem, Hochstadt-Lieberman theorem and Mochizuki-Trooshin theorem, and prove corresponding uniqueness theorems. The obtained results are generalizations of the similar results for the classical Sturm-Liouville operator on a finite interval.
Weak Characterizations of Stochastic Integrability and Dudley's Theorem in Infinite Dimensions
Czech Academy of Sciences Publication Activity Database
Ondreját, Martin; Veraar, M.
2014-01-01
Roč. 27, č. 4 (2014), s. 1350-1374 ISSN 0894-9840 R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : stochastic integration in Banach spaces * almost sure limit theorems * Dudley representation theorem * universal representation theorem * weak characterization of stochastic integrability * Doob representation theorem Subject RIV: BA - General Mathematics Impact factor: 0.857, year: 2014 http://library.utia.cas.cz/separaty/2013/SI/ondrejat-0392394.pdf
Renaud, Joe P.; Henning, Wade G.
2018-04-01
The advanced rheological models of Andrade and Sundberg & Cooper are compared to the traditional Maxwell model to understand how each affects the tidal dissipation of heat within rocky bodies. We find both Andrade and Sundberg–Cooper rheologies can produce at least 10× the tidal heating compared to a traditional Maxwell model for a warm (1400–1600 K) Io-like satellite. Sundberg–Cooper can cause even larger dissipation around a critical temperature and frequency. These models allow cooler planets to stay tidally active in the face of orbital perturbations—a condition we term “tidal resilience.” This has implications for the time evolution of tidally active worlds and the long-term equilibria they fall into. For instance, if Io’s interior is better modeled by the Andrade or Sundberg–Cooper rheologies, the number of possible resonance-forming scenarios that still produce a hot, modern Io is expanded, and these scenarios do not require an early formation of the Laplace resonance. The two primary empirical parameters that define the Andrade anelasticity are examined in several phase spaces to provide guidance on how their uncertainties impact tidal outcomes, as laboratory studies continue to constrain their real values. We provide detailed reference tables on the fully general equations required for others to insert the models of Andrade and Sundberg–Cooper into standard tidal formulae. Lastly, we show that advanced rheologies can greatly impact the heating of short-period exoplanets and exomoons, while the properties of tidal resilience could mean a greater number of tidally active worlds among all extrasolar systems.
CFD for wind and tidal offshore turbines
Montlaur, Adeline
2015-01-01
The book encompasses novel CFD techniques to compute offshore wind and tidal applications. Computational fluid dynamics (CFD) techniques are regarded as the main design tool to explore the new engineering challenges presented by offshore wind and tidal turbines for energy generation. The difficulty and costs of undertaking experimental tests in offshore environments have increased the interest in the field of CFD which is used to design appropriate turbines and blades, understand fluid flow physical phenomena associated with offshore environments, predict power production or characterise offshore environments, amongst other topics.
Short period tidal variations of earth rotation
Yoder, C. F.; Williams, J. G.; Parke, M. E.; Dickey, J. O.
1981-01-01
It is explained that the tidal deformation of the earth's polar moment of inertia by the moon and sun cause periodic variations in rotation. The short period oscillations give rise to a meter-sized, diurnal signature in the lunar laser ranging data obtained at McDonald Observatory. A solution is given for the scale parameter k/C at fortnightly and monthly tidal frequencies. The results are compared with those obtained by other investigators and with a theoretical estimate which includes the effect of oceans and a decoupled fluid core.
Using Computers To Teach the Concepts of the Central Limit Theorem.
Mittag, Kathleen Cage
A pivotal theorem which is of critical importance to statistical inference in probability and statistics is the Central Limit Theorem (CLT). The theorem concerns the sampling distribution of random samples taken from a population, including population distributions that do not have to be normal distributions. This paper contains a brief history of…
Action-angle variables and a KAM theorem for b-Poisson manifolds
Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey
2015-01-01
In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [14] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved.
Two fixed point theorems on quasi-metric spaces via mw- distances
Energy Technology Data Exchange (ETDEWEB)
Alegre, C.
2017-07-01
In this paper we prove a Banach-type fixed point theorem and a Kannan-type theorem in the setting of quasi-metric spaces using the notion of mw-distance. These theorems generalize some results that have recently appeared in the literature. (Author)
Logical strength of complexity theory and a formalization of the PCP theorem in bounded arithmetic
Pich, Ján
2014-01-01
We present several known formalizations of theorems from computational complexity in bounded arithmetic and formalize the PCP theorem in the theory PV1 (no formalization of this theorem was known). This includes a formalization of the existence and of some properties of the (n,d,{\\lambda})-graphs in PV1.
NOAA Historical Tidal Current Data for the Coastal United States
National Oceanic and Atmospheric Administration, Department of Commerce — Knowledge of the timing and strength of tidal currents is extremely important for safe navigation in coastal waters. Tidal currents are almost always the strongest...
Tidal flow characteristics at Kasheli (Kalwa/ Bassein creek), Bombay
Digital Repository Service at National Institute of Oceanography (India)
Swamy, G.N.; Suryanarayana, A.
