Bohr orbit theory revisited

International Nuclear Information System (INIS)

Harcourt, R.D.

1987-01-01

Bohr orbit theory is used to calculate energies for the 1S, 2P, 3D, 4F and 5G states of the helium muonic atom, when the muon is excited. These energies are close to those which have been calculated variationally by Huang (1977, Phys. Rev. A 15 1832-8). (author)

De novo nonsense mutations in ASXL1 cause Bohring-Opitz syndrome

DEFF Research Database (Denmark)

Hoischen, Alexander; van Bon, Bregje W M; Rodríguez-Santiago, Benjamín

2011-01-01

Bohring-Opitz syndrome is characterized by severe intellectual disability, distinctive facial features and multiple congenital malformations. We sequenced the exomes of three individuals with Bohring-Opitz syndrome and in each identified heterozygous de novo nonsense mutations in ASXL1, which...... is required for maintenance of both activation and silencing of Hox genes. In total, 7 out of 13 subjects with a Bohring-Opitz phenotype had de novo ASXL1 mutations, suggesting that the syndrome is genetically heterogeneous....

Reconstructing Bohr's Reply to EPR in Algebraic Quantum Theory

Science.gov (United States)

Ozawa, Masanao; Kitajima, Yuichiro

2012-04-01

Halvorson and Clifton have given a mathematical reconstruction of Bohr's reply to Einstein, Podolsky and Rosen (EPR), and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr's reply. In the present paper, we generalize the above consistency theorem, with a rather elementary proof, to a general formulation of EPR states applicable to both non-relativistic quantum mechanics and algebraic quantum field theory; and we clarify the elements of reality in EPR states in terms of Bohr's requirements of classicality and objectivity, in a general formulation of algebraic quantum theory.

De novo nonsense mutations in ASXL1 cause Bohring-Opitz syndrome

NARCIS (Netherlands)

Hoischen, Alexander; van Bon, Bregje W. M.; Rodríguez-Santiago, Benjamín; Gilissen, Christian; Vissers, Lisenka E. L. M.; de Vries, Petra; Janssen, Irene; van Lier, Bart; Hastings, Rob; Smithson, Sarah F.; Newbury-Ecob, Ruth; Kjaergaard, Susanne; Goodship, Judith; McGowan, Ruth; Bartholdi, Deborah; Rauch, Anita; Peippo, Maarit; Cobben, Jan M.; Wieczorek, Dagmar; Gillessen-Kaesbach, Gabriele; Veltman, Joris A.; Brunner, Han G.; de Vries, Bert B. B. A.

2011-01-01

Bohring-Opitz syndrome is characterized by severe intellectual disability, distinctive facial features and multiple congenital malformations. We sequenced the exomes of three individuals with Bohring-Opitz syndrome and in each identified heterozygous de novo nonsense mutations in ASXL1, which is

Nil Bohr-sets and almost automorphy of higher order

CERN Document Server

Huang, Wen; Ye, Xiangdong

2016-01-01

Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any d\\in \\mathbb{N} does the collection of \\{n\\in \\mathbb{Z}: S\\cap (S-n)\\cap\\ldots\\cap (S-dn)\

Christian Bohr og De syv små Djaevle: Et laerestykke i 4 akter om iltdiffusionsstriden mellem Christian Bohr og August Krogh

DEFF Research Database (Denmark)

Gjedde, Albert

2004-01-01

The author explores novel lessons emerging from the oxygen diffusion controversy between Christian Bohr on one side and August and Marie Krogh on the other. THe controversy found its emphatic expression in August and Marie Krogh's "Seven Little Devils", a series of papers published back-to-back i......The author explores novel lessons emerging from the oxygen diffusion controversy between Christian Bohr on one side and August and Marie Krogh on the other. THe controversy found its emphatic expression in August and Marie Krogh's "Seven Little Devils", a series of papers published back...

Niels Bohr and the Atomic Structure

Indian Academy of Sciences (India)

IAS Admin

principle with the restriction that no more than two electrons occupy a given ... displacement laws. Early in his ... The only difference between them is their atomic weight. F Soddy ... validity, Bohr took his theory to Rutherford. Unfortunately,.

Correction of the exciton Bohr radius in monolayer transition metal dichalcogenides

Science.gov (United States)

Li, Run-Ze; Dong, Xi-Ying; Li, Zhi-Qing; Wang, Zi-Wu

2018-07-01

We theoretically investigate the correction of exciton Bohr radius in monolayer transition metal dichalcogenides (TMDCs) on different polar substrates arising from the exciton-optical phonon coupling, in which both the intrinsic longitudinal optical phonon and surface optical phonon modes couple with the exciton are taken into account. We find that the exciton Bohr radius is enlarged markedly due to these coupling. Moreover, it can be changed on a large scale by modulating the polarizability of polar substrate and the internal distance between the monolayer TMDCs and polar substrate. Theoretical result provides a potential explanation for the variation of the exciton Bohr radius in experimental measurement.

Bohr's Philosophy of Wave–Particle Complementarity

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 18; Issue 10. Bohr's Philosophy of Wave–Particle Complementarity. Dipankar Home. General Article Volume 18 Issue 10 October 2013 pp 905-916. Fulltext. Click here to view fulltext PDF. Permanent link:

Bohr effect of human hemoglobin: Separation of tertiary and quaternary contributions based on the Wyman equation.

Science.gov (United States)

Okonjo, Kehinde Onwochei

2017-09-01

As a prelude to separating tertiary from quaternary structure contributions to the Bohr effect, we employed the Wyman equation to analyze Bohr data for human hemoglobin to which 2,3-bisphosphoglycerate, 2,3-BPG, is bound. Changes in the pK a s of the histidine Bohr groups result in a net reduction of their contributions to the Bohr effect at pH 7.4 compared to their contributions in stripped hemoglobin. The non-histidine 2,3-BPG binding groups - the β-chain terminal amino group and Lys82β - make negative and positive contributions, respectively, to the Bohr effect. The final result is that the Bohr effect at physiological pH is higher for 2,3-BPG bound compared to stripped hemoglobin. Contributions linked to His2β, His77β and His143β enable us to separate tertiary from quaternary Bohr contributions in stripped and in 2,3-BPG bound hemoglobin. Both contributions serve to make the Bohr effect for 2,3-BPG bound hemoglobin higher than for stripped hemoglobin at physiological pH. Copyright © 2017 Elsevier B.V. All rights reserved.

Atoms, metaphors and paradoxes Niels Bohr and the construction of a new physics

CERN Document Server

Petruccioli, Sandro

2006-01-01

This book gives a detailed study of the development and the interpretation given to Niels Bohr's Principle of Correspondence. It also describes the role that this principle played in guiding Bohr's research over the critical period from 1920 to 1927. Quantum mechanics, developed in the 1920s and 1930s by Bohr, Heisenberg, Born, Schrödinger and Dirac, represents one of the most profound turning points in science. This theory required a wholly new kind of physics in which many of the principles, concepts and models representing reality, that had formed the basis of classical physics since Galileo and Newton, had to be abandoned. This book re-examines the birth of quantum mechanics, in particular examining the development of crucial and original insights of Niels Bohr.

EPR, kvantemekanik og Bohr

OpenAIRE

Nielsen, Morten Klockmann

2007-01-01

Dette projekt omhandler området hvor filosofi og fysik smelter sammen. Kvantemekanikkens tilblivelse fik en hård medfart hvilket diskussionerne mellem især Albert Einstein og Niels Bohr vidner om. De var hovedpersoner i striden om hvordan kvantemekanikken skulle fortolkes, og diskussionen kulminerede i 1935 hvor Einstein sammen med kollegerne Podolsky og Rosen offentliggjorde en artikel med titlen “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” (EPR-artiklen)....

The BOHR Effect before Perutz

Science.gov (United States)

Brunori, Maurizio

2012-01-01

Before the outbreak of World War II, Jeffries Wyman postulated that the "Bohr effect" in hemoglobin demanded the oxygen linked dissociation of the imidazole of two histidines of the polypeptide. This proposal emerged from a rigorous analysis of the acid-base titration curves of oxy- and deoxy-hemoglobin, at a time when the information on the…

Love, literature and the quantum atom Niels Bohr's 1913 trilogy revisited

CERN Document Server

Aaserud, Finn

2013-01-01

Niels Bohr ranks with Einstein among the physicists of the 20th century. He rose to this status through his invention of the quantum theory of the atom and his leadership in its defense and development. He also ranks with Einstein in his humanism and his sense of responsibility to his science and the society that enabled him to create it. Our book presents unpublished excerpts from extensive correspondence between Bohr and his immediate family, and uses it to describe and analyze the psychological and cultural background to his invention. The book also contains a reprinting of the three papers of 1913 - the "Trilogy" - in which Bohr worked out the provisional basis of a quantum theory of the atom.

One Hundred Years of Bohr Model

Indian Academy of Sciences (India)

IAS Admin

In this article I shall present a brief review of the .... By 1900, the amount of information available about .... resulting value was in quite good agreement with the .... It is fair to say that Bohr's model of the atom is simple, elegant, revolutionary but ...

Bohr's Electron was Problematic for Einstein: String Theory Solved the Problem

Science.gov (United States)

Webb, William

2013-04-01

Neils Bohr's 1913 model of the hydrogen electron was problematic for Albert Einstein. Bohr's electron rotates with positive kinetic energies +K but has addition negative potential energies - 2K. The total net energy is thus always negative with value - K. Einstein's special relativity requires energies to be positive. There's a Bohr negative energy conflict with Einstein's positive energy requirement. The two men debated the problem. Both would have preferred a different electron model having only positive energies. Bohr and Einstein couldn't find such a model. But Murray Gell-Mann did! In the 1960's, Gell-Mann introduced his loop-shaped string-like electron. Now, analysis with string theory shows that the hydrogen electron is a loop of string-like material with a length equal to the circumference of the circular orbit it occupies. It rotates like a lariat around its centered proton. This loop-shape has no negative potential energies: only positive +K relativistic kinetic energies. Waves induced on loop-shaped electrons propagate their energy at a speed matching the tangential speed of rotation. With matching wave speed and only positive kinetic energies, this loop-shaped electron model is uniquely suited to be governed by the Einstein relativistic equation for total mass-energy. Its calculated photon emissions are all in excellent agreement with experimental data and, of course, in agreement with those -K calculations by Neils Bohr 100 years ago. Problem solved!

Complementarity beyond physics Niels Bohr's parallels

CERN Document Server

Bala, Arun

2017-01-01

In this study Arun Bala examines the implications that Niels Bohr’s principle of complementarity holds for fields beyond physics. Bohr, one of the founding figures of modern quantum physics, argued that the principle of complementarity he proposed for understanding atomic processes has parallels in psychology, biology, and social science, as well as in Buddhist and Taoist thought. But Bohr failed to offer any explanation for why complementarity might extend beyond physics, and his claims have been widely rejected by scientists as empty speculation. Scientific scepticism has only been reinforced by the naïve enthusiasm of postmodern relativists and New Age intuitionists, who seize upon Bohr’s ideas to justify anti-realist and mystical positions. Arun Bala offers a detailed defence of Bohr’s claim that complementarity has far-reaching implications for the biological and social sciences, as well as for comparative philosophies of science, by explaining Bohr’s parallels as responses to the omnipresence...

Development by Niels Bohr of the quantum theory of the atom and of the correspondence principle

International Nuclear Information System (INIS)

El'yashevich, M.A.

1985-01-01

Bohr's investigations in 1912-1923 on the quantum theory of atoms are considered. The sources of N. Bohr's works on this subject are analyzed, and the beginning of his quantum research in 1912 is described. A detailed analysis is given of N. Bohr's famous paper on the hydrogen atom theory and on the origin of spectra. The further development of Bohr's ideas on atomic structure is considered, special attention is being payed to his postulates of stationary states and of radiation transitions and to the development of the correspondence principle. It is shown how well N. Bohr understood the difficulties of the model theory and how be tried to obtain a deep understanding of quantum phenomena

El modelo semicuántico de Bohr en los libros de texto The Bohr's quantum model in the textbook

Directory of Open Access Journals (Sweden)

Jorge Eliécer Moreno Ramírez

2010-01-01

Full Text Available La didáctica de las ciencias naturales está cuestionando la transposición de los modelos científicos en modelos didácticos. Otras investigaciones muestran que el conocimiento científico convertido en conocimiento escolar produce deformaciones de la actividad científica y la simplificación de modelos, contribuyendo con la actitud negativa de los estudiantes hacia las ciencias y al fracaso escolar reportado por algunos estudios. Se pregunta si el modelo atómico de Bohr que se muestra en los textos se corresponde histórica y epistemológicamente con las actividades científicas y cuáles son las posibles deformaciones que de ésta se hace cuando se muestra el modelo en los libros. Los resultados de la investigación muestran una clara diferencia entre la propuesta de Bohr (1913 y la transposición del modelo, lo que invita a una reflexión profunda acerca de la confiabilidad que pueden tener los textos utilizados para la enseñanza de la ciencia químicaNatural science teaching is questioning the transposition that is made of scientific models into didactic models, because research has shown that when scientific knowledge is transformed into scholarly knowledge in order to be taught it causes the deformation of the scientific activity and the simplification of the models. This contributes to the negative attitude of students towards science, and student failure shown in some studies. This research inquired if the transposition of Bohr's atomic model that is shown in textbooks corresponds historically and epistemologically to scientific activity and what the possible deformations are that, coming from this model, are made to the scientific activity that comes from the transposition. The research results show differences between what Bohr (1913 proposed and the transposition of the model in textbooks. This information will contribute to the analysis that is being done regarding the dependability of textbooks.

Bohr's Creation of his Quantum Atom

Science.gov (United States)

Heilbron, John

2013-04-01

Fresh letters throw new light on the content and state of Bohr's mind before and during his creation of the quantum atom. His mental furniture then included the atomic models of the English school, the quantum puzzles of Continental theorists, and the results of his own studies of the electron theory of metals. It also included the poetry of Goethe, plays of Ibsen and Shakespeare, novels of Dickens, and rhapsodies of Kierkegaard and Carlyle. The mind that held these diverse ingredients together oscillated between enthusiasm and dejection during the year in which Bohr took up the problem of atomic structure. He spent most of that year in England, which separated him for extended periods from his close-knit family and friends. Correspondence with his fianc'ee, Margrethe Nørlund, soon to be published, reports his ups and downs as he adjusted to J.J. Thomson, Ernest Rutherford, the English language, and the uneven course of his work. In helping to smooth out his moods, Margrethe played an important and perhaps an enabling role in his creative process.

Bohr--Sommerfeld Lagrangians of moduli spaces of Higgs bundles

DEFF Research Database (Denmark)

Biswas, Indranil; Gammelgaard, Niels Leth; Logares, Marina

Let $X$ be a compact connected Riemann surface of genus at least two. Let $M_H(r,d)$ denote the moduli space of semistable Higgs bundles on $X$ of rank $r$ and degree $d$. We prove that the compact complex Bohr-Sommerfeld Lagrangians of $M_H(r,d)$ are precisely the irreducible components of the n......Let $X$ be a compact connected Riemann surface of genus at least two. Let $M_H(r,d)$ denote the moduli space of semistable Higgs bundles on $X$ of rank $r$ and degree $d$. We prove that the compact complex Bohr-Sommerfeld Lagrangians of $M_H(r,d)$ are precisely the irreducible components...

Il danese tranquillo Niels Bohr, un fisico e il suo tempo, 1885-1962

CERN Document Server

Pais, Abraham

1993-01-01

Niels Bohr è una figura centrale nella fisica del Novecento, padre fondatore della teoria atomica e della meccanica quantistica. La storia della sua vita, ricca e piena anche sul piano affettivo e personale, non può dunque ridursi a un resoconto dei suoi successi scientifici e Pais, allievo e poi amico di Bohr, ne è perfettamente consapevole. Il libro si sviluppa su vari piani: capitoli strettamente biografici o storico-scientifici si alternano a discussioni sulle idee di Bohr in campo politico e filosofico, sui suoi rapporti con Einstein, sul suo ruolo nei drammatici anni della guerra e su molti altri aspetti della vicenda umana.

How Sommerfeld extended Bohr's model of the atom (1913-1916)

Science.gov (United States)

Eckert, Michael

2014-04-01

Sommerfeld's extension of Bohr's atomic model was motivated by the quest for a theory of the Zeeman and Stark effects. The crucial idea was that a spectral line is made up of coinciding frequencies which are decomposed in an applied field. In October 1914 Johannes Stark had published the results of his experimental investigation on the splitting of spectral lines in hydrogen (Balmer lines) in electric fields, which showed that the frequency of each Balmer line becomes decomposed into a multiplet of frequencies. The number of lines in such a decomposition grows with the index of the line in the Balmer series. Sommerfeld concluded from this observation that the quantization in Bohr's model had to be altered in order to allow for such decompositions. He outlined this idea in a lecture in winter 1914/15, but did not publish it. The First World War further delayed its elaboration. When Bohr published new results in autumn 1915, Sommerfeld finally developed his theory in a provisional form in two memoirs which he presented in December 1915 and January 1916 to the Bavarian Academy of Science. In July 1916 he published the refined version in the Annalen der Physik. The focus here is on the preliminary Academy memoirs whose rudimentary form is better suited for a historical approach to Sommerfeld's atomic theory than the finished Annalen-paper. This introductory essay reconstructs the historical context (mainly based on Sommerfeld's correspondence). It will become clear that the extension of Bohr's model did not emerge in a singular stroke of genius but resulted from an evolving process.

Noninvasive measurement of mean alveolar carbon dioxide tension and Bohr's dead space during tidal breathing.

Science.gov (United States)

Koulouris, N G; Latsi, P; Dimitroulis, J; Jordanoglou, B; Gaga, M; Jordanoglou, J

2001-06-01

The lack of methodology for measuring the alveolar carbon dioxide tension (PA,CO2) has forced investigators to make several assumptions, such as that PA,CO2 is equal to end-tidal (PET,CO2) and arterial CO2 tension (Pa,CO2). The present study measured the mean PA,CO2 and Bohr's dead space ratio (Bohr's dead space/tidal volume (VD,Bohr/VT)) during tidal breathing. The method used is a new, simple and noninvasive technique, based on the analysis of the expired CO2 volume per breath (VCO2) versus the exhaled VT. This curve was analysed in 21 normal, healthy subjects and 35 chronic obstructive pulmonary disease (COPD) patients breathing tidally through a mouthpiece apparatus in the sitting position. It is shown that: 1) PA,CO2 is similar to Pa,CO2 in normal subjects, whilst it is significantly lower than Pa,CO2 in COPD patients; 2) PA,CO2 is significantly higher than PET,CO2 in all subjects, especially in COPD patients; 3) VD,Bohr/VT is increased in COPD patients as compared to normal subjects; and 4) VD,Bohr/VT is lower than the "physiological" dead space ratio (VD,phys/VT) in COPD patients. It is concluded that the expired carbon dioxide versus tidal volume curve is a useful tool for research and clinical work, because it permits the noninvasive and accurate measurement of Bohr's dead space and mean alveolar carbon dioxide tension accurately during spontaneous breathing.

Complementarity in the Einstein-Bohr photon box

NARCIS (Netherlands)

Dieks, D.G.B.J.; Lam, S

2008-01-01

The Bohr-Einstein photon box thought experiment is a forerunner of the EPR experiment: a packet of radiation escapes from a box, and the box-plus-radiation state remains entangled. Hence, a measurement on the box makes a difference for the state of the far-away radiation long after its escape. This

Niels Bohr collected works, volume 9: Nuclear physics (1929-1952)

International Nuclear Information System (INIS)

Peierls, R.

1985-01-01

This volume deals with Bohr's work on nuclear physics which began in the pre-1932 days with his thinking deeply, but inconclusively about the seeming contradictions then presented by the evidence about the nucleus. In 1936 Bohr recognized and described the insights provided by neutron scattering experiments and the excitement of this new understanding and its extension and consolidation occupied much of the subsequent years. In 1939 he was again first in understanding the essential features of the newly discovered phenomenon of fission, applying successfully the point of view of nuclear reactions which he had developed over the past three years. Later, in 1949-50, he was impressed by the success of the nuclear shell model, which on the face of it seemed hard to reconcile with the picture of the closely interacting nucleons which he had pioneered in 1936 and he put much effort into clarifying this paradox. As in earlier volumes the published papers are supported by appropriate selections from unpublished notes and drafts, and by relevant correspondence. CONTENTS: Foreword. Part I: Papers and Manuscripts Related to Nuclear Physics. Part II: Selected Correspondence (1929-1949). Inventory of Relevant Manuscripts in the Niels Bohr Archive. Index

Why has the bohr-sommerfeld model of the atom been ignoredby general chemistry textbooks?

Science.gov (United States)

Niaz, Mansoor; Cardellini, Liberato

2011-12-01

Bohr's model of the atom is considered to be important by general chemistry textbooks. A major shortcoming of this model was that it could not explain the spectra of atoms containing more than one electron. In order to increase the explanatory power of the model, Sommerfeld hypothesized the existence of elliptical orbits. This study has the following objectives: 1) Formulation of criteria based on a history and philosophy of science framework; and 2) Evaluation of university-level general chemistry textbooks based on the criteria, published in Italy and U.S.A. Presentation of a textbook was considered to be "satisfactory" if it included a description of the Bohr-Sommerfeld model along with diagrams of the elliptical orbits. Of the 28 textbooks published in Italy that were analyzed, only five were classified as "satisfactory". Of the 46 textbooks published in U.S.A., only three were classified as "satisfactory". This study has the following educational implications: a) Sommerfeld's innovation (auxiliary hypothesis) by introducing elliptical orbits, helped to restore the viability of Bohr's model; b) Bohr-Sommerfeld's model went no further than the alkali metals, which led scientists to look for other models; c) This clearly shows that scientific models are tentative in nature; d) Textbook authors and chemistry teachers do not consider the tentative nature of scientific knowledge to be important; e) Inclusion of the Bohr-Sommerfeld model in textbooks can help our students to understand how science progresses.

Bohr quantum theory of the magnetic monopoles and classical electron electromagnetic mass problem

OpenAIRE

Pankovic, Vladan

2010-01-01

In the first part of this work we apply Bohr (old or naive quantum atomic) theory for analysis of the remarkable electro-dynamical problem of magnetic monopoles. We reproduce formally exactly some basic elements of the Dirac magnetic monopoles theory, especially Dirac electric/magnetic charge quantization condition. It follows after application of Bohr theory at the system, simply called magnetic monopole "atom", consisting of the practically standing, massive magnetic monopole as the "nucleu...

The language of Orthodox theology & quantum mechanics: St Gregory Palamas and Niels Bohr

DEFF Research Database (Denmark)

Tanev, Stoyan

2013-01-01

The objective of this chapter is to provide an analytical framework that would enable the comparison of the ways of using words and language in the cases of St. Gregory Palamas and Niels Bohr. The main motivation will be to explore Christos Yannaras’ point about the opportunity of using quantum....... The focus on epistemological issues could be justified by the fact that both St. Gregory Palamas and Niels Bohr have been acknowledged for their epistemological insights....

The Bohr-Heisenberg correspondence principle viewed from phase space

DEFF Research Database (Denmark)

Dahl, Jens Peder

2002-01-01

Phase-space representations play an increasingly important role in several branches of physics. Here, we review the author's studies of the Bohr-Heisenberg correspondence principle within the Weyl-Wigner phase-space representation. The analysis leads to refined correspondence rules that can...

Niels Bohr - his life and scientific achievements

International Nuclear Information System (INIS)

Kailas, S.

2013-01-01

Niels Bohr, a Nobel laureate and a celebrated scientist of the 20th century is remembered for his lasting contributions to atomic and nuclear physics. His pioneering works on Energy loss by charged particles, the structure of the atom, the compound nucleus model and the mechanism of nuclear fission are indeed remarkable. In this article a brief account of his life and scientific achievements is provided. (author)

Niels Bohr and Complementarity An Introduction

CERN Document Server

Plotnitsky, Arkady

2012-01-01

This book offers a discussion of Niels Bohr’s conception of “complementarity,” arguably his greatest contribution to physics and philosophy. By tracing Bohr’s work from his 1913 atomic theory to the introduction and then refinement of the idea of complementarity, and by explicating different meanings of “complementarity” in Bohr and the relationships between it and Bohr’s other concepts, the book aims to offer a contained and accessible, and yet sufficiently comprehensive account of Bohr’s work on complementarity and its significance.

The coupling one quasi-particle to a Bohr core

International Nuclear Information System (INIS)

Lewenkopf, C.H.

1988-01-01

Odd nuclei are studied coupling one quasi-particle to a Bohr's core, solved by Kumar Baranger's method. Calculations are performed for energies and transition rates for the following isotopes: 133 Xe, 183 W, 99 Tc and 101 Rh. Limitations of the model are discussed. (author) [pt

The Bohr--Einstein ''weighing-of-energy'' debate and the principle of equivalence

International Nuclear Information System (INIS)

Hughes, R.J.

1990-01-01

The Bohr--Einstein debate over the ''weighing of energy'' and the validity of the time--energy uncertainty relation is reexamined in the context of gravitation theories that do not respect the equivalence principle. Bohr's use of the equivalence principle is shown to be sufficient, but not necessary, to establish the validity of this uncertainty relation in Einstein's ''weighing-of-energy'' gedanken experiment. The uncertainty relation is shown to hold in any energy-conserving theory of gravity, and so a failure of the equivalence principle does not engender a failure of quantum mechanics. The relationship between the gravitational redshift and the equivalence principle is reviewed

A new relation of parameters of Bohr-Mottelson rotational spectra formula

International Nuclear Information System (INIS)

Li Mingliang; Xu Fuxin

2003-01-01

With the first three terms of Harris formula included and Mottelson's method followed, a new relation of the parameters of Bohr-Mottelson rotational spectra formula is brought forward. Superdeformed bands of even-even nuclei and normal deformed bands of nuclei in actinide and rare-earth are fitted with four-parameter Bohr-Mottelson rotational spectra formula. The relations of the parameters A, B, C, D are studied. The result show, for normal deformed bands, the new relation approach the experiment value in the same degree as the relation deduced from ab formula, but for superdeformed bands, the new relation is closer to the experiment than the relation deduced from ab formula. Three-parameter Harris formula may have better convergence than two-parameter Harris formula

Diophantine approximation and Dirichlet series

CERN Document Server

Queffélec, Hervé

2013-01-01

This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...

Spectrum of hydrogen atom, Niels Bohr and their impact on contemporary science: a glimpse of modern spectroscopy

International Nuclear Information System (INIS)

Sastry, M.D.

2013-01-01

This contribution reviews developments in the atomic spectroscopy subsequent to Bohr's model. This follows a brief description of Bohr's model of hydrogen atom that accounts for sharp line spectra of hydrogen atom. The developments include the effects of electron and nuclear spins, spectroscopy of multi electron atom which involve electron-electron repulsion and different angular momentum coupling schemes. More recently, Bohr's atom model has found application to processes at nano dimensions of semiconducting materials. It has now become possible to create a hydrogen-like atom, an exciton, with its size comparable or even more than that of the particle it self. This brings in extra quantization and has profound effects on the motion of the particles involved viz electron and hole. (author)

The Niels Bohr Archive is Placing Collections on its Website

DEFF Research Database (Denmark)

Aaserud, Finn

2010-01-01

this supplement, the documents of which we hope to make available on our website by 2013, the centennial for Bohr's model of the nuclear atom. We have found the task of digitizing our collections generally complex, sometimes frustrating, and in the end satisfying. At this stage it is particularly important...

The Life and Work of Niels Bohr – A Brief Sketch

Indian Academy of Sciences (India)

IAS Admin

Niels Henrik David Bohr was born to affluent parents on. 7 October 1885 in ... two years older; while his brother Harald, to whom he was ... sions from a very young age. ... married on 1 August 1912, the beginning of a 50-year relationship.

Niels Bohr's complementarity its structure, history, and intersections with hermeneutics and deconstruction

CERN Document Server

Katsumori, Makoto

2011-01-01

Through detailed textual and conceptual analysis, and with special attention to the potentially conflicting elements of Bohr's thought, this volume's fresh approach analyzes the relations between realism and antirealism through the prism of complementarity.

EPR before EPR: A 1930 Einstein-Bohr thought Experiment Revisited

Science.gov (United States)

Nikolic, Hrvoje

2012-01-01

In 1930, Einstein argued against the consistency of the time-energy uncertainty relation by discussing a thought experiment involving a measurement of the mass of the box which emitted a photon. Bohr seemingly prevailed over Einstein by arguing that Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit…

Probing the (empirical quantum structure embedded in the periodic table with an effective Bohr model

Directory of Open Access Journals (Sweden)

Wellington Nardin Favaro

2013-01-01

Full Text Available The atomic shell structure can be observed by inspecting the experimental periodic properties of the Periodic Table. The (quantum shell structure emerges from these properties and in this way quantum mechanics can be explicitly shown considering the (semi-quantitative periodic properties. These periodic properties can be obtained with a simple effective Bohr model. An effective Bohr model with an effective quantum defect (u was considered as a probe in order to show the quantum structure embedded in the Periodic Table. u(Z shows a quasi-smoothed dependence of Z, i.e., u(Z ≈ Z2/5 - 1.

Multilevel fitting of 235U resonance data sensitive to Bohr-and Brosa-fission channels

International Nuclear Information System (INIS)

Moore, M.S.

1995-01-01

The recent determination of the K, J dependence of the neutron induced fission cross section of 235 U by the Dubna group has led to a renewed interest in the mechanism of fission from saddle to scission. The K quantum numbers designate the so-called Bohr fission channels, which describe the fission properties at the saddle point. Certain other fission properties, e.g., the fragment mass and kinetic-energy distribution, are related to the properties of the scission point. The neutron energy dependence of the fragment kinetic energies has been measured by Hambsch et al., who analyzed their data according to a channel description of Brosa et al. How these two channel descriptions, the saddle-point Bohr channels and the scission-point Brosa channels, relate to one another is an open question, and is the subject matter of the present paper. We use the correlation coefficient between various data sets, in which variations are reported from resonance to resonance, as a measure of both-the statistical reliability of the data and of the degree to which different scission variables relate to different Bohr channels. We have carried out an adjustment of the ENDF/B-VI multilevel evaluation of the fission cross section of 235 U, one that provides a reasonably good fit to the energy dependence of the fission, capture, and total cross sections below 100 eV, and to the Bohr-channel structure deduced from an earlier measurement by Pattenden and Postma. We have also further explored the possibility of describing the data of Hambsch et al. in the Brosa-channel framework with the same set of fission-width vectors, only in a different reference system. While this approach shows promise, it is clear that better data are also needed for the neutron energy variation of the scission-point variables

Darwinism in disguise? A comparison between Bohr's view on quantum mechanics and QBism.

Science.gov (United States)

Faye, Jan

2016-05-28

The Copenhagen interpretation is first and foremost associated with Niels Bohr's philosophy of quantum mechanics. In this paper, I attempt to lay out what I see as Bohr's pragmatic approach to science in general and to quantum physics in particular. A part of this approach is his claim that the classical concepts are indispensable for our understanding of all physical phenomena, and it seems as if the claim is grounded in his reflection upon how the evolution of language is adapted to experience. Another, recent interpretation, QBism, has also found support in Darwin's theory. It may therefore not be surprising that sometimes QBism is said to be of the same breed as the Copenhagen interpretation. By comparing the two interpretations, I conclude, nevertheless, that there are important differences. © 2016 The Author(s).