Tidal flow characteristics of waters at Kasheli, connected to the sea through Thane and Bassein Creeks in Bombay, Maharashtra, India are investigated based on tide and current observations carried out in 1980-81. The results establish that the tidal...
Tidal capture of stars by a massive black hole
Novikov, I. D.; Pethick, C. J.; Polnarev, A. G.
1992-01-01
The processes leading to tidal capture of stars by a massive black hole and the consequences of these processes in a dense stellar cluster are discussed in detail. When the amplitude of a tide and the subsequent oscillations are sufficiently large, the energy deposited in a star after periastron passage and formation of a bound orbit cannot be estimated directly using the linear theory of oscillations of a spherical star, but rather numerical estimates must be used. The evolution of a star after tidal capture is discussed. The maximum ratio R of the cross-section for tidal capture to that for tidal disruption is about 3 for real systems. For the case of a stellar system with an empty capture loss cone, even in the case when the impact parameter for tidal capture only slightly exceeds the impact parameter for direct tidal disruption, tidal capture would be much more important than tidal disruption.
Tidal Power Potential in the Submerged Channels of Dar es
African Journals Online (AJOL)
Results from in-situ measurements show that currents on the sandbank and the tidal flat, in water depths from 0.5 m to 3.0 m, are directed opposite the main tidal current in the deeper waters. Current velocities vary during a tidal cycle and are strongest in the middle of the cycle. Generally, velocities on the tidal flat are around ...
Tidal Marshes: The Boundary between Land and Ocean.
Gosselink, James
An overview of the ecology of the tidal marshes along the gulf coast of the United States is presented. The following topics are included: (1) the human impact on tidal marshes; (2) the geologic origins of tidal marshes; (3) a description of the physical characteristics and ecosystem of the marshlands; (4) a description of the marshland food chain…
Field migration rates of tidal meanders recapitulate fluvial morphodynamics.
Finotello, Alvise; Lanzoni, Stefano; Ghinassi, Massimiliano; Marani, Marco; Rinaldo, Andrea; D'Alpaos, Andrea
2018-02-13
The majority of tidal channels display marked meandering features. Despite their importance in oil-reservoir formation and tidal landscape morphology, questions remain on whether tidal-meander dynamics could be understood in terms of fluvial processes and theory. Key differences suggest otherwise, like the periodic reversal of landscape-forming tidal flows and the widely accepted empirical notion that tidal meanders are stable landscape features, in stark contrast with their migrating fluvial counterparts. On the contrary, here we show that, once properly normalized, observed migration rates of tidal and fluvial meanders are remarkably similar. Key to normalization is the role of tidal channel width that responds to the strong spatial gradients of landscape-forming flow rates and tidal prisms. We find that migration dynamics of tidal meanders agree with nonlinear theories for river meander evolution. Our results challenge the conventional view of tidal channels as stable landscape features and suggest that meandering tidal channels recapitulate many fluvial counterparts owing to large gradients of tidal prisms across meander wavelengths. Copyright © 2018 the Author(s). Published by PNAS.
Detecting areal changes in tidal flats after sea dike construction ...
Indian Academy of Sciences (India)
remote sensing, however, may be used for mapping tidal flats in a rapid and accurate manner. Orbital remote sensing may be used to effectively assess tidal flat accretion due to its repetitive and synop- tic nature (Sanjeevi 1996). Many researchers have used remote sensing images to classify tidal flats and analyze their.
Subtidal flow division at a shallow tidal junction
Buschman, F.A.; Hoitink, A.J.F.; Vegt, M. van der; Hoekstra, P.
2010-01-01
Tides influence distribution of river discharge at tidally affected channel junctions. At the apex of a channel network in an Indonesian delta, observations of flow division suggest that tidally averaged flow division depends on the tidal range. To understand the mechanisms governing the subtidal
Tidal freshwater wetlands, the fresh dimension of the estuary
Barendregt, A.
2016-01-01
Upstream in the estuary, where the river ends, the tidal energy is still present but the constant input from the river creates permanent fresh water conditions. The physical, chemical and biological conditions differ from the brackish part of the tidal area, but by processes from the tidal wave also
Field migration rates of tidal meanders recapitulate fluvial morphodynamics
Finotello, Alvise; Lanzoni, Stefano; Ghinassi, Massimiliano; Marani, Marco; Rinaldo, Andrea; D'Alpaos, Andrea
2018-02-01
The majority of tidal channels display marked meandering features. Despite their importance in oil-reservoir formation and tidal landscape morphology, questions remain on whether tidal-meander dynamics could be understood in terms of fluvial processes and theory. Key differences suggest otherwise, like the periodic reversal of landscape-forming tidal flows and the widely accepted empirical notion that tidal meanders are stable landscape features, in stark contrast with their migrating fluvial counterparts. On the contrary, here we show that, once properly normalized, observed migration rates of tidal and fluvial meanders are remarkably similar. Key to normalization is the role of tidal channel width that responds to the strong spatial gradients of landscape-forming flow rates and tidal prisms. We find that migration dynamics of tidal meanders agree with nonlinear theories for river meander evolution. Our results challenge the conventional view of tidal channels as stable landscape features and suggest that meandering tidal channels recapitulate many fluvial counterparts owing to large gradients of tidal prisms across meander wavelengths.