Traffic restrictions on Routes Bloch, Maxwell and Bohr

CERN Multimedia

IT Department

2008-01-01

Excavation and pipework is being carried out in the framework of the transfer of the waste water treatment plant for the effluents from the surface treatment workshops from Building 254 to Building 676, currently under construction. This work may encroach onto Routes Bloch, Maxwell and Bohr and disrupt the flow of traffic. Users are requested to comply with the road signs that will be erected. The work is expected to last until the beginning of December 2008. Thank you for your understanding. TS/CE and TS/FM Groups Tel.7 4188 or 16 4314

Niels Bohr. Physicist and philospher of the atomic era

International Nuclear Information System (INIS)

Fischer, Ernst Peter

2012-01-01

The physicist and Nobel-prize carrier Niels Bohr (1885-1962) changed by his research our view to the world. By his atomic model for the first time the stability of matter could be explained, but simultaneously the atomic physics and nuclear technique based on this made our world so dangerous as never before. In an impressive portrait Ernst Peter Fischer describes the life and action of this fascinating man, his great physical finding, as well as his political engagement.

Des images et des paraboles : Niels Bohr et le discours descriptif en physique quantique

Directory of Open Access Journals (Sweden)

Ilias Yocaris

2011-01-01

Full Text Available Cette étude porte sur l’importance accordée aux images verbales dans le discours descriptif utilisé en mécanique quantique, et plus précisément sur la conception de la langue scientifique qui est celle de Niels Bohr (1885-1962 : en raison d’une série de considérations techniques, méthodologiques et épistémologiques que nous nous proposons d’analyser in extenso, Bohr considère effectivement que les phénomènes subatomiques ne peuvent être évoqués directement (sans référence au contexte observationnel, par le biais d’un langage dénotatif non figural, mais uniquement de manière métaphorique, détournée, ce qui réduit à ses yeux le discours descriptif des physiciens à « des images et des paraboles ». En examinant les textes de Bohr à la lumière d’un certain nombre de travaux épistémologiques, de commentaires et d’expérimentations auxquels ils ont donné lieu ultérieurement, nous nous proposons de décrire les implications conceptuelles d’une telle prise de position, qui constitue une vraie révolution sur le plan philosophique.

Quantum Humor: The Playful Side of Physics at Bohr's Institute for Theoretical Physics

Science.gov (United States)

Halpern, Paul

2012-09-01

From the 1930s to the 1950s, a period of pivotal developments in quantum, nuclear, and particle physics, physicists at Niels Bohr's Institute for Theoretical Physics in Copenhagen took time off from their research to write humorous articles, letters, and other works. Best known is the Blegdamsvej Faust, performed in April 1932 at the close of one of the Institute's annual conferences. I also focus on the Journal of Jocular Physics, a humorous tribute to Bohr published on the occasions of his 50th, 60th, and 70th birthdays in 1935, 1945, and 1955. Contributors included Léon Rosenfeld, Victor Weisskopf, George Gamow, Oskar Klein, and Hendrik Casimir. I examine their contributions along with letters and other writings to show that they offer a window into some issues in physics at the time, such as the interpretation of complementarity and the nature of the neutrino, as well as the politics of the period.

Quasi-particle excitations and dynamical structure function of trapped Bose-condensates in the WKB approximation

OpenAIRE

Csordás, András; Graham, Robert; Szépfalusy, Péter

1997-01-01

The Bogoliubov equations of the quasi-particle excitations in a weakly interacting trapped Bose-condensate are solved in the WKB approximation in an isotropic harmonic trap, determining the discrete quasi-particle energies and wave functions by torus (Bohr-Sommerfeld) quantization of the integrable classical quasi-particle dynamics. The results are used to calculate the position and strengths of the peaks in the dynamic structure function which can be observed by off-resonance inelastic light...

Bohring-Opitz (Oberklaid-Danks) syndrome: clinical study, review of the literature, and discussion of possible pathogenesis

DEFF Research Database (Denmark)

Hastings, Rob; Cobben, Jan-Maarten; Gillessen-Kaesbach, Gabriele

2011-01-01

Bohring-Opitz syndrome (BOS) is a rare congenital disorder of unknown etiology diagnosed on the basis of distinctive clinical features. We suggest diagnostic criteria for this condition, describe ten previously unreported patients, and update the natural history of four previously reported patients...

Wave-particle duality and Bohr's complementarity principle in quantum mechanics

International Nuclear Information System (INIS)

Sen, D.; Basu, A.N.; Sengupta, S.

1995-01-01

Interest on Bohr's complementarity principle has recently been revived particularly because of several thought experiments and some actually performed experiments to test the validity of mutual exclusiveness of wave and particle properties. A critical review of the situation is undertaken and it is pointed out that the problem with mutual exclusiveness arises because of some vagueness in the conventional formulation. An attempt is made to remove this vagueness by connecting the origin of mutual exclusiveness to some principles of quantum mechanics. Accordingly, it becomes obvious that to contradict complementarity principle without contradicting quantum mechanics would be impossible. Some of the recent experiments are critically analysed. (author). 31 refs., 3 ills

Oxygen affinity and Bohr effect responses to 2,3-diphosphoglycerate in equine and human blood.

Science.gov (United States)

diBella, G; Scandariato, G; Suriano, O; Rizzo, A

1996-05-01

The dependence of blood oxygen affinity and the Bohr effect on the concentration of 2,3-diphosphoglycerate (DPG) in erythrocytes was investigated in 24 trotter horses and 24 healthy men. The oxygen tension at half saturation and standard conditions (P50st at pH 7.4, PCO2(40) mmHg and 37 degrees C) and the carbon dioxide or fixed-acid-induced Bohr effect (dlogP50/dpH) were determined. Samples of fresh blood and blood depleted of or enriched with DPG were studied. In the absence of measurable DPG, the equine and human blood had similar mean (SD) values of P50st (16.6 [0.6] and 16.2 [0.7] mmHg, respectively). In both species these values increased with increasing DPG, but the response of equine blood was significantly lower, at least up to physiological values (P50st = 24.6 [0.6] and 26.2 [0.7]) mmHg; DPG = 14([1.8] and 12.8 [1.2] mumol gHb-1, respectively, in fresh blood). For concentrations above 20 to 25 mumol gHb-1 of DPG the difference between the values of P50st in the two species tended to decrease because the response in human blood reached a plateau. The interactions between the Bohr effect and the concentration of DPG showed that in the horses, as in the men, the level of DPG played an important role in governing the relative magnitude of carbon dioxide and fixed acid factors. The difference between them, which is associated with the oxylabile carbamino binding, was greatest in DPG-depleted blood, but whereas in the men the difference was suppressed by an above normal DPG concentration, in the horses it was still measurable.

Systematic measurements of the Bohr-Weisskopf effect at ISOLDE

CERN Multimedia

Nojiri, Y; Matsuki, S; Ragnarsson, I; Neugart, R; Redi, O; Stroke, H H; Duong, H T; Marescaux, D; Pinard, J; Juncar, P; Ekstrom, C; Pellarin, M; Vialle, J-L; Inamura, T

2002-01-01

The " Bohr-Weisskopf " effect, or " hyperfine structure (hfs) anomaly ", which results from the effect of the distribution of nuclear magnetization on the electro-nuclear interaction, will be measured systematically at the PS Booster ISOLDE, first for a long chain of radioactive cesium isotopes, analogously to previous isotope shift and hfs studies. In addition to the direct measurement of magnetic moment values, the results are expected to provide independent data for testing nuclear wavefunctions, these will be of importance for interpreting systematic parity non-conservation experiments, complementary to the single isotope study which requires a high precision knowledge of the electron wavefunction. Substantial progress in these calculations has been achieved recently. Precision measurements of the hfs splittings and nuclear magnetic moments are required, with sensitivity adequate for the radioactive isotopes produced. A triple resonance atomic beam magnetic resonance apparatus with optical pumping state s...

Systematic Measurements of the Bohr-Weisskopf Effect at ISOLDE

CERN Multimedia

2002-01-01

Nuclear electric and magnetic structure properties are measurable by high-resolution atomic spectroscopy through isotope shifts and the Bohr-Weisskopf effect (hyperfine structure anomalies). \\\\ \\\\ The greatest value of these measurements is when made systematically over a large number of isotopes. This has been done in the case of isotopes shifts most extensively by the experiment at ISOLDE. To date the magnetic distribution studies are few and isolated. Here we propose to intitiate a program at ISOLDE to measure hfs anomalies systematically. The experiments, requiring high-precision data on magnetic dipole constants as well as on nuclear g-factors, will be done by atomic-beam magnetic resonance with the use of laser excitation for polarization of the beam and a sixpole magnet acting as an analyser. \\\\ \\\\ The heavy alkali elements are the most promising candidates for hfs anomaly studies because of the large effect expected, the high production yields at ISOLDE and most importantly, the interesting variations...

Diffusive insights: on the disagreement of Christian Bohr and August Krogh at the Centennial of the Seven Little Devils

DEFF Research Database (Denmark)

Gjedde, Albert

2010-01-01

The year 2010 is the centennial of the publication of the “Seven Little Devils” in the predecessor of Acta Physiologica. In these seven papers, August and Marie Krogh sought to refute Christian Bohr's theory that oxygen diffusion from the lungs to the circulation is not entirely passive but rather...

Inspirations from the theories of Bohr and Mottelson: a Canadian perspective

International Nuclear Information System (INIS)

Ward, D; Waddington, J C; Svensson, C E

2016-01-01

The theories developed by Bohr and Mottelson have inspired much of the world-wide experimental investigation into the structure of the atomic nucleus. On the occasion of the 40th anniversary of the awarding of their Nobel prize, we reflect on some of the experimental developments made in understanding the structure of nuclei. We have chosen to focus on experiments performed in Canada, or having strong ties to Canada, and the work included here spans virtually the whole of the second half of the 20th century. The 8π Spectrometer, which figures prominently in this story, was a novel departure for funding science in Canada that involved an intimate collaboration between a Crown Corporation (Atomic Energy of Canada Ltd) and University research, and enabled many of the insights discussed here. (invited comment)

Bohr Hamiltonian with an energy-dependent γ-unstable Coulomb-like potential

Energy Technology Data Exchange (ETDEWEB)

Budaca, R. [Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele (Romania)

2016-10-15

An exact analytical solution for the Bohr Hamiltonian with an energy-dependent Coulomb-like γ-unstable potential is presented. Due to the linear energy dependence of the potential's coupling constant, the corresponding spectrum in the asymptotic limit of the slope parameter resembles the spectral structure of the spherical vibrator, however with a different state degeneracy. The parameter free energy spectrum as well as the transition rates for this case are given in closed form and duly compared with those of the harmonic U(5) dynamical symmetry. The model wave functions are found to exhibit properties that can be associated to shape coexistence. A possible experimental realization of the model is found in few medium nuclei with a very low second 0{sup +} state known to exhibit competing prolate, oblate and spherical shapes. (orig.)

Diffusive Insights: On the Disagreement of Christian Bohr and August Krogh at the Centennial of the Seven Little Devils

Science.gov (United States)

Gjedde, Albert

2010-01-01

The year 2010 is the centennial of the publication of the "Seven Little Devils" in the predecessor of "Acta Physiologica". In these seven papers, August and Marie Krogh sought to refute Christian Bohr's theory that oxygen diffusion from the lungs to the circulation is not entirely passive but rather facilitated by a specific cellular activity…

Effectiveness of an Asynchronous Online Module on University Students' Understanding of the Bohr Model of the Hydrogen Atom

Science.gov (United States)

Farina, William J., Jr.; Bodzin, Alec M.

2018-01-01

Web-based learning is a growing field in education, yet empirical research into the design of high quality Web-based university science instruction is scarce. A one-week asynchronous online module on the Bohr Model of the atom was developed and implemented guided by the knowledge integration framework. The unit design aligned with three identified…

The divine clockwork: Bohr's correspondence principle and Nelson's stochastic mechanics for the atomic elliptic state

International Nuclear Information System (INIS)

Durran, Richard; Neate, Andrew; Truman, Aubrey

2008-01-01

We consider the Bohr correspondence limit of the Schroedinger wave function for an atomic elliptic state. We analyze this limit in the context of Nelson's stochastic mechanics, exposing an underlying deterministic dynamical system in which trajectories converge to Keplerian motion on an ellipse. This solves the long standing problem of obtaining Kepler's laws of planetary motion in a quantum mechanical setting. In this quantum mechanical setting, local mild instabilities occur in the Keplerian orbit for eccentricities greater than (1/√(2)) which do not occur classically

Investigation of Bohr Hamiltonian in presence of Killingbeck potential using bi-confluent Heun functions

Science.gov (United States)

Sobhani, Hadi; Hassanabadi, Hassan; Chung, Won Sang

2018-05-01

In this study, Bohr Hamiltonian is studied for the triaxial and rotational cases. In both cases, Killingbeck potential is used as interaction. The wave function and energy of these cases are found using bi-confluent Heun functions. The results are examined by reproducing experimental data of some isotopes for each case. Energy levels of the isotopes are shown graphically as well as theoretical results for staggering in γ bands of the isotopes is discussed. In the next step, we argue about B (E 2) transition rates of the isotopes for each case. The results have a good agreement with experimental data.

Excited collective states of nuclei within Bohr Hamiltonian with Tietz-Hua potential

Energy Technology Data Exchange (ETDEWEB)

Chabab, M.; El Batoul, A.; Lahbas, A.; Oulne, M. [Cadi Ayyad University, High Energy Physics and Astrophysics Laboratory, Faculty of Sciences Semlalia, Marrakesh (Morocco); Hamzavi, M. [University of Zanjan, Department of Physics, Zanjan (Iran, Islamic Republic of)

2017-07-15

In this paper, we present new analytical solutions of the Bohr Hamiltonian problem that we derived with the Tietz-Hua potential, here used for describing the β-part of the nuclear collective potential plus that of the harmonic oscillator for the γ-part. Also, we proceed to a systematic comparison of the numerical results obtained with this kind of β-potential with others which are widely used in such a framework as well as with the experiment. The calculations are carried out for energy spectra and electromagnetic transition probabilities for γ-unstable and axially symmetric deformed nuclei. In the same frame, we show the effect of the shape flatness of the β-potential beyond its minimum on transition rates calculations. (orig.)

The quest for reality Bohr and Wittgenstein : two complementary views

CERN Document Server

Stenholm, Stig

2015-01-01

In both science and philosophy, the twentieth century saw a radical breakdown of certainty in the human worldview, as quantum uncertainty and linguistic ambiguity destroyed the comfortable certitudes of the past. As these disciplines form the foundation for a human position in the world, a major epistemological reorganization had to take place. In this book, quantum theorist Stig Stenholm presents Bohr and Wittgenstein, in physics and in philosophy, as central figures representing this revision. Each of them took up the challenge of replacing apparent order and certainty with a provisional understanding based on limited concepts in constant flux. Stenholm concludes that the modern synthesis created by their heirs is far from satisfactory, and the story is so far an unfinished one. The book will appeal to any researcher in either discipline curious about the foundation of modern science, and works to provoke a renewal of discussion, and the eventual emergence of a reformed clarity and understanding.

A novel system for transcutaneous application of carbon dioxide causing an "artificial Bohr effect" in the human body.

Directory of Open Access Journals (Sweden)

Yoshitada Sakai

Full Text Available BACKGROUND: Carbon dioxide (CO(2 therapy refers to the transcutaneous administration of CO(2 for therapeutic purposes. This effect has been explained by an increase in the pressure of O(2 in tissues known as the Bohr effect. However, there have been no reports investigating the oxygen dissociation of haemoglobin (Hb during transcutaneous application of CO(2in vivo. In this study, we investigate whether the Bohr effect is caused by transcutaneous application of CO2 in human living body. METHODS: We used a novel system for transcutaneous application of CO(2 using pure CO(2 gas, hydrogel, and a plastic adaptor. The validity of the CO(2 hydrogel was confirmed in vitro using a measuring device for transcutaneous CO(2 absorption using rat skin. Next, we measured the pH change in the human triceps surae muscle during transcutaneous application of CO(2 using phosphorus-31 magnetic resonance spectroscopy ((31P-MRS in vivo. In addition, oxy- and deoxy-Hb concentrations were measured with near-infrared spectroscopy in the human arm with occulted blood flow to investigate O2 dissociation from Hb caused by transcutaneous application of CO(2. RESULTS: The rat skin experiment showed that CO(2 hydrogel enhanced CO(2 gas permeation through the rat skin. The intracellular pH of the triceps surae muscle decreased significantly 10 min. after transcutaneous application of CO(2. The NIRS data show the oxy-Hb concentration decreased significantly 4 min. after CO(2 application, and deoxy-Hb concentration increased significantly 2 min. after CO(2 application in the CO(2-applied group compared to the control group. Oxy-Hb concentration significantly decreased while deoxy-Hb concentration significantly increased after transcutaneous CO(2 application. CONCLUSIONS: Our novel transcutaneous CO(2 application facilitated an O(2 dissociation from Hb in the human body, thus providing evidence of the Bohr effect in vivo.

Reply to ''Comments on 'Time-symmetric, approximately relativistic particle interactions and radiation' ''

International Nuclear Information System (INIS)

Krizan, J.E.

1982-01-01

The inclusion of screening effects, as argued by Jones, effectively brings in terms of higher order than c -2 . The Darwin Hamiltonian, like the Darwin Lagrangian, usually is written in perturbative expansion, to order c -2 . The physical effects of the Cerenkov radiation (order c -2 ) and the Bohr polarization effect result from a weak-damping analysis with the Darwin Hamiltonian; contact has been made also in previous agreement with quantum field-theoretic calculations for degenerate systems, with the same Hamiltonian. The significance of adding screening should be examined within an approximation which includes c -3 terms and higher: so neither the Darwin Hamiltonian nor the Darwin Lagrangian is sufficient to analyze these situations. The medium modifications of Jones involve macroscopic considerations and higher orders and so the criticism of the microscopic Darwin Hamiltonian is misplaced

Large boson number IBM calculations and their relationship to the Bohr model

International Nuclear Information System (INIS)

Thiamova, G.; Rowe, D.J.

2009-01-01

Recently, the SO(5) Clebsch-Gordan (CG) coefficients up to the seniority v max =40 were computed in floating point arithmetic (T.A. Welsh, unpublished (2008)); and, in exact arithmetic, as square roots of rational numbers (M.A. Caprio et al., to be published in Comput. Phys. Commun.). It is shown in this paper that extending the QQQ model calculations set up in the work by D.J. Rowe and G. Thiamova (Nucl. Phys. A 760, 59 (2005)) to N=v max =40 is sufficient to obtain the IBM results converged to its Bohr contraction limit. This will be done by comparing some important matrix elements in both models, by looking at the seniority decomposition of low-lying states and at the behavior of the energy and B(E2) transition strengths ratios with increasing seniority. (orig.)

Can we close the Bohr-Einstein quantum debate?

Science.gov (United States)

Kupczynski, Marian

2017-11-13

Recent experiments allow one to conclude that Bell-type inequalities are indeed violated; thus, it is important to understand what this means and how we can explain the existence of strong correlations between outcomes of distant measurements. Do we have to announce that Einstein was wrong, Nature is non-local and non-local correlations are produced due to quantum magic and emerge, somehow, from outside space-time? Fortunately, such conclusions are unfounded because, if supplementary parameters describing measuring instruments are correctly incorporated in a theoretical model, then Bell-type inequalities may not be proved. We construct a simple probabilistic model allowing these correlations to be explained in a locally causal way. In our model, measurement outcomes are neither predetermined nor produced in an irreducibly random way. We explain why, contrary to the general belief, the introduction of setting-dependent parameters does not restrict experimenters' freedom of choice. Since the violation of Bell-type inequalities does not allow the conclusion that Nature is non-local and that quantum theory is complete, the Bohr-Einstein quantum debate may not be closed. The continuation of this debate is important not only for a better understanding of Nature but also for various practical applications of quantum phenomena.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).

Can we close the Bohr-Einstein quantum debate?

Science.gov (United States)

Kupczynski, Marian

2017-10-01

Recent experiments allow one to conclude that Bell-type inequalities are indeed violated; thus, it is important to understand what this means and how we can explain the existence of strong correlations between outcomes of distant measurements. Do we have to announce that Einstein was wrong, Nature is non-local and non-local correlations are produced due to quantum magic and emerge, somehow, from outside space-time? Fortunately, such conclusions are unfounded because, if supplementary parameters describing measuring instruments are correctly incorporated in a theoretical model, then Bell-type inequalities may not be proved. We construct a simple probabilistic model allowing these correlations to be explained in a locally causal way. In our model, measurement outcomes are neither predetermined nor produced in an irreducibly random way. We explain why, contrary to the general belief, the introduction of setting-dependent parameters does not restrict experimenters' freedom of choice. Since the violation of Bell-type inequalities does not allow the conclusion that Nature is non-local and that quantum theory is complete, the Bohr-Einstein quantum debate may not be closed. The continuation of this debate is important not only for a better understanding of Nature but also for various practical applications of quantum phenomena. This article is part of the themed issue `Second quantum revolution: foundational questions'.

The Compton Radius, the de Broglie Radius, the Planck Constant, and the Bohr Orbits

Directory of Open Access Journals (Sweden)

Daywitt W. C.

2011-04-01

Full Text Available The Bohr orbits of the hydrogen atom and the Planck constant can be derived classically from the Maxwell equations and the assumption that there is a variation in the electron's velocity about its average value. The resonant nature of the circulating electron and its induced magnetic and Faraday fields prevents a radiative collapse of the electron into the nuclear proton. The derived Planck constant is $h=2pi e^2/alpha c$, where $e$, $alpha$, and $c$ are the electronic charge, the fine structure constant, and the speed of light. The fact that the Planck vacuum (PV theory derives the same Planck constant independently of the above implies that the two derivations are related. The following highlights that connection.

The Compton Radius, the de Broglie Radius, the Planck Constant, and the Bohr Orbits

Directory of Open Access Journals (Sweden)

Daywitt W. C.

2011-04-01

Full Text Available The Bohr orbits of the hydrogen atom and the Planck constant can be derived classically from the Maxwell equations and the assumption that there is a variation in the electron’s velocity about its average value [1]. The resonant nature of the circulating electron and its induced magnetic and Faraday fields prevents a radiative collapse of the electron into the nuclear proton. The derived Planck constant is h = 2 e 2 = c , where e , , and c are the electronic charge, the fine structure constant, and the speed of light. The fact that the Planck vacuum (PV theory [2] derives the same Planck constant independently of the above implies that the two derivations are related. The following highlights that connection.

Gravity, Special Relativity, and the Strong Force A Bohr-Einstein-de Broglie Model for the Formation of Hadrons

CERN Document Server

Vayenas, Constantinos G

2012-01-01

This book shows that the strong interaction forces, which keep hadrons and nuclei together, are relativistic gravitational forces exerted between very small particles in the mass range of neutrinos. First, this book considers the problematic motion of two charged particles under the influence of electrostatic and gravitational forces only, which shows that bound states are formed by following the same semi-classical methodology used by Bohr to describe the H atom. This approach is also coupled with Newton's gravitational law and with Einstein's special relativity. The results agree with experi

Hydrogen atom as test field of theoretical models

International Nuclear Information System (INIS)

Baiquni, A.

1976-01-01

Semi classical theory, covering Bohr atom theory, Bohr Sommerfeld theory, Sommerfeld relativistic theory, and quantum theory such as particle and complementarity dualism, wave mechanics, approximation method, relativistic quantum mechanics, and hydrogen atom fine structure, are discussed. (SMN)

Bohr model description of the critical point for the first order shape phase transition

Science.gov (United States)

Budaca, R.; Buganu, P.; Budaca, A. I.

2018-01-01

The critical point of the shape phase transition between spherical and axially deformed nuclei is described by a collective Bohr Hamiltonian with a sextic potential having simultaneous spherical and deformed minima of the same depth. The particular choice of the potential as well as the scaled and decoupled nature of the total Hamiltonian leads to a model with a single free parameter connected to the height of the barrier which separates the two minima. The solutions are found through the diagonalization in a basis of Bessel functions. The basis is optimized for each value of the free parameter by means of a boundary deformation which assures the convergence of the solutions for a fixed basis dimension. Analyzing the spectral properties of the model, as a function of the barrier height, revealed instances with shape coexisting features which are considered for detailed numerical applications.

Erik Rasmussen, Niels Bohr og Værdirelativismen - i anledning af Kasper Lippert-Rasmussens bog om Erik Rasmussen

DEFF Research Database (Denmark)

Ougaard, Morten

2015-01-01

En svaghed ved Kasper Lippert-Rasmussens i øvrigt udmærkede bog om Erik Rasmussen er, at den forbigår den sene Rasmussens bog om komplementaritet og statskundskab. Bogen var vigtig for Rasmussen, og den bør indgå i hans faglige eftermæle. Den rummer videnskabsteoretiske argumenter af stor relevans...... ikke mindst forholdet mellem normative og kognitive udsagn. Efter mødet med Niels Bohrs filosofi står Rasmussens værdirelativisme både skarpere og stærkere end før, og Kasper Lippert-Rasmussens karakteristik af denne position som et ubegrundet dogme i dansk politologi er ikke overbevisende....

Roles of the β 146 histidyl residue in the molecular basis of the Bohr Effect of hemoglobin: A proton nuclear magnetic resonance study

International Nuclear Information System (INIS)

Busch, M.R.; Mace, J.E.; Ho, N.T.; Ho, Chien

1991-01-01

Assessment of the roles of the carboxyl-terminal β146 histidyl residues in the alkaline Bohr effect in human and normal adult hemoglobin by high-resolution proton nuclear magnetic resonance spectroscopy requires assignment of the resonances corresponding to these residues. By a careful spectroscopic study of human normal adult hemoglobin, enzymatically prepared des(His146β)-hemoglobin, and the mutant hemoglobins Cowtown (β146His → Leu) and York (β146His → Pro), the authors have resolved some of these conflicting results. By a close incremental variation of pH over a wide range in chloride-free 0.1 M N-(2-hydroxyethyl)piperazine-N'-2-ethanesulfonic acid buffer, a single resonance has been found to be consistently missing in the proton nuclear magnetic resonance spectra of these hemoglobin variants. The results indicate that the contribution of the β146 histidyl residues is 0.52 H + /hemoglobin tetramer at pH 7.6, markedly less than 0.8 H + /hemoglobin tetramer estimated by study of the mutant hemoglobin Cowtown (β146His → Leu) by Shih and Perutz. They have found that at least two histidyl residues in the carbonmonoxy form of this mutant have pK values that are perturbed, and they suggest that these pK differences may in part account for this discrepancy. The results show that the pK values of β146 histidyl residues in the carbonmonoxy form of hemoglobin are substantially affected by the presence of chloride and other anions in the solvent, and thus, the contribution of this amino acid residue to the alkaline Bohr effect can be shown to vary widely in magnitude, depending on the solvent composition. These results demonstrate that the detailed molecular mechanisms of the alkaline Bohr effect are not unique but are affected both by the hemoglobin structure and by the interactions with the solvent components in which the hemoglobin molecule resides

Bohr model description of the critical point for the first order shape phase transition

Directory of Open Access Journals (Sweden)

R. Budaca

2018-01-01

Full Text Available The critical point of the shape phase transition between spherical and axially deformed nuclei is described by a collective Bohr Hamiltonian with a sextic potential having simultaneous spherical and deformed minima of the same depth. The particular choice of the potential as well as the scaled and decoupled nature of the total Hamiltonian leads to a model with a single free parameter connected to the height of the barrier which separates the two minima. The solutions are found through the diagonalization in a basis of Bessel functions. The basis is optimized for each value of the free parameter by means of a boundary deformation which assures the convergence of the solutions for a fixed basis dimension. Analyzing the spectral properties of the model, as a function of the barrier height, revealed instances with shape coexisting features which are considered for detailed numerical applications.

What is complementarity?: Niels Bohr and the architecture of quantum theory

Science.gov (United States)

Plotnitsky, Arkady

2014-12-01

This article explores Bohr’s argument, advanced under the heading of ‘complementarity,’ concerning quantum phenomena and quantum mechanics, and its physical and philosophical implications. In Bohr, the term complementarity designates both a particular concept and an overall interpretation of quantum phenomena and quantum mechanics, in part grounded in this concept. While the argument of this article is primarily philosophical, it will also address, historically, the development and transformations of Bohr’s thinking, under the impact of the development of quantum theory and Bohr’s confrontation with Einstein, especially their exchange concerning the EPR experiment, proposed by Einstein, Podolsky and Rosen in 1935. Bohr’s interpretation was progressively characterized by a more radical epistemology, in its ultimate form, which was developed in the 1930s and with which I shall be especially concerned here, defined by his new concepts of phenomenon and atomicity. According to this epistemology, quantum objects are seen as indescribable and possibly even as inconceivable, and as manifesting their existence only in the effects of their interactions with measuring instruments upon those instruments, effects that define phenomena in Bohr’s sense. The absence of causality is an automatic consequence of this epistemology. I shall also consider how probability and statistics work under these epistemological conditions.

What is complementarity?: Niels Bohr and the architecture of quantum theory

International Nuclear Information System (INIS)

Plotnitsky, Arkady

2014-01-01

This article explores Bohr’s argument, advanced under the heading of ‘complementarity,’ concerning quantum phenomena and quantum mechanics, and its physical and philosophical implications. In Bohr, the term complementarity designates both a particular concept and an overall interpretation of quantum phenomena and quantum mechanics, in part grounded in this concept. While the argument of this article is primarily philosophical, it will also address, historically, the development and transformations of Bohr’s thinking, under the impact of the development of quantum theory and Bohr’s confrontation with Einstein, especially their exchange concerning the EPR experiment, proposed by Einstein, Podolsky and Rosen in 1935. Bohr’s interpretation was progressively characterized by a more radical epistemology, in its ultimate form, which was developed in the 1930s and with which I shall be especially concerned here, defined by his new concepts of phenomenon and atomicity. According to this epistemology, quantum objects are seen as indescribable and possibly even as inconceivable, and as manifesting their existence only in the effects of their interactions with measuring instruments upon those instruments, effects that define phenomena in Bohr’s sense. The absence of causality is an automatic consequence of this epistemology. I shall also consider how probability and statistics work under these epistemological conditions. (paper)

Complementarity and the Nature of Uncertainty Relations in Einstein–Bohr Recoiling Slit Experiment

Directory of Open Access Journals (Sweden)

Shogo Tanimura

2015-07-01

Full Text Available A model of the Einstein–Bohr recoiling slit experiment is formulated in a fully quantum theoretical setting. In this model, the state and dynamics of a movable wall that has two slits in it, as well as the state of a particle incoming to the two slits, are described by quantum mechanics. Using this model, we analyzed complementarity between exhibiting an interference pattern and distinguishing the particle path. Comparing the Kennard–Robertson type and the Ozawa-type uncertainty relations, we conclude that the uncertainty relation involved in the double-slit experiment is not the Ozawa-type uncertainty relation but the Kennard-type uncertainty relation of the position and the momentum of the double-slit wall. A possible experiment to test the complementarity relation is suggested. It is also argued that various phenomena which occur at the interface of a quantum system and a classical system, including distinguishability, interference, decoherence, quantum eraser, and weak value, can be understood as aspects of entanglement. Quanta 2015; 4: 1–9.

Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length

Directory of Open Access Journals (Sweden)

Jun Tao

2015-01-01

Full Text Available In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up to Oβ2. We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point. The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method. We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length.

Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF

Science.gov (United States)

Li, Chen; Requist, Ryan; Gross, E. K. U.

2018-02-01

We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length R = Rc, where an avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the R-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-nuclear coupling produces a sizable elongation of the critical Rc by 0.5 bohr. This effect is very accurately captured by a simple and rigorously derived correction, with an M-1 prefactor, to the exchange-correlation potential in density functional theory, M = reduced nuclear mass. Since this nonadiabatic term depends on gradients of the nuclear wave function and conditional electronic density, ∇Rχ(R) and ∇Rn(r, R), it couples the Kohn-Sham equations at neighboring R points. Motivated by an observed localization of nonadiabatic effects in nuclear configuration space, we propose a local conditional density approximation—an approximation that reduces the search for nonadiabatic density functionals to the search for a single function y(n).

Niels Bohr, Max Delbruck and the paradox of light and life

International Nuclear Information System (INIS)

Scott, G.P.

1983-01-01

This paper features a concise, interdisciplinary history of philosophical issues which were the basis of Delbruck's scientific career. The paradox in living behavior of freedom-to-adapt versus deterministic atomism required complete reassessment with the advent of quantum mechanics. Apparent contradictions implied, for example, by the wave-particle model led Bohr to a belief in the ''complementarity of nature,'' which in 1932 he applied to biology. His claim was that purely physicochemical explanations of purposeful life functions such as ''self-generation and freedom of the will'' were impossible since mutually exclusive situations were involved. Thus Delbruck was challenged to spend his career investigating these vital functions. Beginning with ''fruit-fly photochemistry'' he established the molecular nature of the gene and then collected a world-wide group for a research effort on phage virus, which culminated in discovery of the DNA double helix by Watson and Crick. The second phase of his career featured a study of the total stimulus-response system of the fungus Phycomuces, which is still in progress. The extreme light-sensitivity observed, approaching one-quantum response, has raised the question of the survival value of amplified quantum noise. In critical comments to the author, Delbruck opposed the ''Compton-switch model'' for mind-body interaction; and in his lecture, ''Mind from Matter?'' he revealed his ''a priori concept of truth,'' which embraces a neutral monism and rejects the language of emergent evolution. His views are contrasted with those expressed in Popper's First Darwin Lecture

Classical photodissociation dynamics with Bohr quantization: Application to the fragmentation of a van der Waals cluster

International Nuclear Information System (INIS)

Arbelo-González, W.; Bonnet, L.; Larrégaray, P.; Rayez, J.-C.; Rubayo-Soneira, J.

2012-01-01

Graphical abstract: A recent classical description of photodissociation dynamics in a quantum spirit is applied for the first time to a realistic process, the fragmentation of NeBr 2 . Highlights: ► The photo-dissociation of NeBr 2 is studied by means of two approaches. ► The first is the standard classical one with Gaussian binning. ► The second is a new method applied for the first time to a realistic system. ► The new method leads to exactly the same results as the standard one. ► However, it requires about 10 times less trajectories in the present case. - Abstract: The recent classical dynamical approach of photodissociations with Bohr quantization [L. Bonnet, J. Chem. Phys. 133 (2010) 174108] is applied for the first time to a realistic process, the photofragmentation of the van der Waals cluster NeBr 2 . We illustrate the fact that this approach, formally equivalent to the standard one, may be numerically much more efficient.

ToE in a nutshell or reconciliation of Bohr and Einstein

Energy Technology Data Exchange (ETDEWEB)

Kaesser, Juergen

2016-07-01

Unification of particle and gravitational physics is today's major challenge. This book describes a comprehensive theory able to accomplish it. Starting with a few basic assumptions it allows deducting so different features as e.g. the forces, the six quarks, particle mass etc. of the Standard Model or light deflection, perihelion rotation, Shapiro effect, red shift etc. of General Relativity. Furthermore among others it gives answers to open questions like GUT, Dark Mass and eventually Dark Energy, justifies why the behavior of elementary particles in a gravitational field complies with the Schroedinger equation or why the radii of the planets in our solar system are as they are. Einstein and Bohr fiercely struggled for an understanding of quantum physics. Their different perspectives seem to be irreconcilable. Because of the overwhelming success of quantum physics the dissent unsettling the foundation of physics was never resolved. Doing it, as it is tried in this book, comprehensibility for physical processes is regained. Paradoxes like Schroedinger's Cat vanish into thin air. A theory of unification cannot be simple as it has to contain the known physics. Moreover it has to overcome their contradictions as in defining space-time or in postulating separability. Advantage of the here presented approach compared to M-theory or Loop Quantum Gravitation is its ability to deduct observable features. Of course open questions remain being answered requiring the computational effort of actual theories if not even much more. But these items do not define the basic message of the theory but the derivation of specifics.

Effectiveness of an Asynchronous Online Module on University Students' Understanding of the Bohr Model of the Hydrogen Atom

Science.gov (United States)

Farina, William J.; Bodzin, Alec M.

2017-12-01

Web-based learning is a growing field in education, yet empirical research into the design of high quality Web-based university science instruction is scarce. A one-week asynchronous online module on the Bohr Model of the atom was developed and implemented guided by the knowledge integration framework. The unit design aligned with three identified metaprinciples of science learning: making science accessible, making thinking visible, and promoting autonomy. Students in an introductory chemistry course at a large east coast university completed either an online module or traditional classroom instruction. Data from 99 students were analyzed and results showed significant knowledge growth in both online and traditional formats. For the online learning group, findings revealed positive student perceptions of their learning experiences, highly positive feedback for online science learning, and an interest amongst students to learn chemistry within an online environment.

Fission via compound states and JπK A. Bohr's channels: what we can learn from recent studies with slow neutrons

Directory of Open Access Journals (Sweden)

Furman W.I.

2012-02-01

Full Text Available Last data on angular correlations of fission fragments from slow (s-wave neutron induced binary fission of spin-aligned nuclei 235U are discussed in the context of JπK A. Bohrs channels. Special attention is paid to K = 0 channel. Reasons for its suppression are specified for compound nucleus states of negative parity. A brief overview of recent data on T-odd angular correlations in ternary and binary (with emission of a third particle, a neutron or γ-quantum fission induced by slow polarized neutrons is presented. On the basis of the developed theoretical approach it is shown that a valuable information on JπK fission channels at scission point can be inferred from these T-odd angular correlations.

El pabellón Niels Bohr. Tradición Danesa y Modernidad

Directory of Open Access Journals (Sweden)

Carmen García Sánchez

2015-12-01

Full Text Available La casa de invitados de Niels Bohr fue el primer edificio del arquitecto danés Vilhelm Wohlert (1920-2007. Arraigado a la tradición danesa, representa una renovación basada en la absorción de influencias extranjeras: la arquitectura americana y la tradición japonesa. La caja de madera tiene el carácter sensible de un organismo vivo, siempre cambiante según las variaciones de luz del día o temperatura. Puertas plegables y contraventanas generan extensiones de las habitaciones. Cuando se abren, crean una prolongación del espacio interior, que se extiende a la naturaleza circundante, y se expande hacia el espacio exterior, permitiendo su movilización. Se establece una arquitectura de flujos. Protagoniza un ejemplo de la modernidad como refinamiento en la técnica de los límites y la idea de que la arquitectura no es un objeto material, sino el espacio generado en su interior. Podría ser visto como un ikebana; “el arte del espacio”, donde se produce una circulación de aire entre sus componentes; algo vivo que expresa la tercera dimensión, el equilibrio asimétrico, un interés por la materia, su textura y efecto emocional que emana. Hay armonía y equilibrio, que transmiten serenidad y belleza; un encuentro con la naturaleza; un mundo de relaciones amable al ser humano.

O modelo atômico de Bohr e as suas limitações na interpretação do espectro do átomo de hélio

Directory of Open Access Journals (Sweden)

Danielle Nicolodelli Tenfen

2017-05-01

Full Text Available A inserção de tópicos de física moderna e contemporânea na Educação Básica já não é mais algo tão distante. Os livros didáticos aprovados no último Plano Nacional contemplam, de formas distintas, discussões a esse respeito. Porém, sabe-se que a efetiva implementação desses conteúdos em sala de aula depende da formação – tanto conceitual quanto pedagógica – dos professores. Nesse sentido, o presente artigo visa contribuir com professores e estudantes de graduação em Física, apresentando um breve delineamento histórico que enfatiza o contexto de surgimento do modelo atômico de Niels Bohr, conhecido por situar-se em um período de transição entre Física Clássica e Moderna. Ainda, mostram-se detalhadamente as limitações do modelo de Bohr, evidenciando a necessidade das explicações oriundas da nova Mecânica Quântica para uma descrição adequada do espectro do átomo de hélio. Por fim, apresenta-se uma proposta experimental que consiste na construção de um espectroscópio de baixo custo e problematizam-se alguns dados coletados a partir desse aparato.

Direct interaction in nuclear reactions: a theory; L'interaction directe dans les reactions nucleaires: theorie

Energy Technology Data Exchange (ETDEWEB)

Dominicis, C.T. de [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires

1959-07-01

General treatment of the foundations of direct interaction in nuclear reactions; representation of the instantaneous elastic scattering amplitude by the scattering amplitude due to a complex potential; expansion of the instantaneous inelastic scattering amplitude and discussion of the 1. Bohr approximation (distorted waves) contribution to individual and collective states of excitation. (author) [French] Expose general sur les fondements de l'interaction directe dans les reactions nucleaires; representation de l'amplitude de diffusion instantanee elastique par celle due a un potentiel complexe; developpement de l'amplitude de diffusion instantanee inelastique et discussion de la contribution de la premiere approximation de Bohr (sur des distendues) a l'excitation d'etats individuels et collectifs. (auteur)

Collective excitation spectra of transitional even nuclei

International Nuclear Information System (INIS)

Quentin, P.; Paris-11 Univ., 91 - Orsay; Deloncle, I.; Libert, J.; Sauvage, J.

1990-01-01

This talk is dealing with the nuclear low energy collective motion as described in the context of microscopic versions of the Bohr Hamiltonian. Two different ways of building microscopically Bohr collective Hamiltonians will be sketched; one within the framework of the Generator Coordinate Method, the other using the Adiabatic Time-Dependent Hartree-Fock-Boholyubov approximation. A sample of recent results will be presented which pertains to the description of transitional even nuclei and to the newly revisited phenomenon of superdeformation at low spin

Diophantine approximation and badly approximable sets

DEFF Research Database (Denmark)

Kristensen, S.; Thorn, R.; Velani, S.

2006-01-01

. The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...

Relation between the location of elements in the Thomsen-Bohr type periodic table and lysosomal accumulation in tumor and liver

International Nuclear Information System (INIS)

Ando, Atsushi; Ando, Itsuko

1989-01-01

This study was undertaken to evaluate the lysosomal accumulation of radioactive metal ions in tumor and liver, using tumor-bearing animals. From the experimental of lysosomal accumulation and binding substance for nineteen radioactive metal ions, the following results were obtained. Hard and borderline acids which have incomplete d-shells accumulated extensively in lysosomes of tumor and liver with time after administration of these ions. They were bound in these tissues to the acid mucopolysaccharides whose molecular weights exceed 40,000 daltons. Trivalent hard acids (Ga 3+ , In 3+ , Yb 3+ , Tm 3+ ) which have complete d-shells accumulated extensively in the lysosomes of liver, but very little in lysososmes of tumor, and were bound to the acid mucopolysaccharide with a molecular weight of about 10,000 daltons in tissues. It was clear based on these results and the facts reported previously that a very interesting relationship existed between the location of elements in the Thomsen-Bohr type periodic table and the lysosomal accumulation of metal ions

How to understand the tunneling in attosecond experiment?. Bohr-Einstein photon box Gedanken experiment, tunneling time and the wave particle duality

Science.gov (United States)

Kullie, Ossama

2018-02-01

The measurement of the tunneling time (T-time) in today's attosecond and strong field (low-frequency) experiments, despite its controversial discussion, offers a fruitful opportunity to understand time measurement and the time in quantum mechanics. In addition, as we will see in this work, a related controversial issue is the particulate nature of the radiation. The T-time in attosecond experiment and its different aspects and models, is discussed in this work, especially in relation to my model of real T-time (Kullie, 2015), where a good agreement with the experiment and an intriguing similarity to the Bohr-Einstein photon box Gedanken experiment was found. The tunneling process itself is still not well understood, but I am arguing that a scattering mechanism (by the laser wave packet) offers a possibility to understand the tunneling process in the tunneling region. This is related to the question about the corpuscular nature of light which is widely discussed in modern quantum optics experiments.

Entropy of Iterated Function Systems and Their Relations with Black Holes and Bohr-Like Black Holes Entropies

Directory of Open Access Journals (Sweden)

Christian Corda

2018-01-01

Full Text Available In this paper we consider the metric entropies of the maps of an iterated function system deduced from a black hole which are known the Bekenstein–Hawking entropies and its subleading corrections. More precisely, we consider the recent model of a Bohr-like black hole that has been recently analysed in some papers in the literature, obtaining the intriguing result that the metric entropies of a black hole are created by the metric entropies of the functions, created by the black hole principal quantum numbers, i.e., by the black hole quantum levels. We present a new type of topological entropy for general iterated function systems based on a new kind of the inverse of covers. Then the notion of metric entropy for an Iterated Function System ( I F S is considered, and we prove that these definitions for topological entropy of IFS’s are equivalent. It is shown that this kind of topological entropy keeps some properties which are hold by the classic definition of topological entropy for a continuous map. We also consider average entropy as another type of topological entropy for an I F S which is based on the topological entropies of its elements and it is also an invariant object under topological conjugacy. The relation between Axiom A and the average entropy is investigated.

Hierarchical low-rank approximation for high dimensional approximation

KAUST Repository

Nouy, Anthony

2016-01-07

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

Hierarchical low-rank approximation for high dimensional approximation

KAUST Repository

Nouy, Anthony

2016-01-01

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

Loss of Asxl1 Alters Self-Renewal and Cell Fate of Bone Marrow Stromal Cell, Leading to Bohring-Opitz-like Syndrome in Mice

Directory of Open Access Journals (Sweden)

Peng Zhang

2016-06-01

Full Text Available De novo ASXL1 mutations are found in patients with Bohring-Opitz syndrome, a disease with severe developmental defects and early childhood mortality. The underlying pathologic mechanisms remain largely unknown. Using Asxl1-targeted murine models, we found that Asxl1 global loss as well as conditional deletion in osteoblasts and their progenitors led to significant bone loss and a markedly decreased number of bone marrow stromal cells (BMSCs compared with wild-type littermates. Asxl1−/− BMSCs displayed impaired self-renewal and skewed differentiation, away from osteoblasts and favoring adipocytes. RNA-sequencing analysis revealed altered expression of genes involved in cell proliferation, skeletal development, and morphogenesis. Furthermore, gene set enrichment analysis showed decreased expression of stem cell self-renewal gene signature, suggesting a role of Asxl1 in regulating the stemness of BMSCs. Importantly, re-introduction of Asxl1 normalized NANOG and OCT4 expression and restored the self-renewal capacity of Asxl1−/− BMSCs. Our study unveils a pivotal role of ASXL1 in the maintenance of BMSC functions and skeletal development.

(4)He Thermophysical Properties: New Ab Initio Calculations.

Science.gov (United States)

Hurly, John J; Mehl, James B

2007-01-01

Since 2000, atomic physicists have reduced the uncertainty of the helium-helium "ab initio" potential; for example, from approximately 0.6 % to 0.1 % at 4 bohr, and from 0.8 % to 0.1 % at 5.6 bohr. These results led us to: (1) construct a new inter-atomic potential ϕ 07, (2) recalculate values of the second virial coefficient, the viscosity, and the thermal conductivity of (4)He from 1 K to 10,000 K, and (3), analyze the uncertainties of the thermophysical properties that propagate from the uncertainty of ϕ 07 and from the Born-Oppenheimer approximation of the electron-nucleon quantum mechanical system. We correct minor errors in a previous publication [J. J. Hurly and M. R. Moldover, J. Res. Nat. Inst. Standards Technol. 105, 667 (2000)] and compare our results with selected data published after 2000. The ab initio results tabulated here can serve as standards for the measurement of thermophysical properties.

4He Thermophysical Properties: New Ab Initio Calculations

Science.gov (United States)

Hurly, John J.; Mehl, James B.

2007-01-01

Since 2000, atomic physicists have reduced the uncertainty of the helium-helium “ab initio” potential; for example, from approximately 0.6 % to 0.1 % at 4 bohr, and from 0.8 % to 0.1 % at 5.6 bohr. These results led us to: (1) construct a new inter-atomic potential ϕ07, (2) recalculate values of the second virial coefficient, the viscosity, and the thermal conductivity of 4He from 1 K to 10,000 K, and (3), analyze the uncertainties of the thermophysical properties that propagate from the uncertainty of ϕ07 and from the Born-Oppenheimer approximation of the electron-nucleon quantum mechanical system. We correct minor errors in a previous publication [J. J. Hurly and M. R. Moldover, J. Res. Nat. Inst. Standards Technol. 105, 667 (2000)] and compare our results with selected data published after 2000. The ab initio results tabulated here can serve as standards for the measurement of thermophysical properties. PMID:27110456

Theory of collective Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Zhang Qingying

1982-02-01

Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.

New look at the nuclear force

International Nuclear Information System (INIS)

Noyes, P.

1975-07-01

Nuclear force theory and calculations are discussed. It is noted that whether the quark interpretation or the vague bootstrap ideas indicated turn out to be better approximations, it is hoped that the deuteron problem is on the verge of being turned into the Bohr atom of strong interaction physics. 2 references

Self-similar factor approximants

International Nuclear Information System (INIS)

Gluzman, S.; Yukalov, V.I.; Sornette, D.

2003-01-01

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties

Modulated Pade approximant

International Nuclear Information System (INIS)

Ginsburg, C.A.

1980-01-01

In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)

Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

Science.gov (United States)

Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E

2018-06-01

An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.

Direct interaction in nuclear reactions: a theory

International Nuclear Information System (INIS)

Dominicis, C.T. de

1959-01-01

General treatment of the foundations of direct interaction in nuclear reactions; representation of the instantaneous elastic scattering amplitude by the scattering amplitude due to a complex potential; expansion of the instantaneous inelastic scattering amplitude and discussion of the 1. Bohr approximation (distorted waves) contribution to individual and collective states of excitation. (author) [fr

Loss of Asxl1 Alters Self-Renewal and Cell Fate of Bone Marrow Stromal Cell, Leading to Bohring-Opitz-like Syndrome in Mice.

Science.gov (United States)

Zhang, Peng; Xing, Caihong; Rhodes, Steven D; He, Yongzheng; Deng, Kai; Li, Zhaomin; He, Fuhong; Zhu, Caiying; Nguyen, Lihn; Zhou, Yuan; Chen, Shi; Mohammad, Khalid S; Guise, Theresa A; Abdel-Wahab, Omar; Xu, Mingjiang; Wang, Qian-Fei; Yang, Feng-Chun

2016-06-14

De novo ASXL1 mutations are found in patients with Bohring-Opitz syndrome, a disease with severe developmental defects and early childhood mortality. The underlying pathologic mechanisms remain largely unknown. Using Asxl1-targeted murine models, we found that Asxl1 global loss as well as conditional deletion in osteoblasts and their progenitors led to significant bone loss and a markedly decreased number of bone marrow stromal cells (BMSCs) compared with wild-type littermates. Asxl1(-/-) BMSCs displayed impaired self-renewal and skewed differentiation, away from osteoblasts and favoring adipocytes. RNA-sequencing analysis revealed altered expression of genes involved in cell proliferation, skeletal development, and morphogenesis. Furthermore, gene set enrichment analysis showed decreased expression of stem cell self-renewal gene signature, suggesting a role of Asxl1 in regulating the stemness of BMSCs. Importantly, re-introduction of Asxl1 normalized NANOG and OCT4 expression and restored the self-renewal capacity of Asxl1(-/-) BMSCs. Our study unveils a pivotal role of ASXL1 in the maintenance of BMSC functions and skeletal development. Copyright © 2016 The Author(s). Published by Elsevier Inc. All rights reserved.

Atomic structure in black hole

International Nuclear Information System (INIS)

Nagatani, Yukinori

2006-01-01

We propose that any black hole has atomic structure in its inside and has no horizon as a model of black holes. Our proposal is founded on a mean field approximation of gravity. The structure of our model consists of a (charged) singularity at the center and quantum fluctuations of fields around the singularity, namely, it is quite similar to that of atoms. Any properties of black holes, e.g. entropy, can be explained by the model. The model naturally quantizes black holes. In particular, we find the minimum black hole, whose structure is similar to that of the hydrogen atom and whose Schwarzschild radius is approximately 1.1287 times the Planck length. Our approach is conceptually similar to Bohr's model of the atomic structure, and the concept of the minimum Schwarzschild radius is similar to that of the Bohr radius. The model predicts that black holes carry baryon number, and the baryon number is rapidly violated. This baryon number violation can be used as verification of the model. (author)

Approximate symmetries of Hamiltonians

Science.gov (United States)

Chubb, Christopher T.; Flammia, Steven T.

2017-08-01

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

Heating electrons with ion irradiation: A first-principles approach

International Nuclear Information System (INIS)

Pruneda, J.M.; Sanchez-Portal, D.; Arnau, A.; Juaristi, J.I.; Artacho, E.

2009-01-01

Using time-dependent density functional theory we calculate from first-principles the rate of energy transfer from a moving charged particle to the electrons in an insulating material. The behavior of the electronic stopping power in LiF (a wide band gap insulator) versus projectile velocity displays an effective threshold velocity of 8.2 Bohr/asec for the proton, consistent with recent experimental observations. The calculated proton/antiproton stopping power ratio is 2.4 at velocities slightly above the threshold (16.5 Bohr/asec) as compared to the experimental value of 2.1. The approximations introduced in this new non-perturbative methodology are discussed, and results on the velocity dependence of the stopping power, the locality of the energy transfer, and other characteristics of the host material are presented.

Geometric approximation algorithms

CERN Document Server

Har-Peled, Sariel

2011-01-01

Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

Sparse approximation with bases

CERN Document Server

2015-01-01

This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications.  The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

Approximating distributions from moments

Science.gov (United States)

Pawula, R. F.

1987-11-01

A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.

General Rytov approximation.

Science.gov (United States)

Potvin, Guy

2015-10-01

We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.

17th Poincaré Seminar 2013

CERN Document Server

Duplantier, Bertrand; Raimond, Jean-Michel; Rivasseau, Vincent

2016-01-01

This fourteenth volume in the Poincaré Seminar Series is devoted to Niels Bohr, his foundational contributions to understanding atomic structure and quantum theory and their continuing importance today. This book contains the following chapters: - Tomas Bohr, Keeping Things Open; - Olivier Darrigol, Bohr's Trilogy of 1913; -John Heilbron, The Mind that Created the Bohr Atom; - Serge Haroche & Jean-Michel Raimond, Bohr's Legacy in Cavity QED; - Alain Aspect, From Einstein, Bohr, Schrödinger to Bell and Feynman: a New Quantum Revolution?; - Antoine Browaeys, Interacting Cold Rydberg Atoms: A Toy Many-Body System; - Michel Bitbol & Stefano Osnaghi, Bohr´s Complementarity and Kant´s Epistemology. Dating from their origin in lectures to a broad scientific audience these seven chapters are of high educational value. This volume is of general interest to physicists, mathematicians and historians.

Approximation techniques for engineers

CERN Document Server

Komzsik, Louis

2006-01-01

Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.

International Conference Approximation Theory XV

CERN Document Server

Schumaker, Larry

2017-01-01

These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...

Ordered cones and approximation

CERN Document Server

Keimel, Klaus

1992-01-01

This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

Semiclassical approach to Regge poles trajectories calculations for nonsingular potentials: Thomas-Fermi type

International Nuclear Information System (INIS)

Belov, S M; Avdonina, N B; Felfli, Z; Marletta, M; Msezane, A Z; Naboko, S N

2004-01-01

A simple semiclassical approach, based on the investigation of anti-Stokes line topology, is presented for calculating Regge poles for nonsingular (Thomas-Fermi type) potentials, namely potentials with singularities at the origin weaker than order -2. The anti-Stokes lines for Thomas-Fermi potentials have a more complicated structure than those of singular potentials and require careful application of complex analysis. The explicit solution of the Bohr-Sommerfeld quantization condition is used to obtain approximate Regge poles. We introduce and employ three hypotheses to obtain several terms of the Regge pole approximation

CONTRIBUTIONS TO RATIONAL APPROXIMATION,

Science.gov (United States)

Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

Exact constants in approximation theory

CERN Document Server

Korneichuk, N

1991-01-01

This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base

Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation

DEFF Research Database (Denmark)

Sadegh, Payman; Spall, J. C.

1998-01-01

simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...

Approximate kernel competitive learning.

Science.gov (United States)

Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang

2015-03-01

Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.

Approximate cohomology in Banach algebras | Pourabbas ...

African Journals Online (AJOL)

We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate cohomologies. As a special case, approximate Hochschild cohomology is ...

International Conference Approximation Theory XIV

CERN Document Server

Schumaker, Larry

2014-01-01

This volume developed from papers presented at the international conference Approximation Theory XIV,  held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.

Forms of Approximate Radiation Transport

CERN Document Server

Brunner, G

2002-01-01

Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.

Approximate and renormgroup symmetries

International Nuclear Information System (INIS)

Ibragimov, Nail H.; Kovalev, Vladimir F.

2009-01-01

''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

Approximations of Fuzzy Systems

Directory of Open Access Journals (Sweden)

Vinai K. Singh

2013-03-01

Full Text Available A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems, with product inference, centroid defuzzification and Gaussian functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions

Approximate and renormgroup symmetries

Energy Technology Data Exchange (ETDEWEB)

Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling

2009-07-01

''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix

International Nuclear Information System (INIS)

Miller, William H.; Cotton, Stephen J.

2016-01-01

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory—e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states—and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix.

Science.gov (United States)

Miller, William H; Cotton, Stephen J

2016-08-28

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory-e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states-and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix

Energy Technology Data Exchange (ETDEWEB)

Miller, William H., E-mail: millerwh@berkeley.edu; Cotton, Stephen J., E-mail: StephenJCotton47@gmail.com [Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)

2016-08-28

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory—e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states—and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.

Cosmological applications of Padé approximant

International Nuclear Information System (INIS)

Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

2014-01-01

As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation

Cosmological applications of Padé approximant

Science.gov (United States)

Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

2014-01-01

As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.

Prestack wavefield approximations

KAUST Repository

Alkhalifah, Tariq

2013-01-01

The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

Prestack wavefield approximations

KAUST Repository

Alkhalifah, Tariq

2013-09-01

The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

Expectation Consistent Approximate Inference

DEFF Research Database (Denmark)

Opper, Manfred; Winther, Ole

2005-01-01

We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...

Approximate number and approximate time discrimination each correlate with school math abilities in young children.

Science.gov (United States)

Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin

2016-01-01

What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright �

Approximation and Computation

CERN Document Server

Gautschi, Walter; Rassias, Themistocles M

2011-01-01

Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg

Constrained Optimization via Stochastic approximation with a simultaneous perturbation gradient approximation

DEFF Research Database (Denmark)

Sadegh, Payman

1997-01-01

This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...... of the optimization parameters. It is shown that, under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point, The procedure is illustrated by a numerical example, (C) 1997 Elsevier Science Ltd....

Some results in Diophantine approximation

DEFF Research Database (Denmark)

Pedersen, Steffen Højris

the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered......This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...

Bounded-Degree Approximations of Stochastic Networks

Energy Technology Data Exchange (ETDEWEB)

Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar

2017-06-01

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.

Approximation by planar elastic curves

DEFF Research Database (Denmark)

Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge

2016-01-01

We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....

Limitations of shallow nets approximation.

Science.gov (United States)

Lin, Shao-Bo

2017-10-01

In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

Approximate circuits for increased reliability

Science.gov (United States)

Hamlet, Jason R.; Mayo, Jackson R.

2015-08-18

Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.

Mapping moveout approximations in TI media

KAUST Repository

Stovas, Alexey; Alkhalifah, Tariq Ali

2013-01-01

Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

Analytical approximation of neutron physics data

International Nuclear Information System (INIS)

Badikov, S.A.; Vinogradov, V.A.; Gaj, E.V.; Rabotnov, N.S.

1984-01-01

The method for experimental neutron-physical data analytical approximation by rational functions based on the Pade approximation is suggested. It is shown that the existence of the Pade approximation specific properties in polar zones is an extremely favourable analytical property essentially extending the convergence range and increasing its rate as compared with polynomial approximation. The Pade approximation is the particularly natural instrument for resonance curve processing as the resonances conform to the complex poles of the approximant. But even in a general case analytical representation of the data in this form is convenient and compact. Thus representation of the data on the neutron threshold reaction cross sections (BOSPOR constant library) in the form of rational functions lead to approximately twenty fold reduction of the storaged numerical information as compared with the by-point calculation at the same accWracy

Mapping moveout approximations in TI media

KAUST Repository

Stovas, Alexey

2013-11-21

Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

Nuclear Hartree-Fock approximation testing and other related approximations

International Nuclear Information System (INIS)

Cohenca, J.M.

1970-01-01

Hartree-Fock, and Tamm-Dancoff approximations are tested for angular momentum of even-even nuclei. Wave functions, energy levels and momenta are comparatively evaluated. Quadripole interactions are studied following the Elliott model. Results are applied to Ne 20 [pt

Approximate Implicitization Using Linear Algebra

Directory of Open Access Journals (Sweden)

Oliver J. D. Barrowclough

2012-01-01

Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.

Risk approximation in decision making: approximative numeric abilities predict advantageous decisions under objective risk.

Science.gov (United States)

Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias

2018-01-22

Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.

Nonlinear approximation with dictionaries I. Direct estimates

DEFF Research Database (Denmark)

Gribonval, Rémi; Nielsen, Morten

2004-01-01

We study various approximation classes associated with m-term approximation by elements from a (possibly) redundant dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation w...

Spline approximation, Part 1: Basic methodology

Science.gov (United States)

Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar

2018-04-01

In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.

The efficiency of Flory approximation

International Nuclear Information System (INIS)

Obukhov, S.P.

1984-01-01

The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)

Rutherford and Bohr*

Indian Academy of Sciences (India)

IAS Admin

He was always concerned about hurting any person's feelings, and he found great ... classical picture might be modified by using Planck's quantum of action. A first manuscript .... problem soon was made academic by Rutherford moving to Cambridge. ..... I hope it will not have too much of a reaction on them'. And later: 'I am ...

Weighted approximation with varying weight

CERN Document Server

Totik, Vilmos

1994-01-01

A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

Bent approximations to synchrotron radiation optics

International Nuclear Information System (INIS)

Heald, S.

1981-01-01

Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors

INTOR cost approximation

International Nuclear Information System (INIS)

Knobloch, A.F.

1980-01-01

A simplified cost approximation for INTOR parameter sets in a narrow parameter range is shown. Plausible constraints permit the evaluation of the consequences of parameter variations on overall cost. (orig.) [de

A unified approach to the Darwin approximation

International Nuclear Information System (INIS)

Krause, Todd B.; Apte, A.; Morrison, P. J.

2007-01-01

There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting

An Approximate Approach to Automatic Kernel Selection.

Science.gov (United States)

Ding, Lizhong; Liao, Shizhong

2016-02-02

Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

Approximate error conjugation gradient minimization methods

Science.gov (United States)

Kallman, Jeffrey S

2013-05-21

In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.

Self-similar continued root approximants

International Nuclear Information System (INIS)

Gluzman, S.; Yukalov, V.I.

2012-01-01

A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Padé approximants. A theorem on the convergence of the self-similar continued roots is proved. The method is illustrated by several examples from condensed-matter physics.

 Higher Order Improvements for Approximate Estimators

DEFF Research Database (Denmark)

Kristensen, Dennis; Salanié, Bernard

Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties of such appr......Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties...... of such approximate estimators at a low computational cost. The first two methods correct the objective function so as to remove the leading term of the bias due to the approximation. One variant provides an analytical bias adjustment, but it only works for estimators based on stochastic approximators......, such as simulation-based estimators. Our second bias correction is based on ideas from the resampling literature; it eliminates the leading bias term for non-stochastic as well as stochastic approximators. Finally, we propose an iterative procedure where we use Newton-Raphson (NR) iterations based on a much finer...

Exact and approximate multiple diffraction calculations

International Nuclear Information System (INIS)

Alexander, Y.; Wallace, S.J.; Sparrow, D.A.

1976-08-01

A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation

On Covering Approximation Subspaces

Directory of Open Access Journals (Sweden)

Xun Ge

2009-06-01

Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

Prestack traveltime approximations

KAUST Repository

Alkhalifah, Tariq Ali

2011-01-01

Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.

Approximation methods in probability theory

CERN Document Server

Čekanavičius, Vydas

2016-01-01

This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.

Fractional Schroedinger equation

International Nuclear Information System (INIS)

Laskin, Nick

2002-01-01

Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations

Comparison of the Born series and rational approximants in potential scattering. [Pade approximants, Yikawa and exponential potential

Energy Technology Data Exchange (ETDEWEB)

Garibotti, C R; Grinstein, F F [Rosario Univ. Nacional (Argentina). Facultad de Ciencias Exactas e Ingenieria

1976-05-08

It is discussed the real utility of Born series for the calculation of atomic collision processes in the Born approximation. It is suggested to make use of Pade approximants and it is shown that this approach provides very fast convergent sequences over all the energy range studied. Yukawa and exponential potential are explicitly considered and the results are compared with high-order Born approximation.

Spherical Approximation on Unit Sphere

Directory of Open Access Journals (Sweden)

Eman Samir Bhaya

2018-01-01

Full Text Available In this paper we introduce a Jackson type theorem for functions in LP spaces on sphere And study on best approximation of  functions in  spaces defined on unit sphere. our central problem is to describe the approximation behavior of functions in    spaces for  by modulus of smoothness of functions.

Collective excitations at low energy: microscopic study of rotation, vibration and their coupling in even-even nuclei; Excitations collectives a basse energie: Etude microscopique de la rotation, de la vibration et de leur couplage dans les noyaux pair-pairs

Energy Technology Data Exchange (ETDEWEB)

Deloncle, I.

1989-10-23

In this study we have built the quadrupolar collective Bohr Hamiltonian in a purely microscopic way by using an approximation of the time-dependant Hartree-Fock adiabatic approach. The purpose of this work was to obtain a quantitative description of the collective properties in the low energy range of intermediate and heavy nuclei by using a 2-body effective interaction of Skyrme-type. We consider low energy processes as dynamic regimes in which the collective movement is adiabatic when compared with modes associated to individual freedom. In the N-body solution we propose, we have assumed that: -) a mean field exists at any moment, -) some collective variables exist whose temporal variations include all the dynamics, and -) the collective movement is adiabatic. This work is a microscopic formulation and an efficient approach to resolve the Bohr and Mottelson unified model. Low energy spectra have been computed for 4 nuclei: Ge{sup 74}, Se{sup 76}, Cd{sup 110} and Pt{sup 186} and they agree well with experimental data.

Energy straggling determination for charged particles in thick targets

International Nuclear Information System (INIS)

Lopez M, J.

1980-01-01

Energy straggling is reported for deuterons in carbon and protons in silicon, and the data obtained is compared with predictions of Bohr and Bethe. The experimental method used is based on a reaction resonance widening, observed at backward angles in the thick targets. The incident energy determines the depth at which the resonant scattering occurs and the energy straggling can be measured from the backscattering spectra. The data obtained for the energy straggling of deuterons are approximately two times bigger than those predicted by Bohr's theory; nevertheless, the values found for the energy straggling of protons in silicon are in agreement with the values predicted by the aforesaid theory. This disagreement was explained by the fact that carbon targets used were amorphous and porous, in contrast with those of cristal silicon, (it is an experimental fact that porous materials are expected to give higher stragglings than non-porous ones). Thus, the method reviewed in this work is valid, but the porosity effects should be taken into account in comparing results among materials with different densities. (author)

Analysis of corrections to the eikonal approximation

Science.gov (United States)

Hebborn, C.; Capel, P.

2017-11-01

Various corrections to the eikonal approximations are studied for two- and three-body nuclear collisions with the goal to extend the range of validity of this approximation to beam energies of 10 MeV/nucleon. Wallace's correction does not improve much the elastic-scattering cross sections obtained at the usual eikonal approximation. On the contrary, a semiclassical approximation that substitutes the impact parameter by a complex distance of closest approach computed with the projectile-target optical potential efficiently corrects the eikonal approximation. This opens the possibility to analyze data measured down to 10 MeV/nucleon within eikonal-like reaction models.

Ancilla-approximable quantum state transformations

International Nuclear Information System (INIS)

Blass, Andreas; Gurevich, Yuri

2015-01-01

We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation

Ancilla-approximable quantum state transformations

Energy Technology Data Exchange (ETDEWEB)

Blass, Andreas [Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 (United States); Gurevich, Yuri [Microsoft Research, Redmond, Washington 98052 (United States)

2015-04-15

We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation.

Recognition of computerized facial approximations by familiar assessors.

Science.gov (United States)

Richard, Adam H; Monson, Keith L

2017-11-01

Studies testing the effectiveness of facial approximations typically involve groups of participants who are unfamiliar with the approximated individual(s). This limitation requires the use of photograph arrays including a picture of the subject for comparison to the facial approximation. While this practice is often necessary due to the difficulty in obtaining a group of assessors who are familiar with the approximated subject, it may not accurately simulate the thought process of the target audience (friends and family members) in comparing a mental image of the approximated subject to the facial approximation. As part of a larger process to evaluate the effectiveness and best implementation of the ReFace facial approximation software program, the rare opportunity arose to conduct a recognition study using assessors who were personally acquainted with the subjects of the approximations. ReFace facial approximations were generated based on preexisting medical scans, and co-workers of the scan donors were tested on whether they could accurately pick out the approximation of their colleague from arrays of facial approximations. Results from the study demonstrated an overall poor recognition performance (i.e., where a single choice within a pool is not enforced) for individuals who were familiar with the approximated subjects. Out of 220 recognition tests only 10.5% resulted in the assessor selecting the correct approximation (or correctly choosing not to make a selection when the array consisted only of foils), an outcome that was not significantly different from the 9% random chance rate. When allowed to select multiple approximations the assessors felt resembled the target individual, the overall sensitivity for ReFace approximations was 16.0% and the overall specificity was 81.8%. These results differ markedly from the results of a previous study using assessors who were unfamiliar with the approximated subjects. Some possible explanations for this disparity in

Approximating The DCM

DEFF Research Database (Denmark)

Madsen, Rasmus Elsborg

2005-01-01

The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM...

An approximation for kanban controlled assembly systems

NARCIS (Netherlands)

Topan, E.; Avsar, Z.M.

2011-01-01

An approximation is proposed to evaluate the steady-state performance of kanban controlled two-stage assembly systems. The development of the approximation is as follows. The considered continuous-time Markov chain is aggregated keeping the model exact, and this aggregate model is approximated

Low Rank Approximation Algorithms, Implementation, Applications

CERN Document Server

Markovsky, Ivan

2012-01-01

Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...

Space distribution and energy straggling of charged particles via Fokker-Planck equation

International Nuclear Information System (INIS)

Manservisi, S.; Molinari, V.; Nespoli, A.

1996-01-01

The Fokker-Planck equation describing a beam of charged particles entering a homogeneous medium is solved here for a stationary case. Interactions are taken into account through Coulomb cross-section. Starting from the charged-particle distribution as a function of velocity and penetration depth, some important kinetic quantities are calculated, like mean velocity, range and the loss of energy per unit space. In such quantities the energy straggling is taken into account. This phenomenon is not considered in the continuous slowing-down approximation that is commonly used to obtain the range and the stopping power. Finally the well-know Bohr of Bethe formula is found as a first-order approximation of the Fokker-Planck equation

Shearlets and Optimally Sparse Approximations

DEFF Research Database (Denmark)

Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q

2012-01-01

Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....

Multilevel weighted least squares polynomial approximation

KAUST Repository

Haji-Ali, Abdul-Lateef

2017-06-30

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

Improved Dutch Roll Approximation for Hypersonic Vehicle

Directory of Open Access Journals (Sweden)

Liang-Liang Yin

2014-06-01

Full Text Available An improved dutch roll approximation for hypersonic vehicle is presented. From the new approximations, the dutch roll frequency is shown to be a function of the stability axis yaw stability and the dutch roll damping is mainly effected by the roll damping ratio. In additional, an important parameter called roll-to-yaw ratio is obtained to describe the dutch roll mode. Solution shows that large-roll-to-yaw ratio is the generate character of hypersonic vehicle, which results the large error for the practical approximation. Predictions from the literal approximations derived in this paper are compared with actual numerical values for s example hypersonic vehicle, results show the approximations work well and the error is below 10 %.

Regression with Sparse Approximations of Data

DEFF Research Database (Denmark)

Noorzad, Pardis; Sturm, Bob L.

2012-01-01

We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...

Rational approximation of vertical segments

Science.gov (United States)

Salazar Celis, Oliver; Cuyt, Annie; Verdonk, Brigitte

2007-08-01

In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.

On Nash-Equilibria of Approximation-Stable Games

Science.gov (United States)

Awasthi, Pranjal; Balcan, Maria-Florina; Blum, Avrim; Sheffet, Or; Vempala, Santosh

One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ɛ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ɛ-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ɛ,Δ) approximation-stable games must have an ɛ-equilibrium of support O(Δ^{2-o(1)}/ɛ2{log n}), yielding an immediate n^{O(Δ^{2-o(1)}/ɛ^2log n)}-time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ɛ are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.

Legendre-tau approximations for functional differential equations

Science.gov (United States)

Ito, K.; Teglas, R.

1986-01-01

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

Approximate maximum parsimony and ancestral maximum likelihood.

Science.gov (United States)

Alon, Noga; Chor, Benny; Pardi, Fabio; Rapoport, Anat

2010-01-01

We explore the maximum parsimony (MP) and ancestral maximum likelihood (AML) criteria in phylogenetic tree reconstruction. Both problems are NP-hard, so we seek approximate solutions. We formulate the two problems as Steiner tree problems under appropriate distances. The gist of our approach is the succinct characterization of Steiner trees for a small number of leaves for the two distances. This enables the use of known Steiner tree approximation algorithms. The approach leads to a 16/9 approximation ratio for AML and asymptotically to a 1.55 approximation ratio for MP.

Local density approximations for relativistic exchange energies

International Nuclear Information System (INIS)

MacDonald, A.H.

1986-01-01

The use of local density approximations to approximate exchange interactions in relativistic electron systems is reviewed. Particular attention is paid to the physical content of these exchange energies by discussing results for the uniform relativistic electron gas from a new point of view. Work on applying these local density approximations in atoms and solids is reviewed and it is concluded that good accuracy is usually possible provided self-interaction corrections are applied. The local density approximations necessary for spin-polarized relativistic systems are discussed and some new results are presented

L’ULTIMO ASSOLUTO DELLA RELATIVITÀ

Directory of Open Access Journals (Sweden)

Andrea Roselli

2014-03-01

Full Text Available Si mostra come la celebre disputa tra Einstein e Bohr riguardi i concetti di realtà retrostanti le loro relative concezioni della realtà fisica; conseguentemente, viene suggerita una significativa connessione tra le teorie di Copenaghen e la relatività einsteiniana. Bohr considerava la descrizione della realtà offerta dalla meccanica quantistica completa; Einstein, al contrario (nonostante il contributo apportato alla sua nascita, continuava a cercare una teoria deterministica. Quando nel 1935 Einstein, Podolsky e Rosen pubblicarono il famoso EPR, Bohr replicò centrando l’attenzione sul ragionevole criterio di realtà proposto dagli autori, rimarcando l’inconsistenza concettuale dell’esistenza indipendente di un costitutivo “inconoscibile”. La fisica, attraverso la grande lezione epistemologica – come era solito dirne Niels Bohr – rappresentata dalla MQ, si trovava di fronte ad una capitale questione filosofica: che cosa è la realtà? Viene infine suggerita una giustapposizione della problematizzazione einsteiniana del concetto di simultaneità e del carattere reciproco delle misurazioni quantomeccaniche esposto da Bohr, che suggerisce l’abbandono dell’ultimo grande assoluto: una realtà assoluta.

Some relations between entropy and approximation numbers

Institute of Scientific and Technical Information of China (English)

郑志明

1999-01-01

A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.

Saddlepoint approximation methods in financial engineering

CERN Document Server

Kwok, Yue Kuen

2018-01-01

This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables.  The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quanti...

Approximating centrality in evolving graphs: toward sublinearity

Science.gov (United States)

Priest, Benjamin W.; Cybenko, George

2017-05-01

The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.

Axiomatic Characterizations of IVF Rough Approximation Operators

Directory of Open Access Journals (Sweden)

Guangji Yu

2014-01-01

Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.

Approximation properties of fine hyperbolic graphs

Indian Academy of Sciences (India)

2016-08-26

Aug 26, 2016 ... In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use ... Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, People's Republic of China ...

Efficient automata constructions and approximate automata

NARCIS (Netherlands)

Watson, B.W.; Kourie, D.G.; Ngassam, E.K.; Strauss, T.; Cleophas, L.G.W.A.

2008-01-01

In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at least L. Such automata can be used in a variety of practical applications, including network security pattern

Efficient automata constructions and approximate automata

NARCIS (Netherlands)

Watson, B.W.; Kourie, D.G.; Ngassam, E.K.; Strauss, T.; Cleophas, L.G.W.A.; Holub, J.; Zdárek, J.

2006-01-01

In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at least L. Such automata can be used in a variety of practical applications, including network security pattern

Approximation of the semi-infinite interval

Directory of Open Access Journals (Sweden)

A. McD. Mercer

1980-01-01

Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.

Rational approximations for tomographic reconstructions

International Nuclear Information System (INIS)

Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas

2013-01-01

We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp–Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image. (paper)

'LTE-diffusion approximation' for arc calculations

International Nuclear Information System (INIS)

Lowke, J J; Tanaka, M

2006-01-01

This paper proposes the use of the 'LTE-diffusion approximation' for predicting the properties of electric arcs. Under this approximation, local thermodynamic equilibrium (LTE) is assumed, with a particular mesh size near the electrodes chosen to be equal to the 'diffusion length', based on D e /W, where D e is the electron diffusion coefficient and W is the electron drift velocity. This approximation overcomes the problem that the equilibrium electrical conductivity in the arc near the electrodes is almost zero, which makes accurate calculations using LTE impossible in the limit of small mesh size, as then voltages would tend towards infinity. Use of the LTE-diffusion approximation for a 200 A arc with a thermionic cathode gives predictions of total arc voltage, electrode temperatures, arc temperatures and radial profiles of heat flux density and current density at the anode that are in approximate agreement with more accurate calculations which include an account of the diffusion of electric charges to the electrodes, and also with experimental results. Calculations, which include diffusion of charges, agree with experimental results of current and heat flux density as a function of radius if the Milne boundary condition is used at the anode surface rather than imposing zero charge density at the anode

Nonlinear approximation with general wave packets

DEFF Research Database (Denmark)

Borup, Lasse; Nielsen, Morten

2005-01-01

We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...

Approximations for stop-loss reinsurance premiums

NARCIS (Netherlands)

Reijnen, Rajko; Albers, Willem/Wim; Kallenberg, W.C.M.

2005-01-01

Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are

Approximation properties of haplotype tagging

Directory of Open Access Journals (Sweden)

Dreiseitl Stephan

2006-01-01

Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.

Approximation for the adjoint neutron spectrum

International Nuclear Information System (INIS)

Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

2002-01-01

The proposal of this work is the determination of an analytical approximation which is capable to reproduce the adjoint neutron flux for the energy range of the narrow resonances (NR). In a previous work we developed a method for the calculation of the adjoint spectrum which was calculated from the adjoint neutron balance equations, that were obtained by the collision probabilities method, this method involved a considerable quantity of numerical calculation. In the analytical method some approximations were done, like the multiplication of the escape probability in the fuel by the adjoint flux in the moderator, and after these approximations, taking into account the case of the narrow resonances, were substituted in the adjoint neutron balance equation for the fuel, resulting in an analytical approximation for the adjoint flux. The results obtained in this work were compared to the results generated with the reference method, which demonstrated a good and precise results for the adjoint neutron flux for the narrow resonances. (author)

Operator approximant problems arising from quantum theory

CERN Document Server

Maher, Philip J

2017-01-01

This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.

Non-Linear Approximation of Bayesian Update

KAUST Repository

Litvinenko, Alexander

2016-01-01

We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

Quirks of Stirling's Approximation

Science.gov (United States)

Macrae, Roderick M.; Allgeier, Benjamin M.

2013-01-01

Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…

Non-Linear Approximation of Bayesian Update

KAUST Repository

Litvinenko, Alexander

2016-06-23

We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

Approximations to camera sensor noise

Science.gov (United States)

Jin, Xiaodan; Hirakawa, Keigo

2013-02-01

Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.

APPROXIMATIONS TO PERFORMANCE MEASURES IN QUEUING SYSTEMS

Directory of Open Access Journals (Sweden)

Kambo, N. S.

2012-11-01

Full Text Available Approximations to various performance measures in queuing systems have received considerable attention because these measures have wide applicability. In this paper we propose two methods to approximate the queuing characteristics of a GI/M/1 system. The first method is non-parametric in nature, using only the first three moments of the arrival distribution. The second method treads the known path of approximating the arrival distribution by a mixture of two exponential distributions by matching the first three moments. Numerical examples and optimal analysis of performance measures of GI/M/1 queues are provided to illustrate the efficacy of the methods, and are compared with benchmark approximations.

Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities

KAUST Repository

Cheon, Sooyoung

2013-02-16

Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.

Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities

KAUST Repository

Cheon, Sooyoung; Liang, Faming; Chen, Yuguo; Yu, Kai

2013-01-01

Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.

Approximate Bayesian evaluations of measurement uncertainty

Science.gov (United States)

Possolo, Antonio; Bodnar, Olha

2018-04-01

The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

Improved radiative corrections for (e,e'p) experiments: Beyond the peaking approximation and implications of the soft-photon approximation

International Nuclear Information System (INIS)

Weissbach, F.; Hencken, K.; Rohe, D.; Sick, I.; Trautmann, D.

2006-01-01

Analyzing (e,e ' p) experimental data involves corrections for radiative effects which change the interaction kinematics and which have to be carefully considered in order to obtain the desired accuracy. Missing momentum and energy due to bremsstrahlung have so far often been incorporated into the simulations and the experimental analyses using the peaking approximation. It assumes that all bremsstrahlung is emitted in the direction of the radiating particle. In this article we introduce a full angular Monte Carlo simulation method which overcomes this approximation. As a test, the angular distribution of the bremsstrahlung photons is reconstructed from H(e,e ' p) data. Its width is found to be underestimated by the peaking approximation and described much better by the approach developed in this work. The impact of the soft-photon approximation on the photon angular distribution is found to be minor as compared to the impact of the peaking approximation. (orig.)

Trajectory averaging for stochastic approximation MCMC algorithms

KAUST Repository

Liang, Faming

2010-10-01

The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.

Toward a consistent random phase approximation based on the relativistic Hartree approximation

International Nuclear Information System (INIS)

Price, C.E.; Rost, E.; Shepard, J.R.; McNeil, J.A.

1992-01-01

We examine the random phase approximation (RPA) based on a relativistic Hartree approximation description for nuclear ground states. This model includes contributions from the negative energy sea at the one-loop level. We emphasize consistency between the treatment of the ground state and the RPA. This consistency is important in the description of low-lying collective levels but less important for the longitudinal (e,e') quasielastic response. We also study the effect of imposing a three-momentum cutoff on negative energy sea contributions. A cutoff of twice the nucleon mass improves agreement with observed spin-orbit splittings in nuclei compared to the standard infinite cutoff results, an effect traceable to the fact that imposing the cutoff reduces m * /m. Consistency is much more important than the cutoff in the description of low-lying collective levels. The cutoff model also provides excellent agreement with quasielastic (e,e') data

Seismic wave extrapolation using lowrank symbol approximation

KAUST Repository

Fomel, Sergey

2012-04-30

We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.

Approximation algorithms for guarding holey polygons ...

African Journals Online (AJOL)

Guarding edges of polygons is a version of art gallery problem.The goal is finding the minimum number of guards to cover the edges of a polygon. This problem is NP-hard, and to our knowledge there are approximation algorithms just for simple polygons. In this paper we present two approximation algorithms for guarding ...

Approximation properties of fine hyperbolic graphs

Indian Academy of Sciences (India)

2010 Mathematics Subject Classification. 46L07. 1. Introduction. Given a countable discrete group G, some nice approximation properties for the reduced. C∗-algebras C∗ r (G) can give us the approximation properties of G. For example, Lance. [7] proved that the nuclearity of C∗ r (G) is equivalent to the amenability of G; ...

Interaction potential for two different atoms

International Nuclear Information System (INIS)

Kuzmichev, V.E.; Peresypkin, V.V.

1991-01-01

Using the rigorous approach to the nonrelativistic four Coulomb particle problem the interaction potentials between an ordinary hydrogen and muonic-hydrogen atoms at large: R>a e +a μ (1), and intermediate: a e >R>>a μ (2) distances, where a e and a μ are the Bohr radii, are calculated in the adiabatic approximation. The van der Waals potential constants in the region (1) and an explicit potential form in the region (2) taking into account both the polarization effects and the electron screening corrections are determined. 10 refs

Introduction to the theory of magnetism

CERN Document Server

Wagner, D

2013-01-01

Introduction to the Theory of Magnetism is an introductory text on the theory of magnetism. The discussions are organized around diamagnetism, paramagnetism, and ferromagnetism. The exchange interaction and the resulting many-particle problem for a system of atomic spins are also considered, and the properties of this system are examined in several approximations. This book is comprised of three chapters and begins with a review of the fundamental effects of diamagnetism, paying particular attention to the Bohr-van Leeuwen theorem, the Fermi gas, Landau levels, and cyclotron resonance. The dia

Approximate number word knowledge before the cardinal principle.

Science.gov (United States)

Gunderson, Elizabeth A; Spaepen, Elizabet; Levine, Susan C

2015-02-01

Approximate number word knowledge-understanding the relation between the count words and the approximate magnitudes of sets-is a critical piece of knowledge that predicts later math achievement. However, researchers disagree about when children first show evidence of approximate number word knowledge-before, or only after, they have learned the cardinal principle. In two studies, children who had not yet learned the cardinal principle (subset-knowers) produced sets in response to number words (verbal comprehension task) and produced number words in response to set sizes (verbal production task). As evidence of approximate number word knowledge, we examined whether children's numerical responses increased with increasing numerosity of the stimulus. In Study 1, subset-knowers (ages 3.0-4.2 years) showed approximate number word knowledge above their knower-level on both tasks, but this effect did not extend to numbers above 4. In Study 2, we collected data from a broader age range of subset-knowers (ages 3.1-5.6 years). In this sample, children showed approximate number word knowledge on the verbal production task even when only examining set sizes above 4. Across studies, children's age predicted approximate number word knowledge (above 4) on the verbal production task when controlling for their knower-level, study (1 or 2), and parents' education, none of which predicted approximation ability. Thus, children can develop approximate knowledge of number words up to 10 before learning the cardinal principle. Furthermore, approximate number word knowledge increases with age and might not be closely related to the development of exact number word knowledge. Copyright © 2014 Elsevier Inc. All rights reserved.

Approximate Bayesian computation.

Directory of Open Access Journals (Sweden)

Mikael Sunnåker

Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.

Pawlak algebra and approximate structure on fuzzy lattice.

Science.gov (United States)

Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai

2014-01-01

The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.

Dynamical cluster approximation plus semiclassical approximation study for a Mott insulator and d-wave pairing

Science.gov (United States)

Kim, SungKun; Lee, Hunpyo

2017-06-01

Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.

Methods of Fourier analysis and approximation theory

CERN Document Server

Tikhonov, Sergey

2016-01-01

Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

Optimization and approximation

CERN Document Server

Pedregal, Pablo

2017-01-01

This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

Uniform analytic approximation of Wigner rotation matrices

Science.gov (United States)

Hoffmann, Scott E.

2018-02-01

We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

Multilevel Monte Carlo in Approximate Bayesian Computation

KAUST Repository

Jasra, Ajay

2017-02-13

In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.

Einstein's Materialism and Modern Tests of Quantum Mechanics

Science.gov (United States)

Vigier, J. P.

After a presentation of Einstein's and Bohr's antagonistic point of view on the interpretation of Quantum Mechanics an illustration of their conflicting positions in the particular case of Young's double slit experiment is presented. It is then shown that in their most recent form (i. e. time dependent neutron interferometry) these experiments suggest (if one accepts absolute energymomentum conservation in all individual microprocesses) that Einstein was right in the Bohr-Einstein controversy.Translated AbstractEinsteins Materialismus und heutige Tests der QuantenmechanikNach einer Darstellung von Einsteins und Bohrs antagonistischen Standpunkten in der Interpretation der Quantenmechanik werden ihre widersprüchlichen Positionen im speziellen Fall des Youngschen Doppelspaltexperiments dargestellt. Es wird dann gezeigt, daß diese Experimente in ihrer neuesten Form (d. h. zeitabhängige Neutroneninterferometrie) Einstein in der Bohr-Einsteinkontroverse recht gaben (wenn man absolute Energie-Impulserhaltung bei allen individuellen Mikroprozessen annimmt).

Hybrid Quantum Mechanical-Quasi-Classical Model for Evaluating Ionization and Stripping Cross Sections in Atom-Ion Collisions

CERN Document Server

Kaganovich, I D; Startsev, E

2005-01-01

Ion-atom ionization cross sections are needed in many applications employing the propagation of fast ions through matter. When experimental data or full-scale theoretical calculations are non-existent, approximate methods must be used. The most robust and easy-to-use approximations include the Born approximation of quantum mechanics and the quasi-classical approach utilizing classical mechanics together with the Bohr-Sommerfeld quantization rule.* The simplest method to extend the validity of both approaches is to combine them, i.e., use the two different approaches but only for the regions of impact parameters in which they are valid, and sum the results to obtain the total cross section. We have recently investigated theoretically and experimentally the stripping of more than 18 different pairs of projectile and target atoms in the range of 3-38 MeV/amu to study the range of validity of various approximations. The results of the modified approach agree better with the experimental data than either the Born ...

Approximation Properties of Certain Summation Integral Type Operators

Directory of Open Access Journals (Sweden)

Patel P.

2015-03-01

Full Text Available In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

Semiclassical initial value approximation for Green's function.

Science.gov (United States)

Kay, Kenneth G

2010-06-28

A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincare surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.

Einstein and the Quantum: The Secret Life of EPR

Science.gov (United States)

Fine, Arthur

2006-05-01

Locality, separation and entanglement -- 1930s style. Starting with Solvay 1927, we'll explore the background to the 1935 paper by Einstein, Podolsky and Rosen: how it was composed, the actual argument and principles used, and how the paper was received by Schroedinger, and others. We'll also look at Bohr's response: the extent to which Bohr connects with what Einstein was after in EPR and the extent to which EPR marks a shift in Bohr's thinking about the quantum theory. Time permitting, we will contrast EPR with Bell's theorem.

The adiabatic approximation in multichannel scattering

International Nuclear Information System (INIS)

Schulte, A.M.

1978-01-01

Using two-dimensional models, an attempt has been made to get an impression of the conditions of validity of the adiabatic approximation. For a nucleon bound to a rotating nucleus the Coriolis coupling is neglected and the relation between this nuclear Coriolis coupling and the classical Coriolis force has been examined. The approximation for particle scattering from an axially symmetric rotating nucleus based on a short duration of the collision, has been combined with an approximation based on the limitation of angular momentum transfer between particle and nucleus. Numerical calculations demonstrate the validity of the new combined method. The concept of time duration for quantum mechanical collisions has also been studied, as has the collective description of permanently deformed nuclei. (C.F.)

Minimal entropy approximation for cellular automata

International Nuclear Information System (INIS)

Fukś, Henryk

2014-01-01

We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim. (paper)

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

Bohr's complementarity principle; quantum mechanics; mutual exclusiveness; quantum entanglement; uncertainty principle. ... casting light on the origin of complementarity in quantum interferometric experiments, the whole issue is reviewed on the basis of our earlier precise formulation of Bohr's complementarity principle.

Function approximation using combined unsupervised and supervised learning.

Science.gov (United States)

Andras, Peter

2014-03-01

Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.

Hardness and Approximation for Network Flow Interdiction

OpenAIRE

Chestnut, Stephen R.; Zenklusen, Rico

2015-01-01

In the Network Flow Interdiction problem an adversary attacks a network in order to minimize the maximum s-t-flow. Very little is known about the approximatibility of this problem despite decades of interest in it. We present the first approximation hardness, showing that Network Flow Interdiction and several of its variants cannot be much easier to approximate than Densest k-Subgraph. In particular, any $n^{o(1)}$-approximation algorithm for Network Flow Interdiction would imply an $n^{o(1)}...

Approximate reasoning in physical systems

International Nuclear Information System (INIS)

Mutihac, R.

1991-01-01

The theory of fuzzy sets provides excellent ground to deal with fuzzy observations (uncertain or imprecise signals, wavelengths, temperatures,etc.) fuzzy functions (spectra and depth profiles) and fuzzy logic and approximate reasoning. First, the basic ideas of fuzzy set theory are briefly presented. Secondly, stress is put on application of simple fuzzy set operations for matching candidate reference spectra of a spectral library to an unknown sample spectrum (e.g. IR spectroscopy). Thirdly, approximate reasoning is applied to infer an unknown property from information available in a database (e.g. crystal systems). Finally, multi-dimensional fuzzy reasoning techniques are suggested. (Author)

Face Recognition using Approximate Arithmetic

DEFF Research Database (Denmark)

Marso, Karol

Face recognition is image processing technique which aims to identify human faces and found its use in various different fields for example in security. Throughout the years this field evolved and there are many approaches and many different algorithms which aim to make the face recognition as effective...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....

Stochastic quantization and mean field approximation

International Nuclear Information System (INIS)

Jengo, R.; Parga, N.

1983-09-01

In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)

Approximative solutions of stochastic optimization problem

Czech Academy of Sciences Publication Activity Database

Lachout, Petr

2010-01-01

Roč. 46, č. 3 (2010), s. 513-523 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic optimization problem * sensitivity * approximative solution Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/lachout-approximative solutions of stochastic optimization problem.pdf

Trajectory averaging for stochastic approximation MCMC algorithms

KAUST Repository

Liang, Faming

2010-01-01

to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic

Reduction of Linear Programming to Linear Approximation

OpenAIRE

Vaserstein, Leonid N.

2006-01-01

It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.

Thin-wall approximation in vacuum decay: A lemma

Science.gov (United States)

Brown, Adam R.

2018-05-01

The "thin-wall approximation" gives a simple estimate of the decay rate of an unstable quantum field. Unfortunately, the approximation is uncontrolled. In this paper I show that there are actually two different thin-wall approximations and that they bracket the true decay rate: I prove that one is an upper bound and the other a lower bound. In the thin-wall limit, the two approximations converge. In the presence of gravity, a generalization of this lemma provides a simple sufficient condition for nonperturbative vacuum instability.

The Bohr Correspondence Principle

Indian Academy of Sciences (India)

IAS Admin

Deepak Dhar. Keywords. Correspondence principle, hy- drogen atom, Kepler orbit. Deepak Dhar works at the. Tata Institute of Funda- mental Research,. Mumbai. His research interests are mainly in the area of statistical physics. We consider the quantum-mechanical non-relati- vistic hydrogen atom. We show that for bound.

The Bohr Correspondence Principle

Indian Academy of Sciences (India)

Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 4. Current Issue Volume 23 | Issue 4. April 2018. Home · Volumes & Issues · Categories · Special Issues · Search · Editorial Board · Information for Authors · Subscription ...

Smooth function approximation using neural networks.

Science.gov (United States)

Ferrari, Silvia; Stengel, Robert F

2005-01-01

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

An improved saddlepoint approximation.

Science.gov (United States)

Gillespie, Colin S; Renshaw, Eric

2007-08-01

Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents. However, it suffers from the problem of not always yielding full support, and whilst [S. Wang, General saddlepoint approximations in the bootstrap, Prob. Stat. Lett. 27 (1992) 61.] neat scaling approach provides a solution to this hurdle, it leads to potentially inaccurate and aberrant results. We therefore propose several new ways of surmounting such difficulties, including: extending the inversion of the cumulant generating function to second-order; selecting an appropriate probability structure for higher-order cumulants (the standard moment closure procedure takes them to be zero); and, making subtle changes to the target cumulants and then optimising via the simplex algorithm.

Topology, calculus and approximation

CERN Document Server

Komornik, Vilmos

2017-01-01

Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...

Comparison of four support-vector based function approximators

NARCIS (Netherlands)

de Kruif, B.J.; de Vries, Theodorus J.A.

2004-01-01

One of the uses of the support vector machine (SVM), as introduced in V.N. Vapnik (2000), is as a function approximator. The SVM and approximators based on it, approximate a relation in data by applying interpolation between so-called support vectors, being a limited number of samples that have been

Coefficients Calculation in Pascal Approximation for Passive Filter Design

Directory of Open Access Journals (Sweden)

George B. Kasapoglu

2018-02-01

Full Text Available The recently modified Pascal function is further exploited in this paper in the design of passive analog filters. The Pascal approximation has non-equiripple magnitude, in contrast of the most well-known approximations, such as the Chebyshev approximation. A novelty of this work is the introduction of a precise method that calculates the coefficients of the Pascal function. Two examples are presented for the passive design to illustrate the advantages and the disadvantages of the Pascal approximation. Moreover, the values of the passive elements can be taken from tables, which are created to define the normalized values of these elements for the Pascal approximation, as Zverev had done for the Chebyshev, Elliptic, and other approximations. Although Pascal approximation can be implemented to both passive and active filter designs, a passive filter design is addressed in this paper, and the benefits and shortcomings of Pascal approximation are presented and discussed.

Recursive B-spline approximation using the Kalman filter

Directory of Open Access Journals (Sweden)

Jens Jauch

2017-02-01

Full Text Available This paper proposes a novel recursive B-spline approximation (RBA algorithm which approximates an unbounded number of data points with a B-spline function and achieves lower computational effort compared with previous algorithms. Conventional recursive algorithms based on the Kalman filter (KF restrict the approximation to a bounded and predefined interval. Conversely RBA includes a novel shift operation that enables to shift estimated B-spline coefficients in the state vector of a KF. This allows to adapt the interval in which the B-spline function can approximate data points during run-time.

Approximate Computing Techniques for Iterative Graph Algorithms

Energy Technology Data Exchange (ETDEWEB)

Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh; Kalyanaraman, Anantharaman; Chavarria Miranda, Daniel G.; Krishnamoorthy, Sriram

2017-12-18

Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with low impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.

Conditional Density Approximations with Mixtures of Polynomials

DEFF Research Database (Denmark)

Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre

2015-01-01

Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce...... two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities...

Mathematical analysis, approximation theory and their applications

CERN Document Server

Gupta, Vijay

2016-01-01

Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

On Love's approximation for fluid-filled elastic tubes

International Nuclear Information System (INIS)

Caroli, E.; Mainardi, F.

1980-01-01

A simple procedure is set up to introduce Love's approximation for wave propagation in thin-walled fluid-filled elastic tubes. The dispersion relation for linear waves and the radial profile for fluid pressure are determined in this approximation. It is shown that the Love approximation is valid in the low-frequency regime. (author)

WKB approximation in atomic physics

International Nuclear Information System (INIS)

Karnakov, Boris Mikhailovich

2013-01-01

Provides extensive coverage of the Wentzel-Kramers-Brillouin approximation and its applications. Presented as a sequence of problems with highly detailed solutions. Gives a concise introduction for calculating Rydberg states, potential barriers and quasistationary systems. This book has evolved from lectures devoted to applications of the Wentzel-Kramers-Brillouin- (WKB or quasi-classical) approximation and of the method of 1/N -expansion for solving various problems in atomic and nuclear physics. The intent of this book is to help students and investigators in this field to extend their knowledge of these important calculation methods in quantum mechanics. Much material is contained herein that is not to be found elsewhere. WKB approximation, while constituting a fundamental area in atomic physics, has not been the focus of many books. A novel method has been adopted for the presentation of the subject matter, the material is presented as a succession of problems, followed by a detailed way of solving them. The methods introduced are then used to calculate Rydberg states in atomic systems and to evaluate potential barriers and quasistationary states. Finally, adiabatic transition and ionization of quantum systems are covered.

Dead space and slope indices from the expiratory carbon dioxide tension-volume curve

NARCIS (Netherlands)

A.H. Kars (Alice); J.M. Bogaard (Jan); Th. Stijnen (Theo); J. de Vries; A.F.M. Verbraak (Anton); C. Hilvering

1997-01-01

textabstractThe slope of phase 3 and three noninvasively determined dead space estimates derived from the expiratory carbon dioxide tension (PCO2) versus volume curve, including the Bohr dead space (VD,Bohr), the Fowler dead space (VD,Fowler) and pre-interface expirate

SFU-driven transparent approximation acceleration on GPUs

NARCIS (Netherlands)

Li, A.; Song, S.L.; Wijtvliet, M.; Kumar, A.; Corporaal, H.

2016-01-01

Approximate computing, the technique that sacrifices certain amount of accuracy in exchange for substantial performance boost or power reduction, is one of the most promising solutions to enable power control and performance scaling towards exascale. Although most existing approximation designs

Approximate Networking for Universal Internet Access

Directory of Open Access Journals (Sweden)

Junaid Qadir

2017-12-01

Full Text Available Despite the best efforts of networking researchers and practitioners, an ideal Internet experience is inaccessible to an overwhelming majority of people the world over, mainly due to the lack of cost-efficient ways of provisioning high-performance, global Internet. In this paper, we argue that instead of an exclusive focus on a utopian goal of universally accessible “ideal networking” (in which we have a high throughput and quality of service as well as low latency and congestion, we should consider providing “approximate networking” through the adoption of context-appropriate trade-offs. In this regard, we propose to leverage the advances in the emerging trend of “approximate computing” that rely on relaxing the bounds of precise/exact computing to provide new opportunities for improving the area, power, and performance efficiency of systems by orders of magnitude by embracing output errors in resilient applications. Furthermore, we propose to extend the dimensions of approximate computing towards various knobs available at network layers. Approximate networking can be used to provision “Global Access to the Internet for All” (GAIA in a pragmatically tiered fashion, in which different users around the world are provided a different context-appropriate (but still contextually functional Internet experience.

Variational Gaussian approximation for Poisson data

Science.gov (United States)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Approximation in two-stage stochastic integer programming

NARCIS (Netherlands)

W. Romeijnders; L. Stougie (Leen); M. van der Vlerk

2014-01-01

htmlabstractApproximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solution value.

Approximation in two-stage stochastic integer programming

NARCIS (Netherlands)

Romeijnders, W.; Stougie, L.; van der Vlerk, M.H.

2014-01-01

Approximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solution value. However,

Magnus approximation in the adiabatic picture

International Nuclear Information System (INIS)

Klarsfeld, S.; Oteo, J.A.

1991-01-01

A simple approximate nonperturbative method is described for treating time-dependent problems that works well in the intermediate regime far from both the sudden and the adiabatic limits. The method consists of applying the Magnus expansion after transforming to the adiabatic basis defined by the eigenstates of the instantaneous Hamiltonian. A few exactly soluble examples are considered in order to assess the domain of validity of the approximation. (author) 32 refs., 4 figs

Decay and fission of the oriented nuclei

CERN Document Server

Kadmenskij, S G

2002-01-01

The fragment angular distributions for binary decay of oriented spherical and deformed nuclei with taking into account the correct transformational properties of wave functions under time inversion have been investigated. It has been shown that for description of fragment angular distributions the adiabatic approximation for collective rotational nuclear degrees of freedom is not correct. It has been demonstrated that this approximation is valid for description of spontaneous and induced low-energy nuclear fission. The dependence of partial fission widths on the orientation of the internal axes spins, projections of spins, and relative angular moments of fission fragments has been analyzed. It has been shown that the adiabatic approximation results in coherent interference of wave functions of fragments relative movement. This interference forms fragments the universal angular distributions of fission fragments for oriented nuclei. For these distributions the deviations from A. Bohr's formula have been invest...

Nuclei far from stability. Individual and collective excitations at low energy

International Nuclear Information System (INIS)

Meyer, M.

1984-01-01

The low energy structure of exotic nuclei is discussed in terms of self-consistent microscopic models. The experimental striking features of the spectroscopy of these nuclei are briefly surveyed and the schematic steps performed to obtain from effective N-N interactions their spectroscopic properties are presented. Their saturation and deformation properties are given by the Hartree-Fock approximation (HF). Then it is shown how to describe the dynamics of even-even exotic nuclei excited states by solving the complete Bohr Hamiltonian, built microscopically using the HF approximation and the adiabatic limit (and its derivatives) of the time-dependent HF approximation (ATDHF). The structure of odd and doubly odd nuclei is discussed in the framework of the unified model, ie the microscopic rotor + quasiparticles model. Finally possible future directions of experimental research concerning exotic nuclei are described and improvements or new theoretical approaches discussed [fr

Space-efficient path-reporting approximate distance oracles

DEFF Research Database (Denmark)

Elkin, Michael; Neiman, Ofer; Wulff-Nilsen, Christian

2016-01-01

We consider approximate path-reporting distance oracles, distance labeling and labeled routing with extremely low space requirements, for general undirected graphs. For distance oracles, we show how to break the nlog⁡n space bound of Thorup and Zwick if approximate paths rather than distances need...

Aspects of three field approximations: Darwin, frozen, EMPULSE

International Nuclear Information System (INIS)

Boyd, J.K.; Lee, E.P.; Yu, S.S.

1985-01-01

The traditional approach used to study high energy beam propagation relies on the frozen field approximation. A minor modification of the frozen field approximation yields the set of equations applied to the analysis of the hose instability. These models are constrasted with the Darwin field approximation. A statement is made of the Darwin model equations relevant to the analysis of the hose instability

On Convex Quadratic Approximation

NARCIS (Netherlands)

den Hertog, D.; de Klerk, E.; Roos, J.

2000-01-01

In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

All-Norm Approximation Algorithms

NARCIS (Netherlands)

Azar, Yossi; Epstein, Leah; Richter, Yossi; Woeginger, Gerhard J.; Penttonen, Martti; Meineche Schmidt, Erik

2002-01-01

A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different ℓ p norms. We address this problem by introducing the concept of an All-norm ρ-approximation

Approximation by Cylinder Surfaces

DEFF Research Database (Denmark)

Randrup, Thomas

1997-01-01

We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...

Approximate Noether symmetries and collineations for regular perturbative Lagrangians

Science.gov (United States)

Paliathanasis, Andronikos; Jamal, Sameerah

2018-01-01

Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying manifold. In particular we determine the generic Noether symmetry conditions for the approximate point symmetries and we find that for a class of perturbed Lagrangians, Noether symmetries are related to the elements of the Homothetic algebra of the metric which is defined by the unperturbed Lagrangian. Moreover, we discuss how exact symmetries become approximate symmetries. Finally, some applications are presented.

The Kantian framework of complementarity

Science.gov (United States)

Cuffaro, Michael

A growing number of commentators have, in recent years, noted the important affinities in the views of Immanuel Kant and Niels Bohr. While these commentators are correct, the picture they present of the connections between Bohr and Kant is painted in broad strokes; it is open to the criticism that these affinities are merely superficial. In this essay, I provide a closer, structural, analysis of both Bohr's and Kant's views that makes these connections more explicit. In particular, I demonstrate the similarities between Bohr's argument, on the one hand, that neither the wave nor the particle description of atomic phenomena pick out an object in the ordinary sense of the word, and Kant's requirement, on the other hand, that both 'mathematical' (having to do with magnitude) and 'dynamical' (having to do with an object's interaction with other objects) principles must be applicable to appearances in order for us to determine them as objects of experience. I argue that Bohr's 'complementarity interpretation' of quantum mechanics, which views atomic objects as idealizations, and which licenses the repeal of the principle of causality for the domain of atomic physics, is perfectly compatible with, and indeed follows naturally from a broadly Kantian epistemological framework.

Square well approximation to the optical potential

International Nuclear Information System (INIS)

Jain, A.K.; Gupta, M.C.; Marwadi, P.R.

1976-01-01

Approximations for obtaining T-matrix elements for a sum of several potentials in terms of T-matrices for individual potentials are studied. Based on model calculations for S-wave for a sum of two separable non-local potentials of Yukawa type form factors and a sum of two delta function potentials, it is shown that the T-matrix for a sum of several potentials can be approximated satisfactorily over all the energy regions by the sum of T-matrices for individual potentials. Based on this, an approximate method for finding T-matrix for any local potential by approximating it by a sum of suitable number of square wells is presented. This provides an interesting way to calculate the T-matrix for any arbitary potential in terms of Bessel functions to a good degree of accuracy. The method is applied to the Saxon-Wood potentials and good agreement with exact results is found. (author)

Uncertainty relations for approximation and estimation

Energy Technology Data Exchange (ETDEWEB)

Lee, Jaeha, E-mail: jlee@post.kek.jp [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Tsutsui, Izumi, E-mail: izumi.tsutsui@kek.jp [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)

2016-05-27

We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for proxy functions used for the approximation is given by Aharonov's weak value, which also determines the classical Fisher information in parameter estimation, turning our inequality into the genuine Cramér–Rao inequality. Since the standard form of the uncertainty relation arises as a special case of our inequality, and since the parameter estimation is available as well, our inequality can treat both the position–momentum and the time–energy relations in one framework albeit handled differently. - Highlights: • Several inequalities interpreted as uncertainty relations for approximation/estimation are derived from a single ‘versatile inequality’. • The ‘versatile inequality’ sets a limit on the approximation of an observable and/or the estimation of a parameter by another observable. • The ‘versatile inequality’ turns into an elaboration of the Robertson–Kennard (Schrödinger) inequality and the Cramér–Rao inequality. • Both the position–momentum and the time–energy relation are treated in one framework. • In every case, Aharonov's weak value arises as a key geometrical ingredient, deciding the optimal choice for the proxy functions.

Uncertainty relations for approximation and estimation

International Nuclear Information System (INIS)

Lee, Jaeha; Tsutsui, Izumi

2016-01-01

We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for proxy functions used for the approximation is given by Aharonov's weak value, which also determines the classical Fisher information in parameter estimation, turning our inequality into the genuine Cramér–Rao inequality. Since the standard form of the uncertainty relation arises as a special case of our inequality, and since the parameter estimation is available as well, our inequality can treat both the position–momentum and the time–energy relations in one framework albeit handled differently. - Highlights: • Several inequalities interpreted as uncertainty relations for approximation/estimation are derived from a single ‘versatile inequality’. • The ‘versatile inequality’ sets a limit on the approximation of an observable and/or the estimation of a parameter by another observable. • The ‘versatile inequality’ turns into an elaboration of the Robertson–Kennard (Schrödinger) inequality and the Cramér–Rao inequality. • Both the position–momentum and the time–energy relation are treated in one framework. • In every case, Aharonov's weak value arises as a key geometrical ingredient, deciding the optimal choice for the proxy functions.

Diophantine approximation

CERN Document Server

Schmidt, Wolfgang M

1980-01-01

"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)

Approximate Inference and Deep Generative Models

CERN Multimedia

CERN. Geneva

2018-01-01

Advances in deep generative models are at the forefront of deep learning research because of the promise they offer for allowing data-efficient learning, and for model-based reinforcement learning. In this talk I'll review a few standard methods for approximate inference and introduce modern approximations which allow for efficient large-scale training of a wide variety of generative models. Finally, I'll demonstrate several important application of these models to density estimation, missing data imputation, data compression and planning.

Approximation of the inverse G-frame operator

Indian Academy of Sciences (India)

... projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we like using finite-dimensional linear algebra.

Optical approximation in the theory of geometric impedance

International Nuclear Information System (INIS)

Stupakov, G.; Bane, K.L.F.; Zagorodnov, I.

2007-02-01

In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually equivalent to the approximation of geometric optics in electromagnetic theory. Using this approximation, we derive equations for the longitudinal impedance for arbitrary offsets, with respect to a reference orbit, of source and test particles. With the help of the Panofsky-Wenzel theorem we also obtain expressions for the transverse impedance (also for arbitrary offsets). We further simplify these expressions for the case of the small offsets that are typical for practical applications. Our final expressions for the impedance, in the general case, involve two dimensional integrals over various cross-sections of the transition. We further demonstrate, for several known axisymmetric examples, how our method is applied to the calculation of impedances. Finally, we discuss the accuracy of the optical approximation and its relation to the diffraction regime in the theory of impedance. (orig.)

APPROXIMATION OF FREE-FORM CURVE – AIRFOIL SHAPE

Directory of Open Access Journals (Sweden)

CHONG PERK LIN

2013-12-01

Full Text Available Approximation of free-form shape is essential in numerous engineering applications, particularly in automotive and aircraft industries. Commercial CAD software for the approximation of free-form shape is based almost exclusively on parametric polynomial and rational parametric polynomial. The parametric curve is defined by vector function of one independent variable R(u = (x(u, y(u, z(u, where 0≤u≤1. Bézier representation is one of the parametric functions, which is widely used in the approximating of free-form shape. Given a string of points with the assumption of sufficiently dense to characterise airfoil shape, it is desirable to approximate the shape with Bézier representation. The expectation is that the representation function is close to the shape within an acceptable working tolerance. In this paper, the aim is to explore the use of manual and automated methods for approximating section curve of airfoil with Bézier representation.

Conference on Abstract Spaces and Approximation

CERN Document Server

Szökefalvi-Nagy, B; Abstrakte Räume und Approximation; Abstract spaces and approximation

1969-01-01

The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici­ pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, Wiener-Hopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs littl...

Kullback-Leibler divergence and the Pareto-Exponential approximation.

Science.gov (United States)

Weinberg, G V

2016-01-01

Recent radar research interests in the Pareto distribution as a model for X-band maritime surveillance radar clutter returns have resulted in analysis of the asymptotic behaviour of this clutter model. In particular, it is of interest to understand when the Pareto distribution is well approximated by an Exponential distribution. The justification for this is that under the latter clutter model assumption, simpler radar detection schemes can be applied. An information theory approach is introduced to investigate the Pareto-Exponential approximation. By analysing the Kullback-Leibler divergence between the two distributions it is possible to not only assess when the approximation is valid, but to determine, for a given Pareto model, the optimal Exponential approximation.

Diagonal Pade approximations for initial value problems

International Nuclear Information System (INIS)

Reusch, M.F.; Ratzan, L.; Pomphrey, N.; Park, W.

1987-06-01

Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab

A test of the adhesion approximation for gravitational clustering

Science.gov (United States)

Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.

1993-01-01

We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

Hydrogen: Beyond the Classic Approximation

International Nuclear Information System (INIS)

Scivetti, Ivan

2003-01-01

The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position

Simultaneous approximation in scales of Banach spaces

International Nuclear Information System (INIS)

Bramble, J.H.; Scott, R.

1978-01-01

The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods

On transparent potentials: a Born approximation study

International Nuclear Information System (INIS)

Coudray, C.

1980-01-01

In the frame of the scattering inverse problem at fixed energy, a class of potentials transparent in Born approximation is obtained. All these potentials are spherically symmetric and are oscillating functions of the reduced radial variable. Amongst them, the Born approximation of the transparent potential of the Newton-Sabatier method is found. In the same class, quasi-transparent potentials are exhibited. Very general features of potentials transparent in Born approximation are then stated. And bounds are given for the exact scattering amplitudes corresponding to most of the potentials previously exhibited. These bounds, obtained at fixed energy, and for large values of the angular momentum, are found to be independent on the energy

A critical review on some aspects of the theory of fission

International Nuclear Information System (INIS)

Pauli, H.C.

1981-01-01

The lecture notes display briefly some of the facets which eventually will be part of a theory for the fission process. They cover some important aspects of our present understanding in a qualitative fashion and complement the existing review articles rather than replacing them. The notes include sections on (I) The Bohr-Wheeler Fission of a Drop, (II) The Strutinsky-Swiatecki Quantum Droplet, (III) The Question of Inertias of a Fluid in Motion, (IV) Some Selected Aspects of the Distributions of Mass and Kinetic Energy, and (V) Possible Relations Between the Phenomenological Models and Self-Consistent Field Approximations. (author)

A new vibrational level of the H2+ molecular ion

International Nuclear Information System (INIS)

Carbonell, J.; Lazauskas, R.; Delande, D.; Hilico, L.; Kilic, S.; Hilico, L.; Kilic, S.

2003-01-01

A new vibrational level of the molecular ion H 2 + with binding energy of 1.09 x 10 -9 a.u. ∼ 30 neV below the first dissociation limit is predicted, using highly accurate numerical non-relativistic quantum calculations, which go beyond the Born-Oppenheimer approximation. It is the first-excited vibrational level v=1 of the 2pσ u electronic state, antisymmetric with respect to the exchange of the two protons, with orbital angular momentum L=0. It manifests itself as a huge p - H scattering length of a = 750 ± 5 Bohr radii. (authors)

Low-energy coupling of individual and collective degrees of freedom: a general microscopic approach

International Nuclear Information System (INIS)

Quentin, P.; Meyer, M.

1988-01-01

A general microscopic approach of low energy coupling of individual and collective degrees of freedom is presented. The ingredients of a Bohr-Mottelson unified model description are determined consistently from the Skyrme SIII effective interaction, through the adiabatic limit of the time-dependent Hartree-Fock-Bogoliubov approximation. Three specific aspects will be mostly developed: i) the effect of pairing correlations on adiabatic mass parameters and collective dynamics; ii) a consistent coupling of collective and individual degrees of freedom to describe odd nuclei; iii) a study of spectroscopic data in odd-odd nuclei as a test of effective nucleon-nucleon interactions. (author)

Approximate supernova remnant dynamics with cosmic ray production

Science.gov (United States)

Voelk, H. J.; Drury, L. O.; Dorfi, E. A.

1985-01-01

Supernova explosions are the most violent and energetic events in the galaxy and have long been considered probably sources of Cosmic Rays. Recent shock acceleration models treating the Cosmic Rays (CR's) as test particles nb a prescribed Supernova Remnant (SNR) evolution, indeed indicate an approximate power law momentum distribution f sub source (p) approximation p(-a) for the particles ultimately injected into the Interstellar Medium (ISM). This spectrum extends almost to the momentum p = 1 million GeV/c, where the break in the observed spectrum occurs. The calculated power law index approximately less than 4.2 agrees with that inferred for the galactic CR sources. The absolute CR intensity can however not be well determined in such a test particle approximation.

Approximate supernova remnant dynamics with cosmic ray production

International Nuclear Information System (INIS)

Voelk, H.J.; Drury, L.O.; Dorfi, E.A.

1985-01-01

Supernova explosions are the most violent and energetic events in the galaxy and have long been considered probable sources of cosmic rays. Recent shock acceleration models treating the cosmic rays (CR's) as test particles nb a prescribed supernova remnant (SNR) evolution, indeed indicate an approximate power law momentum distribution f sub source (p) approximation p(-a) for the particles ultimately injected into the interstellar medium (ISM). This spectrum extends almost to the momentum p = 1 million GeV/c, where the break in the observed spectrum occurs. The calculated power law index approximately less than 4.2 agrees with that inferred for the galactic CR sources. The absolute CR intensity can however not be well determined in such a test particle approximation

Geometric convergence of some two-point Pade approximations

International Nuclear Information System (INIS)

Nemeth, G.

1983-01-01

The geometric convergences of some two-point Pade approximations are investigated on the real positive axis and on certain infinite sets of the complex plane. Some theorems concerning the geometric convergence of Pade approximations are proved, and bounds on geometric convergence rates are given. The results may be interesting considering the applications both in numerical computations and in approximation theory. As a specific case, the numerical calculations connected with the plasma dispersion function may be performed. (D.Gy.)

Standard filter approximations for low power Continuous Wavelet Transforms.

Science.gov (United States)

Casson, Alexander J; Rodriguez-Villegas, Esther

2010-01-01

Analogue domain implementations of the Continuous Wavelet Transform (CWT) have proved popular in recent years as they can be implemented at very low power consumption levels. This is essential for use in wearable, long term physiological monitoring systems. Present analogue CWT implementations rely on taking mathematical a approximation of the wanted mother wavelet function to give a filter transfer function that is suitable for circuit implementation. This paper investigates the use of standard filter approximations (Butterworth, Chebyshev, Bessel) as an alternative wavelet approximation technique. This extends the number of approximation techniques available for generating analogue CWT filters. An example ECG analysis shows that signal information can be successfully extracted using these CWT approximations.

Ordering, symbols and finite-dimensional approximations of path integrals

International Nuclear Information System (INIS)

Kashiwa, Taro; Sakoda, Seiji; Zenkin, S.V.

1994-01-01

We derive general form of finite-dimensional approximations of path integrals for both bosonic and fermionic canonical systems in terms of symbols of operators determined by operator ordering. We argue that for a system with a given quantum Hamiltonian such approximations are independent of the type of symbols up to terms of O(ε), where ε of is infinitesimal time interval determining the accuracy of the approximations. A new class of such approximations is found for both c-number and Grassmannian dynamical variables. The actions determined by the approximations are non-local and have no classical continuum limit except the cases of pq- and qp-ordering. As an explicit example the fermionic oscillator is considered in detail. (author)

Hardness of approximation for strip packing

DEFF Research Database (Denmark)

Adamaszek, Anna Maria; Kociumaka, Tomasz; Pilipczuk, Marcin

2017-01-01

Strip packing is a classical packing problem, where the goal is to pack a set of rectangular objects into a strip of a given width, while minimizing the total height of the packing. The problem has multiple applications, for example, in scheduling and stock-cutting, and has been studied extensively......)-approximation by two independent research groups [FSTTCS 2016,WALCOM 2017]. This raises a questionwhether strip packing with polynomially bounded input data admits a quasi-polynomial time approximation scheme, as is the case for related twodimensional packing problems like maximum independent set of rectangles or two...

Adaptive control using neural networks and approximate models.

Science.gov (United States)

Narendra, K S; Mukhopadhyay, S

1997-01-01

The NARMA model is an exact representation of the input-output behavior of finite-dimensional nonlinear discrete-time dynamical systems in a neighborhood of the equilibrium state. However, it is not convenient for purposes of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate methods are used for realizing the neural controllers to overcome computational complexity. In this paper, we introduce two classes of models which are approximations to the NARMA model, and which are linear in the control input. The latter fact substantially simplifies both the theoretical analysis as well as the practical implementation of the controller. Extensive simulation studies have shown that the neural controllers designed using the proposed approximate models perform very well, and in many cases even better than an approximate controller designed using the exact NARMA model. In view of their mathematical tractability as well as their success in simulation studies, a case is made in this paper that such approximate input-output models warrant a detailed study in their own right.

Analytical models approximating individual processes: a validation method.

Science.gov (United States)

Favier, C; Degallier, N; Menkès, C E

2010-12-01

Upscaling population models from fine to coarse resolutions, in space, time and/or level of description, allows the derivation of fast and tractable models based on a thorough knowledge of individual processes. The validity of such approximations is generally tested only on a limited range of parameter sets. A more general validation test, over a range of parameters, is proposed; this would estimate the error induced by the approximation, using the original model's stochastic variability as a reference. This method is illustrated by three examples taken from the field of epidemics transmitted by vectors that bite in a temporally cyclical pattern, that illustrate the use of the method: to estimate if an approximation over- or under-fits the original model; to invalidate an approximation; to rank possible approximations for their qualities. As a result, the application of the validation method to this field emphasizes the need to account for the vectors' biology in epidemic prediction models and to validate these against finer scale models. Copyright © 2010 Elsevier Inc. All rights reserved.

The Hartree-Fock seniority approximation

International Nuclear Information System (INIS)

Gomez, J.M.G.; Prieto, C.

1986-01-01

A new self-consistent method is used to take into account the mean-field and the pairing correlations in nuclei at the same time. We call it the Hartree-Fock seniority approximation, because the long-range and short-range correlations are treated in the frameworks of Hartree-Fock theory and the seniority scheme. The method is developed in detail for a minimum-seniority variational wave function in the coordinate representation for an effective interaction of the Skyrme type. An advantage of the present approach over the Hartree-Fock-Bogoliubov theory is the exact conservation of angular momentum and particle number. Furthermore, the computational effort required in the Hartree-Fock seniority approximation is similar to that ofthe pure Hartree-Fock picture. Some numerical calculations for Ca isotopes are presented. (orig.)

Quasi-fractional approximation to the Bessel functions

International Nuclear Information System (INIS)

Guerrero, P.M.L.

1989-01-01

In this paper the authors presents a simple Quasi-Fractional Approximation for Bessel Functions J ν (x), (- 1 ≤ ν < 0.5). This has been obtained by extending a method published which uses simultaneously power series and asymptotic expansions. Both functions, exact and approximated, coincide in at least two digits for positive x, and ν between - 1 and 0,4

Scattering theory and effective medium approximations to heterogeneous materials

International Nuclear Information System (INIS)

Gubernatis, J.E.

1977-01-01

The formal analogy existing between problems studied in the microscopic theory of disordered alloys and problems concerned with the effective (macroscopic) behavior of heterogeneous materials is discussed. Attention is focused on (1) analogous approximations (effective medium approximations) developed for the microscopic problems by scattering theory concepts and techniques, but for the macroscopic problems principally by intuitive means, (2) the link, provided by scattering theory, of the intuitively developed approximations to a well-defined perturbative analysis, (3) the possible presence of conditionally convergent integrals in effective medium approximations

Approximate modal analysis using Fourier decomposition

International Nuclear Information System (INIS)

Kozar, Ivica; Jericevic, Zeljko; Pecak, Tatjana

2010-01-01

The paper presents a novel numerical approach for approximate solution of eigenvalue problem and investigates its suitability for modal analysis of structures with special attention on plate structures. The approach is based on Fourier transformation of the matrix equation into frequency domain and subsequent removal of potentially less significant frequencies. The procedure results in a much reduced problem that is used in eigenvalue calculation. After calculation eigenvectors are expanded and transformed back into time domain. The principles are presented in Jericevic [1]. Fourier transform can be formulated in a way that some parts of the matrix that should not be approximated are not transformed but are fully preserved. In this paper we present formulation that preserves central or edge parts of the matrix and compare it with the formulation that performs transform on the whole matrix. Numerical experiments on transformed structural dynamic matrices describe quality of the approximations obtained in modal analysis of structures. On the basis of the numerical experiments, from the three approaches to matrix reduction one is recommended.

A Gaussian Approximation Potential for Silicon

Science.gov (United States)

Bernstein, Noam; Bartók, Albert; Kermode, James; Csányi, Gábor

We present an interatomic potential for silicon using the Gaussian Approximation Potential (GAP) approach, which uses the Gaussian process regression method to approximate the reference potential energy surface as a sum of atomic energies. Each atomic energy is approximated as a function of the local environment around the atom, which is described with the smooth overlap of atomic environments (SOAP) descriptor. The potential is fit to a database of energies, forces, and stresses calculated using density functional theory (DFT) on a wide range of configurations from zero and finite temperature simulations. These include crystalline phases, liquid, amorphous, and low coordination structures, and diamond-structure point defects, dislocations, surfaces, and cracks. We compare the results of the potential to DFT calculations, as well as to previously published models including Stillinger-Weber, Tersoff, modified embedded atom method (MEAM), and ReaxFF. We show that it is very accurate as compared to the DFT reference results for a wide range of properties, including low energy bulk phases, liquid structure, as well as point, line, and plane defects in the diamond structure.

Development of the relativistic impulse approximation

International Nuclear Information System (INIS)

Wallace, S.J.

1985-01-01

This talk contains three parts. Part I reviews the developments which led to the relativistic impulse approximation for proton-nucleus scattering. In Part II, problems with the impulse approximation in its original form - principally the low energy problem - are discussed and traced to pionic contributions. Use of pseudovector covariants in place of pseudoscalar ones in the NN amplitude provides more satisfactory low energy results, however, the difference between pseudovector and pseudoscalar results is ambiguous in the sense that it is not controlled by NN data. Only with further theoretical input can the ambiguity be removed. Part III of the talk presents a new development of the relativistic impulse approximation which is the result of work done in the past year and a half in collaboration with J.A. Tjon. A complete NN amplitude representation is developed and a complete set of Lorentz invariant amplitudes are calculated based on a one-meson exchange model and appropriate integral equations. A meson theoretical basis for the important pair contributions to proton-nucleus scattering is established by the new developments. 28 references

Local approximation of a metapopulation's equilibrium.

Science.gov (United States)

Barbour, A D; McVinish, R; Pollett, P K

2018-04-18

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously.

Approximate Bayesian recursive estimation

Czech Academy of Sciences Publication Activity Database

Kárný, Miroslav

2014-01-01

Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf

Pion-nucleus cross sections approximation

International Nuclear Information System (INIS)

Barashenkov, V.S.; Polanski, A.; Sosnin, A.N.

1990-01-01

Analytical approximation of pion-nucleus elastic and inelastic interaction cross-section is suggested, with could be applied in the energy range exceeding several dozens of MeV for nuclei heavier than beryllium. 3 refs.; 4 tabs

Causality problem in atomic physics

Energy Technology Data Exchange (ETDEWEB)

Bor, N

1985-10-01

The casuality problem in atomic physics is analysed by Bohr in a wide methodological context. The first part of the paper is a short historical essay picturing the entry of statistical concepts into physics. Bohr underlines a close relationship between an unavoidably probabilitic nature of the quantum theory and quantum postulates introducing the alien-to-classical-physics concepts of integrity, individuality of atomic processes. In the second central part of the paper Bohr discusses the casuality problems in atomic physics in detail and shows that their solution requires a careful analysis of the observation process. Proceeding from the program methodological requirement to describe the measuring instrumentation operation and observation results in the language of classical physics, he explains that the statistical character of the uncertainty relationships expresses a substantial specifically quantum constraint to the applicifically of classical conceptions analyses of microphenomena. Then Bohr refines in principle the notion ''phenomenon'', as one of the central notions among those he employed for the formulation of his complementarity principle. According to bohr a phenomenon should be under-stood as an unambiguously present situation of a completed experiment. Therefore, it is erroneous to speak of the phenomenon perturbation by the observation. The final part of the article deals with the discussion of methodological parallels of the quantum theory and relativity theory.

The causality problem in atomic physics

International Nuclear Information System (INIS)

Bor, N.

1985-01-01

The casuality problem in atomic physics is analysed by Bohr in a wide methodological context. The first part of the paper is a short historical essay picturing the entry of statistical concepts into physics. Bohr underlines a close relationship between an unavoidably probabilitic nature of the quantum theory and quantum postulates introducing the alien-to-classical-physics concepts of integrity, individuality of atomic processes. In the second central part of the paper Bohr discusses the casuality problems in atomic physics in detail and shows that their solution requires a careful analysis of the observation process. Proceeding from the program methodological requirement to describe the measuring instrumentation operation and observation results in the language of classical physics, he explains that the statistical character of the uncertainty relationships expresses a substantial specifically quantum constraint to the applicifically of classical conceptions analyses of microphenomena. Then Bohr refines in principle the notion ''phenomenon'', as one of the central notions among those he employed for the formulation of his complementarity principle. According to bohr a phenomenon should be under-stood as an unambiguously present situation of a completed experiment. Therefore, it is erroneous to speak of the phenomenon perturbation by the observation. The final part of the article deals with the discussion of methodological parallels of the quantum theory and relativity theory

Approximal morphology as predictor of approximal caries in primary molar teeth

DEFF Research Database (Denmark)

Cortes, A; Martignon, S; Qvist, V

2018-01-01

consent was given, participated. Upper and lower molar teeth of one randomly selected side received a 2-day temporarily separation. Bitewing radiographs and silicone impressions of interproximal area (IPA) were obtained. One-year procedures were repeated in 52 children (84%). The morphology of the distal...... surfaces of the first molar teeth and the mesial surfaces on the second molar teeth (n=208) was scored from the occlusal aspect on images from the baseline resin models resulting in four IPA variants: concave-concave; concave-convex; convex-concave, and convex-convex. Approximal caries on the surface...

Finite Element Approximation of the FENE-P Model

OpenAIRE

Barrett , John ,; Boyaval , Sébastien

2017-01-01

We extend our analysis on the Oldroyd-B model in Barrett and Boyaval [1] to consider the finite element approximation of the FENE-P system of equations, which models a dilute polymeric fluid, in a bounded domain $D $\\subset$ R d , d = 2 or 3$, subject to no flow boundary conditions. Our schemes are based on approximating the pressure and the symmetric conforma-tion tensor by either (a) piecewise constants or (b) continuous piecewise linears. In case (a) the velocity field is approximated by c...

Nuclear data processing, analysis, transformation and storage with Pade-approximants

International Nuclear Information System (INIS)

Badikov, S.A.; Gay, E.V.; Guseynov, M.A.; Rabotnov, N.S.

1992-01-01

A method is described to generate rational approximants of high order with applications to neutron data handling. The problems considered are: The approximations of neutron cross-sections in resonance region producing the parameters for Adler-Adler type formulae; calculations of resulting rational approximants' errors given in analytical form allowing to compute the error at any energy point inside the interval of approximation; calculations of the correlation coefficient of error values in two arbitrary points provided that experimental errors are independent and normally distributed; a method of simultaneous generation of a few rational approximants with identical set of poles; functionals other than LSM; two-dimensional approximation. (orig.)

Lattice quantum chromodynamics with approximately chiral fermions

International Nuclear Information System (INIS)

Hierl, Dieter

2008-05-01

In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the Θ + pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

Lattice quantum chromodynamics with approximately chiral fermions

Energy Technology Data Exchange (ETDEWEB)

Hierl, Dieter

2008-05-15

In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

Rollout sampling approximate policy iteration

NARCIS (Netherlands)

Dimitrakakis, C.; Lagoudakis, M.G.

2008-01-01

Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a

Using function approximation to determine neural network accuracy

International Nuclear Information System (INIS)

Wichman, R.F.; Alexander, J.

2013-01-01

Many, if not most, control processes demonstrate nonlinear behavior in some portion of their operating range and the ability of neural networks to model non-linear dynamics makes them very appealing for control. Control of high reliability safety systems, and autonomous control in process or robotic applications, however, require accurate and consistent control and neural networks are only approximators of various functions so their degree of approximation becomes important. In this paper, the factors affecting the ability of a feed-forward back-propagation neural network to accurately approximate a non-linear function are explored. Compared to pattern recognition using a neural network for function approximation provides an easy and accurate method for determining the network's accuracy. In contrast to other techniques, we show that errors arising in function approximation or curve fitting are caused by the neural network itself rather than scatter in the data. A method is proposed that provides improvements in the accuracy achieved during training and resulting ability of the network to generalize after training. Binary input vectors provided a more accurate model than with scalar inputs and retraining using a small number of the outlier x,y pairs improved generalization. (author)

Methods of Approximation Theory in Complex Analysis and Mathematical Physics

CERN Document Server

Saff, Edward

1993-01-01

The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...

Beyond the random phase approximation

DEFF Research Database (Denmark)

Olsen, Thomas; Thygesen, Kristian S.

2013-01-01

We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...... functional theory and the adiabatic connection fluctuation-dissipation theorem and contains no fitted parameters. The new kernel is shown to preserve the accurate description of dispersive interactions from RPA while significantly improving the description of short-range correlation in molecules, insulators......, and metals. For molecular atomization energies, the rALDA is a factor of 7 better than RPA and a factor of 4 better than the Perdew-Burke-Ernzerhof (PBE) functional when compared to experiments, and a factor of 3 (1.5) better than RPA (PBE) for cohesive energies of solids. For transition metals...

Vacancy-rearrangement theory in the first Magnus approximation

International Nuclear Information System (INIS)

Becker, R.L.

1984-01-01

In the present paper we employ the first Magnus approximation (M1A), a unitarized Born approximation, in semiclassical collision theory. We have found previously that the M1A gives a substantial improvement over the first Born approximation (B1A) and can give a good approximation to a full coupled channels calculation of the mean L-shell vacancy probability per electron, p/sub L/, when the L-vacancies are accompanied by a K-shell vacancy (p/sub L/ is obtained experimentally from measurements of K/sub α/-satellite intensities). For sufficiently strong projectile-electron interactions (sufficiently large Z/sub p/ or small v) the M1A ceases to reproduce the coupled channels results, but it is accurate over a much wider range of Z/sub p/ and v than the B1A. 27 references

I grandi della fisica da Platone a Heisenberg

CERN Document Server

Von Weizsäcker, Carl Friedrich

2002-01-01

Parmenide ; Platone ; Aristotele ; Copernico, Keplero, Galilei ; Galileo Galilei ; Cartesio ; Gottfried Wilhelm Leibniz ; Cartesio, Newton, Leibniz, Kant ; Immanuel Kant ; Johann Wolfgang Goethe ; Robert Meyer ; Albert Einstein ; Niels Bohr ; Paul Adrien Maurice Dirac ; Niels Bohr e Werner Heisenberg, un ricordo del 1932 ; Werner Heisenberg ; Heisenberg, fisico e filosofo ; l'interpretazione filosofica della fisica moderna.

Minimax rational approximation of the Fermi-Dirac distribution

Science.gov (United States)

Moussa, Jonathan E.

2016-10-01

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ɛ-1)) poles to achieve an error tolerance ɛ at temperature β-1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. This is particularly beneficial when Δ ≫ Δocc, such as in electronic structure calculations that use a large basis set.

Fast wavelet based sparse approximate inverse preconditioner

Energy Technology Data Exchange (ETDEWEB)

Wan, W.L. [Univ. of California, Los Angeles, CA (United States)

1996-12-31

Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.

Approximate Coulomb effects in the three-body scattering problem

International Nuclear Information System (INIS)

Haftel, M.I.; Zankel, H.

1981-01-01

From the momentum space Faddeev equations we derive approximate expressions which describe the Coulomb-nuclear interference in the three-body elastic scattering, rearrangement, and breakup problems and apply the formalism to p-d elastic scattering. The approximations treat the Coulomb interference as mainly a two-body effect, but we allow for the charge distribution of the deuteron in the p-d calculations. Real and imaginary parts of the Coulomb correction to the elastic scattering phase shifts are described in terms of on-shell quantities only. In the case of pure Coulomb breakup we recover the distorted-wave Born approximation result. Comparing the derived approximation with the full Faddeev p-d elastic scattering calculation, which includes the Coulomb force, we obtain good qualitative agreement in S and P waves, but disagreement in repulsive higher partial waves. The on-shell approximation investigated is found to be superior to other current approximations. The calculated differential cross sections at 10 MeV raise the question of whether there is a significant Coulomb-nuclear interference at backward angles

Framework for sequential approximate optimization

NARCIS (Netherlands)

Jacobs, J.H.; Etman, L.F.P.; Keulen, van F.; Rooda, J.E.

2004-01-01

An object-oriented framework for Sequential Approximate Optimization (SAO) isproposed. The framework aims to provide an open environment for thespecification and implementation of SAO strategies. The framework is based onthe Python programming language and contains a toolbox of Python

Perturbative corrections for approximate inference in gaussian latent variable models

DEFF Research Database (Denmark)

Opper, Manfred; Paquet, Ulrich; Winther, Ole

2013-01-01

Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact b...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....

Approximating the physical inner product of loop quantum cosmology

International Nuclear Information System (INIS)

Bahr, Benjamin; Thiemann, Thomas

2007-01-01

In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We find that the approximation is able to recover the analytic solution of the problem, which consolidates hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity

Two-body potentials in the collective model

International Nuclear Information System (INIS)

Draayer, J.P.; Rosensteel, G.; Arizona State Univ., Tempe

1982-01-01

The question, 'How well can a 1+2-body shell-model interaction represent a many-body potential.', is addressed by optimally expanding the (1+2+3)-body potential β 3 cos 3γ and the (1+2+3+4)-body potential β 4 of the Bohr-Mottelson collective model in terms of (1+2)-body operators. It is found that the correlation of β 4 with its approximation is greater than 97% throughout the sd shell. Although β 3 cos 3γ is also well approximated in the first half of the sd shell where it has more than 80% correlation with its approximation, the correlation drops abruptly at 28 Si to 50% and remains low in the second half of the shell. The approximations are primarily sums of the various components of the quadrupole-quadrupole interaction connecting different major oscillator shells. The results suggest that axially-symmetric deformation can be represented by simple (1+2)-body operators, whereas asymmetric shapes require non-simple 3-body terms. (orig.)

Polynomial approximation of functions in Sobolev spaces

International Nuclear Information System (INIS)

Dupont, T.; Scott, R.

1980-01-01

Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces

Nernst effect beyond the relaxation-time approximation

OpenAIRE

Pikulin, D. I.; Hou, Chang-Yu; Beenakker, C. W. J.

2011-01-01

Motivated by recent interest in the Nernst effect in cuprate superconductors, we calculate this magneto-thermo-electric effect for an arbitrary (anisotropic) quasiparticle dispersion relation and elastic scattering rate. The exact solution of the linearized Boltzmann equation is compared with the commonly used relaxation-time approximation. We find qualitative deficiencies of this approximation, to the extent that it can get the sign wrong of the Nernst coefficient. Ziman's improvement of the...

Contribution to the projected Hartree-Fock method and microscopic theory of coupling between rotation bands

International Nuclear Information System (INIS)

Brut, F.

1982-01-01

The spectroscopy of odd-A nuclei, in the 1p and 2s-1d shells, is studied in the framework of the projected Hartree-Fock method and by the generator coordinate method. The nuclear effective interactions of Cohen and Kurath, on the one hand, and of Kuo or Preedom-Wildenthal, on the other hand, are used. The binding energies, the nuclear spectra, the static moments and the electromagnetic transitions obtained by these two approaches are compared to the same quantities given by a complete diagonalization in the shell model basis. This study of light nuclei gives some possibilities to put in order the energy levels by coupled rotational bands. In the microscopic approach, thus we find all the elements of the unified model of Bohr and Mottelson. To give evidence of such a relation, the functions of the angle β, in the integrals of the projection method of Peierls and Yoccoz, for a Slater determinant, are developed in the vicinity of the bounds β = O and β = π. The microscopic coefficients are evaluated in the Hartree-Fock approximation, using the particle-hole formalism. Calculations are made for 20 Ne and 21 Ne and the resulting microscopic coefficients are compared with the corresponding terms of the unified model of Bohr and Mottelson [fr

Resonance journal of science education

Indian Academy of Sciences (India)

IAS Admin

Sketch made by Niels Bohr in 1944 to illustrate the content of his debate with Einstein on the uncertainty principle at the 6th Solvay Conference in 1930. Niels Bohr (1885–1962). Sketch by Homi Bhabha. (Courtesy: TIFR, Bombay). Front Cover. 871. Science Smiles. Ayan Guha. 876. Back Cover. 948. Classics. Biology and ...

Consistent dynamical and statistical description of fission and comparison

Energy Technology Data Exchange (ETDEWEB)

Shunuan, Wang [Chinese Nuclear Data Center, Beijing, BJ (China)

1996-06-01

The research survey of consistent dynamical and statistical description of fission is briefly introduced. The channel theory of fission with diffusive dynamics based on Bohr channel theory of fission and Fokker-Planck equation and Kramers-modified Bohr-Wheeler expression according to Strutinsky method given by P.Frobrich et al. are compared and analyzed. (2 figs.).

Approximate Reanalysis in Topology Optimization

DEFF Research Database (Denmark)

Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole

2009-01-01

In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...

Approximate spatio-temporal top-k publish/subscribe

KAUST Repository

Chen, Lisi

2018-04-26

Location-based publish/subscribe plays a significant role in mobile information disseminations. In this light, we propose and study a novel problem of processing location-based top-k subscriptions over spatio-temporal data streams. We define a new type of approximate location-based top-k subscription, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription, that continuously feeds users with relevant spatio-temporal messages by considering textual similarity, spatial proximity, and information freshness. Different from existing location-based top-k subscriptions, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription can automatically adjust the triggering condition by taking the triggering score of other subscriptions into account. The group filtering efficacy can be substantially improved by sacrificing the publishing result quality with a bounded guarantee. We conduct extensive experiments on two real datasets to demonstrate the performance of the developed solutions.

Approximate spatio-temporal top-k publish/subscribe

KAUST Repository

Chen, Lisi; Shang, Shuo

2018-01-01

Location-based publish/subscribe plays a significant role in mobile information disseminations. In this light, we propose and study a novel problem of processing location-based top-k subscriptions over spatio-temporal data streams. We define a new type of approximate location-based top-k subscription, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription, that continuously feeds users with relevant spatio-temporal messages by considering textual similarity, spatial proximity, and information freshness. Different from existing location-based top-k subscriptions, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription can automatically adjust the triggering condition by taking the triggering score of other subscriptions into account. The group filtering efficacy can be substantially improved by sacrificing the publishing result quality with a bounded guarantee. We conduct extensive experiments on two real datasets to demonstrate the performance of the developed solutions.

Resummation of perturbative QCD by pade approximants

International Nuclear Information System (INIS)

Gardi, E.

1997-01-01

In this lecture I present some of the new developments concerning the use of Pade Approximants (PA's) for resuming perturbative series in QCD. It is shown that PA's tend to reduce the renormalization scale and scheme dependence as compared to truncated series. In particular it is proven that in the limit where the β function is dominated by the 1-loop contribution, there is an exact symmetry that guarantees invariance of diagonal PA's under changing the renormalization scale. In addition it is shown that in the large β 0 approximation diagonal PA's can be interpreted as a systematic method for approximating the flow of momentum in Feynman diagrams. This corresponds to a new multiple scale generalization of the Brodsky-Lepage-Mackenzie (BLM) method to higher orders. I illustrate the method with the Bjorken sum rule and the vacuum polarization function. (author)

The log-linear return approximation, bubbles, and predictability

DEFF Research Database (Denmark)

Engsted, Tom; Pedersen, Thomas Quistgaard; Tanggaard, Carsten

We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividendprice ratio. Next, we simulate various rational bubbles which have explosive conditional expec...

On root mean square approximation by exponential functions

OpenAIRE

Sharipov, Ruslan

2014-01-01

The problem of root mean square approximation of a square integrable function by finite linear combinations of exponential functions is considered. It is subdivided into linear and nonlinear parts. The linear approximation problem is solved. Then the nonlinear problem is studied in some particular example.

Approximate estimation of system reliability via fault trees

International Nuclear Information System (INIS)

Dutuit, Y.; Rauzy, A.

2005-01-01

In this article, we show how fault tree analysis, carried out by means of binary decision diagrams (BDD), is able to approximate reliability of systems made of independent repairable components with a good accuracy and a good efficiency. We consider four algorithms: the Murchland lower bound, the Barlow-Proschan lower bound, the Vesely full approximation and the Vesely asymptotic approximation. For each of these algorithms, we consider an implementation based on the classical minimal cut sets/rare events approach and another one relying on the BDD technology. We present numerical results obtained with both approaches on various examples

Usefulness of bound-state approximations in reaction theory

International Nuclear Information System (INIS)

Adhikari, S.K.

1981-01-01

A bound-state approximation when applied to certain operators, such as the many-body resolvent operator for a two-body fragmentation channel, in many-body scattering equations, reduces such equations to equivalent two-body scattering equations which are supposed to provide a good description of the underlying physical process. In this paper we test several variants of bound-state approximations in the soluble three-boson Amado model and find that such approximations lead to weak and unacceptable kernels for the equivalent two-body scattering equations and hence to a poor description of the underlying many-body process

Quenched Approximation to ΔS = 1 K Decay

International Nuclear Information System (INIS)

Christ, Norman H.

2005-01-01

The importance of explicit quark loops in the amplitudes contributing to ΔS = 1, K meson decays raises potential ambiguities when these amplitudes are evaluated in the quenched approximation. Using the factorization of these amplitudes into short- and long-distance parts provided by the standard low-energy effective weak Hamiltonian, we argue that the quenched approximation can be conventionally justified if it is applied to the long-distance portion of each amplitude. The result is a reasonably well-motivated definition of the quenched approximation that is close to that employed in the RBC and CP-PACS calculations of these quantities

Discovering approximate-associated sequence patterns for protein-DNA interactions

KAUST Repository

Chan, Tak Ming

2010-12-30

Motivation: The bindings between transcription factors (TFs) and transcription factor binding sites (TFBSs) are fundamental protein-DNA interactions in transcriptional regulation. Extensive efforts have been made to better understand the protein-DNA interactions. Recent mining on exact TF-TFBS-associated sequence patterns (rules) has shown great potentials and achieved very promising results. However, exact rules cannot handle variations in real data, resulting in limited informative rules. In this article, we generalize the exact rules to approximate ones for both TFs and TFBSs, which are essential for biological variations. Results: A progressive approach is proposed to address the approximation to alleviate the computational requirements. Firstly, similar TFBSs are grouped from the available TF-TFBS data (TRANSFAC database). Secondly, approximate and highly conserved binding cores are discovered from TF sequences corresponding to each TFBS group. A customized algorithm is developed for the specific objective. We discover the approximate TF-TFBS rules by associating the grouped TFBS consensuses and TF cores. The rules discovered are evaluated by matching (verifying with) the actual protein-DNA binding pairs from Protein Data Bank (PDB) 3D structures. The approximate results exhibit many more verified rules and up to 300% better verification ratios than the exact ones. The customized algorithm achieves over 73% better verification ratios than traditional methods. Approximate rules (64-79%) are shown statistically significant. Detailed variation analysis and conservation verification on NCBI records demonstrate that the approximate rules reveal both the flexible and specific protein-DNA interactions accurately. The approximate TF-TFBS rules discovered show great generalized capability of exploring more informative binding rules. © The Author 2010. Published by Oxford University Press. All rights reserved.

An approximate analytical approach to resampling averages

DEFF Research Database (Denmark)

Malzahn, Dorthe; Opper, M.

2004-01-01

Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach for appr...... for approximate Bayesian inference. We demonstrate our approach on regression with Gaussian processes. A comparison with averages obtained by Monte-Carlo sampling shows that our method achieves good accuracy....

Approximate convex hull of affine iterated function system attractors

International Nuclear Information System (INIS)

Mishkinis, Anton; Gentil, Christian; Lanquetin, Sandrine; Sokolov, Dmitry

2012-01-01

Highlights: ► We present an iterative algorithm to approximate affine IFS attractor convex hull. ► Elimination of the interior points significantly reduces the complexity. ► To optimize calculations, we merge the convex hull images at each iteration. ► Approximation by ellipses increases speed of convergence to the exact convex hull. ► We present a method of the output convex hull simplification. - Abstract: In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output approximate convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximate convex hull without loss of accuracy.

The high intensity approximation applied to multiphoton ionization

International Nuclear Information System (INIS)

Brandi, H.S.; Davidovich, L.; Zagury, N.

1980-08-01

It is shown that the most commonly used high intensity approximations as applied to ionization by strong electromagnetic fields are related. The applicability of the steepest descent method in these approximations, and the relation between them and first-order perturbation theory, are also discussed. (Author) [pt

The Log-Linear Return Approximation, Bubbles, and Predictability

DEFF Research Database (Denmark)

Engsted, Tom; Pedersen, Thomas Quistgaard; Tanggaard, Carsten

2012-01-01

We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividend-price ratio. Next, we simulate various rational bubbles which have explosive conditional expe...

Truthful approximations to range voting

DEFF Research Database (Denmark)

Filos-Ratsika, Aris; Miltersen, Peter Bro

We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare...

Ultrafast Approximation for Phylogenetic Bootstrap

NARCIS (Netherlands)

Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt

Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and

An Approximate Method for Solving Optimal Control Problems for Discrete Systems Based on Local Approximation of an Attainability Set

Directory of Open Access Journals (Sweden)

V. A. Baturin

2017-03-01

Full Text Available An optimal control problem for discrete systems is considered. A method of successive improvements along with its modernization based on the expansion of the main structures of the core algorithm about the parameter is suggested. The idea of the method is based on local approximation of attainability set, which is described by the zeros of the Bellman function in the special problem of optimal control. The essence of the problem is as follows: from the end point of the phase is required to find a path that minimizes functional deviations of the norm from the initial state. If the initial point belongs to the attainability set of the original controlled system, the value of the Bellman function equal to zero, otherwise the value of the Bellman function is greater than zero. For this special task Bellman equation is considered. The support approximation and Bellman equation are selected. The Bellman function is approximated by quadratic terms. Along the allowable trajectory, this approximation gives nothing, because Bellman function and its expansion coefficients are zero. We used a special trick: an additional variable is introduced, which characterizes the degree of deviation of the system from the initial state, thus it is obtained expanded original chain. For the new variable initial nonzero conditions is selected, thus obtained trajectory is lying outside attainability set and relevant Bellman function is greater than zero, which allows it to hold a non-trivial approximation. As a result of these procedures algorithms of successive improvements is designed. Conditions for relaxation algorithms and conditions for the necessary conditions of optimality are also obtained.

Performance approximation of pick-to-belt orderpicking systems

NARCIS (Netherlands)

M.B.M. de Koster (René)

1994-01-01

textabstractIn this paper, an approximation method is discussed for the analysis of pick-to-belt orderpicking systems. The aim of the approximation method is to provide an instrument for obtaining rapid insight in the performance of designs of pick-to-belt orderpicking systems. It can be used to

Modified semiclassical approximation for trapped Bose gases

International Nuclear Information System (INIS)

Yukalov, V.I.

2005-01-01

A generalization of the semiclassical approximation is suggested allowing for an essential extension of its region of applicability. In particular, it becomes possible to describe Bose-Einstein condensation of a trapped gas in low-dimensional traps and in traps of low confining dimensions, for which the standard semiclassical approximation is not applicable. The result of the modified approach is shown to coincide with purely quantum-mechanical calculations for harmonic traps, including the one-dimensional harmonic trap. The advantage of the semiclassical approximation is in its simplicity and generality. Power-law potentials of arbitrary powers are considered. The effective thermodynamic limit is defined for any confining dimension. The behavior of the specific heat, isothermal compressibility, and density fluctuations is analyzed, with an emphasis on low confining dimensions, where the usual semiclassical method fails. The peculiarities of the thermodynamic characteristics in the effective thermodynamic limit are discussed

On Born approximation in black hole scattering

Science.gov (United States)

Batic, D.; Kelkar, N. G.; Nowakowski, M.

2011-12-01

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordström and Reissner-Nordström-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.

Efficient solution of parabolic equations by Krylov approximation methods

Science.gov (United States)

Gallopoulos, E.; Saad, Y.

1990-01-01

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Diversity comparison of Pareto front approximations in many-objective optimization.

Science.gov (United States)

Li, Miqing; Yang, Shengxiang; Liu, Xiaohui

2014-12-01

Diversity assessment of Pareto front approximations is an important issue in the stochastic multiobjective optimization community. Most of the diversity indicators in the literature were designed to work for any number of objectives of Pareto front approximations in principle, but in practice many of these indicators are infeasible or not workable when the number of objectives is large. In this paper, we propose a diversity comparison indicator (DCI) to assess the diversity of Pareto front approximations in many-objective optimization. DCI evaluates relative quality of different Pareto front approximations rather than provides an absolute measure of distribution for a single approximation. In DCI, all the concerned approximations are put into a grid environment so that there are some hyperboxes containing one or more solutions. The proposed indicator only considers the contribution of different approximations to nonempty hyperboxes. Therefore, the computational cost does not increase exponentially with the number of objectives. In fact, the implementation of DCI is of quadratic time complexity, which is fully independent of the number of divisions used in grid. Systematic experiments are conducted using three groups of artificial Pareto front approximations and seven groups of real Pareto front approximations with different numbers of objectives to verify the effectiveness of DCI. Moreover, a comparison with two diversity indicators used widely in many-objective optimization is made analytically and empirically. Finally, a parametric investigation reveals interesting insights of the division number in grid and also offers some suggested settings to the users with different preferences.

Approximating Preemptive Stochastic Scheduling

OpenAIRE

Megow Nicole; Vredeveld Tjark

2009-01-01

We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...

Precise analytic approximations for the Bessel function J1 (x)

Science.gov (United States)

Maass, Fernando; Martin, Pablo

2018-03-01

Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.

Approximate Likelihood

CERN Multimedia

CERN. Geneva

2015-01-01

Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...

Some properties of dual and approximate dual of fusion frames

OpenAIRE

Arefijamaal, Ali Akbar; Neyshaburi, Fahimeh Arabyani

2016-01-01

In this paper we extend the notion of approximate dual to fusion frames and present some approaches to obtain dual and approximate alternate dual fusion frames. Also, we study the stability of dual and approximate alternate dual fusion frames.

Geometrical-optics approximation of forward scattering by coated particles.

Science.gov (United States)

Xu, Feng; Cai, Xiaoshu; Ren, Kuanfang

2004-03-20

By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0 degrees-60 degrees) for coated particles illuminated by a collimated incident beam. Phases of emerging rays are exactly calculated to improve the approximation precision. This method proves effective for transparent and tiny absorbent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. When the absorption coefficient of a particle is greater than 0.01, the geometrical optics approximation is effective only for forward small angles, typically less than 10 degrees or so.

Inertial parameters in the interacting boson fermion approximation

International Nuclear Information System (INIS)

Dukelsky, J.; Lima, C.

1986-06-01

The Hartree-Bose-Fermi and the adiabatic approximations are used to derive analytic formulas for the moment of inertia and the decoupling parameter of the interacting boson fermion approximation for deformed systems. These formulas are applied to the SU(3) dynamical symmetry, obtaining perfect agreement with the exact results. (Authors) [pt

Approximation of bivariate copulas by patched bivariate Fréchet copulas

KAUST Repository

Zheng, Yanting; Yang, Jingping; Huang, Jianhua Z.

2011-01-01

Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums. © 2010 Elsevier B.V.

Approximation of bivariate copulas by patched bivariate Fréchet copulas

KAUST Repository

Zheng, Yanting

2011-03-01

Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums. © 2010 Elsevier B.V.

On badly approximable complex numbers

DEFF Research Database (Denmark)

Esdahl-Schou, Rune; Kristensen, S.

We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...

Approximation of Surfaces by Cylinders

DEFF Research Database (Denmark)

Randrup, Thomas

1998-01-01

We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...

Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

Science.gov (United States)

Gordon, Sheldon P.; Yang, Yajun

2017-01-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

PWL approximation of nonlinear dynamical systems, part I: structural stability

International Nuclear Information System (INIS)

Storace, M; De Feo, O

2005-01-01

This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes the approximation method and applies it to some particularly significant dynamical systems (topological normal forms). The structural stability of the PWL approximations of such systems is investigated through a bifurcation analysis (via continuation methods)

Dynamic Analyses of Result Quality in Energy-Aware Approximate Programs

Science.gov (United States)

RIngenburg, Michael F.

Energy efficiency is a key concern in the design of modern computer systems. One promising approach to energy-efficient computation, approximate computing, trades off output precision for energy efficiency. However, this tradeoff can have unexpected effects on computation quality. This thesis presents dynamic analysis tools to study, debug, and monitor the quality and energy efficiency of approximate computations. We propose three styles of tools: prototyping tools that allow developers to experiment with approximation in their applications, online tools that instrument code to determine the key sources of error, and online tools that monitor the quality of deployed applications in real time. Our prototyping tool is based on an extension to the functional language OCaml. We add approximation constructs to the language, an approximation simulator to the runtime, and profiling and auto-tuning tools for studying and experimenting with energy-quality tradeoffs. We also present two online debugging tools and three online monitoring tools. The first online tool identifies correlations between output quality and the total number of executions of, and errors in, individual approximate operations. The second tracks the number of approximate operations that flow into a particular value. Our online tools comprise three low-cost approaches to dynamic quality monitoring. They are designed to monitor quality in deployed applications without spending more energy than is saved by approximation. Online monitors can be used to perform real time adjustments to energy usage in order to meet specific quality goals. We present prototype implementations of all of these tools and describe their usage with several applications. Our prototyping, profiling, and autotuning tools allow us to experiment with approximation strategies and identify new strategies, our online tools succeed in providing new insights into the effects of approximation on output quality, and our monitors succeed in

An improved corrective smoothed particle method approximation for second‐order derivatives

NARCIS (Netherlands)

Korzilius, S.P.; Schilders, W.H.A.; Anthonissen, M.J.H.

2013-01-01

To solve (partial) differential equations it is necessary to have good numerical approximations. In SPH, most approximations suffer from the presence of boundaries. In this work a new approximation for the second-order derivative is derived and numerically compared with two other approximation

Blind sensor calibration using approximate message passing

International Nuclear Information System (INIS)

Schülke, Christophe; Caltagirone, Francesco; Zdeborová, Lenka

2015-01-01

The ubiquity of approximately sparse data has led a variety of communities to take great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying them to real data can be problematic if imperfect sensing devices introduce deviations from this ideal signal acquisition process, caused by sensor decalibration or failure. We propose a message passing algorithm called calibration approximate message passing (Cal-AMP) that can treat a variety of such sensor-induced imperfections. In addition to deriving the general form of the algorithm, we numerically investigate two particular settings. In the first, a fraction of the sensors is faulty, giving readings unrelated to the signal. In the second, sensors are decalibrated and each one introduces a different multiplicative gain to the measurements. Cal-AMP shares the scalability of approximate message passing, allowing us to treat large sized instances of these problems, and experimentally exhibits a phase transition between domains of success and failure. (paper)

The binary collision approximation: Background and introduction

International Nuclear Information System (INIS)

Robinson, M.T.

1992-08-01

The binary collision approximation (BCA) has long been used in computer simulations of the interactions of energetic atoms with solid targets, as well as being the basis of most analytical theory in this area. While mainly a high-energy approximation, the BCA retains qualitative significance at low energies and, with proper formulation, gives useful quantitative information as well. Moreover, computer simulations based on the BCA can achieve good statistics in many situations where those based on full classical dynamical models require the most advanced computer hardware or are even impracticable. The foundations of the BCA in classical scattering are reviewed, including methods of evaluating the scattering integrals, interaction potentials, and electron excitation effects. The explicit evaluation of time at significant points on particle trajectories is discussed, as are scheduling algorithms for ordering the collisions in a developing cascade. An approximate treatment of nearly simultaneous collisions is outlined and the searching algorithms used in MARLOWE are presented

An inductive algorithm for smooth approximation of functions

International Nuclear Information System (INIS)

Kupenova, T.N.

2011-01-01

An inductive algorithm is presented for smooth approximation of functions, based on the Tikhonov regularization method and applied to a specific kind of the Tikhonov parametric functional. The discrepancy principle is used for estimation of the regularization parameter. The principle of heuristic self-organization is applied for assessment of some parameters of the approximating function

Gauge-invariant intense-field approximations to all orders

International Nuclear Information System (INIS)

Faisal, F H M

2007-01-01

We present a gauge-invariant formulation of the so-called strong-field KFR approximations in the 'velocity' and 'length' gauges and demonstrate their equivalence in all orders. The theory thus overcomes a longstanding discrepancy between the strong-field velocity and the length-gauge approximations for non-perturbative processes in intense laser fields. (fast track communication)

On the convergence of multigroup discrete-ordinates approximations

International Nuclear Information System (INIS)

Victory, H.D. Jr.; Allen, E.J.; Ganguly, K.

1987-01-01

Our analysis is divided into two distinct parts which we label for convenience as Part A and Part B. In Part A, we demonstrate that the multigroup discrete-ordinates approximations are well-defined and converge to the exact transport solution in any subcritical setting. For the most part, we focus on transport in two-dimensional Cartesian geometry. A Nystroem technique is used to extend the discrete ordinates multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ collectively compact operator theory to deduce stability and convergence of the approximates. In Part B, we perform a thorough convergence analysis for the multigroup discrete-ordinates method for an anisotropically-scattering subcritical medium in slab geometry. The diamond-difference and step-characteristic spatial approximation methods are each studied. The multigroup neutron fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution. This is the first thorough convergence analysis for the fully-discretized multigroup neutron transport equations

Approximation theorems by Meyer-Koenig and Zeller type operators

International Nuclear Information System (INIS)

Ali Ozarslan, M.; Duman, Oktay

2009-01-01

This paper is mainly connected with the approximation properties of Meyer-Koenig and Zeller (MKZ) type operators. We first introduce a general sequence of MKZ operators based on q-integers and then obtain a Korovkin-type approximation theorem for these operators. We also compute their rates of convergence by means of modulus of continuity and the elements of Lipschitz class functionals. Furthermore, we give an rth order generalization of our operators in order to get some explicit approximation results.

Space-angle approximations in the variational nodal method

International Nuclear Information System (INIS)

Lewis, E. E.; Palmiotti, G.; Taiwo, T.

1999-01-01

The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2) bilinear finite subelement trial functions for the treatment of fuel assembly sized nodes in which fuel-pin cell cross sections are represented explicitly. Polynomial and subelement trial functions are applied to benchmark water-reactor problems containing MOX fuel using spherical harmonic and simplified spherical harmonic approximations. The resulting accuracy and computing costs are compared

Subquadratic medial-axis approximation in $\\mathbb{R}^3$

Directory of Open Access Journals (Sweden)

Christian Scheffer

2015-09-01

Full Text Available We present an algorithm that approximates the medial axis of a smooth manifold in $\\mathbb{R}^3$ which is given by a sufficiently dense point sample. The resulting, non-discrete approximation is shown to converge to the medial axis as the sampling density approaches infinity. While all previous algorithms guaranteeing convergence have a running time quadratic in the size $n$ of the point sample, we achieve a running time of at most $\\mathcal{O}(n\\log^3 n$. While there is no subquadratic upper bound on the output complexity of previous algorithms for non-discrete medial axis approximation, the output of our algorithm is guaranteed to be of linear size.

Merging Belief Propagation and the Mean Field Approximation

DEFF Research Database (Denmark)

Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro

2010-01-01

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence......) as a starting point. In this method message passing fixed point equations (which correspond to the update rules in a message passing algorithm) are then obtained by imposing different region-based approximations and constraints on the mean field and belief propagation parts of the corresponding factor graph....... Our results can be applied, for example, to algorithms that perform joint channel estimation and decoding in iterative receivers. This is demonstrated in a simple example....

Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

Science.gov (United States)

Freund, Roland

1989-01-01

Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.

APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING MODELS

Directory of Open Access Journals (Sweden)

T. I. Aliev

2013-03-01

Full Text Available For probability distributions with variation coefficient, not equal to unity, mathematical dependences for approximating distributions on the basis of first two moments are derived by making use of multi exponential distributions. It is proposed to approximate distributions with coefficient of variation less than unity by using hypoexponential distribution, which makes it possible to generate random variables with coefficient of variation, taking any value in a range (0; 1, as opposed to Erlang distribution, having only discrete values of coefficient of variation.

An approximate fractional Gaussian noise model with computational cost

KAUST Repository

Sørbye, Sigrunn H.

2017-09-18

Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\\\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\\\\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.

Sharp Bounds for Symmetric and Asymmetric Diophantine Approximation

Institute of Scientific and Technical Information of China (English)

Cornelis KRAAIKAMP; Ionica SMEETS

2011-01-01

In 2004,Tong found bounds for the approximation quality of a regular continued fraction convergent to a rational number,expressed in bounds for both the previous and next approximation.The authors sharpen his results with a geometric method and give both sharp upper and lower bounds.The asymptotic frequencies that these bounds occur are also calculated.

evaluation of approximate design procedures for biaxially loaded

African Journals Online (AJOL)

The approximation according to the ACI is based on the work by Parme [9] who chose to approximate a as a logarithmic function 9f a parameter /3 representing an actual point on· the non-dimensional load contour, where the two moment components, . related to the respective uniaxial capacities are equal,. i.e. f3=;: my lmuy ...

Effective medium super-cell approximation for interacting disordered systems: an alternative real-space derivation of generalized dynamical cluster approximation

International Nuclear Information System (INIS)

Moradian, Rostam

2006-01-01

We develop a generalized real-space effective medium super-cell approximation (EMSCA) method to treat the electronic states of interacting disordered systems. This method is general and allows randomness both in the on-site energies and in the hopping integrals. For a non-interacting disordered system, in the special case of randomness in the on-site energies, this method is equivalent to the non-local coherent potential approximation (NLCPA) derived previously. Also, for an interacting system the EMSCA method leads to the real-space derivation of the generalized dynamical cluster approximation (DCA) for a general lattice structure. We found that the original DCA and the NLCPA are two simple cases of this technique, so the EMSCA is equivalent to the generalized DCA where there is included interaction and randomness in the on-site energies and in the hopping integrals. All of the equations of this formalism are derived by using the effective medium theory in real space

On the atomic-number similarity of the binding energies of electrons in filled shells of elements of the periodic table

Science.gov (United States)

Karpov, V. Ya.; Shpatakovskaya, G. V.

2017-03-01

An expression for the binding energies of electrons in the ground state of an atom is derived on the basis of the Bohr-Sommerfeld quantization rule within the Thomas-Fermi model. The validity of this relation for all elements from neon to uranium is tested within a more perfect quantum-mechanical model with and without the inclusion of relativistic effects, as well as with experimental binding energies. As a result, the ordering of electronic levels in filled atomic shells is established, manifested in an approximate atomic-number similarity. It is proposed to use this scaling property to analytically estimate the binding energies of electrons in an arbitrary atom.

Faster and Simpler Approximation of Stable Matchings

Directory of Open Access Journals (Sweden)

Katarzyna Paluch

2014-04-01

Full Text Available We give a 3 2 -approximation algorithm for finding stable matchings that runs in O(m time. The previous most well-known algorithm, by McDermid, has the same approximation ratio but runs in O(n3/2m time, where n denotes the number of people andm is the total length of the preference lists in a given instance. In addition, the algorithm and the analysis are much simpler. We also give the extension of the algorithm for computing stable many-to-many matchings.

On the dipole approximation with error estimates

Science.gov (United States)

Boßmann, Lea; Grummt, Robert; Kolb, Martin

2018-01-01

The dipole approximation is employed to describe interactions between atoms and radiation. It essentially consists of neglecting the spatial variation of the external field over the atom. Heuristically, this is justified by arguing that the wavelength is considerably larger than the atomic length scale, which holds under usual experimental conditions. We prove the dipole approximation in the limit of infinite wavelengths compared to the atomic length scale and estimate the rate of convergence. Our results include N-body Coulomb potentials and experimentally relevant electromagnetic fields such as plane waves and laser pulses.

On approximation of Lie groups by discrete subgroups

Indian Academy of Sciences (India)

2016-08-26

Aug 26, 2016 ... The notion of approximation of Lie groups by discrete subgroups was introduced by Tôyama in Kodai Math. Sem. Rep. 1 (1949) 36–37 and investigated in detail by Kuranishi in Nagoya Math. J. 2 (1951) 63–71. It is known as a theorem of Tôyama that any connected Lie group approximated by discrete ...

A simple approximation method for dilute Ising systems

International Nuclear Information System (INIS)

Saber, M.

1996-10-01

We describe a simple approximate method to analyze dilute Ising systems. The method takes into consideration the fluctuations of the effective field, and is based on a probability distribution of random variables which correctly accounts for all the single site kinematic relations. It is shown that the simplest approximation gives satisfactory results when compared with other methods. (author). 12 refs, 2 tabs

The modified signed likelihood statistic and saddlepoint approximations

DEFF Research Database (Denmark)

Jensen, Jens Ledet

1992-01-01

SUMMARY: For a number of tests in exponential families we show that the use of a normal approximation to the modified signed likelihood ratio statistic r * is equivalent to the use of a saddlepoint approximation. This is also true in a large deviation region where the signed likelihood ratio...... statistic r is of order √ n. © 1992 Biometrika Trust....

Confidence Intervals for Asbestos Fiber Counts: Approximate Negative Binomial Distribution.

Science.gov (United States)

Bartley, David; Slaven, James; Harper, Martin

2017-03-01

The negative binomial distribution is adopted for analyzing asbestos fiber counts so as to account for both the sampling errors in capturing only a finite number of fibers and the inevitable human variation in identifying and counting sampled fibers. A simple approximation to this distribution is developed for the derivation of quantiles and approximate confidence limits. The success of the approximation depends critically on the use of Stirling's expansion to sufficient order, on exact normalization of the approximating distribution, on reasonable perturbation of quantities from the normal distribution, and on accurately approximating sums by inverse-trapezoidal integration. Accuracy of the approximation developed is checked through simulation and also by comparison to traditional approximate confidence intervals in the specific case that the negative binomial distribution approaches the Poisson distribution. The resulting statistics are shown to relate directly to early research into the accuracy of asbestos sampling and analysis. Uncertainty in estimating mean asbestos fiber concentrations given only a single count is derived. Decision limits (limits of detection) and detection limits are considered for controlling false-positive and false-negative detection assertions and are compared to traditional limits computed assuming normal distributions. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.

Nonresonant approximations to the optical potential

International Nuclear Information System (INIS)

Kowalski, K.L.

1982-01-01

A new class of approximations to the optical potential, which includes those of the multiple-scattering variety, is investigated. These approximations are constructed so that the optical potential maintains the correct unitarity properties along with a proper treatment of nucleon identity. The special case of nucleon-nucleus scattering with complete inclusion of Pauli effects is studied in detail. The treatment is such that the optical potential receives contributions only from subsystems embedded in their own physically correct antisymmetrized subspaces. It is found that a systematic development of even the lowest-order approximations requires the use of the off-shell extension due to Alt, Grassberger, and Sandhas along with a consistent set of dynamical equations for the optical potential. In nucleon-nucleus scattering a lowest-order optical potential is obtained as part of a systematic, exact, inclusive connectivity expansion which is expected to be useful at moderately high energies. This lowest-order potential consists of an energy-shifted (trho)-type term with three-body kinematics plus a heavy-particle exchange or pickup term. The natural appearance of the exchange term additivity in the optical potential clarifies the role of the elastic distortion in connection with the treatment of these processes. The relationship of the relevant aspects of the present analysis of the optical potential to conventional multiple scattering methods is discussed

Sequential function approximation on arbitrarily distributed point sets

Science.gov (United States)

Wu, Kailiang; Xiu, Dongbin

2018-02-01

We present a randomized iterative method for approximating unknown function sequentially on arbitrary point set. The method is based on a recently developed sequential approximation (SA) method, which approximates a target function using one data point at each step and avoids matrix operations. The focus of this paper is on data sets with highly irregular distribution of the points. We present a nearest neighbor replacement (NNR) algorithm, which allows one to sample the irregular data sets in a near optimal manner. We provide mathematical justification and error estimates for the NNR algorithm. Extensive numerical examples are also presented to demonstrate that the NNR algorithm can deliver satisfactory convergence for the SA method on data sets with high irregularity in their point distributions.

Semiclassical approximation to time-dependent Hartree--Fock theory

International Nuclear Information System (INIS)

Dworzecka, M.; Poggioli, R.

1976-01-01

Working within a time-dependent Hartree-Fock framework, one develops a semiclassical approximation appropriate for large systems. It is demonstrated that the standard semiclassical approach, the Thomas-Fermi approximation, is inconsistent with Hartree-Fock theory when the basic two-body interaction is short-ranged (as in nuclear systems, for example). However, by introducing a simple extension of the Thomas-Fermi approximation, one overcomes this problem. One also discusses the infinite nuclear matter problem and point out that time-dependent Hartree-Fock theory yields collective modes of the zero sound variety instead of ordinary hydrodynamic (first) sound. One thus emphasizes that one should be extremely circumspect when attempting to cast the equations of motion of time-dependent Hartree-Fock theory into a hydrodynamic-like form

Good and Bad Neighborhood Approximations for Outlier Detection Ensembles

DEFF Research Database (Denmark)

Kirner, Evelyn; Schubert, Erich; Zimek, Arthur

2017-01-01

Outlier detection methods have used approximate neighborhoods in filter-refinement approaches. Outlier detection ensembles have used artificially obfuscated neighborhoods to achieve diverse ensemble members. Here we argue that outlier detection models could be based on approximate neighborhoods...... in the first place, thus gaining in both efficiency and effectiveness. It depends, however, on the type of approximation, as only some seem beneficial for the task of outlier detection, while no (large) benefit can be seen for others. In particular, we argue that space-filling curves are beneficial...

APPROXIMATE DEVELOPMENTS FOR SURFACES OF REVOLUTION

Directory of Open Access Journals (Sweden)

Mădălina Roxana Buneci

2016-12-01

Full Text Available The purpose of this paper is provide a set of Maple procedures to construct approximate developments of a general surface of revolution generalizing the well-known gore method for sphere

The complex variable boundary element method: Applications in determining approximative boundaries

Science.gov (United States)

Hromadka, T.V.

1984-01-01

The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.

Gaussian and 1/N approximations in semiclassical cosmology

International Nuclear Information System (INIS)

Mazzitelli, F.D.; Paz, J.P.

1989-01-01

We study the λphi 4 theory and the interacting O(N) model in a curved background using the Gaussian approximation for the former and the large-N approximation for the latter. We obtain the renormalized version of the semiclassical Einstein equations having in mind a future application of these models to investigate the physics of the very early Universe. We show that, while the Gaussian approximation has two different phases, in the large-N limit only one is present. The different features of the two phases are analyzed at the level of the effective field equations. We discuss the initial-value problem and find the initial conditions that make the theory renormalizable. As an example, we study the de Sitter self-consistent solutions of the semiclassical Einstein equations. Finally, for an identically zero mean value of the field we find the evolution equations for the classical field Ω(x) = (λ 2 >)/sup 1/2/ and the spacetime metric. They are very similar to the ones obtained by replacing the classical potential by the one-loop effective potential in the classical equations but do not have the drawbacks of the one-loop approximation

Approximate Matching of Hierarchial Data

DEFF Research Database (Denmark)

Augsten, Nikolaus

-grams of a tree are all its subtrees of a particular shape. Intuitively, two trees are similar if they have many pq-grams in common. The pq-gram distance is an efficient and effective approximation of the tree edit distance. We analyze the properties of the pq-gram distance and compare it with the tree edit...

Pythagorean Approximations and Continued Fractions

Science.gov (United States)

Peralta, Javier

2008-01-01

In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…

An Origami Approximation to the Cosmic Web

Science.gov (United States)

Neyrinck, Mark C.

2016-10-01

The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in `polygonal' or `polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls to be more easily understood, and may aid in understanding spin correlations between nearby galaxies. This contribution explores kinematic origami-approximation models giving velocity fields for the first time.

Function approximation of tasks by neural networks

International Nuclear Information System (INIS)

Gougam, L.A.; Chikhi, A.; Mekideche-Chafa, F.

2008-01-01

For several years now, neural network models have enjoyed wide popularity, being applied to problems of regression, classification and time series analysis. Neural networks have been recently seen as attractive tools for developing efficient solutions for many real world problems in function approximation. The latter is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. In a previous contribution, we have used a well known simplified architecture to show that it provides a reasonably efficient, practical and robust, multi-frequency analysis. We have investigated the universal approximation theory of neural networks whose transfer functions are: sigmoid (because of biological relevance), Gaussian and two specified families of wavelets. The latter have been found to be more appropriate to use. The aim of the present contribution is therefore to use a m exican hat wavelet a s transfer function to approximate different tasks relevant and inherent to various applications in physics. The results complement and provide new insights into previously published results on this problem

Approximate particle number projection in hot nuclei

International Nuclear Information System (INIS)

Kosov, D.S.; Vdovin, A.I.

1995-01-01

Heated finite systems like, e.g., hot atomic nuclei have to be described by the canonical partition function. But this is a quite difficult technical problem and, as a rule, the grand canonical partition function is used in the studies. As a result, some shortcomings of the theoretical description appear because of the thermal fluctuations of the number of particles. Moreover, in nuclei with pairing correlations the quantum number fluctuations are introduced by some approximate methods (e.g., by the standard BCS method). The exact particle number projection is very cumbersome and an approximate number projection method for T ≠ 0 basing on the formalism of thermo field dynamics is proposed. The idea of the Lipkin-Nogami method to perform any operator as a series in the number operator powers is used. The system of equations for the coefficients of this expansion is written and the solution of the system in the next approximation after the BCS one is obtained. The method which is of the 'projection after variation' type is applied to a degenerate single j-shell model. 14 refs., 1 tab

Finite elements and approximation

CERN Document Server

Zienkiewicz, O C

2006-01-01

A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

Roadworks around the "Les Cèdres" car park

CERN Multimedia

SMB Department

2016-01-01

Diversions will be in place on Route Scherrer and Route Bohr from 4 to 31 July.   As we announced in a previous article, the SMB department is currently installing vehicle registration plate readers at the entrances and exits of the Les Cèdres car park and of the Building 4 and 5 car park, both on the Meyrin site. Please note that, due to the installation work involved: access to Buildings 50 and 52 via Route Scherrer (passing under the Building 50 walkway) will be closed from 4 to 8 July, access to the Les Cèdres car park via Route Scherrer will be closed from 4 to 14 July, access to the Les Cèdres car park via Route Bohr will be closed from 16 to 31 July, Route Bohr will be closed between Route Greinacher and Route Bell from 16 to 31 July. Please also note that, following the completion of the work, the Les Cèdres car park will operate as a one-way system, with entry only from Route Scherrer and exit only onto Route Bohr. Thank you for your understand...

An approximation to the interference term using Frobenius Method

Energy Technology Data Exchange (ETDEWEB)

Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C. da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear; E-mail: aquilino@lmp.ufrj.br

2007-07-01

An analytical approximation of the interference term {chi}(x,{xi}) is proposed. The approximation is based on the differential equation to {chi}(x,{xi}) using the Frobenius method and the parameter variation. The analytical expression of the {chi}(x,{xi}) obtained in terms of the elementary functions is very simple and precise. In this work one applies the approximations to the Doppler broadening functions and to the interference term in determining the neutron cross sections. Results were validated for the resonances of the U{sup 238} isotope for different energies and temperature ranges. (author)

An approximation to the interference term using Frobenius Method

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C. da

2007-01-01

An analytical approximation of the interference term χ(x,ξ) is proposed. The approximation is based on the differential equation to χ(x,ξ) using the Frobenius method and the parameter variation. The analytical expression of the χ(x,ξ) obtained in terms of the elementary functions is very simple and precise. In this work one applies the approximations to the Doppler broadening functions and to the interference term in determining the neutron cross sections. Results were validated for the resonances of the U 238 isotope for different energies and temperature ranges. (author)

The mathematical structure of the approximate linear response relation

International Nuclear Information System (INIS)

Yasuda, Muneki; Tanaka, Kazuyuki

2007-01-01

In this paper, we study the mathematical structures of the linear response relation based on Plefka's expansion and the cluster variation method in terms of the perturbation expansion, and we show how this linear response relation approximates the correlation functions of the specified system. Moreover, by comparing the perturbation expansions of the correlation functions estimated by the linear response relation based on these approximation methods with exact perturbative forms of the correlation functions, we are able to explain why the approximate techniques using the linear response relation work well

Efficient approximation of random fields for numerical applications

KAUST Repository

Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus

2015-01-01

We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.

Efficient approximation of random fields for numerical applications

KAUST Repository

Harbrecht, Helmut

2015-01-07

We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.

Intensity-based hierarchical elastic registration using approximating splines.

Science.gov (United States)

Serifovic-Trbalic, Amira; Demirovic, Damir; Cattin, Philippe C

2014-01-01

We introduce a new hierarchical approach for elastic medical image registration using approximating splines. In order to obtain the dense deformation field, we employ Gaussian elastic body splines (GEBS) that incorporate anisotropic landmark errors and rotation information. Since the GEBS approach is based on a physical model in form of analytical solutions of the Navier equation, it can very well cope with the local as well as global deformations present in the images by varying the standard deviation of the Gaussian forces. The proposed GEBS approximating model is integrated into the elastic hierarchical image registration framework, which decomposes a nonrigid registration problem into numerous local rigid transformations. The approximating GEBS registration scheme incorporates anisotropic landmark errors as well as rotation information. The anisotropic landmark localization uncertainties can be estimated directly from the image data, and in this case, they represent the minimal stochastic localization error, i.e., the Cramér-Rao bound. The rotation information of each landmark obtained from the hierarchical procedure is transposed in an additional angular landmark, doubling the number of landmarks in the GEBS model. The modified hierarchical registration using the approximating GEBS model is applied to register 161 image pairs from a digital mammogram database. The obtained results are very encouraging, and the proposed approach significantly improved all registrations comparing the mean-square error in relation to approximating TPS with the rotation information. On artificially deformed breast images, the newly proposed method performed better than the state-of-the-art registration algorithm introduced by Rueckert et al. (IEEE Trans Med Imaging 18:712-721, 1999). The average error per breast tissue pixel was less than 2.23 pixels compared to 2.46 pixels for Rueckert's method. The proposed hierarchical elastic image registration approach incorporates the GEBS

Lognormal Approximations of Fault Tree Uncertainty Distributions.

Science.gov (United States)

El-Shanawany, Ashraf Ben; Ardron, Keith H; Walker, Simon P

2018-01-26

Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed-form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling-based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed-form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks's method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models. © 2018 Society for Risk Analysis.

Direct application of Padé approximant for solving nonlinear differential equations.

Science.gov (United States)

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

2014-01-01

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

Continuum orbital approximations in weak-coupling theories for inelastic electron scattering

International Nuclear Information System (INIS)

Peek, J.M.; Mann, J.B.

1977-01-01

Two approximations, motivated by heavy-particle scattering theory, are tested for weak-coupling electron-atom (ion) inelastic scattering theory. They consist of replacing the one-electron scattering orbitals by their Langer uniform approximations and the use of an average trajectory approximation which entirely avoids the necessity for generating continuum orbitals. Numerical tests for a dipole-allowed and a dipole-forbidden event, based on Coulomb-Born theory with exchange neglected, reveal the error trends. It is concluded that the uniform approximation gives a satisfactory prediction for traditional weak-coupling theories while the average approximation should be limited to collision energies exceeding at least twice the threshold energy. The accuracy for both approximations is higher for positive ions than for neutral targets. Partial-wave collision-strength data indicate that greater care should be exercised in using these approximations to predict quantities differential in the scattering angle. An application to the 2s 2 S-2p 2 P transition in Ne VIII is presented

Self-consistent approximations beyond the CPA: Part II

International Nuclear Information System (INIS)

Kaplan, T.; Gray, L.J.

1982-01-01

This paper concentrates on a self-consistent approximation for random alloys developed by Kaplan, Leath, Gray, and Diehl. The construction of the augmented space formalism for a binary alloy is sketched, and the notation to be used derived. Using the operator methods of the augmented space, the self-consistent approximation is derived for the average Green's function, and for evaluating the self-energy, taking into account the scattering by clusters of excitations. The particular cluster approximation desired is derived by treating the scattering by the excitations with S /SUB T/ exactly. Fourier transforms on the disorder-space clustersite labels solve the self-consistent set of equations. Expansion to short range order in the alloy is also discussed. A method to reduce the problem to a computationally tractable form is described

Perturbation expansions generated by an approximate propagator

International Nuclear Information System (INIS)

Znojil, M.

1987-01-01

Starting from a knowledge of an approximate propagator R at some trial energy guess E 0 , a new perturbative prescription for p-plet of bound states and of their energies is proposed. It generalizes the Rayleigh-Schroedinger (RS) degenerate perturbation theory to the nondiagonal operators R (eliminates a RS need of their diagnolisation) and defines an approximate Hamiltonian T by mere inversion. The deviation V of T from the exact Hamiltonian H is assumed small only after a substraction of a further auxiliary Hartree-Fock-like separable ''selfconsistent'' potential U of rank p. The convergence is illustrated numerically on the anharmonic oscillator example

Congruence Approximations for Entrophy Endowed Hyperbolic Systems

Science.gov (United States)

Barth, Timothy J.; Saini, Subhash (Technical Monitor)

1998-01-01

Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

Multilevel weighted least squares polynomial approximation

KAUST Repository

Haji-Ali, Abdul-Lateef; Nobile, Fabio; Tempone, Raul; Wolfers, Sö ren

2017-01-01

, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose

Approximating the ground state of gapped quantum spin systems

Energy Technology Data Exchange (ETDEWEB)

Michalakis, Spyridon [Los Alamos National Laboratory; Hamza, Eman [NON LANL; Nachtergaele, Bruno [NON LANL; Sims, Robert [NON LANL

2009-01-01

We consider quantum spin systems defined on finite sets V equipped with a metric. In typical examples, V is a large, but finite subset of Z{sup d}. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset {chi} {contained_in} V the ground state projector can be approximated by the product of two projections, one supported on {chi} and one supported on {chi}{sup c}, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. Such an approximation was useful in proving an area law in one dimension, and this result corresponds to a multi-dimensional analogue.

Atoms – How Small, and How Large!

Indian Academy of Sciences (India)

IAS Admin

found in the Bohr atom model, the birth centenary of which is celebrated in the year 2013. Neils Bohr intro- duced in his model the quantization (occurrence of dis- ... free or isolated H-atom is of the order of 1 Å = 10. −10 m. The quantity a0 is quite fundamental and it serves as a unit of length in the atomic–molecular physics.

Polynomial approximation on polytopes

CERN Document Server

Totik, Vilmos

2014-01-01

Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.

Discussion of CoSA: Clustering of Sparse Approximations

Energy Technology Data Exchange (ETDEWEB)

Armstrong, Derek Elswick [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-03-07

The purpose of this talk is to discuss the possible applications of CoSA (Clustering of Sparse Approximations) to the exploitation of HSI (HyperSpectral Imagery) data. CoSA is presented by Moody et al. in the Journal of Applied Remote Sensing (“Land cover classification in multispectral imagery using clustering of sparse approximations over learned feature dictionaries”, Vol. 8, 2014) and is based on machine learning techniques.

Approximate reasoning in decision analysis

Energy Technology Data Exchange (ETDEWEB)

Gupta, M M; Sanchez, E

1982-01-01

The volume aims to incorporate the recent advances in both theory and applications. It contains 44 articles by 74 contributors from 17 different countries. The topics considered include: membership functions; composite fuzzy relations; fuzzy logic and inference; classifications and similarity measures; expert systems and medical diagnosis; psychological measurements and human behaviour; approximate reasoning and decision analysis; and fuzzy clustering algorithms.

Green-Ampt approximations: A comprehensive analysis

Science.gov (United States)

Ali, Shakir; Islam, Adlul; Mishra, P. K.; Sikka, Alok K.

2016-04-01

Green-Ampt (GA) model and its modifications are widely used for simulating infiltration process. Several explicit approximate solutions to the implicit GA model have been developed with varying degree of accuracy. In this study, performance of nine explicit approximations to the GA model is compared with the implicit GA model using the published data for broad range of soil classes and infiltration time. The explicit GA models considered are Li et al. (1976) (LI), Stone et al. (1994) (ST), Salvucci and Entekhabi (1994) (SE), Parlange et al. (2002) (PA), Barry et al. (2005) (BA), Swamee et al. (2012) (SW), Ali et al. (2013) (AL), Almedeij and Esen (2014) (AE), and Vatankhah (2015) (VA). Six statistical indicators (e.g., percent relative error, maximum absolute percent relative error, average absolute percent relative errors, percent bias, index of agreement, and Nash-Sutcliffe efficiency) and relative computer computation time are used for assessing the model performance. Models are ranked based on the overall performance index (OPI). The BA model is found to be the most accurate followed by the PA and VA models for variety of soil classes and infiltration periods. The AE, SW, SE, and LI model also performed comparatively better. Based on the overall performance index, the explicit models are ranked as BA > PA > VA > LI > AE > SE > SW > ST > AL. Results of this study will be helpful in selection of accurate and simple explicit approximate GA models for solving variety of hydrological problems.

Nonlinear Ritz approximation for Fredholm functionals

Directory of Open Access Journals (Sweden)

Mudhir A. Abdul Hussain

2015-11-01

Full Text Available In this article we use the modify Lyapunov-Schmidt reduction to find nonlinear Ritz approximation for a Fredholm functional. This functional corresponds to a nonlinear Fredholm operator defined by a nonlinear fourth-order differential equation.

An overview on Approximate Bayesian computation*

Directory of Open Access Journals (Sweden)

Baragatti Meïli

2014-01-01

Full Text Available Approximate Bayesian computation techniques, also called likelihood-free methods, are one of the most satisfactory approach to intractable likelihood problems. This overview presents recent results since its introduction about ten years ago in population genetics.

Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations

International Nuclear Information System (INIS)

Peng, Degao; Yang, Yang; Zhang, Peng; Yang, Weitao

2014-01-01

In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N 4 ). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as 〈S ^2 〉 are also developed and tested

Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations

Energy Technology Data Exchange (ETDEWEB)

Peng, Degao; Yang, Yang; Zhang, Peng [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Yang, Weitao, E-mail: weitao.yang@duke.edu [Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708 (United States)

2014-12-07

In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N{sup 4}). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as 〈S{sup ^2}〉 are also developed and tested.

Comment on 'Approximation for a large-angle simple pendulum period'

International Nuclear Information System (INIS)

Yuan Qingxin; Ding Pei

2009-01-01

In a recent letter, Belendez et al (2009 Eur. J. Phys. 30 L25-8) proposed an alternative of approximation for the period of a simple pendulum suggested earlier by Hite (2005 Phys. Teach. 43 290-2) who set out to improve on the Kidd and Fogg formula (2002 Phys. Teach. 40 81-3). As a response to the approximation scheme, we obtain another analytical approximation for the large-angle pendulum period, which owns the simplicity and accuracy in evaluating the exact period, and moreover, for amplitudes less than 144 deg. the analytical approximate expression is more accurate than others in the literature. (letters and comments)

Reply to Steele & Ferrer: Modeling Oscillation, Approximately or Exactly?

Science.gov (United States)

Oud, Johan H. L.; Folmer, Henk

2011-01-01

This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…

Approximations for Markovian multi-class queues with preemptive priorities

NARCIS (Netherlands)

van der Heijden, Matthijs C.; van Harten, Aart; Sleptchenko, Andrei

2004-01-01

We discuss the approximation of performance measures in multi-class M/M/k queues with preemptive priorities for large problem instances (many classes and servers) using class aggregation and server reduction. We compared our approximations to exact and simulation results and found that our approach

Approximations for W-Pair Production at Linear-Collider Energies

CERN Document Server

Denner, A

1997-01-01

We determine the accuracy of various approximations to the O(alpha) corrections for on-shell W-pair production. While an approximation based on the universal corrections arising from initial-state radiation, from the running of alpha, and from corrections proportional to m_t^2 fails in the Linear-Collider energy range, a high-energy approximation improved by the exact universal corrections is sufficiently good above about 500GeV. These results indicate that in Monte Carlo event generators for off-shell W-pair production the incorporation of the universal corrections is not sufficient and more corrections should be included.

Applicability of point-dipoles approximation to all-dielectric metamaterials

DEFF Research Database (Denmark)

Kuznetsova, S. M.; Andryieuski, Andrei; Lavrinenko, Andrei

2015-01-01

All-dielectric metamaterials consisting of high-dielectric inclusions in a low-dielectric matrix are considered as a low-loss alternative to resonant metal-based metamaterials. In this paper we investigate the applicability of the point electric and magnetic dipoles approximation to dielectric meta......-atoms on the example of a dielectric ring metamaterial. Despite the large electrical size of high-dielectric meta-atoms, the dipole approximation allows for accurate prediction of the metamaterials properties for the rings with diameters up to approximate to 0.8 of the lattice constant. The results provide important...... guidelines for design and optimization of all-dielectric metamaterials....

Globally convergent optimization algorithm using conservative convex separable diagonal quadratic approximations

NARCIS (Netherlands)

Groenwold, A.A.; Wood, D.W.; Etman, L.F.P.; Tosserams, S.

2009-01-01

We implement and test a globally convergent sequential approximate optimization algorithm based on (convexified) diagonal quadratic approximations. The algorithm resides in the class of globally convergent optimization methods based on conservative convex separable approximations developed by

Fractal image coding by an approximation of the collage error

Science.gov (United States)

Salih, Ismail; Smith, Stanley H.

1998-12-01

In fractal image compression an image is coded as a set of contractive transformations, and is guaranteed to generate an approximation to the original image when iteratively applied to any initial image. In this paper we present a method for mapping similar regions within an image by an approximation of the collage error; that is, range blocks can be approximated by a linear combination of domain blocks.

Thermodynamic properties of sticky electrolytes in the HNC/MS approximation

International Nuclear Information System (INIS)

Herrera, J.N.; Blum, L.

1991-01-01

We study an approximation for a model which combines the sticky potential of Baxter and charged spheres. In the hypernetted chain (HNC)/mean spherical approximation (MSA), simple expressions for the thermodynamic functions are obtained. There equations should be useful in representing the properties of real electrolytes. Approximate expressions that are similar to those of the primitive model are obtained, for low densities (concentrations) of the electrolyte (Author)

An overview on polynomial approximation of NP-hard problems

Directory of Open Access Journals (Sweden)

Paschos Vangelis Th.

2009-01-01

Full Text Available The fact that polynomial time algorithm is very unlikely to be devised for an optimal solving of the NP-hard problems strongly motivates both the researchers and the practitioners to try to solve such problems heuristically, by making a trade-off between computational time and solution's quality. In other words, heuristic computation consists of trying to find not the best solution but one solution which is 'close to' the optimal one in reasonable time. Among the classes of heuristic methods for NP-hard problems, the polynomial approximation algorithms aim at solving a given NP-hard problem in poly-nomial time by computing feasible solutions that are, under some predefined criterion, as near to the optimal ones as possible. The polynomial approximation theory deals with the study of such algorithms. This survey first presents and analyzes time approximation algorithms for some classical examples of NP-hard problems. Secondly, it shows how classical notions and tools of complexity theory, such as polynomial reductions, can be matched with polynomial approximation in order to devise structural results for NP-hard optimization problems. Finally, it presents a quick description of what is commonly called inapproximability results. Such results provide limits on the approximability of the problems tackled.

Dissociation between exact and approximate addition in developmental dyslexia.

Science.gov (United States)

Yang, Xiujie; Meng, Xiangzhi

2016-09-01

Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.

RATIONAL APPROXIMATIONS TO GENERALIZED HYPERGEOMETRIC FUNCTIONS.

Science.gov (United States)

Under weak restrictions on the various free parameters, general theorems for rational representations of the generalized hypergeometric functions...and certain Meijer G-functions are developed. Upon specialization, these theorems yield a sequency of rational approximations which converge to the

The generalized gradient approximation in solids and molecules

International Nuclear Information System (INIS)

Haas, P.

2010-01-01

Today, most methods are based on theoretical calculations of the electronic structure of molecules, surfaces and solids on density functional theory (DFT) and the resulting Kohn-Sham equations. Unfortunately, the exact analytical expression for the exchange-correlation functional is not known and has to be approximated. The reliability of such a Kohn-Sham calculation depends i) from the numerical accuracy and ii) from the used approximation for the exchange-correlation energy. To solve the Kohn-Sham equations, the WIEN2k code, which is one of the most accurate methods for solid-state calculations, is used. The search for better approximations for the exchange-correlation energy is an intense field of research in chemistry and physics. The main objectives of the dissertation is the development, implementation and testing of advanced exchange-correlation functionals and the analysis of existing functionals. The focus of this work are GGA - functionals. Such GGA functionals are still the most widely used functionals, in particular because they are easy to implement and require little computational effort. Several recent studies have shown that an improvement of the GGA should be possible. A detailed analysis of the results will allow us to understand why a particular GGA approximation for a class of elements (compounds) works better than for another. (Kancsar) [de

An approximation method for diffusion based leaching models

International Nuclear Information System (INIS)

Shukla, B.S.; Dignam, M.J.

1987-01-01

In connection with the fixation of nuclear waste in a glassy matrix equations have been derived for leaching models based on a uniform concentration gradient approximation, and hence a uniform flux, therefore requiring the use of only Fick's first law. In this paper we improve on the uniform flux approximation, developing and justifying the approach. The resulting set of equations are solved to a satisfactory approximation for a matrix dissolving at a constant rate in a finite volume of leachant to give analytical expressions for the time dependence of the thickness of the leached layer, the diffusional and dissolutional contribution to the flux, and the leachant composition. Families of curves are presented which cover the full range of all the physical parameters for this system. The same procedure can be readily extended to more complex systems. (author)

Approximation of ruin probabilities via Erlangized scale mixtures

DEFF Research Database (Denmark)

Peralta, Oscar; Rojas-Nandayapa, Leonardo; Xie, Wangyue

2018-01-01

In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cramér–Lundbergreserve process having absolutely continuous but otherwise general claim size distributions. We employ a dense class of distributions that we denominate Erlangized scale...... a simple methodology for constructing a sequence of distributions having the form Π⋆G with the purpose of approximating the integrated tail distribution of the claim sizes. Then we adapt a recent result which delivers an explicit expression for the probability of ruin in the case that the claim size...... distribution is modeled as an Erlangized scale mixture. We provide simplified expressions for the approximation of the probability of ruin and construct explicit bounds for the error of approximation. We complement our results with a classical example where the claim sizes are heavy-tailed....

Approximate models for broken clouds in stochastic radiative transfer theory

International Nuclear Information System (INIS)

Doicu, Adrian; Efremenko, Dmitry S.; Loyola, Diego; Trautmann, Thomas

2014-01-01

This paper presents approximate models in stochastic radiative transfer theory. The independent column approximation and its modified version with a solar source computed in a full three-dimensional atmosphere are formulated in a stochastic framework and for arbitrary cloud statistics. The nth-order stochastic models describing the independent column approximations are equivalent to the nth-order stochastic models for the original radiance fields in which the gradient vectors are neglected. Fast approximate models are further derived on the basis of zeroth-order stochastic models and the independent column approximation. The so-called “internal mixing” models assume a combination of the optical properties of the cloud and the clear sky, while the “external mixing” models assume a combination of the radiances corresponding to completely overcast and clear skies. A consistent treatment of internal and external mixing models is provided, and a new parameterization of the closure coefficient in the effective thickness approximation is given. An efficient computation of the closure coefficient for internal mixing models, using a previously derived vector stochastic model as a reference, is also presented. Equipped with appropriate look-up tables for the closure coefficient, these models can easily be integrated into operational trace gas retrieval systems that exploit absorption features in the near-IR solar spectrum. - Highlights: • Independent column approximation in a stochastic setting. • Fast internal and external mixing models for total and diffuse radiances. • Efficient optimization of internal mixing models to match reference models

Plasma Physics Approximations in Ares

International Nuclear Information System (INIS)

Managan, R. A.

2015-01-01

Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, Fn( μ/θ ), the chemical potential, μ or ζ = ln(1+e μ/θ ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A α (ζ ),A β (ζ ), ζ, f(ζ ) = (1 + e -μ/θ )F 1/2 (μ/θ), F 1/2 '/F 1/2 , F c α , and F c β . In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.

Approximate first integrals of a chaotic Hamiltonian system | Unal ...

African Journals Online (AJOL)

Approximate first integrals (conserved quantities) of a Hamiltonian dynamical system with two-degrees of freedom which arises in the modeling of galaxy have been obtained based on the approximate Noether symmetries for the resonance ω1 = ω2. Furthermore, Kolmogorov-Arnold-Moser (KAM) curves have been ...

On a saddlepoint approximation to the Markov binomial distribution

DEFF Research Database (Denmark)

Jensen, Jens Ledet

A nonstandard saddlepoint approximation to the distribution of a sum of Markov dependent trials is introduced. The relative error of the approximation is studied, not only for the number of summands tending to infinity, but also for the parameter approaching the boundary of its definition range...

Efficient approximation of black-box functions and Pareto sets

NARCIS (Netherlands)

Rennen, G.

2009-01-01

In the case of time-consuming simulation models or other so-called black-box functions, we determine a metamodel which approximates the relation between the input- and output-variables of the simulation model. To solve multi-objective optimization problems, we approximate the Pareto set, i.e. the

36 CFR 254.11 - Exchanges at approximately equal value.

Science.gov (United States)

2010-07-01

... equal value. 254.11 Section 254.11 Parks, Forests, and Public Property FOREST SERVICE, DEPARTMENT OF AGRICULTURE LANDOWNERSHIP ADJUSTMENTS Land Exchanges § 254.11 Exchanges at approximately equal value. (a) The authorized officer may exchange lands which are of approximately equal value upon a determination that: (1...

Modification of linear response theory for mean-field approximations

NARCIS (Netherlands)

Hütter, M.; Öttinger, H.C.

1996-01-01

In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the

On the mathematical treatment of the Born-Oppenheimer approximation

International Nuclear Information System (INIS)

Jecko, Thierry

2014-01-01

Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics

On the mathematical treatment of the Born-Oppenheimer approximation

Energy Technology Data Exchange (ETDEWEB)

Jecko, Thierry, E-mail: thierry.jecko@u-cergy.fr [AGM, UMR 8088 du CNRS, Université de Cergy-Pontoise, Département de mathématiques, site de Saint Martin, 2 avenue Adolphe Chauvin, F-95000 Pontoise (France)

2014-05-15

Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.

Nonstandard approximation schemes for lower dimensional quantum field theories

International Nuclear Information System (INIS)

Fitzpatrick, D.A.

1981-01-01

The purpose of this thesis has been to apply two different nonstandard approximation schemes to a variety of lower-dimensional schemes. In doing this, we show their applicability where (e.g., Feynman or Rayleigh-Schroedinger) approximation schemes are inapplicable. We have applied the well-known mean-field approximation scheme by Guralnik et al. to general lower dimensional theories - the phi 4 field theory in one dimension, and the massive and massless Thirring models in two dimensions. In each case, we derive a bound-state propagator and then expand the theory in terms of the original and bound-state propagators. The results obtained can be compared with previously known results thereby show, in general, reasonably good convergence. In the second half of the thesis, we develop a self-consistent quantum mechanical approximation scheme. This can be applied to any monotonic polynomial potential. It has been applied in detail to the anharmonic oscillator, and the results in several analytical domains are very good, including extensive tables of numerical results

APPECT: An Approximate Backbone-Based Clustering Algorithm for Tags

DEFF Research Database (Denmark)

Zong, Yu; Xu, Guandong; Jin, Pin

2011-01-01

algorithm for Tags (APPECT). The main steps of APPECT are: (1) we execute the K-means algorithm on a tag similarity matrix for M times and collect a set of tag clustering results Z={C1,C2,…,Cm}; (2) we form the approximate backbone of Z by executing a greedy search; (3) we fix the approximate backbone...... as the initial tag clustering result and then assign the rest tags into the corresponding clusters based on the similarity. Experimental results on three real world datasets namely MedWorm, MovieLens and Dmoz demonstrate the effectiveness and the superiority of the proposed method against the traditional...... Agglomerative Clustering on tagging data, which possess the inherent drawbacks, such as the sensitivity of initialization. In this paper, we instead make use of the approximate backbone of tag clustering results to find out better tag clusters. In particular, we propose an APProximate backbonE-based Clustering...

Breakdown of the few-level approximation in collective systems

International Nuclear Information System (INIS)

Kiffner, M.; Evers, J.; Keitel, C. H.

2007-01-01

The validity of the few-level approximation in dipole-dipole interacting collective systems is discussed. As an example system, we study the archetype case of two dipole-dipole interacting atoms, each modeled by two complete sets of angular momentum multiplets. We establish the breakdown of the few-level approximation by first proving the intuitive result that the dipole-dipole induced energy shifts between collective two-atom states depend on the length of the vector connecting the atoms, but not on its orientation, if complete and degenerate multiplets are considered. A careful analysis of our findings reveals that the simplification of the atomic level scheme by artificially omitting Zeeman sublevels in a few-level approximation generally leads to incorrect predictions. We find that this breakdown can be traced back to the dipole-dipole coupling of transitions with orthogonal dipole moments. Our interpretation enables us to identify special geometries in which partial few-level approximations to two- or three-level systems are valid

Analytic approximation for the modified Bessel function I -2/3(x)

Science.gov (United States)

Martin, Pablo; Olivares, Jorge; Maass, Fernando

2017-12-01

In the present work an analytic approximation to modified Bessel function of negative fractional order I -2/3(x) is presented. The validity of the approximation is for every positive value of the independent variable. The accuracy is high in spite of the small number (4) of parameters used. The approximation is a combination of elementary functions with rational ones. Power series and assymptotic expansions are simultaneously used to obtain the approximation.

Ranking Support Vector Machine with Kernel Approximation.

Science.gov (United States)

Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.

Ranking Support Vector Machine with Kernel Approximation

Directory of Open Access Journals (Sweden)

Kai Chen

2017-01-01

Full Text Available Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels can give higher accuracy than linear RankSVM (RankSVM with a linear kernel for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.

Traveling-cluster approximation for uncorrelated amorphous systems

International Nuclear Information System (INIS)

Sen, A.K.; Mills, R.; Kaplan, T.; Gray, L.J.

1984-01-01

We have developed a formalism for including cluster effects in the one-electron Green's function for a positionally disordered (liquid or amorphous) system without any correlation among the scattering sites. This method is an extension of the technique known as the traveling-cluster approximation (TCA) originally obtained and applied to a substitutional alloy by Mills and Ratanavararaksa. We have also proved the appropriate fixed-point theorem, which guarantees, for a bounded local potential, that the self-consistent equations always converge upon iteration to a unique, Herglotz solution. To our knowledge, this is the only analytic theory for considering cluster effects. Furthermore, we have performed some computer calculations in the pair TCA, for the model case of delta-function potentials on a one-dimensional random chain. These results have been compared with ''exact calculations'' (which, in principle, take into account all cluster effects) and with the coherent-potential approximation (CPA), which is the single-site TCA. The density of states for the pair TCA clearly shows some improvement over the CPA and yet, apparently, the pair approximation distorts some of the features of the exact results

Unambiguous results from variational matrix Pade approximants

International Nuclear Information System (INIS)

Pindor, Maciej.

1979-10-01

Variational Matrix Pade Approximants are studied as a nonlinear variational problem. It is shown that although a stationary value of the Schwinger functional is a stationary value of VMPA, the latter has also another stationary value. It is therefore proposed that instead of looking for a stationary point of VMPA, one minimizes some non-negative functional and then one calculates VMPA at the point where the former has the absolute minimum. This approach, which we call the Method of the Variational Gradient (MVG) gives unambiguous results and is also shown to minimize a distance between the approximate and the exact stationary values of the Schwinger functional

Lagrangians for plasmas in drift-fluid approximation

International Nuclear Information System (INIS)

Pfirsch, D.; Correa-Restrepo, D.

1996-10-01

For drift waves and related instabilities conservation laws can play a crucial role. In an ideal theory these conservation laws are guaranteed when a Lagrangian can be found from which the equations for the various quantities result by Hamilton's principle. Such a Lagrangian for plasmas in drift-fluid approximation was obtained by a heuristic method in a recent paper by Pfirsch and Correa-Restrepo. In the present paper the same Lagrangian is derived from the exact multi-fluid Lagrangian via an iterative approximation procedure which resembles the standard method usually applied to the equations of motion. That method, however, does not guarantee all the conservation laws to hold. (orig.)

Error Estimates for the Approximation of the Effective Hamiltonian

International Nuclear Information System (INIS)

Camilli, Fabio; Capuzzo Dolcetta, Italo; Gomes, Diogo A.

2008-01-01

We study approximation schemes for the cell problem arising in homogenization of Hamilton-Jacobi equations. We prove several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian, both in the optimal control setting and as well as in the calculus of variations setting

Mean-field approximation for spacing distribution functions in classical systems

Science.gov (United States)

González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

2012-01-01

We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

Approximation Algorithms for Model-Based Diagnosis

NARCIS (Netherlands)

Feldman, A.B.

2010-01-01

Model-based diagnosis is an area of abductive inference that uses a system model, together with observations about system behavior, to isolate sets of faulty components (diagnoses) that explain the observed behavior, according to some minimality criterion. This thesis presents greedy approximation

Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

Science.gov (United States)

Wei, Qinglai; Li, Benkai; Song, Ruizhuo

2018-04-01

In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers

Directory of Open Access Journals (Sweden)

Emily Szkudlarek

2018-05-01

Full Text Available Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1 compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2 to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children (n = 158 were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers.

Science.gov (United States)

Szkudlarek, Emily; Brannon, Elizabeth M

2018-01-01

Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1) compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2) to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children ( n = 158) were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that approximate arithmetic

Approximate Dispersion Relations for Waves on Arbitrary Shear Flows

Science.gov (United States)

Ellingsen, S. À.; Li, Y.

2017-12-01

An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential flow, is shown to produce good approximations at all wavelengths for a wide range of naturally occuring shear flows as well as widely used model flows. The relation reduces in many cases to a 3-D generalization of the much used approximation by Skop (1987), developed further by Kirby and Chen (1989), but is shown to be more robust, succeeding in situations where the Kirby and Chen model fails. The two approximations incur the same numerical cost and difficulty. While the Kirby and Chen approximation is excellent for a wide range of currents, the exact criteria for its applicability have not been known. We explain the apparently serendipitous success of the latter and derive proper conditions of applicability for both approximate dispersion relations. Our new model has a greater range of applicability. A second order approximation is also derived. It greatly improves accuracy, which is shown to be important in difficult cases. It has an advantage over the corresponding second-order expression proposed by Kirby and Chen that its criterion of accuracy is explicitly known, which is not currently the case for the latter to our knowledge. Our second-order term is also arguably significantly simpler to implement, and more physically transparent, than its sibling due to Kirby and Chen.Plain Language SummaryIn order to answer key questions such as how the ocean surface affects the climate, erodes the coastline and transports nutrients, we must understand how waves move. This is not so easy when depth varying currents are present, as they often are in coastal waters. We have developed a modeling tool for accurately predicting wave properties in such situations, ready for use, for example, in the complex oceanographic computer models. Our

Approximated solutions to Born-Infeld dynamics

International Nuclear Information System (INIS)

Ferraro, Rafael; Nigro, Mauro

2016-01-01

The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.

Approximated solutions to Born-Infeld dynamics

Energy Technology Data Exchange (ETDEWEB)

Ferraro, Rafael [Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA),Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina); Nigro, Mauro [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina)

2016-02-01

The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.

A domian Decomposition Method for Transient Neutron Transport with Pomrning-Eddington Approximation

International Nuclear Information System (INIS)

Hendi, A.A.; Abulwafa, E.E.

2008-01-01

The time-dependent neutron transport problem is approximated using the Pomraning-Eddington approximation. This approximation is two-flux approximation that expands the angular intensity in terms of the energy density and the net flux. This approximation converts the integro-differential Boltzmann equation into two first order differential equations. The A domian decomposition method that used to solve the linear or nonlinear differential equations is used to solve the resultant two differential equations to find the neutron energy density and net flux, which can be used to calculate the neutron angular intensity through the Pomraning-Eddington approximation

Approximate viability for nonlinear evolution inclusions with application to controllability

Directory of Open Access Journals (Sweden)

Omar Benniche

2016-12-01

Full Text Available We investigate approximate viability for a graph with respect to fully nonlinear quasi-autonomous evolution inclusions. As application, an approximate null controllability result is given.

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)

Radiative transfer in disc galaxies - V. The accuracy of the KB approximation

Science.gov (United States)

Lee, Dukhang; Baes, Maarten; Seon, Kwang-Il; Camps, Peter; Verstocken, Sam; Han, Wonyong

2016-12-01

We investigate the accuracy of an approximate radiative transfer technique that was first proposed by Kylafis & Bahcall (hereafter the KB approximation) and has been popular in modelling dusty late-type galaxies. We compare realistic galaxy models calculated with the KB approximation with those of a three-dimensional Monte Carlo radiative transfer code SKIRT. The SKIRT code fully takes into account of the contribution of multiple scattering whereas the KB approximation calculates only single scattered intensity and multiple scattering components are approximated. We find that the KB approximation gives fairly accurate results if optically thin, face-on galaxies are considered. However, for highly inclined (I ≳ 85°) and/or optically thick (central face-on optical depth ≳1) galaxy models, the approximation can give rise to substantial errors, sometimes, up to ≳40 per cent. Moreover, it is also found that the KB approximation is not always physical, sometimes producing infinite intensities at lines of sight with high optical depth in edge-on galaxy models. There is no `simple recipe' to correct the errors of the KB approximation that is universally applicable to any galaxy models. Therefore, it is recommended that the full radiative transfer calculation be used, even though it is slower than the KB approximation.

Compound Poisson Approximations for Sums of Random Variables

OpenAIRE

Serfozo, Richard F.

1986-01-01

We show that a sum of dependent random variables is approximately compound Poisson when the variables are rarely nonzero and, given they are nonzero, their conditional distributions are nearly identical. We give several upper bounds on the total-variation distance between the distribution of such a sum and a compound Poisson distribution. Included is an example for Markovian occurrences of a rare event. Our bounds are consistent with those that are known for Poisson approximations for sums of...

Upper bounds on minimum cardinality of exact and approximate reducts

KAUST Repository

Chikalov, Igor

2010-01-01

In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case. © 2010 Springer-Verlag Berlin Heidelberg.

PWL approximation of nonlinear dynamical systems, part II: identification issues

International Nuclear Information System (INIS)

De Feo, O; Storace, M

2005-01-01

This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes a black-box identification method based on state space reconstruction and PWL approximation, and applies it to some particularly significant dynamical systems (two topological normal forms and the Colpitts oscillator)

Analysis of the dynamical cluster approximation for the Hubbard model

OpenAIRE

Aryanpour, K.; Hettler, M. H.; Jarrell, M.

2002-01-01

We examine a central approximation of the recently introduced Dynamical Cluster Approximation (DCA) by example of the Hubbard model. By both analytical and numerical means we study non-compact and compact contributions to the thermodynamic potential. We show that approximating non-compact diagrams by their cluster analogs results in a larger systematic error as compared to the compact diagrams. Consequently, only the compact contributions should be taken from the cluster, whereas non-compact ...

Multijet final states: exact results and the leading pole approximation

International Nuclear Information System (INIS)

Ellis, R.K.; Owens, J.F.

1984-09-01

Exact results for the process gg → ggg are compared with those obtained using the leading pole approximation. Regions of phase space where the approximation breaks down are discussed. A specific example relevant for background estimates to W boson production is presented. It is concluded that in this instance the leading pole approximation may underestimate the standard QCD background by more than a factor of two in certain kinematic regions of physical interest

Integral approximants for functions of higher monodromic dimension

Energy Technology Data Exchange (ETDEWEB)

Baker, G.A. Jr.

1987-01-01

In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.